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Taking into account the fluctuation of the growth rate on the left and right sides of the classic QGLF, a quadratic exponential quality gain-loss function (QGLF) is created based on the asymmetric QGLF. The two scenarios of non-normal distribution (triangular distribution) and truncated normal distribution of quality characteristic values are optimized using the quadratic exponential quality gain-loss process mean. Through the case study approaches, the empirical validity and applicability of the quadratic exponential QGLF model are thoroughly assessed, confirming its effectiveness in improving quality management practices.

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The distribution of motor errors can influence optimal motor planning (where to aim). In football instep kicking, it was shown that ball landing locations exhibit the right-up-left-down elliptical distribution in right-footed kickers and vice versa. However, this was reported as a result of mixed multiple kickers; the individual-level error distribution has been unclear. Here we show substantial inter-individual variability in error shape and error direction in the 30 kicks aimed at a target (1.7 m high, 11.0 m in front) by 27 male football players. All players exhibit right-up-left-down distributions with ellipticity (minor/major radius ratio of the 95% confidence ellipse) ranging from 0.25 to 0.77 and major axis angle ranging from 13 to 67° from the horizontal axis. The mean absolute error and the area of the 95% confidence ellipse are not significantly correlated with major axis angle (ρ ≤ 0.312) and ellipticity (|r| ≤ 0.343). By simulating shots aimed at the top-right and top-left edges of a goal with these observed ranges and normalised ellipse area, we reveal a wide range of probability of shots on goal (top-right: 2.7-fold difference, top-left: 1.5-fold difference) due to inter-individual variability in error shape and direction independent of error size. Further simulation shows that, depending on the shape-direction combination, the aiming points with the same 80% probability of shots on goal change by up to 0.3 m vertically, even for the same minimal error size. We highlight the importance for football players to consider not only accuracy/precision, but also error shape and direction to optimise motor planning.

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Introduction: The HGSHS:A is one of the most commonly used measures of hypnotic suggestibility. However, this test suffers from low feasibility due to a time requirement exceeding 1 h, and from a questionable representation of the normal population. Recently, a short version of HGSHS-5:G was developed and published, and now the first results are available. The scope of this investigation was to verify the assumption of equally positioned and normally distributed scores, resulting in equally sized suggestibility groups in a number of different studies with full or short versions of HGSHS, and to compare the results of the 11-item score with the 5-item score, the latter being calculated from either the full version or the short version test. Methods: Data from 21 studies with testing for HGSHS were analyzed, 15 using the HGSHS:A full version and six using the HGSHS-5:G short version, for a total of 2,529 data sets. Position and distribution of both the 11-item score and the 5-item score were tested. Linear regression analysis was used to compare the two scores, as well as cross-table and weighted Cohen's kappa to determine the match of grouping into low and high suggestibility. To evaluate contributing factors to the observed differences in the study results, a multifactorial analysis of variance was performed. Results: In the different studies, position and distribution of scores, as well as group sizes for low and high suggestibles, varied. All score distributions were found to be non-normal and shifted to the right from the middle score; the shift was more extensive with the 11-item score. The correlation between both scores calculated from full version tests was moderate (R 2 = 0.69), as was the match of suggestibility grouping (κ = 0.58). Studies using the short version involving less student-dominated populations showed sufficient agreement with the full version, but lower scores were caused by an increase in the zero score. Conclusion: A normal population is not represented in most applications of HGSHS, and grouping into low and high suggestibles varies, mainly due to different positions of score distributions. A direct comparison of full and short versions of HGSHS tested in the same subjects is still missing.

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In this article, we develop a new control chart based on the Exponentially Weighted Moving Average (EWMA) statistic, termed the New Extended Exponentially Weighted Moving Average (NEEWMA) statistic, designed to recognize slight changes in the process mean. We derive expressions for the mean and variance of the NEEWMA statistic, ensuring an unbiased estimation of the mean, with simulation results showing lower variance compared to traditional EWMA charts. Evaluating its performance using Average Run Length (ARL), our analysis reveals that the NEEWMA control chart outperforms EWMA and Extended EWMA (EEWMA) charts in swiftly recognizing shifts in the process mean. Illustrating its operational methodology through Monte Carlo simulations, an illustrative example using practical data is also provided to showcase its effectiveness.

