Modeling the response of a population of olfactory receptor neurons to an odorant

We modeled the firing rate of populations of olfactory receptor neurons (ORNs) responding to an odorant at different concentrations. Two cases were considered: a population of ORNs that all express the same olfactory receptor (OR), and a population that expresses many different ORs. To take into account ORN variability, we replaced single parameter values in a biophysical ORN model with values drawn from statistical distributions, chosen to correspond to experimental data. For ORNs expressing the same OR, we found that the distributions of firing frequencies are Gaussian at all concentrations, with larger mean and standard deviation at higher concentrations. For a population expressing different ORs, the distribution of firing frequencies can be described as the superposition of a Gaussian distribution and a lognormal distribution. Distributions of maximum value and dynamic range of spiking frequencies in the simulated ORN population were similar to experimental results.     

江苏主要常绿阔叶树种的分布与热量关系的初步研究

植物分布主要受气候因子制约,在气候因子中温度又起主导作用。这一观点作为植物地理学的一条原理早已为人们所接受。可是,植物分布与温度之间的定量研究工作在我国做得还比较少。日本大阪大学吉良教授(1967,1977)曾用两种热量指标(温暖指标Warmth index和寒冷指标Coldness index)分析日本森林带的分布与热量之间的关系。朝鲜学者任良宰     

Statistical characteristics of spontaneous and evoked unit activity in the cat superior colliculus

Spontaneous and evoked unit activity of the superior colliculus was studied in cats immobilized with gallamine or with the spinal cord divided (encephalé isolé). Statistical parameters of unit activity were calculated in light and darkness and in the presence of a moving photic stimulus. Spontaneously active neurons were divided into four main groups: 1) with a mean interspike interval of about 300 msec, coefficient of variation 1.9, and with two modes in the autocorrelation histogram; 2) with similar statistical parameters but distinguished by correlation with saccadic eye movements; 3) histogram of interspike intervals exponential in type, autocorrelation histogram flat, mean interval and standard deviation about 100 msec; 4) with symmetrical distribution of interspike intervals, mean interval about 50 msec, coefficient of variation 0.4–0.5. Spontaneous activity in light and darkness differed only in the neurons of the second group. Comparison of the statistical parameters of the spontaneous and evoked activity shows that encoding of the stimulus could be carried out by neurons of groups 3 and 4. In some cases the mode of the histogram of interspike intervals and the standard deviation changed significantly and activity appeared regularly in the autocorrelation histogram.     

Statistical and physiological distinction of constitution types

Most conventional human health and function evaluation methods are based on a traditional notion that all the population characteristics follow the Gaussian distribution law with the parameters M and s forming the basis of the norm conception. But some known facts contradict this idea that requires checking the statistical homogeneity of population characteristics. Analysis of statistical distribution and central tendencies for simple measured indices in population and somatotypes samples proved an idea of natural population distinctions by a broad set of morpho-functional features (by means of 23-D matrix cluster analysis for different indices) and provided the scientific grounds to use a constitutional approach in human sciences and physical education as well. Gaussian distribution law was found within somatotype groups permitting the use of its parameters for norm evaluation. In practice for somatotype determination the relative girth body dimensions (normalized by body height) were proved to be preferable.     

Population genetics approach to the problem of the nonspecific biological resistance of the human body. I. Statement of the problem and basis for the approach. Distribution parameters of anthropometric markers of normal and ill newborn infants and nurslings

Distributions of two metrical characters-the weight and the body length at birth are considered in several groups of healthy, diseased and dead newborns and infants. Significant differences in statistical parameters of these distributions (mean, standard deviation, skewness and kurtosis) are demonstrated for normal and malformated children. The increased number of children with minimal deviations from the mean values of characters (adaptive norm) is observed among healthy newborns, while in groups of diseased and dead children the frequency of individuals with extreme (especially low) values is increased. The principle of classification of individuals based simultaneously on two characteris is suggested and the problem of "average phenotype" classification by the number of characters is discussed.     

Analysis of phosphorescence in heterogeneous systems using distributions of quencher concentration.

