Effects of rock properties on specific cutting energy in linear cutting of sandstones by picks

Specific cutting energy (SE) has been widely used to assess the rock cuttability for mechanical excavation purposes. Some prediction models were developed for SE through correlating rock properties with SE values. However, some of the textural and compositional rock parameters i.e. texture coefficient and feldspar, mafic, and felsic mineral contents were not considered. The present study is to investigate the effects of previously ignored rock parameters along with engineering rock properties on SE. Mineralogical and petrographic analyses, rock mechanics, and linear rock cutting tests were performed on sandstone samples taken from sites around Ankara, Turkey. Relationships between SE and rock properties were evaluated using bivariate correlation and linear regression analyses. The tests and subsequent analyses revealed that the texture coefficient and feldspar content of sandstones affected rock cuttability, evidenced by significant correlations between these parameters and SE at a 90% confidence level. Felsic and mafic mineral contents of sandstones did not exhibit any statistically significant correlation against SE. Cementation coefficient, effective porosity, and pore volume had good correlations against SE. Poisson's ratio, Brazilian tensile strength, Shore scleroscope hardness, Schmidt hammer hardness, dry density, and point load strength index showed very strong linear correlations against SE at confidence levels of 95% and above, all of which were also found suitable to be used in predicting SE individually, depending on the results of regression analysis, ANOVA, Student's t-tests, and R-2 values. Poisson's ratio exhibited the highest correlation with SE and seemed to be the most reliable SE prediction tool in sandstones.

Statnote 27: Principal components analysis (PCA)

In Statnotes 24 and 25, multiple linear regression, a statistical method that examines the relationship between a single dependent variable (Y) and two or more independent variables (X), was described. The principle objective of such an analysis was to determine which of the X variables had a significant influence on Y and to construct an equation that predicts Y from the X variables. ‘Principal components analysis’ (PCA) and ‘factor analysis’ (FA) are also methods of examining the relationships between different variables but they differ from multiple regression in that no distinction is made between the dependent and independent variables, all variables being essentially treated the same. Originally, PCA and FA were regarded as distinct methods but in recent times they have been combined into a single analysis, PCA often being the first stage of a FA. The basic objective of a PCA/FA is to examine the relationships between the variables or the ‘structure’ of the variables and to determine whether these relationships can be explained by a smaller number of ‘factors’. This statnote describes the use of PCA/FA in the analysis of the differences between the DNA profiles of different MRSA strains introduced in Statnote 26.

Statnote 16: fitting a regression line to data

Fitting a linear regression to data provides much more information about the relationship between two variables than a simple correlation test. A goodness of fit test of the line should always be carried out. Hence, ‘r squared’ estimates the strength of the relationship between Y and X, ANOVA whether a statistically significant line is present, and the ‘t’ test whether the slope of the line is significantly different from zero. In addition, it is important to check whether the data fit the assumptions for regression analysis and, if not, whether a transformation of the Y and/or X variables is necessary.

Data methods in optometry. Part 6: fitting a regression line to data

1. Fitting a linear regression to data provides much more information about the relationship between two variables than a simple correlation test. A goodness of fit test of the line should always be carried out. Hence, r squared estimates the strength of the relationship between Y and X, ANOVA whether a statistically significant line is present, and the ‘t’ test whether the slope of the line is significantly different from zero. 2. Always check whether the data collected fit the assumptions for regression analysis and, if not, whether a transformation of the Y and/or X variables is necessary. 3. If the regression line is to be used for prediction, it is important to determine whether the prediction involves an individual y value or a mean. Care should be taken if predictions are made close to the extremities of the data and are subject to considerable error if x falls beyond the range of the data. Multiple predictions require correction of the P values. 3. If several individual regression lines have been calculated from a number of similar sets of data, consider whether they should be combined to form a single regression line. 4. If the data exhibit a degree of curvature, then fitting a higher-order polynomial curve may provide a better fit than a straight line. In this case, a test of whether the data depart significantly from a linear regression should be carried out.