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In the mechanical cutting industry, trial production is used for predicting and evaluating the quality of product processes before batch production, and it can be expressed through the qualification rate. However, it cannot objectively and comprehensively evaluate the quality of product processes. This study optimizes the analysis of outliers and stability in mathematical statistics to better apply it in the mechanical cutting industry; then, it combines them with process capability analysis. Simultaneously, considering the non-normal distribution of process parameters, a batch production-prediction model is proposed. The reliability of batch production-prediction model is verified by the diameter, roundness and roughness of structural common samples. Meanwhile, for other mechanical parts in the mechanical cutting industry, the model proposed in this paper can be used to quickly and accurately predict and evaluate batch production.

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For a micro-indentation hardness test with non-destructivity, the Nix-Gao model is widely used to describe tested hardness or microhardness variation with an indentation depth induced by indentation size effect, in which tested hardness approaches the macrohardness when the indentation depth is large enough. Based on an analysis of hardness measurements on 10 body-centered cubic steels with diverse microstructure, this paper proposes an analytical relation between microhardness to macrohardness ratio and the indentation depth by explicitly linking characteristic indentation depth (a data-fitting parameter) to grain size and ferrite volume fraction using two different methods. In addition, the normal distribution theory is incorporated to consider the inevitable scatter of identical measurements resulting from material heterogeneity and machining/testing errors. Results show that the proposed model, with 96% reliability, can effectively predict microhardness variation with the indentation depth and its scatter.

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Gaussian signal detection models with equal variance are commonly used in simple yes-no detection and discrimination tasks whereas more flexible models with unequal variance require additional information. Here, a hierarchical Bayesian model with equal variance is extended to an unequal-variance model by exploiting variability of hit and false-alarm rates in a random sample of participants. This hierarchical model is investigated analytically, in simulations and in applications to existing data sets. The results suggest that signal variance and other parameters can be accurately estimated if plausible assumptions are met. It is concluded that the model provides a promising alternative to the ubiquitous equal-variance model for binary data.

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Chemical mechanical planarization (CMP) reduces film thickness, eliminates step height, and achieves high levels of planarity in semiconductor manufacturing. However, research into its mechanisms is still in progress, and there are many issues to be resolved. To solve problems in CMP, it is necessary to understand the contact phenomenon that occurs at the pad-wafer interface, especially pad asperity. Moreover, understanding the non-uniform distribution of pad asperity, such as height and radius, is essential for predicting the material removal rate (MRR). In this study, based on the existing Greenwood-Williamson (GW) theory and probability density function (PDF), a modified mathematical model that includes changes in asperity distribution was developed and validated experimentally. The contact model proposed in this study included functions that calculated the time-dependent height and radius wear of the pad asperities. Specifically, the experimentally obtained values were compared with the values obtained by the model, and the comparison results were analyzed. Thereby, it was found that the contact model and MRR model considering the change in asperity wear and distribution due to CMP proposed in this study are in better agreement with the experimental results than the existing model, which shows that the MRR can be predicted by a mathematical model using the change in asperity distribution.

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A biodegradable hybrid polymer patch was invented at the University of Cincinnati to cover gaps on the skin over the spinal column of a growing fetus, characterized by the medical condition spina bifida. The inserted patch faces amniotic fluid (AF) on one side and cerebrospinal fluid on the other side. The goal is to provide a profile of the roughness of a patch over time at 0, 4, 8, 12, and 16 weeks with a 95% confidence band. The patch is soaked in a test tube filled with either amniotic fluid (AF) or phosphate-buffered saline (PBS) in the lab. If roughness is measured at any time point for a patch, the patch is destroyed. Thus, it is impossible to measure roughness at all weeks of interest for any patch. It is important to assess the roughness of a patch because the rougher the patch is, the faster the skin grows under the patch. We use a model-based approach with Monte Carlo simulations to estimate the profile over time with a 95% confidence band. The roughness profiles are similar with both liquids. The profile can be used as a template for future experiments on the composition of patches.