A continuous distribution approach, instead of the traditional mono- and multiexponential analysis, for determining quencher concentration in a heterogeneous system has been developed. A mathematical model of phosphorescence decay inside a volume with homogeneous concentration of phosphor and heterogeneous concentration of quencher was formulated to obtain pulse-response fitting functions for four different distributions of quencher concentration: rectangular, normal (Gaussian), gamma, and multimodal. The analysis was applied to parameter estimates of a heterogeneous distribution of oxygen tension (PO2) within a volume. Simulated phosphorescence decay data were randomly generated for different distributions and heterogeneity of PO2 inside the excitation/emission volume, consisting of 200 domains, and then fit with equations developed for the four models. Analysis using a monoexponential fit yielded a systematic error (underestimate) in mean PO2 that increased with the degree of heterogeneity. The fitting procedures based on the continuous distribution approach returned more accurate values for parameters of the generated PO2 distribution than did the monoexponential fit. The parameters of the fit (M = mean; sigma = standard deviation) were investigated as a function of signal-to-noise ratio (SNR = maximum signal amplitude/peak-to-peak noise). The best-fit parameter values were stable when SNR > or = 20. All four fitting models returned accurate values of M and sigma for different PO2 distributions. The ability of our procedures to resolve two different heterogeneous compartments was also demonstrated using a bimodal fitting model. An approximate scheme was formulated to allow calculation of the first moments of a spatial distribution of quencher without specifying the distribution. In addition, a procedure for the recovery of a histogram, representing the quencher concentration distribution, was developed and successfully tested.     

Prediction of Random Effects in Linear and Generalized Linear Models under Model Misspecification

Summary Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with the assumption that the random effects follow a Gaussian distribution. Via theoretical and numerical calculations and simulation, we investigate the impact of misspecification of this distribution on both how well the predicted values recover the true underlying distribution and the accuracy of prediction of the realized values of the random effects. We show that, although the predicted values can vary with the assumed distribution, the prediction accuracy, as measured by mean square error, is little affected for mild‐to‐moderate violations of the assumptions. Thus, standard approaches, readily available in statistical software, will often suffice. The results are illustrated using data from the Heart and Estrogen/Progestin Replacement Study using models to predict future blood pressure values.     

Vegetation gradients in relation to temporal fluctuation of environmental factors in Bekanbeushi peatland, Hokkaido, Japan

The relationship between vegetation gradients and temporal variation of groundwater table depth, groundwater pH and electrical conductivity was studied in Bekanbeushi peatland, northern Japan. These environmental factors were expressed using four statistical parameters: maximum, minimum, mean and standard deviation or coefficient of variation during the growing season. The bog–fen–swamp/marsh gradient was primarily explained by minimum, maximum and mean groundwater table depth and minimum pH. The separation between the bog and the fen by minimum pH was particularly clear. Minimum conductivity was secondarily important for explaining this vegetation gradient. The swamp–marsh gradient was explained by the standard deviation of groundwater table depth. Maximum pH and conductivity were not significant in explaining either of these gradients. This study suggests that parameters that are obtained from the consecutive measurement of environmental factors may have differing significance in explaining vegetation gradients in these peatlands, and values from a single sampling may miss important ecological information.     

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.     

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.     

Genetic and Statistical Analyses of Strong Selection on Polygenic Traits: What,Me Normal?

We develop a general population genetic framework for analyzing selection on many loci, and apply it to strong truncation and disruptive selection on an additive polygenic trait. We first present statistical methods for analyzing the infinitesimal model, in which offspring breeding values are normally distributed around the mean of the parents, with fixed variance. These show that the usual assumption of a Gaussian distribution of breeding values in the population gives remarkably accurate predictions for the mean and the variance, even when disruptive selection generates substantial deviations from normality. We then set out a general genetic analysis of selection and recombination. The population is represented by multilocus cumulants describing the distribution of haploid genotypes, and selection is described by the relation between mean fitness and these cumulants. We provide exact recursions in terms of generating functions for the effects of selection on non-central moments. The effects of recombination are simply calculated as a weighted sum over all the permutations produced by meiosis. Finally, the new cumulants that describe the next generation are computed from the non-central moments. Although this scheme is applied here in detail only to selection on an additive trait, it is quite general. For arbitrary epistasis and linkage, we describe a consistent infinitesimal limit in which the short-term selection response is dominated by infinitesimal allele frequency changes and linkage disequilibria. Numerical multilocus results show that the standard Gaussian approximation gives accurate predictions for the dynamics of the mean and genetic variance in this limit. Even with intense truncation selection, linkage disequilibria of order three and higher never cause much deviation from normality. Thus, the empirical deviations frequently found between predicted and observed responses to artificial selection are not caused by linkage-disequilibrium-induced departures from normality. Disruptive selection can generate substantial four-way disequilibria, and hence kurtosis; but even then, the Gaussian assumption predicts the variance accurately. In contrast to the apparent simplicity of the infinitesimal limit, data suggest that changes in genetic variance after 10 or more generations of selection are likely to be dominated by allele frequency dynamics that depend on genetic details.     

