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Single particle level microscopy of immobilized FAPbBr3 nanocrystals (NCs) has elucidated the involvement of different processes in their photoluminescence (PL) intermittency. Four different blinking patterns are observed in the data from more than 100 NCs. The dependence of PL decays on PL intensities brought out in fluorescence lifetime intensity distribution (FLID) plots is rationalized by the interplay of exciton- and trion-mediated recombinations along with hot carrier (HC) trapping. The high intensity-long lifetime component is attributed to neutral exciton recombination, the low intensity-short lifetime component is attributed to trion assisted recombination, and the low intensity-long lifetime component is attributed to hot carrier recombination. Change-point analysis (CPA) of the PL blinking data reveals the involvement of multiple intermediate states. Truncated power law distribution is found to be more appropriate than power law and lognormal distribution for on and off events. Probability distributions of PL trajectories of single NCs are obtained for two different excitation fluences and wavelengths (λex = 400, 440 nm). Trapping rate (kT) prevails at higher power densities for both excitation wavelengths. From a careful analysis of the FLID and probability distributions, it is concluded that there is competition between the HC and trion assisted blinking pathways and that the contribution of these mechanisms varies with excitation wavelength as well as fluence. [ABSTRACT FROM AUTHOR]

The lognormal moment sequence is considered. Using the fractional moments technique, it is first proved that the lognormal has the largest differential entropy among the infinite positively supported probability densities with the same lognormal-moments. Then, relying on previous theoretical results on entropy convergence obtained by the authors concerning the indeterminate Stieltjes moment problem, the lognormal distribution is accurately reconstructed by the maximum entropy technique using only its integer moment sequence, although it is not uniquely determined by moments. [ABSTRACT FROM AUTHOR]

Based on the materials of the Royal Greenwich Observatory catalog, the study of two different sunspot group populations continued: LLG – large long-lived, and SSG – small short-lived groups. The task of achieving a higher accuracy of the population separation parameter than before (Nagovitsyn & Pevtsov 2016, 2021) is being solved. A procedure for randomizing the lifetimes of sunspot groups observed once a day is proposed, which allows for statistical studies to achieve a higher time resolution. The form of the Gnevyshev-Waldmeier Rule is taken, which linearly connects the logarithm of the log S area and the lifetime of the sunspot group LT (over limited time intervals). It is shown that it has coefficients significantly different for SSG and LLG populations. The range of values of the group lifetime parameter separating the populations was found as LT ∗ = 4.75 ± 0.53 days, which is in agreement with the threshold values obtained earlier for the number of days of sunspot group observation: m SSG ⩽ 5 days and m LLG > 5 days. It is shown that the parameters of the bilognormal distribution of the sunspot group areas, obtained from their common grouped sample statistically by Levenberg–Marquardt method and with a preliminary division into lognormal distributions by lifetime, correspond to each other. It was clarified that, with an accuracy of up to a tenth of a day, the SSG population corresponds to the lifetimes of groups ⩽ 4.6 days, and the LLG population corresponds to times ⩾ 4.7 days. The results obtained make it possible to study various physical properties of SSG and LLG populations independently of each other in order to compare them and study their nature. [ABSTRACT FROM AUTHOR]

Radon is a radioactive, carcinogenic gas formed by the radioactive decay of uranium and radium that occur naturally in small amounts in all rocks and soils. It is the largest single source of radiation exposure to the UK population, contributing to more than 1 100 lung cancer deaths each year according to an analysis conducted in 2005. Regulations exist to protect employees (and other persons) where radon concentrations exceed the reference level of 300 Bq m−3. Once the reference level is exceeded, annual doses of more than the public dose limit of 1 mSv a−1 are considered to be excessive. A radon measurement campaign for schools, which started in 2009, generated a large dataset, including those with high numbers of simultaneous radon measurements. Radon data between buildings (e.g. homes) have been shown to correspond broadly to the lognormal distribution, after the additive contribution of outside air has been removed. However, there are fewer studies of the distribution of radon levels within a single, large property. Radon data collected from 533 UK schools with at least 20 valid, simultaneous results were analysed against several statistical models. In approximately 50% of schools the radon levels could be represented by the lognormal distribution and in 60% by the loglogistic lognormal distribution, the latter being a better fit probably owing to its lower sensitivity to the tails of the distribution. Qualitatively, the lognormal and the loglogistic probability plots appeared to be indistinguishable. These findings indicate that the lognormal and loglogistic might be appropriate models to characterise the distribution of radon in most large workplaces. For each statistical model, the two distribution parameters can be used to provide a better estimate of the average dose to the occupants. However, caution is required when assessing doses, since the average estimator of the radon concentration does not predict the highest value and may significantly underestimate or overestimate the dose in specific areas. [ABSTRACT FROM AUTHOR]

Abstract.Under the comprehensive model of assets which satisfy the triple conditions of stochastic jump, stochastic volatility, and stochastic interest rate, the pricing problem of reset options with default risk is investigated. First, two-dimensional log-normal distribution and radical process with reverting property are applied to describe sudden jump of assets and time-varying characteristics of volatility and interest rate, respectively. Further, through the principle of risk neutral pricing with the characteristic function method, we establish the joint characteristic function related to the options. Second, according to measure transform and payoff function decomposition, the analytical pricing and hedging share formulas of vulnerable reset options are given. Third, 3-D fast Fourier transform is constructed to obtain a fast and asymptotic solution of option prices. Finally, the accuracy and stability of 3-D fast Fourier transform is analyzed through numerical examples. The experimental results show that the proposed method can solve the complex pricing problem of vulnerable reset options more efficiently. [ABSTRACT FROM AUTHOR]

Several sugar mills operate as waste-to-energy plants. The shredder is the initial high-energy machine in the production chain and prepares sugarcane. Its hammers, essential spare parts, require continuous replacement. Then, the search for intelligent strategies to extend the lifetime of these hammers is fundamental. This paper presents (a) a dynamic data-driven model for estimating the deterioration and predicting remaining life of the sugarcane shredder hammers during operation, for which the real data of the entering sugarcane flow and the power required to prepare the sugarcane are analyzed, and (b) a management architecture intended for online decision-making assistance to extend the hammers' life by making a trade-off between the desired lifetime, along with a nominal shredder work satisfaction criterion. The deterioration model is validated with real data achieving an accuracy of 84.41%. The remaining life prognostic is within a confidence zone calculated from the historical sugarcane flow, with a probability close to 99%, fitting a lognormal probability distribution. A numerical example is also provided to illustrate a closed loop control, where the proposed architecture is used to extend the useful life of the hammers during operation, adjusting the incoming sugarcane flow while maintaining the nominal work satisfaction of the shredder. [ABSTRACT FROM AUTHOR]