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BACKGROUND: This study addresses the significant challenge of low survival rates in patients with cause-specific lung cancer accompanied by bone or brain metastases. Recognizing the critical need for an effective predictive model, the research aims to establish survival prediction models using both parametric and non-parametric approaches. METHODS: Clinical data from lung cancer patients with at least one bone or brain metastasis between 2000 and 2020 from the SEER database were utilized. Four models were constructed: Cox proportional hazard, Weibull accelerated failure time (AFT), log-normal AFT, and Zografos-Balakrishnan log-normal (ZBLN). Independent prognostic factors for cause-specific survival were identified, and model fit was evaluated using Akaike's and Bayesian information criteria. Internal validation assessed predictive accuracy and discriminability through the Harriel Concordance Index (C-index) and calibration plots. RESULTS: A total of 20,412 patients were included, with 14,290 (70%) as the training cohort and 6122 (30%) validation. Independent prognostic factors selected for the study were age, race, sex, primary tumor site, disease grade, total malignant tumor in situ, metastases, treatment modality, and histology. Among the accelerated failure time (AFT) models considered, the ZBLN distribution exhibited the most robust model fit for the 3- and 5-year survival, as evidenced by the lowest values of Akaike's information criterion of 6322 and 79,396, and the Bayesian information criterion of 63,495 and 79,396, respectively. This outperformed other AFT and Cox models (AIC = [156,891, 211,125]; BIC = [158,848, 211,287]). Regarding predictive accuracy, the ZBLN AFT model achieved the highest concordance C-index (0.682, 0.667), a better performance than the Cox model (0.669, 0.643). The calibration curves of the ZBLN AFT model demonstrated a high degree of concordance between actual and predicted values. All variables considered in this study demonstrated significance at the 0.05 level for the ZBLN AFT model. However, differences emerged in the significant variations in survival times between subgroups. The study revealed that patients with only bone metastases have a higher chance of survival compared to only brain and those with bone and brain metastases. CONCLUSIONS: The study highlights the underutilized but accurate nature of the accelerated failure time model in predicting lung cancer survival and identifying prognostic factors. These findings have implications for individualized clinical decisions, indicating the potential for screening and professional care of lung cancer patients with at least one bone or brain metastasis in the future.

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Carbonylated sites are the determining factors for functional changes or deletions in carbonylated proteins, so identifying carbonylated sites is essential for understanding the process of protein carbonylated and exploring the pathogenesis of related diseases. The current wet experimental methods for predicting carbonylated modification sites ae not only expensive and time-consuming, but also have limited protein processing capabilities and cannot meet the needs of researchers. The identification of carbonylated sites using computational methods not only improves the functional characterization of proteins, but also provides researchers with free tools for predicting carbonylated sites. Therefore, it is essential to establish a model using computational methods that can accurately predict protein carbonylated sites. In this study, a prediction model, CarSitePred, is proposed to identify carbonylation sites. In CarSitePred, specific location amino acid hydrophobic hydrophilic, one-to-one numerical conversion of amino acids, and AlexNet convolutional neural networks convert preprocessed carbonylated sequences into valid numerical features. The K-means Normal Distribution-based Undersampling Algorithm (KNDUA) and Localized Normal Distribution Oversampling Technology (LNDOT) were firstly proposed and employed to balance the K, P, R and T carbonylation training dataset. And for the first time, carbonylation modification sites were transformed into the form of images and directly inputted into AlexNet convolutional neural network to extract features for fitting SVM classifiers. The 10-fold cross-validation and independent testing results show that CarSitePred achieves better prediction performance than the best currently available prediction models. Availability: https://github.com/zuoyun123/CarSitePred.Communicated by Ramaswamy H. Sarma.

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There is a limited understanding of the survival responses of Campylobacter jejuni during thermal processing, which must be investigated for appropriate risk assessment and processing. Therefore, we aimed to elucidate the survival response of C. jejuni and develop a predictive model considering strain variability and uncertainty, which are important for quantitative microbial risk assessment (QMRA) or risk-based processing control measures. We employed the most probable curve (MPC) method to consider the uncertainty in cell concentrations. Further, the multivariate normal (MVN) distribution served as a model for strain variability in bacterial survival behavior. The prediction curves from the MVN successfully captured the parameter variability of the most probable curves of each strain. More than ten reference strains effectively described the strain variability in parameters using the MVN distribution. The findings indicated that, with sufficient strain data, the MVN could estimate the strain variability, including unknown strains. The multi-level model for strain variability can potentially become a specialized tool for QMRA and risk-based processing controls. The combined approach of MPC and MVN provides valuable insights into strain variability, emphasizing the importance of accounting for variability and uncertainty in predictive models for QMRA and risk-based processing control measures.