Statistical analysis in microbiology:statnotes

This book is aimed primarily at microbiologists who are undertaking research and who require a basic knowledge of statistics to analyse their experimental data. Computer software employing a wide range of data analysis methods is widely available to experimental scientists. The availability of this software, however, makes it essential that investigators understand the basic principles of statistics. Statistical analysis of data can be complex with many different methods of approach, each of which applies in a particular experimental circumstance. Hence, it is possible to apply an incorrect statistical method to data and to draw the wrong conclusions from an experiment. The purpose of this book, which has its origin in a series of articles published in the Society for Applied Microbiology journal ‘The Microbiologist’, is an attempt to present the basic logic of statistics as clearly as possible and therefore, to dispel some of the myths that often surround the subject. The 28 ‘Statnotes’ deal with various topics that are likely to be encountered, including the nature of variables, the comparison of means of two or more groups, non-parametric statistics, analysis of variance, correlating variables, and more complex methods such as multiple linear regression and principal components analysis. In each case, the relevant statistical method is illustrated with examples drawn from experiments in microbiological research. The text incorporates a glossary of the most commonly used statistical terms and there are two appendices designed to aid the investigator in the selection of the most appropriate test.

Statnote 24: Multiple regression

In previous statnotes, the application of correlation and regression methods to the analysis of two variables (X,Y) was described. These methods can be used to determine whether there is a linear relationship between the two variables, whether the relationship is positive or negative, to test the degree of significance of the linear relationship, and to obtain an equation relating Y to X. This Statnote extends the methods of linear correlation and regression to situations where there are two or more X variables, i.e., 'multiple linear regression’.

Pronounced reduction of postprandial glucagon by lixisenatide:a meta-analysis of randomized clinical trials

Glucagon-like peptide-1 (GLP-1) receptor agonists improve islet function and delay gastric emptying in patients with type 2 diabetes mellitus (T2DM). This meta-analysis aimed to investigate the effects of the once-daily prandial GLP-1 receptor agonist lixisenatide on postprandial plasma glucose (PPG), glucagon and insulin levels. Methods: Six randomized, placebo-controlled studies of lixisenatide 20μg once daily were included in this analysis: lixisenatide as monotherapy (GetGoal-Mono), as add-on to oral antidiabetic drugs (OADs; GetGoal-M, GetGoal-S) or in combination with basal insulin (GetGoal-L, GetGoal-Duo-1 and GetGoal-L-Asia). Change in 2-h PPG and glucose excursion were evaluated across six studies. Change in 2-h glucagon and postprandial insulin were evaluated across two studies. A meta-analysis was performed on least square (LS) mean estimates obtained from analysis of covariance (ANCOVA)-based linear regression. Results: Lixisenatide significantly reduced 2-h PPG from baseline (LS mean difference vs. placebo: -4.9mmol/l, p<0.001) and glucose excursion (LS mean difference vs. placebo: -4.5mmol/l, p<0.001). As measured in two studies, lixisenatide also reduced postprandial glucagon (LS mean difference vs. placebo: -19.0ng/l, p<0.001) and insulin (LS mean difference vs. placebo: -64.8 pmol/l, p<0.001). There was a stronger correlation between 2-h postprandial glucagon and 2-h PPG with lixisenatide than with placebo. Conclusions: Lixisenatide significantly reduced 2-h PPG and glucose excursion together with a marked reduction in postprandial glucagon and insulin; thus, lixisenatide appears to have biological effects on blood glucose that are independent of increased insulin secretion. These effects may be, in part, attributed to reduced glucagon secretion. © 2014 John Wiley and Sons Ltd.

On the Lp-Norm Regression Models for Estimating Value-at-Risk

Analysis of risk measures associated with price series data movements and its predictions are of strategic importance in the financial markets as well as to policy makers in particular for short- and longterm planning for setting up economic growth targets. For example, oilprice risk-management focuses primarily on when and how an organization can best prevent the costly exposure to price risk. Value-at-Risk (VaR) is the commonly practised instrument to measure risk and is evaluated by analysing the negative/positive tail of the probability distributions of the returns (profit or loss). In modelling applications, least-squares estimation (LSE)-based linear regression models are often employed for modeling and analyzing correlated data. These linear models are optimal and perform relatively well under conditions such as errors following normal or approximately normal distributions, being free of large size outliers and satisfying the Gauss-Markov assumptions. However, often in practical situations, the LSE-based linear regression models fail to provide optimal results, for instance, in non-Gaussian situations especially when the errors follow distributions with fat tails and error terms possess a finite variance. This is the situation in case of risk analysis which involves analyzing tail distributions. Thus, applications of the LSE-based regression models may be questioned for appropriateness and may have limited applicability. We have carried out the risk analysis of Iranian crude oil price data based on the Lp-norm regression models and have noted that the LSE-based models do not always perform the best. We discuss results from the L1, L2 and L∞-norm based linear regression models. ACM Computing Classification System (1998): B.1.2, F.1.3, F.2.3, G.3, J.2.