Thanks to the performance improvement introduced by micro sized functional fillers, application of epoxy composites for electrical insulation purposes has become popular. This paper investigates the dielectric properties of epoxy micro-composites filled with alumina (Al2O3). In particular, measurements of relative permittivity, dissipation factor, and electrical breakdown are performed, and a comprehensive statistical analysis on dielectric properties was conducted. AC breakdown strength (AC-BDS) was analyzed for normal distribution using four methods (Anderson–Darling, Shapiro–Wilk, Ryan–Joiner, and Kolmogorov–Smirnov). In addition, the AC-BDS was analyzed at risk probabilities of 1%, 5%, 10%, and 50% using Weibull distribution functions. Both normal and Weibull distributions were evaluated using the Anderson–Darling (A-D) statistic and p-value. Additionally, the log-normal, gamma, and exponential distributions of AC-BDS were examined by A-D goodness-of-fit test. The hypothesis test results of AC-BDS were fit by normal and Weibull distributions, and the compliance was evaluated by p-value and each method statistics. In addition, the experimental results of AC-BDS were fit by log-normal and gamma distributions, and the goodness-of-fit was evaluated by p-value and A-D testing. On the other hand, exponential distribution was not suitable for p-value and A-D testing. The results showed that the distributions of AC-BDS were the best using log-normal distribution. Meanwhile, statistical analysis results verified the apparent effect of temperature on dielectric properties using a paired t-test. The analysis results of this paper not only contribute to better characterization of epoxy/Al2O3 micro-composites but also introduce a comprehensive approach for performing statistical analysis for electrical insulation materials. [ABSTRACT FROM AUTHOR]

Estimating the exposure time to single infectious pathogens and the associated incubation period, based on symptom onset data, is crucial for identifying infection sources and implementing public health interventions. However, data from rapid surveillance systems designed for early outbreak warning often come with outliers originated from individuals who were not directly exposed to the initial source of infection (i.e. tertiary and subsequent infection cases), making the estimation of exposure time challenging. To address this issue, this study uses a three-parameter lognormal distribution and proposes a new γ-divergence-based robust approach for estimating the parameter corresponding to exposure time with a tailored optimization procedure using the majorization-minimization algorithm, which ensures the monotonic decreasing property of the objective function. Comprehensive numerical experiments and real data analyses suggest that our method is superior to conventional methods in terms of bias, mean squared error, and coverage probability of 95% confidence intervals. [ABSTRACT FROM AUTHOR]

Seismic risk expresses the expected degree of damage and loss following a catastrophic event. An efficient tool for assessing the seismic risk of embankments is fragility curves. This research investigates the influence of embankment's geometry, the depth of rupture occurrence, and the underlying sandy soil's conditions on the embankment's fragility. To achieve this, the response of three highway embankments resting on sandy soil was examined through quasi-static parametric numerical analyses. For the establishment of fragility curves, a cumulative lognormal probability distribution function was used. The maximum vertical displacement of the embankments' external surface and the fault displacement were considered as the damage indicator and the intensity measure, respectively. Damage levels were categorized into three qualitative thresholds: minor, moderate, and extensive. All fragility curves were generated for normal and reverse faults, as well as the combination of those fault types (dip-slip fault). Finally, the proposed curves were verified via their comparison with those provided by HAZUS. It was concluded that embankment geometry and depth of fault rupture appearance do not significantly affect fragility, as exceedance probabilities show minimal differences (<4%). However, an embankment founded on dense sandy soil reveals slightly higher fragility compared to the one founded on loose sand. Differences regarding the probability of exceedance of a certain damage level are restricted by a maximum of 7%. [ABSTRACT FROM AUTHOR]

Accurate prediction of material properties is essential in structural engineering design to ensure reliability and safety. Traditional approaches often rely on Gaussian distributions to model material variability. However, our research reveals limitations with Gaussian assumptions, particularly when covariance parameters exceed certain thresholds, leading to physically unrealistic negative values for material properties. To overcome these limitations, we investigate an alternative approach using lognormal distributions for material property modeling. Through Monte Carlo simulations employing Cholesky decomposition, we compare the performance of lognormal distributions with Gaussian counterparts. Our findings demonstrate that lognormal distributions offer a viable alternative, providing more accurate representations of material variability while maintaining computational efficiency. Furthermore, we utilize finite element method (FEM) data from Monte Carlo simulations to predict beam deflection using deep neural networks (DNNs). Leveraging inverse modeling techniques, we showcase the ability to predict elastic modulus from beam deflection data under both normal and lognormal distribution assumptions. By integrating lognormal modeling and inverse modeling techniques into structural analysis, we enhance the realism and accuracy of predictions, thereby improving reliability in engineering design. This paper discusses the implications of our findings and emphasizes the importance of considering alternative probability distributions for material property modeling in structural engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the optimal experimental planning for multi-level stress testing with Type-II censoring when the test units can be put into coherent systems for the experiment. Based on the notion of system signatures of coherent systems and assuming the lifetimes of the test units follow a distribution in a general log-location-scale family of distributions, the maximum likelihood estimators of the model parameters and the Fisher information matrix are derived. For optimal experimental planning, in addition to some commonly used optimality criteria, such as D-optimality, A-optimality, and V-optimality, we also consider the total time of the experiment and the total time on test. Then, motivated by a real-life application in the reliability study of furniture joints, we focus on using series systems in multi-level stress experiments. The methodology is illustrated by considering lognormal and Weibull distributed test units. Numerical and Monte Carlo simulation studies are used to demonstrate the advantages and disadvantages of using series systems in life-testing experiments. A numerical example based on furniture joints with sensitivity analysis is used to elucidate how the proposed methods can be used in planning a life-testing experiment. Finally, some concluding remarks with some future research directions are provided. [ABSTRACT FROM AUTHOR]

Background Reproducibility has been well studied in the field of food analysis; the RSD is said to follow a Horwitz curve with certain exceptions. However, little systematic research has been done on predicting repeatability or intermediate precision. Objective We developed a regression method to estimate within-laboratory SDs using hierarchical Bayesian modeling and analyzing duplicate measurement data obtained from actual laboratory tests. Methods The Hamiltonian Monte Carlo method was employed and implemented using R with Stan. The basic structure of the statistical model was assumed to be a Chi-squared distribution, the fixed effect of the predictor was assumed to be a nonlinear function with a constant term and a concentration-dependent term, and the random effects were assumed to follow a lognormal distribution as a hierarchical prior. Results By analyzing over 300 instances, we obtained regression results that fit well with the assumed model, except for moisture, which was a method-defined analyte. The developed method applies to a wide variety of analytes measured using general principles, including spectroscopy, GC, and HPLC. Although the estimated precisions were within the Horwitz ratio criteria for repeatability, some cases using high-sensitivity detectors, such as mass spectrometers, showed SDs below that range. Conclusion We propose utilizing the within-laboratory precision predicted by the model established in this study for internal QC and measurement uncertainty estimation without considering sample matrices. Highlights Performing statistical modeling on data from double analysis, which is conducted as a part of internal QCs, will simplify the estimation of the precision that fits each analytical system in a laboratory. [ABSTRACT FROM AUTHOR]

