Mesenchymal progenitor cell markers in human articular cartilage: normal distribution and changes in osteoarthritis

INTRODUCTION: Recent findings suggest that articular cartilage contains mesenchymal progenitor cells. The aim of this study was to examine the distribution of stem cell markers (Notch-1, Stro-1 and VCAM-1) and of molecules that modulate progenitor differentiation (Notch-1 and Sox9) in normal adult human articular cartilage and in osteoarthritis (OA) cartilage. METHODS: Expression of the markers was analyzed by immunohistochemistry (IHC) and flow cytometry. Hoechst 33342 dye was used to identify and sort the cartilage side population (SP). Multilineage differentiation assays including chondrogenesis, osteogenesis and adipogenesis were performed on SP and non-SP (NSP) cells. RESULTS: A surprisingly high number (>45%) of cells were positive for Notch-1, Stro-1 and VCAM-1 throughout normal cartilage. Expression of these markers was higher in the superficial zone (SZ) of normal cartilage as compared to the middle zone (MZ) and deep zone (DZ). Non-fibrillated OA cartilage SZ showed reduced Notch-1 and Sox9 staining frequency, while Notch-1, Stro-1 and VCAM-1 positive cells were increased in the MZ. Most cells in OA clusters were positive for each molecule tested. The frequency of SP cells in cartilage was 0.14 +/- 0.05% and no difference was found between normal and OA. SP cells displayed chondrogenic and osteogenic but not adipogenic differentiation potential. CONCLUSIONS: These results show a surprisingly high number of cells that express putative progenitor cell markers in human cartilage. In contrast, the percentage of SP cells is much lower and within the range of expected stem cell frequency. Thus, markers such as Notch-1, Stro-1 or VCAM-1 may not be useful to identify progenitors in cartilage. Instead, their increased expression in OA cartilage implicates involvement in the abnormal cell activation and differentiation process characteristic of OA.

Reliability studies of the skew normal distribution

It has been observed in various practical applications that data do not conform to the normal distribution, which is symmetric with no skewness. The skew normal distribution proposed by Azzalini(1985) is appropriate for the analysis of data which is unimodal but exhibits some skewness. The skew normal distribution includes the normal distribution as a special case where the skewness parameter is zero. In this thesis, we study the structural properties of the skew normal distribution, with an emphasis on the reliability properties of the model. More specifically, we obtain the failure rate, the mean residual life function, and the reliability function of a skew normal random variable. We also compare it with the normal distribution with respect to certain stochastic orderings. Appropriate machinery is developed to obtain the reliability of a component when the strength and stress follow the skew normal distribution. Finally, IQ score data from Roberts (1988) is analyzed to illustrate the procedure.

The Dynamin-like Protein DLP1 Is Essential for Normal Distribution and Morphology of the Endoplasmic Reticulum and Mitochondria in Mammalian Cells

The dynamin family of large GTPases has been implicated in vesicle formation from both the plasma membrane and various intracellular membrane compartments. The dynamin-like protein DLP1, recently identified in mammalian tissues, has been shown to be more closely related to the yeast dynamin proteins Vps1p and Dnm1p (42%) than to the mammalian dynamins (37%). Furthermore, DLP1 has been shown to associate with punctate vesicles that are in intimate contact with microtubules and the endoplasmic reticulum (ER) in mammalian cells. To define the function of DLP1, we have transiently expressed both wild-type and two mutant DLP1 proteins, tagged with green fluorescent protein, in cultured mammalian cells. Point mutations in the GTP-binding domain of DLP1 (K38A and D231N) dramatically changed its intracellular distribution from punctate vesicular structures to either an aggregated or a diffuse pattern. Strikingly, cells expressing DLP1 mutants or microinjected with DLP1 antibodies showed a marked reduction in ER fluorescence and a significant aggregation and tubulation of mitochondria by immunofluorescence microscopy. Consistent with these observations, electron microscopy of DLP1 mutant cells revealed a striking and quantitative change in the distribution and morphology of mitochondria and the ER. These data support very recent studies by other authors implicating DLP1 in the maintenance of mitochondrial morphology in both yeast and mammalian cells. Furthermore, this study provides the first evidence that a dynamin family member participates in the maintenance and distribution of the ER. How DLP1 might participate in the biogenesis of two presumably distinct organelle systems is discussed.