Estimation of average annual daily traffic (AADT) using geographically weighted regression (GWR) method and geographic information system (GIS)

Annual average daily traffic (AADT) is important information for many transportation planning, design, operation, and maintenance activities, as well as for the allocation of highway funds. Many studies have attempted AADT estimation using factor approach, regression analysis, time series, and artificial neural networks. However, these methods are unable to account for spatially variable influence of independent variables on the dependent variable even though it is well known that to many transportation problems, including AADT estimation, spatial context is important. ^ In this study, applications of geographically weighted regression (GWR) methods to estimating AADT were investigated. The GWR based methods considered the influence of correlations among the variables over space and the spatially non-stationarity of the variables. A GWR model allows different relationships between the dependent and independent variables to exist at different points in space. In other words, model parameters vary from location to location and the locally linear regression parameters at a point are affected more by observations near that point than observations further away. ^ The study area was Broward County, Florida. Broward County lies on the Atlantic coast between Palm Beach and Miami-Dade counties. In this study, a total of 67 variables were considered as potential AADT predictors, and six variables (lanes, speed, regional accessibility, direct access, density of roadway length, and density of seasonal household) were selected to develop the models. ^ To investigate the predictive powers of various AADT predictors over the space, the statistics including local r-square, local parameter estimates, and local errors were examined and mapped. The local variations in relationships among parameters were investigated, measured, and mapped to assess the usefulness of GWR methods. ^ The results indicated that the GWR models were able to better explain the variation in the data and to predict AADT with smaller errors than the ordinary linear regression models for the same dataset. Additionally, GWR was able to model the spatial non-stationarity in the data, i.e., the spatially varying relationship between AADT and predictors, which cannot be modeled in ordinary linear regression. ^

A Q factor analysis of college undergraduate students' study behaviors

The purpose of this study was to better understand the study behaviors and habits of university undergraduate students. It was designed to determine whether undergraduate students could be grouped based on their self-reported study behaviors and if any grouping system could be determined, whether group membership was related to students’ academic achievement. A total of 152 undergraduate students voluntarily participated in the current study by completing the Study Behavior Inventory instrument. All participants were enrolled in fall semester of 2010 at Florida International University. The Q factor analysis technique using principal components extraction and a varimax rotation was used in order to examine the participants in relation to each other and to detect a pattern of intercorrelations among participants based on their self-reported study behaviors. The Q factor analysis yielded a two factor structure representing two distinct student types among participants regarding their study behaviors. The first student type (i.e., Factor 1) describes proactive learners who organize both their study materials and study time well. Type 1 students are labeled “Proactive Learners with Well-Organized Study Behaviors”. The second type (i.e., Factor 2) represents students who are poorly organized as well as being very likely to procrastinate. Type 2 students are labeled Disorganized Procrastinators. Hierarchical linear regression was employed to examine the relationship between student type and academic achievement as measured by current grade point averages (GPAs). The results showed significant differences in GPAs between Type 1 and Type 2 students at the .05 significance level. Furthermore, student type was found to be a significant predictor of academic achievement beyond and above students’ attribute variables including sex, age, major, and enrollment status. The study has several implications for educational researchers, practitioners, and policy makers in terms of improving college students' learning behaviors and outcomes.

Development, validation and uncertainty analysis of quantitative structure and activity relationship models for Log P of disinfection by -products