We estimated the severity of cerebellar ataxia by analyzing gait rhythm. We measured the step times in patients with pure cerebellar ataxia and healthy controls and then analyzed the distribution of the ratios of adjacent times. Gait rhythm displayed the best adaptation when expressed as the sum of the power law and lognormal distributions in both groups, and the groups could be distinguished by the exponent of the power law distribution, reflecting the fractal property of gait rhythm. Gait rhythm might reflect different features of impairment in patients with cerebellar ataxia, making it a useful continuous scale for cerebellar ataxia. • We identified a novel pattern of gait rhythm distribution caused by cerebellar ataxia. • A linear combination of power law and lognormal components optimized the fitting of the cumulative gait rhythm distribution. • The power law was indicative of the fractal property of gait rhythm. • The two components correlated SARA kinetic and gait/posture subscores, respectively. • Gait rhythm analysis could provide a useful continuous scale for cerebellar ataxia. [ABSTRACT FROM AUTHOR]

The synthetic Tukey's control chart (denoted by Syn-TCC) applies a single observation in the process monitoring and is relatively robust to outliers. For a complex process, the probability distribution of quality characteristic must be carefully identified and the loss of quality characteristic, which is defined as the deviation from the target value, must be accurately estimated so that the quality state of the process may be more comprehensively described. However, the literature rarely studied the economic design of the Syn-TCC with Taguchi's loss function under non normality. In the present study, it is assumed that the quality characteristic follows a log-normal distribution and Taguchi's asymmetric linear and quadratic loss functions are involved to develop the economic-statistical design of the Syn-TCC for multiple assignable causes. A case study is presented to illustrate the application of this economic-statistical design of the Syn-TCC to an IC package industry. The sensitivity analysis of this case study reveals that a larger production lot size and larger two coefficients of loss functions generally lead to a higher total expected cost. [ABSTRACT FROM AUTHOR]

For metropolises like Beijing, heavy congestions cause transit passengers' unreliable travel time, including in vehicle time and waiting time. Comparing with other managerial measures, designing a lane for bus use only is an effective method to improve travel reliability, for it can eliminate the influence on bus-driving conditions. This paper proposes a reliable and practical method to determine exclusive bus lanes (EBL). A reliability-based optimization model is established, in which the tradeoff among bus and private car passengers' travel time, reliability, and EBL construction cost are considered. Based on the actual network, a user equilibrium demand assignment model is applied to estimate the dynamic bus flow distribution. Since the model is nonlinear, a two-step method is proposed where tangent lines are introduced to constitute an envelope curve to linearize the model. This work conducts the statistical modeling and fitting analysis with actual bus trajectory data, collected on EBL in Beijing during peak hours. Passenger travel time distributions are fitted to estimate the statistical passenger travel time; Lognormal distribution and Gaussian distribution are the best fit. The optimization results indicate that the passenger travel time reliability can be improved by 5.5% by the optimized EBL location scheme. This study will provide a theoretical basis and methodological support for improving the service level of the public transportation system in large cities through the scientific planning of exclusive bus lanes. [ABSTRACT FROM AUTHOR]

The most common form of solidification of metals is heterogeneous nucleation, in which the particles, regardless of whether they are endogenous or exogenous, nucleate the primary crystal phase, becoming solid crystal particles and, subsequently, initiating into grains during solidification. Explosive grain initiation has been proposed recently for these particles, which have significant nucleation undercooling, in which once nucleation happens, a certain number of solid particles can initiate into grains simultaneously, resulting in recalescence. This is a different form of grain initiation and has high potential for more significant grain refinement in casting alloys. In this work, an analytical model is designed to describe explosive grain initiation, based on which the criteria for the three different grain initiation forms, explosive grain initiation (EGI), hybrid grain initiation (HGI), and progressive grain initiation (PGI), are derived. These criteria are employed to develop a grain initiation map for the Mg-Al alloy system inoculated with nucleant particles having a log-normal size distribution. This work can not only help us to understand the effect of each condition, such as the cooling rate and the solute concentration, on grain initiation behaviors, but also predict the grain size for alloy systems with relatively impotent nucleant particles during solidification. [ABSTRACT FROM AUTHOR]

Globally, the prevalence of multidrug-resistant tuberculosis (MDR-TB) has been increasing recently. This is a major public health concern, as MDR-TB is more difficult to treat and has poorer outcomes compared to drug-sensitive tuberculosis. The main objective of the study was to identify risk factors for recurrent multidrug-resistant tuberculosis, at Alert Specialized Hospital, Addis Ababa, by using different parametric shared frailty models. From January 2016 to December 2021, a retrospective study was conducted on MDR-TB patients at Alert Specialized Hospital in Addis Ababa. The data for the study were collected from the medical records of MDR-TB patients at the hospital during this time period. Gamma and inverse-Gaussian shared frailty models were used to analyze the dataset, with the exponential, Weibull, and lognormal distributions included as baseline hazard functions. The data were analyzed using R statistical software. The median recurrence time of the patients was 12 months, and 149 (34.3%) had recurrences. The clustering effect was statistically significant for multiple drug-resistant tuberculosis patients' recurrence. According to the Weibull-Inverse-Gaussian model, factors that reduced time to MDR-TB recurrence included lower weight (ɸ = 0.944), smoking (ɸ = 0.045), alcohol use (ɸ = 0.631), hemoptysis (ɸ = 0.041), pneumonia (ɸ = 0.564), previous anti-TB treatment (ɸ = 0.106), rural residence (ɸ = 0.163), and chronic diseases like diabetes (ɸ = 0.442) were associated with faster recurrence. While, higher education (ɸ = 3.525) and age (ɸ = 1.021) extended time to recurrence. For weight increment, smokers and alcohol users, clinical complications of hemoptysis and pneumonia, patients with pulmonary disease who had a history of previous anti-TB treatment, and being rural residents are prognostic factors. There was a significant clustering effect at the Alert Specialized Hospital in Addis Ababa, Ethiopia. The Weibull-Inverse Gaussian Shared Frailty Model was chosen as the best model for predicting the time to recurrence of MDR-TB. [ABSTRACT FROM AUTHOR]

An attempt was made to evaluate the elongation level as a stressor on biodegradable starch films reinforced with nanoclay using a simple linear model. A total of 120 film units were subjected to increasing elongation levels and the exact break time of the failed units was monitored. Nine different attempts were made to fit the data distribution and the lognormal distribution was chosen as the most suitable because it resulted in the lowest values of the regression fit indices −2LL, AICc and BIC. Following the selection of the best fit, it was, generally, observed that an increase in the elongation level resulted in the decreasing exact break time of the films. Among several models, the best fit was provided by the simple linear model. Based on this model, the acceleration factor was estimated, and it was shown that it increased exponentially while increasing the elongation level. Finally, the probability of failure and the hazard rate of the film units as a function of the elongation level were estimated, demonstrating the applicability of this method as a tool for food packaging film failure prediction. [ABSTRACT FROM AUTHOR]