Tables of factors for one-sided tolerance limits for normal distribution,

Mode of access: Internet.

Joint Densities of Correlation Coefficients for Samples from Multivariate Standard Normal Distribution

2000 Mathematics Subject Classification: 62H10.

Inferences about Parameters of Trivariate Normal Distribution with Missing Data

Multivariate normal distribution is commonly encountered in any field, a frequent issue is the missing values in practice. The purpose of this research was to estimate the parameters in three-dimensional covariance permutation-symmetric normal distribution with complete data and all possible patterns of incomplete data. In this study, MLE with missing data were derived, and the properties of the MLE as well as the sampling distributions were obtained. A Monte Carlo simulation study was used to evaluate the performance of the considered estimators for both cases when ρ was known and unknown. All results indicated that, compared to estimators in the case of omitting observations with missing data, the estimators derived in this article led to better performance. Furthermore, when ρ was unknown, using the estimate of ρ would lead to the same conclusion.

Stochastic model for simulating maize yield

Maize is one of the most important crops in the world. The products generated from this crop are largely used in the starch industry, the animal and human nutrition sector, and biomass energy production and refineries. For these reasons, there is much interest in figuring the potential grain yield of maize genotypes in relation to the environment in which they will be grown, as the productivity directly affects agribusiness or farm profitability. Questions like these can be investigated with ecophysiological crop models, which can be organized according to different philosophies and structures. The main objective of this work is to conceptualize a stochastic model for predicting maize grain yield and productivity under different conditions of water supply while considering the uncertainties of daily climate data. Therefore, one focus is to explain the model construction in detail, and the other is to present some results in light of the philosophy adopted. A deterministic model was built as the basis for the stochastic model. The former performed well in terms of the curve shape of the above-ground dry matter over time as well as the grain yield under full and moderate water deficit conditions. Through the use of a triangular distribution for the harvest index and a bivariate normal distribution of the averaged daily solar radiation and air temperature, the stochastic model satisfactorily simulated grain productivity, i.e., it was found that 10,604 kg ha(-1) is the most likely grain productivity, very similar to the productivity simulated by the deterministic model and for the real conditions based on a field experiment. © 2012 American Society of Agricultural and Biological Engineers.

A stochastic model of temporal variations in monthly temperature, precipitation, snowfall, and resulting snowpack

We report a Monte Carlo representation of the long-term inter-annual variability of monthly snowfall on a detailed (1 km) grid of points throughout the southwest. An extension of the local climate model of the southwestern United States (Stamm and Craig 1992) provides spatially based estimates of mean and variance of monthly temperature and precipitation. The mean is the expected value from a canonical regression using independent variables that represent controls on climate in this area, including orography. Variance is computed as the standard error of the prediction and provides site-specific measures of (1) natural sources of variation and (2) errors due to limitations of the data and poor distribution of climate stations. Simulation of monthly temperature and precipitation over a sequence of years is achieved by drawing from a bivariate normal distribution. The conditional expectation of precipitation. given temperature in each month, is the basis of a numerical integration of the normal probability distribution of log precipitation below a threshold temperature (3°C) to determine snowfall as a percent of total precipitation. Snowfall predictions are tested at stations for which long-term records are available. At Donner Memorial State Park (elevation 1811 meters) a 34-year simulation - matching the length of instrumental record - is within 15 percent of observed for mean annual snowfall. We also compute resulting snowpack using a variation of the model of Martinec et al. (1983). This allows additional tests by examining spatial patterns of predicted snowfall and snowpack and their hydrologic implications.