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This study investigated the feasibility of using hyperspectral imaging (HSI) technique to detect the saponin content in Panax notoginseng (PN) powder. The reflectance hyperspectral images of PN powder samples were collected in the spectral range of 400.6-999.9 nm. Savitzky-golay (SG) smoothing combined with detrending correction was utilized to preprocess the original spectral data. Two model population analysis (MPA) based methods, namely bootstrapping soft shrinkage (BOSS) and iteratively retains informative variables (IRIV) were employed to extract feature wavelengths from the full spectra. A generalized normal distribution optimization based extreme learning machine (GNDO-ELM) model was proposed to establish calibration model between spectra and saponin content, and compared with existing methods (GA-ELM, PSO-ELM and SSA-ELM). The result showed that the IRIV-GNDO-ELM model gave the best performance, with coefficient of determination for prediction (R2P) of 0.953 and root mean square error for prediction (RMSEP) of 0.115%. Therefore, it is possible to determine the saponin content of PN powder by using HSI technique.

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The membrane bioreactor (MBR) process always offers better wastewater treatment than conventional activated sludge (CAS) treatment. However, the difference in their efficacy of virus reduction remains unknown. To investigate this, we monitored virus concentrations before and after MBR and CAS processes over 2 years. Concentrations of norovirus genotypes I and II (NoV GI and GII), aichivirus (AiV), F-specific RNA phage genotypes I, II, and III (GI-, GII-, and GIII-FRNAPHs), and pepper mild mottle virus (PMMoV) were measured by a quantitative polymerase chain reaction (qPCR) method at two municipal wastewater treatment plants (WWTPs A and B) in Japan. Virus concentration datasets containing left-censored data were estimated by using both maximum likelihood estimation (MLE) and robust regression on order statistics (rROS) approaches. PMMoV was the most prevalent at both WWTPs, with median concentrations of 7.5 to 8.8 log10 copies/L before treatment. Log10 removal values (LRVs) of all viruses based on means and standard deviations of concentrations before and after treatment were consistently higher following MBR than following CAS. We used NoV GII as a model pathogen in a quantitative microbial risk assessment of the treated water, and we estimated the additional reductions required following MBR and CAS processes to meet the guideline of 10-6 DALYs pppy for safe wastewater reuse.

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In this study, we tackle the challenge of optimizing the design of a Brushless Direct Current (BLDC) motor. Utilizing an established analytical model, we introduced the Multi-Objective Generalized Normal Distribution Optimization (MOGNDO) method, a biomimetic approach based on Pareto optimality, dominance, and external archiving. We initially tested MOGNDO on standard multi-objective benchmark functions, where it showed strong performance. When applied to the BLDC motor design with the objectives of either maximizing operational efficiency or minimizing motor mass, the MOGNDO algorithm consistently outperformed other techniques like Ant Lion Optimizer (ALO), Ion Motion Optimization (IMO), and Sine Cosine Algorithm (SCA). Specifically, MOGNDO yielded the most optimal values across efficiency and mass metrics, providing practical solutions for real-world BLDC motor design. The MOGNDO source code is available at: https://github.com/kanak02/MOGNDO.

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The cracking problem of asphalt concrete panels is a crucial consideration in the design of hydraulic asphalt concrete seepage control bodies. Panels experiencing uneven rises or falls of water levels during impoundment may exhibit loading rate effects. Investigating the fracture toughness value of asphalt concrete under varying loading rates is essential. This study employs a statistical method to calculate the fracture index KIC, using the semi-circular bending test (SCB) to examine the effect of loading rates on the Type I fracture mode of hydraulic asphalt concrete. The data are analyzed using the two-parameter Weibull distribution curve, offering insights into the minimum number of KIC test specimens. The results indicate an increase in KIC with loading rate, with greater data dispersion at faster rates. The Weibull distribution curve successfully fits the fracture behavior under different loading rates, providing valuable predictions. This study estimates the minimum number of SCB test specimens to be nine, based on a confidence level of 0.95 and a relative deviation not exceeding 5%.

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Determining if the frequency distribution of a given data set follows a normal distribution or not is among the first steps of data analysis. Visual examination of the data, commonly by Q-Q plot, although is acceptable by many scientists, is considered subjective and not acceptable by other researchers. One-sample Kolmogorov-Smirnov test with Lilliefors correction (for a sample size ≥ 50) and Shapiro-Wilk test (for a sample size < 50) are common statistical tests for checking the normality of a data set quantitatively. As parametric tests, which assume that the data distribution is normal (Gaussian, bell-shaped), are more robust compared to their non-parametric counterparts, we commonly use transformations (e.g., log-transformation, Box-Cox transformation, etc.) to make the frequency distribution of non-normally distributed data close to a normal distribution. Herein, I wish to reflect on presenting how to practically work with these statistical methods through examining of real data sets.