Genome-wide association analysis and genetic architecture of egg weight and egg uniformity in layer chickens

The pioneering work by Professor Soller et al., among others, on the use of genetic markers to analyze quantitative traits has provided opportunities to discover their genetic architecture in livestock by identifying quantitative trait loci (QTL). The recent availability of high-density single nucleotide polymorphism (SNP) panels has advanced such studies by capitalizing on population-wide linkage disequilibrium at positions across the genome. In this study, genomic prediction model Bayes-B was used to identify genomic regions associated with the mean and standard deviation of egg weight at three ages in a commercial brown egg layer line. A total of 24,425 segregating SNPs were evaluated simultaneously using over 2900 genotyped individuals or families. The corresponding phenotypic records were represented as individual measurements or family means from full-sib progeny. A novel approach using the posterior distribution of window variances from the Monte Carlo Markov Chain samples was used to describe genetic architecture and to make statistical inferences about regions with the largest effects. A QTL region on chromosome 4 was found to explain a large proportion of the genetic variance for the mean (30%) and standard deviation (up to 16%) of the weight of eggs laid at specific ages. Additional regions with smaller effects on chromosomes 2, 5, 6, 8, 20, 23, 28 and Z showed suggestive associations with mean egg weight and a region on chromosome 13 with the standard deviation of egg weight at 26-28 weeks of age. The genetic architecture of the analyzed traits was characterized by a limited number of genes or genomic regions with large effects and many regions with small polygenic effects. The region on chromosome 4 can be used to improve both the mean and standard deviation of egg weight by marker-assisted selection.     

Population modeling for a captive squirrel monkey colony

Population modeling for a squirrel monkey colony breeding in a captive laboratory environment was approached with the use of two different mathematical modeling techniques. Deterministic modeling was used initially on a spreadsheet to estimate future census figures for animals in various age/sex classes. Historical data were taken as input parameters for the model, combined with harvesting policies to calculate future population figures in the colony. This was followed by a more sophisticated stochastic model that is capable of accommodating random variations in biological phenomena, as well as smoothing out measurement errors. Point estimates (means) for input parameters used in the deterministic model are replaced by probability distributions fitted into historical data from colony records. With the use of Crystal Ball (Decisioneering, Inc., Denver, CO) software, user-selected distributions are embedded in appropriate cells in the spreadsheet model. A Monte Carlo simulation scheme running within the spreadsheet draws (on each cycle) random values for input parameters from the distribution embedded in each relevant cell, and thus generates output values for forecast variables. After several thousand runs, a distribution is formed at the output end representing estimates for population figures (forecast variables) in the form of probability distributions. Such distributions provide the decision-maker with a mathematical habitat for statistical analysis in a stochastic setting. In addition to providing standard statistical measures (e.g., mean, variance, and range) that describe the location and shape of the distribution, this approach offers the potential for investigating crucial issues such as conditions surrounding the plausibility of extinction.     