Background: Cardiovascular disease (CVD) is the leading cause of premature mortality worldwide. Despite existing research on CVD risk factors, the study of premature CVD mortality in Malaysia remains limited. This study employs survival analysis to model modifiable risk factors associated with premature CVD mortality among Malaysian adults. Method: We utilised data from Malaysia's National Health and Morbidity Survey (NHMS) conducted in 2006, 2011, and 2015, linked with mortality records. The cohort comprised individuals aged 18 to 70 during the NHMS interview. Follow-up extended to 2021, focusing on CVD-related premature mortality between ages 30 and 70. We employed six survival models: a semi-parametric Cox proportional hazard (PH) and five parametric survival models, which were Exponential, Weibull, Gompertz, log-normal and log-logistic distributions using R software. The age standardized incidence rate (ASIR) of premature CVD mortality was calculated per 1000 person-years. Results: Among 63,722 participants, 886 (1.4%) experienced premature CVD mortality, with an ASIR of 1.80 per 1000 person-years. The best-fit models (based on AIC value) were the stratified Cox model by age (semi-parametric) and the log-normal accelerated failure time (AFT) model (parametric). Males had higher risk (Hazard Ratio, HR = 2.68) and experienced 49% shorter survival time (Event Time Ratio, ETR = 0.51) compared to females. Compared to Chinese ethnicity, Indians, Malays, and other Bumiputera had higher HR and lower survival times. Rural residents and those with lower education also faced increased HRs and reduced survival times. Diabetes (diagnosed: HR = 3.26, ETR = 0.37; undiagnosed: HR = 1.63, ETR = 0.63), hypertension (diagnosed: HR = 1.84, ETR = 0.53; undiagnosed: HR = 1.46, ETR = 0.68), and undiagnosed hypercholesterolemia (HR = 1.31, ETR = 0.80) increased risk and decreased survival times. Additionally, current smoking and abdominal obesity elevated risk (HR = 1.38, 1.60) and shortened survival (ETR = 0.81, 0.71). Conclusion: The semi-parametric and parametric survival models both highlight the considerable impact of socioeconomic status and modifiable risk factors on premature CVD mortality, underscoring the imperative for targeted interventions to effectively mitigate these effects. [ABSTRACT FROM AUTHOR]

Simple Summary: Chiggers are common ectoparasites on rodents and other small mammals, and they transmit scrub typhus, a zoonotic disease. Dehong in Yunnan Province of southwest China is located on the China–Myanmar border, and it is a focus of scrub typhus. The present paper reports the infestation and distribution of chiggers on small mammals in Dehong for the first time. From 1760 rodents and other sympatric small mammals, a total of 9309 chiggers were identified, representing 117 species. Most chigger species had low host specificity. Leptotrombidium deliense, a major vector of scrub typhus in China, was the dominant chigger species in Dehong, and it was mainly distributed in flatland areas and indoors. The infestation and community indexes of chiggers in mountainous areas and outdoors were higher than those in flatland areas and indoors. The species abundance distribution of the chigger community conformed to log-normal distribution, and the total number of chigger species was roughly estimated to be 147. The species diversity of the chigger community is high in Dehong, with an obvious environmental heterogeneity. The low host specificity of chiggers and the occurrence of a large number of L. deliense in Dehong would increase the transmission risk of scrub typhus on the China–Myanmar border. Chiggers (chigger mites) are a group of tiny arthropods, and they are the exclusive vector of Orientia tsutsugamushi (Ot), the causative agent of scrub typhus (tsutsugamushi disease). Dehong Prefecture in Yunnan Province of southwest China is located on the China–Myanmar border and is an important focus of scrub typhus. Based on the field surveys in Dehong between 2008 and 2022, the present paper reports the infestation and ecological distribution of chiggers on the body surface of rodents and other sympatric small mammals (shrews, tree shrews, etc.) in the region for the first time. The constituent ratio (Cr), prevalence (PM), mean abundance (MA), and mean intensity (MI) were routinely calculated to reflect the infestation of small-mammal hosts with chiggers. Additionally, the species richness (S), Shannon–Wiener diversity index (H), Simpson dominance index (D), and Pielou's evenness index (E) were calculated to illustrate the chigger community structure. Preston's log-normal model was used to fit the theoretical curve of species abundance distribution, and the Chao 1 formula was used to roughly estimate the expected total species. The "corrplot" package in R software (Version 4.3.1) was used to analyze interspecific relationships, and the online drawing software was used to create a chord diagram to visualize the host–chigger associations. From 1760 small-mammal hosts, a total of 9309 chiggers were identified as belonging to 1 family, 16 genera, and 117 species, with high species diversity. The dominant chigger species were Leptotrombidium deliense, Walchia ewingi, and Gahrliepia longipedalis, with a total Cr = 47.65% (4436/9309), among which L. deliense is the most important vector of Ot in China. The overall infestation indexes (PM, MA, and MI) and community parameters (S, H, and E) of chiggers in the mountainous areas and outdoors were higher than those in the flatland areas and indoors, with an obvious environmental heterogeneity. Leptotrombidium deliense was the dominant species in the flatland and indoors, while G. longipedalis was the prevalent species in the mountainous and outdoor areas. The species abundance distribution of the chigger community conformed to log-normal distribution with the theoretical curve equation: S (R) ′ = 28 e − [ 0.23 (R − 0) ] 2 , indicating the existence of many rare species and only a few dominant species in the community. The expected total number of chigger species was roughly estimated to be 147 species, 30 more than the 117 species actually collected, suggesting that some uncommon species may have been missed in the sampling survey. The host–parasite association analysis revealed that one host species can harbor different chigger species, and one chigger species can parasitize different host species with low host specificity. A positive or negative correlation existed among different chigger species, indicating a cooperative or competitive interspecific relationship. The species diversity of chiggers is high in Dehong on the China–Myanmar border, and a large host sample is recommended to find more uncommon species. There is an obvious environmental heterogeneity of the chigger community, with different species diversity and dominant species in different environments. The low host specificity of chiggers and the occurrence of a large number of L. deliense in Dehong, especially in flatland areas and indoors, would increase the risk of persistent transmission of scrub typhus in the region. [ABSTRACT FROM AUTHOR]