Hydrophobicity as measured by Log P is an important molecular property related to toxicity and carcinogenicity. With increasing public health concerns for the effects of Disinfection By-Products (DBPs), there are considerable benefits in developing Quantitative Structure and Activity Relationship (QSAR) models capable of accurately predicting Log P. In this research, Log P values of 173 DBP compounds in 6 functional classes were used to develop QSAR models, by applying 3 molecular descriptors, namely, Energy of the Lowest Unoccupied Molecular Orbital (ELUMO), Number of Chlorine (NCl) and Number of Carbon (NC) by Multiple Linear Regression (MLR) analysis. The QSAR models developed were validated based on the Organization for Economic Co-operation and Development (OECD) principles. The model Applicability Domain (AD) and mechanistic interpretation were explored. Considering the very complex nature of DBPs, the established QSAR models performed very well with respect to goodness-of-fit, robustness and predictability. The predicted values of Log P of DBPs by the QSAR models were found to be significant with a correlation coefficient R2 from 81% to 98%. The Leverage Approach by Williams Plot was applied to detect and remove outliers, consequently increasing R 2 by approximately 2% to 13% for different DBP classes. The developed QSAR models were statistically validated for their predictive power by the Leave-One-Out (LOO) and Leave-Many-Out (LMO) cross validation methods. Finally, Monte Carlo simulation was used to assess the variations and inherent uncertainties in the QSAR models of Log P and determine the most influential parameters in connection with Log P prediction. The developed QSAR models in this dissertation will have a broad applicability domain because the research data set covered six out of eight common DBP classes, including halogenated alkane, halogenated alkene, halogenated aromatic, halogenated aldehyde, halogenated ketone, and halogenated carboxylic acid, which have been brought to the attention of regulatory agencies in recent years. Furthermore, the QSAR models are suitable to be used for prediction of similar DBP compounds within the same applicability domain. The selection and integration of various methodologies developed in this research may also benefit future research in similar fields.

The mosses of Terra Nova National Park, Eastern Newfoundland, a bryofloristic analysis and interpretation

The known moss flora of Terra Nova National Park, eastern Newfoundland, comp~ises 210 species. Eighty-two percent of the moss species occurring in Terra Nova are widespread or widespread-sporadic in Newfoundland. Other Newfoundland distributional elements present in the Terra Nova moss flora are the northwestern, southern, southeastern, and disjunct elements, but four of the mosses occurring in Terra Nova appear to belong to a previously unrecognized northeastern element of the Newfoundland flora. The majority (70.9%) of Terra Nova's mosses are of boreal affinity and are widely distributed in the North American coniferous forest belt. An additional 10.5 percent of the Terra Nova mosses are cosmopolitan while 9.5 percent are temperate and 4.8 percent are arctic-montane species. The remaining 4.3 percent of the mosses are of montane affinity, and disjunct between eastern and western North America. In Terra Nova, temperate species at their northern limit are concentrated in balsam fir stands, while arctic-montane species are restricted to exposed cliffs, scree slopes, and coastal exposures. Montane species are largely confined to exposed or freshwater habitats. Inability to tolerate high summer temperatures limits the distributions of both arctic-montane and montane species. In Terra Nova, species of differing phytogeographic affinities co-occur on cliffs and scree slopes. The microhabitat relationships of five selected species from such habitats were evaluated by Discriminant Functions Analysis and Multiple Regression Analysis. The five mosses have distinct and different microhabitats on cliffs and scree slopes in Terra Nova, and abundance of all but one is associated with variation in at least one microhabitat variable. Micro-distribution of Grimmia torquata, an arctic-montane species at its southern limit, appears to be deterJ]lined by sensitivity to high summer temperatures. Both southern mosses at their northern limit (Aulacomnium androgynum, Isothecium myosuroides) appear to be limited by water availability and, possibly, by low winter temperatures. The two species whose distributions extend both north and south or the study area (Encalypta procera, Eurhynchium pulchellum) show no clear relationship with microclimate. Dispersal factors have played a significant role in the development of the Terra Nova moss flora. Compared to the most likely colonizing source (i .e. the rest of the island of Newfoundland), species with small diaspores have colonized the study area to a proportionately much greater extent than have species with large diaspores. Hierarchical log-linear analysis indicates that this is so for all affinity groups present in Terra Nova. The apparent dispersal effects emphasize the comparatively recent glaciation of the area, and may also have been enhanced by anthropogenic influences. The restriction of some species to specific habitats, or to narrowly defined microhabitats, appears to strengthen selection for easily dispersed taxa.