Exercise sheet 8 pdf

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Exercise sheet 8

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Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors

In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model`s goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease. Copyright (C) 2008 John Wiley & Sons, Ltd.

STOCHASTIC MODEL FOR SIMULATING MAIZE YIELD

Maize is one of the most important crops in the world. The products generated from this crop are largely used in the starch industry, the animal and human nutrition sector, and biomass energy production and refineries. For these reasons, there is much interest in figuring the potential grain yield of maize genotypes in relation to the environment in which they will be grown, as the productivity directly affects agribusiness or farm profitability. Questions like these can be investigated with ecophysiological crop models, which can be organized according to different philosophies and structures. The main objective of this work is to conceptualize a stochastic model for predicting maize grain yield and productivity under different conditions of water supply while considering the uncertainties of daily climate data. Therefore, one focus is to explain the model construction in detail, and the other is to present some results in light of the philosophy adopted. A deterministic model was built as the basis for the stochastic model. The former performed well in terms of the curve shape of the above-ground dry matter over time as well as the grain yield under full and moderate water deficit conditions. Through the use of a triangular distribution for the harvest index and a bivariate normal distribution of the averaged daily solar radiation and air temperature, the stochastic model satisfactorily simulated grain productivity, i.e., it was found that 10,604 kg ha(-1) is the most likely grain productivity, very similar to the productivity simulated by the deterministic model and for the real conditions based on a field experiment.

Statnote 14: the correlation of two variables (Pearson's 'r')

Pearson's correlation coefficient (‘r’) is one of the most widely used of all statistics. Nevertheless, care needs to be used in interpreting the results because with large numbers of observations, quite small values of ‘r’ become significant and the X variable may only account for a small proportion of the variance in Y. Hence, ‘r squared’ should always be calculated and included in a discussion of the significance of ‘r’. The use of ‘r’ also assumes that the data follow a bivariate normal distribution (see Statnote 17) and this assumption should be examined prior to the study. If the data do not conform to such a distribution, the use of a non-parametric correlation coefficient should be considered. A significant correlation should not be interpreted as indicating ‘causation’ especially in observational studies, in which the two variables may be correlated because of their mutual correlations with other confounding variables.

Data analysis methods in optometry. Part 5: correlation

1. Pearson's correlation coefficient only tests whether the data fit a linear model. With large numbers of observations, quite small values of r become significant and the X variable may only account for a minute proportion of the variance in Y. Hence, the value of r squared should always be calculated and included in a discussion of the significance of r. 2. The use of r assumes that a bivariate normal distribution is present and this assumption should be examined prior to the study. If Pearson's r is not appropriate, then a non-parametric correlation coefficient such as Spearman's rs may be used. 3. A significant correlation should not be interpreted as indicating causation especially in observational studies in which there is a high probability that the two variables are correlated because of their mutual correlations with other variables. 4. In studies of measurement error, there are problems in using r as a test of reliability and the ‘intra-class correlation coefficient’ should be used as an alternative. A correlation test provides only limited information as to the relationship between two variables. Fitting a regression line to the data using the method known as ‘least square’ provides much more information and the methods of regression and their application in optometry will be discussed in the next article.

Univariate and bivariate distribution of growth traits in beef buffaloes from Brazil

The aim of this study was to analyze the weight at birth (BW) and adjusted at 205 (W205), 365 (W365) and 550 (W55O) days in beef buffaloes from Brazil, using two approaches: parametric, by normal distribution, and non-parametric, by kernel function, and thus estimating the genetic, environmental and phenotypic correlation among traits. Information of 5,169 animals at birth (BW), 3,792 at 205 days (W205), 3.883 at 365 days (W365) and 1,524 at 550 days of age (W550) were used. The birth weight distribution presented an evident discrepancy in relation to the normal distribution. However, W205, W365 and W550 presented normal distributions. The birth weight presented weak genetic, environmental, and phenotypic associations with the other weight measurements. on the other hand, the weight traits at 205, 365, 550 days of age showed a high genetic correlation.