This paper introduces bivariate log-symmetric models for analyzing the relationship between two variables, assuming a family of log-symmetric distributions. These models offer greater flexibility than the bivariate lognormal distribution, allowing for better representation of diverse distribution shapes and behaviors in the data. The log-symmetric distribution family is widely used in various scientific fields and includes distributions such as log-normal, log-Student-t, and log-Laplace, among others, providing several options for modeling different data types. However, there are few approaches to jointly model continuous positive and explanatory variables in regression analysis. Therefore, we propose a class of generalized linear model (GLM) regression models based on bivariate log-symmetric distributions, aiming to fill this gap. Furthermore, in the proposed model, covariates are used to describe its dispersion and correlation parameters. This study uses a dataset of anthropometric measurements of newborns to correlate them with various biological factors, proposing bivariate regression models to account for the relationships observed in the data. Such models are crucial for preventing and controlling public health issues. [ABSTRACT FROM AUTHOR]

Sea salt aerosols play a critical role in regulating the global climate through their interactions with solar radiation. The size distribution of these particles is crucial in determining their bulk optical properties. In this study, we analyzed in situ measured size distributions of sea salt aerosols from four field campaigns and used multi-mode lognormal size distributions to fit the data. We employed super-spheroids and coated super-spheroids to account for the particles' non-spherictty, inhomogeneity, and hysteresis effect during the deliquescence and crystallization processes. To compute the single-scattering properties of sea salt aerosols, we used the state-of-the-art invariant imbedding T-matrix method, which allows us to obtain accurate optical properties for sea salt aerosols with a maximum volume-equivalent diameter of 12 µm at a wavelength of 532 nm. Our results demonstrated that the particle models developed in this study were successful in replicating both the measured depolarization and lidar ratios at various relative humidity (RH) levels. Importantly, we observed that large-size particles with diameters larger than 4 µm had a substantial impact on the optical properties of sea salt aerosols, which has not been accounted for in previous studies. Specifically, excluding particles with diameters larger than 4 µm led to underestimating the scattering and backscattering coefficients by 27%–38% and 43%–60%, respectively, for the ACE-Asia field campaign. Additionally, the depolarization ratios were underestimated by 0.15 within the 50%–70% RH range. These findings emphasize the necessity of considering large particle sizes for optical modeling of sea salt aerosols. [ABSTRACT FROM AUTHOR]

There is little information which examines and compares climate zones or geology/topography in their relation to soil thickness along mountain slopes, where soil thickness is a possible contributing factor for the increase of sediment wash-off. In this study, the data obtained from handy penetration tests conducted throughout Japan are collected and attached to information on climate zones and geography/topography with the aim of clarifying the difference in soil thickness according to the climate zone and geological classification. The probability distribution of soil thickness was found to fit roughly with the probability density function of a log-normal distribution, regardless of the climate zone or geological age / lithology. A comparison of μ showed that the soil thickness at target sites in the Pacific climate zone, which have high rainfall, was large, at approximately 2.1 m. Meanwhile, the soil thickness was low, at approximately 1.5 m, at target sites in the Setouchi climate zone, which has low rainfall. A comparison of the geology showed that soil thicknesses of sites where the geology consisted of Tertiary and Quaternary sedimentary rocks were high, at approximately 2.1 m and 2.3 m, respectively. This suggests that, in high-precipitation regions, the weathering of rocks is promoted so that the soil layers tend to increase in thickness. [ABSTRACT FROM AUTHOR]

The stress-induced evolution of coal fractures significantly affects permeability and, consequently, gas extraction efficiency. This study introduces a novel coal fracture evolution model based on assumptions of fracture morphology and log-normal distribution of fracture aspect ratio. This model offers a theoretical framework for understanding the fracture closure process, ultimately depicting fracture evolution as a combined result of elastic compression and closure. It predicts the decay curve of fracture porosity under hydrostatic pressure loading. We conducted uniaxial compression experiments for determining the mechanical parameters of the model and in situ CT experiments with confining pressure ranging from 0 to 25 MPa for validating the model. The findings indicate the following: (1) Initially, the decline in fracture porosity with stress is predominantly due to elastic compression, followed by a rapid transition to closure. (2) Sensitivity analysis reveals that an increase in two physical quantities—the cube root of the product of the peak aspect ratio and the square of the mean aspect ratio (xc) and the bulk modulus of the coal matrix (Km)—results in a decrease in the rate of fracture porosity decay with stress. (3) Tectonic action has a dual effect of augmenting xc and diminishing Km. We define the magnification of xc and the divisor of Km under a common term—scaling factor. When the scaling factor of xc is less than that of Km, the tectonic action promotes the decay of porosity with stress. Conversely, when the scaling factor of xc is greater than that of Km, the effect is reversed. [ABSTRACT FROM AUTHOR]

Recent studies have highlighted leptin, a key hormone that regulates energy intake and induces satiety, due to the worldwide prevalence of obesity. In this study, we analyzed plasma leptin measurements from 18 women with premenopausal obesity before and after bromocriptine treatment. By using underlying pulses recovered through deconvolution, we modeled the leptin secretory pulses as marked point processes and applied statistical distributions to evaluate the dynamics of leptin, including the interpulse intervals and amplitudes of the secretion. We fit the generalized inverse Gaussian and lognormal distributions to the intervals and the Gaussian, lognormal, and gamma distributions to the amplitudes of pulses. We evaluated the models' goodness of fit using statistical metrics including Akaike's information criterion, Kolmogorov-Smirnov plots, and quantile-quantile plots. Our evaluation results revealed the effectiveness of these statistical distributions in modeling leptin secretion. Although the lognormal and gamma distributions performed the best based on the metrics, we found all distributions capable of accurately modeling the timing of secretory events, leading us to a better understanding of the physiology of leptin secretion and providing a basis for leptin monitoring. In terms of pulse amplitude, the evaluation metrics indicated the gamma distribution as the most accurate statistical representation. We found no statistically significant effect of bromocriptine intake on the model parameters except for one distribution model. [ABSTRACT FROM AUTHOR]

This study investigates the influence of spinel crystallization characteristics on vanadium extraction during the converter vanadium slag-cooling process through thermodynamic calculations and experimental investigations. The phase evolution and micro-morphology variations of V-containing slag at different quenching temperatures are characterized via X-ray diffraction and scanning electron microscopy-energy dispersive X-ray spectroscopy, and the grain size of spinel phases is measured using an image processing software. Results indicate that the crystallization sequence in V-containing slag during the cooling process is V-spinel → Ti-spinel → olivine → rhodonite. When the temperature is reduced from 1400 °C to 1000 °C, the grain sizes of spinel exhibit a log-normal distribution, with the mean diameter and leaching rate of vanadium increasing from 15.11 to 27.27 μm and from 82.65 pct to 92.06 pct, respectively. The restrictive step in the crystallization process is the interfacial reaction. When cooled from 1000 °C to 25 °C, Ostwald ripening-type grain size distribution is observed, and the mean diameter increased to 41.9 μm. The vanadium leaching rate decreased to 85 pct due to the encapsulation of V-spinel by Ti-spinel and olivine, and the crystallization process is observed to be controlled by diffusion. [ABSTRACT FROM AUTHOR]