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Street trees play an important role in the city, but large-scale, multi-city inventory data are very limited to date, which can help to define geo-climatic and social development influences on urban forest characteristics. In this paper we speculate that at national level, geocliamtes and street development shape the different street tree characteristics, and large scale street View images (SVIs)-measurements favor the identification of factors responsible for the street tree variations in China. By collecting urban trees from 11 metropolises through SVIs method, an inventory of urban trees in China, including 201,942 trees at 9807 sites, was obtained from a latitude gradient from tropical 18oN to cold-temperate 45oN. Individual tree size-related growth status, tree-shrub-herb-related vertical structure, tree species identity, and street condition and street development (total 20 social development parameters) in the inventory is recorded. We analyzed trends and factors influencing street trees characteristics through latitudinal variation, distribution, linear regression, redundancy (RDA) ordination, and inter-city comparisons. The results showed that 1) with latitude increased, DBH and CPS linearly decreased, together with more highly dense forests (>100 trees/100 m street segment) observed. Latitude independence was in TH and forest vertical structural complexity. 2) All tree size data were in the log-normal distribution pattern when the two-parameter model was used and was best fitted by the Johnson distribution pattern when the >2-parameter model was used. 3) Tree growth status showed strong latitude dependency (R2 > 0.4, p < 0.05), with latitude increase accompanied by a higher percentage of trees with poor growth status (diebacks, dead trees, etc.). 4) The top abundant trees were Populus spp., Cinnamomum camphora, Salix spp., Platanus acerifolia, Ficus macrocarpa (5.5 %-14.6 %), and the arbor-shrub-herb three-layer structured forests took 52.3 % of total sites. With latitude rise, increasing abundance of Populus spp., Salix spp., elm, and pine but decreasing abundance of the unrecognizable tree groups were found (p < 0.05). 5) We also constructed a street tree comprehensive index based on their potential for providing services to citizen from the inventory data and found it was negatively related to latitudes. RDA ordination showed that geo-climatic conditions (49 %-61.5 %) and social developments (21.4 %-52.7 %) were almost equally responsible for tree size, growth status, and vertical structural variations, while road width (lane number of the street) was the most potent predictor (coefficient > 2.0 %, p < 0.01) for these variations. Our study can benefit the national-level management of urban forests and inventory-based various ecological service precise evaluation.

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Background: Pathological conditions may result in certain genes having expression variance that differs markedly from that of the control. Finding such genes from gene expression data can provide invaluable candidates for therapeutic intervention. Under the dominant paradigm for modeling RNA-Seq gene counts using the negative binomial model, tests of differential variability are challenging to develop, owing to dependence of the variance on the mean. Methods: Here, we describe clrDV, a statistical method for detecting genes that show differential variability between two populations. We present the skew-normal distribution for modeling gene-wise null distribution of centered log-ratio transformation of compositional RNA-seq data. Results: Simulation results show that clrDV has false discovery rate and probability of Type II error that are on par with or superior to existing methodologies. In addition, its run time is faster than its closest competitors, and remains relatively constant for increasing sample size per group. Analysis of a large neurodegenerative disease RNA-Seq dataset using clrDV successfully recovers multiple gene candidates that have been reported to be associated with Alzheimer's disease.

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The quantitative description of growth rings is yet incomplete, including the functional division into earlywood and latewood. Methods developed to date, such as the Mork criterion for conifers, can be biased and arbitrary depending on species and growth conditions. We proposed the use of modeling of the statistical distribution of tracheids to determine a universal criterion applicable to all conifer species. Thisstudy was based on 50-year anatomical measurements of Pinus sylvestris L., Pinus sibirica Du Tour, and Picea obovata Ledeb. near the upper tree line in the Western Sayan Mountains (South Siberia). Statistical distributions of the cell wall thickness (CWT)-to-radial-diameter (D) ratio and its slope were investigated for raw and standardized data (divided by the mean). The bimodal distribution of the slope for standardized CWT and D was modeled with beta distributions for earlywood and latewood tracheids and a generalized normal distribution for transition wood to account for the gradual shift in cell traits. The modelcan describe with high accuracy the growth ring structure for species characterized by various proportions of latewood, histometric traits, and gradual or abrupt transition. The proportion of two (or three, including transition wood) zones in the modeled distribution is proposed as a desired criterion.