Multivariate Techniques in Biomechanical Analysis

This work outlines the theoretical advantages of multivariate methods in biomechanical data, validates the proposed methods and outlines new clinical findings relating to knee osteoarthritis that were made possible by this approach. New techniques were based on existing multivariate approaches, Partial Least Squares (PLS) and Non-negative Matrix Factorization (NMF) and validated using existing data sets. The new techniques developed, PCA-PLS-LDA (Principal Component Analysis – Partial Least Squares – Linear Discriminant Analysis), PCA-PLS-MLR (Principal Component Analysis – Partial Least Squares –Multiple Linear Regression) and Waveform Similarity (based on NMF) were developed to address the challenging characteristics of biomechanical data, variability and correlation. As a result, these new structure-seeking technique revealed new clinical findings. The first new clinical finding relates to the relationship between pain, radiographic severity and mechanics. Simultaneous analysis of pain and radiographic severity outcomes, a first in biomechanics, revealed that the knee adduction moment’s relationship to radiographic features is mediated by pain in subjects with moderate osteoarthritis. The second clinical finding was quantifying the importance of neuromuscular patterns in brace effectiveness for patients with knee osteoarthritis. I found that brace effectiveness was more related to the patient’s unbraced neuromuscular patterns than it was to mechanics, and that these neuromuscular patterns were more complicated than simply increased overall muscle activity, as previously thought.

Estimation of Sample Size and Power For Quantile Regression

Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of the response, QR provides an alternative way to model the relationship between quantiles of the response and covariates. Therefore, QR can be widely used to solve problems in econometrics, environmental sciences and health sciences. Sample size is an important factor in the planning stage of experimental design and observational studies. In ordinary linear regression, sample size may be determined based on either precision analysis or power analysis with closed form formulas. There are also methods that calculate sample size based on precision analysis for QR like C.Jennen-Steinmetz and S.Wellek (2005). A method to estimate sample size for QR based on power analysis was proposed by Shao and Wang (2009). In this paper, a new method is proposed to calculate sample size based on power analysis under hypothesis test of covariate effects. Even though error distribution assumption is not necessary for QR analysis itself, researchers have to make assumptions of error distribution and covariate structure in the planning stage of a study to obtain a reasonable estimate of sample size. In this project, both parametric and nonparametric methods are provided to estimate error distribution. Since the method proposed can be implemented in R, user is able to choose either parametric distribution or nonparametric kernel density estimation for error distribution. User also needs to specify the covariate structure and effect size to carry out sample size and power calculation. The performance of the method proposed is further evaluated using numerical simulation. The results suggest that the sample sizes obtained from our method provide empirical powers that are closed to the nominal power level, for example, 80%.

Tooth replacement for partially dentate elders: a willingness-to-pay analysis

Objectives: The primary aim of this study was to investigate partially dentate elders' willingness-to-pay (WTP) for two different tooth replacement strategies: Removable Partial Dentures (RPDs) and, functionally orientated treatment according to the principles of the Shortened Dental Arch (SDA). The secondary aim was to measure the same patient groups' WTP for dental implant treatment.Methods: 55 patients who had completed a previous RCT comparing two tooth replacement strategies (RPDs (n=27) and SDA (n=28)) were recruited (Trial Registration no. ISRCTN26302774). Patients were asked to indicate their WTP for treatment to replace missing teeth in a number of hypothetical scenarios using the payment card method of contingency evaluation coupled to different costs. Data were collected on patients' social class, income levels and other social circumstances. A Mann-Whitney U Test was used to compare differences in WTP between the two treatment groups. To investigate predictive factors for WTP, multiple linear regression analyses were conducted.Results: The median age for the patient sample was 72.0 years (IQR: 71-75 years). Patients who had been provided with RPDs indicated that their WTP for this treatment strategy was significantly higher (€550; IQR: 500-650) than those patients who had received SDA treatment (€500; IQR: 450-550) (p=0.003). However patients provided with RPDs indicated that their WTP for SDA treatment (€650; IQR: 600-650) was also significantly higher than those patients who had actually received functionally orientated treatment (€550; IQR: 500-600) (p<0.001). The results indicated that both current income levels and previous treatment allocation were significantly correlated to WTP for both the RPD and the SDA groups. Patients in both treatment groups exhibited little WTP for dental implant treatment with a median value recorded which was half the market value for this treatment (€1000; IQR: 500-1000).Conclusions: Amongst this patient cohort previous treatment experience had a strong influence on WTP as did current income levels. Both treatment groups indicated a very strong WTP for simpler, functionally orientated care using adhesive fixed prostheses (SDA) over conventional RPDs. Clinical significance: Partially dentate older patients expressed a strong preference for functionally orientated tooth replacement as an alternative to conventional RPDs.