The performance of numerical weather prediction models has improved dramatically recently. However, model biases remain a fundamental limitation prohibiting the direct implementation of model results. There are several ways to describe wind speed data. The Weibull and lognormal distributions are used to obtain the best-fit model for the wind speed data. This study aims to develop a statistical post-processing method based on the distribution-based scaling (DBS) approach, which scales NWP data to fit the distribution derived using recorded wind speed at that site location. The performance of the suggested method was evaluated using four different error measures. The optimal model is anticipated to have the lowest Mean Bias Error (MBE), Mean Absolute Error (MAE), Root Mean square Error (RMSE), and variance (s2) values. It was determined that employing a DBS strategy significantly improved the NWP by at least 75%. [ABSTRACT FROM AUTHOR]

• Smoke and NO x exhaust emissions from a total of 905 construction machines, including 4 different types. • Substantial field measurements were carried out on construction sites in Beijing, giving an indication of real-world emissions. • Measured smoke result indicate that the implementation of strict regulatory policies is contribute to reducing emission. • Measured NO x emissions indicate that stricter emission standard stage cannot control the NO x level. To understand the smoke level and NO x emission characteristics of in-use construction machinery in Beijing, we selected 905 construction machines in Beijing from August 2022 to April 2023 to monitor the emission level of smoke and NO x. The exhaust smoke level and excessive emission situation of different machinery types were identified, and their NO x emission levels were monitored according to the free acceleration method. We investigated the correlation of NO x and smoke emission, and proposed suggestions for controlling pollution discharge from construction machinery in the future. The results show that the exhaust smoke level was 0–2.62 m−1, followed a log-normal distribution (μ = -1.73, δ = 1.09, R 2 = 0.99), with a 5.64% exceedance rate. Differences were observed among machinery types, with low-power engine forklifts showing higher smoke levels. The NO x emission range was 71–1516 ppm, followed a normal distribution (μ = 565.54, δ = 309.51, R 2 = 0.83). Differences among machinery types were relatively small. Engine rated net power had the most significant impact on NO x emissions. Thus, NO x emissions from construction machinery need further attention. Furthermore, we found a weak negative correlation (p < 0.05) between the emission level of smoke and NO x , that is the synergic emission reduction effect is poor, emphasizing the need for NO x emission limits. In the future, the oversight in Beijing should prioritize phasing out China Ⅰ and China Ⅱ machinery, and monitor emissions from high-power engine China Ⅲ machinery. [Display omitted] [ABSTRACT FROM AUTHOR]

Statistical process control consists of sophisticated and well-organized methods which contribute to monitor and improve the quality of a product. Control charts are now routinely used in many applied areas to enhance the quality of products. In this study, a general framework is presented to construct univariate control charts for joint monitoring using the information theoretic approach. To this end, we monitor a process by maximizing the entropy and by minimizing the cross entropy. Information control charts are free from strict distributional assumptions, as information charts are based on information discrepancy between the initial moment μ0 and the data moments rt . These charts can jointly monitor mean and variance and thus provide a unified approach that is helpful in reducing the labor for designing separate charts. Besides real data applications, in this study, Monte Carlo simulations are used to assess the performance of the information charts using the average run length as a performance criterion assuming different distributions including normal, gamma, exponential, lognormal,Weibull and beta. Furthermore, a comparison with the traditional charts is also given for each distribution.

With the rapid urbanization and expansion of rail transit systems, the axle loads of trains, which are a critical aspect of their configuration, have significantly increased. This increase poses substantial potential threats to the safety and service life of existing bridges within urban rail transit networks. Therefore, it is imperative to develop methods for monitoring and identifying train axle loads. In this study, a strain field measurement scheme was devised and implemented for an operational simply supported composite beam bridge in urban rail transit. This involved numerical modeling and validation of the bridge's structural response, followed by the calculation of strain influence lines at specific measurement points. Subsequently, a method for identifying train axle loads, considering the dynamic amplification effect, was established. This method integrates principles from strain influence lines with mathematical optimization techniques. Specifically, the axle loads of locomotives on the forward AC03 type trains of Shanghai Metro Line 3 were found to conform to a logarithmic normal distribution model, while those of middle carriages followed a normal distribution model. Their respective mean axle loads were determined as 9.64 t and 10.77 t, with a shared variance of 0.8. Similarly, the axle loads of locomotives and middle carriages on reverse AC03-type trains also followed normal distribution models, with identical mean values around 10.5 t. The variances for axle loads of locomotives and middle carriages of reverse trains were found to be 1.36 and 0.8, respectively. The developed method effectively enables the monitoring of train axle loads and assessment of their impact on bridge structures, therefore enhancing safety and operational reliability within urban rail transit systems. [ABSTRACT FROM AUTHOR]

Investigating the spatial and size distributions of fracture structures formed by various external stresses in coal is essential for understanding fracture evolution and methane percolation behavior in coal reservoirs. To estimate the characteristics of microscale fractures in three-dimensional space, X-ray computed microtomography was used to establish digital reconstructed fracture models. Two algorithms that reflect topological features were applied to quantitatively characterize coal fractures. The results show that tectonic stress negatively affects the anisotropy of fractures, reducing the frequency of fractures that are approximately parallel or perpendicular to the main direction. A new fracture connectivity evaluation parameter, calculated by the integral average of the linear fitting curve between the coordination number and the corresponding average radius of many maximum spheres in the pore network model, is proposed. This method is more objective for evaluating fracture connectivity. The results indicate that with increasing tectonic action, fracture connectivity improves. Based on skeleton model data, we found a power-law relationship between the equivalent diameter of the fracture and the cumulative volume. Using this relationship and the capillary model assumption, we rederived expressions for total gas seepage flux and permeability applicable to fractures that do not conform to the tortuous fractal theory. Additionally, we discovered that the fracture aperture follows a log-normal distribution and derived an improved cube model's mathematical formula based on this. These findings are significant for revealing how different fracture structures affect gas seepage and provide a foundation for developing theoretical models to predict gas seepage in coal reservoirs. Article Highlights: A quantitative study of different coal fracture structures based on CT Comprehensive investigation on coal fracture properties concerned with gas seepage Evolution of coal fracture orientation distribution with tectonism Connectivity evolution with tectonism [ABSTRACT FROM AUTHOR]