Biophysical models of ciliary activity: Gaussian frequency distributions

A model of a freely rotating exended scatterer is proposed to describe light scattering from beating cilia. Gaussian rotation frequency distributions, characterized by a mean angular frequency and a standard deviation, are introduced in order to simulate intensity autocorrelation functions and to fit the model to experimental data. Thus the ciliary beats are characterized by a mean beat frequency and a standard deviation of the beat frequency distribution. The standard deviation influences the damping of the intensity autocorrelation function of light scattered from cilia. The calculated intensity autocorrelation function shows a more prominent oscillating behaviour the smaller the standard deviation of the beat frequency. The validity of the model is supported by experimental data in two ways: 1) The model fits very well to experimental data in computer evaluations, 2) Neither the model nor information obtained from measurements are dependent on the measuring angle.The contents were presented in part at the 9th International Biophysics Congress in Jerusalem, Israel, August 23–28, 1987 Offprint requests to: P. Thyberg     

Probabilistic model of the spatial distribution of muscle fibres in human muscles

An analytical model and computer simulation model for measuring fibre density in motor units of human skeletal muscles have been described. The model was developed for Gaussian distribution of the fibres in the motor unit territory. It has been shown that fibre density measurement using a triggering fibre was a biased estimate of the actual density of the fibres in the territory. The effects of varying the standard deviation of the spatial distribution on the estimate of fibre density has been investigated, and it has been shown that for high values of standard deviation a uniform distribution of the fibres in the territory was a good first order approximation.     

Show the data, don't conceal them

Current standards of data presentation and analysis in biological journals often fall short of ideal. This is the first of a planned series of short articles, to be published in a number of journals, aiming to highlight the principles of clear data presentation and appropriate statistical analysis. This article considers the methods used to show data, in particular the value of the dot plot, and methods to summarise the distribution of values. The uses of measures such as standard deviation, standard error of the mean, and confidence intervals are contrasted.     

Newtonian versus Special-Relativistic Statistical Predictions for Low-Speed Scattering

The statistical predictions of Newtonian and special-relativistic mechanics, which are calculated from an initially Gaussian ensemble of trajectories, are compared for a low-speed scattering system. The comparisons are focused on the mean dwell time, transmission and reflection coefficients, and the position and momentum means and standard deviations. We find that the statistical predictions of the two theories do not always agree as conventionally expected. The predictions are close if the scattering is non-chaotic but they are radically different if the scattering is chaotic and the initial ensemble is well localized in phase space. Our result indicates that for low-speed chaotic scattering, special-relativistic mechanics must be used, instead of the standard practice of using Newtonian mechanics, to obtain empirically-correct statistical predictions from an initially well-localized Gaussian ensemble.     

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.     

Gender and muscle differences in EMG amplitude and median frequency, and variability during maximal voluntary contractions of the quadriceps femoris.

The purpose of this study was to evaluate gender and muscle differences in electromyographic (EMG) amplitude and median frequency mean and standard deviation during maximal voluntary contractions of the quadriceps femoris. Thirty recreationally active volunteers were assessed for isometric EMG activity of the vastus medialis (VM), vastus lateralis (VL), and rectus femoris (RF) muscles during three 5-s maximal isometric voluntary contractions (MVCs). Median frequency of the three muscles was assessed through a power spectral analysis (fast Fourier transformation, Hanning window processing, 512 points). The power spectral analysis was performed during the middle 3 s of each contraction over 11 consecutive, 512 ms epochs overlapping each other by half their length (256 ms). The median frequency (F(med)) for each of the 11 windows was determined for each muscle. The mean and standard deviation of the F(med) across the 11 overlapping windows were then calculated for each contraction and muscle. EMG amplitude was determined by calculating the root mean square (RMS-50 ms time constant) over the same contraction period for each muscle. The mean amplitude and standard deviation about the mean value were then determined. A three-factor ANOVA with repeated measures was performed on the calculated F(med) mean and standard deviation values, and RMS standard deviations, to assess any gender, muscle, or trial differences, or interactions. A two-factor (gender by muscle) ANOVA with repeated measures was performed on the RMS mean amplitude for each muscle. Intraclass correlation coefficients (ICCs-2,1), standard errors of measurement (SEMs), and associated 95% confidence intervals were then calculated for maximal quadriceps torque and F(med) for each muscle. The results from this study demonstrated that the VL muscle displayed significantly higher F(med) values than the RF and VM muscles. The RF muscle showed significantly higher F(med) values (mean of 11 overlapping windows) than the VM muscle. Intrasession reliability was found to be high for the calculated mean values (ICC=0.85-0.96), but was shown to be low for variability (ICC=0.13-0.45). The major findings of this study support the notion that the EMG signal is "quasi-random" in nature, as demonstrated by the reproducible F(med) means and unreliable variability.