The effects of Si content of steel melts containing 1.5% Al as well as alloying sequence of Si and Al on the evolution of inclusions are investigated. The SiO2 inclusion is primarily formed when Si (=0.5–3.0 wt%) is added to the melts at 1873 K, and the area fraction (AF) of the inclusions decreases over time. The subsequent addition of 1.5% Al to the Si‐alloyed steel (i.e., 3.0Si→1.5Al) increases the AF of inclusions due to the formation of Al2O3. The population density function (PDF) analysis for the preferential Si alloying shows a fractal distribution, indicating that the inclusions grow by a collision mechanism. PDF analysis shows a lognormal distribution because Al2O3 inclusion is formed and grows after subsequent Al alloying. Alternatively, when 1.5% Al is preferentially added to steel, Al2O3 clusters are formed. The AF of Al2O3 cluster decreases over time. When 3.0% Si is subsequently added to the Al‐alloyed steel (i.e., 1.5Al→3.0Si), singular Al2O3 particles are mainly observed. Because the Al alloying results in the formation of Al2O3 regardless of the alloying sequence and Si content, it is important to float up and separate Al2O3 cluster to improve the cleanliness of high‐Si‐Al‐alloyed steels such as electrical steels. [ABSTRACT FROM AUTHOR]

Dating phylogenetic trees to obtain branch lengths in time units is essential for many downstream applications but has remained challenging. Dating requires inferring substitution rates that can change across the tree. While we can assume to have information about a small subset of nodes from the fossil record or sampling times (for fast-evolving organisms), inferring the ages of the other nodes essentially requires extrapolation and interpolation. Assuming a distribution of branch rates, we can formulate dating as a constrained maximum likelihood (ML) estimation problem. While ML dating methods exist, their accuracy degrades in the face of model misspecification, where the assumed parametric statistical distribution of branch rates vastly differs from the true distribution. Notably, most existing methods assume rigid, often unimodal, branch rate distributions. A second challenge is that the likelihood function involves an integral over the continuous domain of the rates, often leading to difficult non-convex optimization problems. To tackle both challenges, we propose a new method called Molecular Dating using Categorical-models (MD-Cat). MD-Cat uses a categorical model of rates inspired by non-parametric statistics and can approximate a large family of models by discretizing the rate distribution into k categories. Under this model, we can use the Expectation-Maximization algorithm to co-estimate rate categories and branch lengths in time units. Our model has fewer assumptions about the true distribution of branch rates than parametric models such as Gamma or LogNormal distribution. Our results on two simulated and real datasets of Angiosperms and HIV and a wide selection of rate distributions show that MD-Cat is often more accurate than the alternatives, especially on datasets with exponential or multimodal rate distributions. [ABSTRACT FROM AUTHOR]

Process capability analysis is a valuable tool in quality assurance, but deviations from normal distribution necessitate adjustments to basic process capability indices. Process control literature offers solutions for non-normality, with data transformation being a common approach. The Box-Cox transformation (BCT) is often used to normalize non-normal data, relying on maximum likelihood estimation (MLE) to determine the transformation parameter, lambda. Alternative methods exist for estimating the single transformation parameter lamda, employing goodness-of-fit tests instead of the MLE method. This study explores two expressions within the Box-Cox transformation (BCT), encompassing both optimal and rounded values of lambda. The primary goal is to identify an effective method for transforming non-normal data into a distribution closer to normality through goodness-of-fit tests, aiming to obtain accurate estimates for process capability analysis in alignment with six sigma standards. Furthermore, this study focuses on the influence of utilizing both optimal and rounded values of lambda when transforming non-normal data to normal, and how these lambda values impact the estimates of process capability analysis. The findings reveal that methods such as Shapiro-Wilk's (SW) and Artificial Covariate (AC) outperform the MLE method. Moreover, employing the optimal lambda value during data transformation leads to improved estimates of process capability. Data simulation and analysis were conducted using Minitab software and the R programming language. [ABSTRACT FROM AUTHOR]

Frazil floc sizes and concentrations have been investigated in a small number of laboratory studies, but no detailed field measurements have been reported previously. In this study, a submersible camera system was deployed a total of 11 times during the principal and residual supercooling phases in the North Saskatchewan, Peace, and Kananaskis rivers to capture time-series images of frazil ice particles and flocs. Images were processed to accurately identify flocs and to calculate their sizes and concentrations. Key hydraulic and meteorological measurements were collected, and air–water heat fluxes were estimated to investigate their influence on floc properties. A lognormal distribution was found to be a good fit for the floc size distribution. The mean floc size ranged from 1.19 to 5.64 mm and the overall mean floc size was 3.80 mm. The mean floc size decreased linearly as the local Reynolds number increased. The average floc number concentration ranged from 1.80×10-4 to 1.15×10-1 cm -3. The average floc volumetric concentration ranged from 2.05×10-7 to 4.56×10-3 and was found to correlate strongly with the fractional height above the river bed. No significant correlations were found between the air–water heat flux and floc properties. Time series analysis showed that during the principal supercooling phase, floc number concentration and mean size increased significantly just prior to peak supercooling and reached a maximum near the end of principal supercooling. During the residual supercooling phase, the mean floc size did not typically vary significantly even 2.5 h after the residual phase had ended and the water temperature had increased above 0 °C. [ABSTRACT FROM AUTHOR]

The synthesis of metal nanoparticles holds significant promise for various applications ranging from electronics to catalysis. Their high specific surface area makes them more applicable in the form of lubricant and sorbent. Some of the metal nano-powders, such as silver, copper, and zinc, possess anti-microbial properties; hence, they are very useful in medical sciences. This paper presents a novel approach to the design and implementation of a compact metal nano-powder generator of 273 MW average power through the electrical explosion of wire method. The design focuses on achieving the automatic and repetitive operation of a compact metal nano-powder generator and minimizing its geometric inductance to achieve a fast rise time current across the exploding wire load. Copper nano-powder is produced with a copper wire of 450 μm thickness and 30 mm length at charging voltages of 8.5, 9.0, and 9.5 kV and achieving a superheat of 1.75, 1.92, and 2.06, respectively. The synthesis process is characterized by a detailed analysis of the copper nano-powder's structural, morphological, and chemical composition using techniques such as x-ray diffraction, scanning electron microscopy, and energy-dispersive x-ray spectroscopy. The particle size distribution studies are performed by adopting the log-normal probability distribution. The results demonstrate the effectiveness of the proposed compact nano-powder generator in producing copper nano-powder with tailored properties suitable for diverse applications. [ABSTRACT FROM AUTHOR]

Spray cooling is an effective solution for high heat flux dissipation challenges. Accurate prediction of heat transfer efficiency by numerical simulation can reduce the cost of spray cooling in engineering applications. To improve the accuracy of numerical simulation, this study develops a mathematical model for droplet collision and heat transfer response based on experimental data. In spray cooling experiments, droplets are sprayed onto a 200 °C aluminum alloy thermal wall using an atomizing nozzle, temperature is monitored, and the curve of heat flux variation during cooling is estimated from temperature data. Analysis of high-speed photography results provides the droplet diameter, velocity, and spatial distribution. We discover that the average Weber number of droplets, We, has a power-law relationship with the volumetric flow rate, Q, as We ∼ Q1.55. The velocity and position of spray droplets approximately follow a normal distribution, while the diameter follows a Log-normal distribution. By analyzing the relation between heat flux and spray distribution, an experimental-data-based model, named Droplet Collision-Associated Heat Transfer Model, is designed. Integrating this experimental-data-based model with the discrete phase model (DPM), the heat transfer evolution process in spray cooling is simulated with high reliability. Particles sources are generated based on the experimentally obtained droplet parameter probability distributions, DPM is used to capture the trajectories of droplets, and the droplet impact heat transfer correlation model calculates the thermal response of the wall. Compared with experimental results, the simulation error is only 7.49%. Simulation results indicate that spray cooling at high flow rates has better temperature uniformity. [ABSTRACT FROM AUTHOR]

We determined the size distribution of helium droplets produced in a pulsed beam in the condensation regime from the gas phase. Following electron-impact ionization, the mass-to-charge ratios of the positively charged droplets were determined by measuring their kinetic energies and velocities using an electrostatic cylindrical deflector setup. Over a range of different source conditions, we observed bimodal velocity distributions and log-normal size distributions. Our results are similar to those reported for continuous beams, but with mean sizes larger by a factor of around 100. The log-normal size distributions reported here differ strongly from the exponential distributions recently reported for a pulsed beam produced using a different nozzle design. [ABSTRACT FROM AUTHOR]

Using a 50‐compartment Python‐coded mathematical lung model, we compared mixed venous blood flow (Q) distributions and arterial oxygen tension/inspired oxygen fraction (PaO2/FiO2) relationships in lungs modeled with log normal distributions (LND) of inspired (VI) versus expired (VA) alveolar gas volumes. In lungs with normal V/Q heterogeneity, Q versus VA/Q and Q versus VI/Q distributions were similar with either approach, and PaO2/FiO2 sequences remained indistinguishable. In V/Q heterogeneous lungs at high FiO2, VILND generated low Q versus VA/Q shoulders and some negative VA units, while VALND preserved Q versus VA/Q log normality by blood flow diversion from low VI/Q units. We managed VILND‐induced negative VA units either by shunt conversion (VI decreased to 0) or VI redistribution simulating collateral ventilation (VI increased till VA = 0). Comparing oxygen transfer: VALND > VILND (redistribution) > VILND (shunt). In V/Q heterogeneous lungs VALND and VILND (redistribution) regained near optimal oxygen transfer on 100% oxygen, while impairment persisted with VILND (shunt). Unlike VALND, VILND (redistribution) produced Q versus VA/Q distributions in V/Q heterogeneity compatible with multiple inert gas (MIGET) reports. VILND (redistribution) is a physiologically–based MIGET–compatible alternative to West's original VALND lung modeling approach. [ABSTRACT FROM AUTHOR]

The present study explores the effect of rotational anisotropy on the bearing capacity responses of the square and rectangular footings using the random finite difference method (RFDM) and Monte Carlo simulation (MCS) technique. Three different aspect ratios (i.e., L/B = 1, 2, and 3) are considered in this study. The lognormal distribution is chosen for the spatial distribution of the tangent of the friction angle. The probabilistic bearing capacity response (μNγ) and the failure probability (pf) of the footings are obtained for different angles of rotation of the soil strata (β) considering different orientations of the footings. The probabilistic results are presented in the form of PDF and CDF for different β and L/B ratios of the footing. The desired safety factors (FSr) corresponding to a specific target failure probability (say pft = 0.01%) are also evaluated for different β. It is found that the orientation of the rectangular footings with respect to the strike direction of the soil strata has significant effects on the μNγ and pf of the footings. [ABSTRACT FROM AUTHOR]

Background The control of the microbial contamination of pharmaceutical products (PP) is crucial to ensure their safety and efficacy. The validity of the monitoring of such contamination depends on the uncertainty of this quantification. Highly uncertain quantifications due to the variability of determinations or the magnitude of systematic effects affecting microbial growth or other analytical operations make analysis unfit for the intended use. The quantification of the measurement uncertainty expressing the combined effects of all random and systematic effects affecting the analysis allows for a sound decision about quantification adequacy for their intended use. The complexity of the quantification of microbial analysis uncertainty led to the development of simplified ways of performing this evaluation. Objective This work assesses the adequacy of the simplified quantification of the uncertainty of the determination of the microbial contamination of PP by log transforming microbial count and dilution factor of the test sample whose uncertainty is combined in a log scale using the uncertainty propagation law. Methods This assessment is performed by a parallel novel bottom-up and accurate evaluation of microbial analysis uncertainty involving the Monte Carlo method simulation of the Poisson log-normal distribution of counts and of the normally distributed measured volumes involved in the analysis. Systematic effects are assessed and corrected on results to compensate for their impact on the determinations. Poisson regression is used to predict precision affecting determinations on unknown test samples. Result Simplified and detailed models of the uncertainty of the measurement of the microbial contamination of PP are provided, allowing objective comparisons of several determinations and those with a maximum contamination level. Conclusions This work concludes that triplicate determinations are required to produce results with adequately low uncertainty and that simplified uncertainty quantification underevaluates or overevaluates the uncertainty from determinations based on low or high colony numbers, respectively. Therefore, detailed uncertainty evaluations are advised for determinations between 50 and 200% of PP's maximum admissible contamination value Highlight User-friendly tools for detailed and simplified evaluations of the uncertainty of the measurement of microbial contamination of PP are provided together with the understanding of when simplifications are adequate. [ABSTRACT FROM AUTHOR]

Tasks of different nature and difficulty levels are a part of people's lives. In this context, there is a scientific interest in the relationship between the difficulty of the task and the persistence need to accomplish it. Despite the generality of this problem, some tasks can be simulated in the form of games. In this way, we employ data from a large online platform, called Steam, to analyze games and the performance of their players. More specifically, we investigated persistence in completing tasks based on the proportion of players who accomplished game achievements. Overall, we present five major findings. First, the probability distribution for the number of achievements is log-normal distribution. Second, the distribution of game players also follows a log-normal. Third, most games require neither a very high degree of persistence nor a very low one. Fourth, players also prefer games that demand a certain intermediate persistence. Fifth, the proportion of players as a function of the number of achievements declines approximately exponentially. As both the log-normal and the exponential functions are memoryless, they are mathematical forms that describe random effects arising from the nature of the system. Therefore our first two findings describe random processes of fragmenting achievements and players while the last three provide a quantitative measure of the human preference in the pursuit of challenging, achievable and justifiable tasks. [ABSTRACT FROM AUTHOR]

The Balise Transmission Module (BTM) unit of the on-board train control system is a crucial component. Due to its unique installation position and complex environment, this unit has a higher fault rate within the on-board train control system. To conduct fault prediction for the BTM unit based on actual fault data, this study proposes a prediction method combining reliability statistics and machine learning, and achieves the fusion of prediction results from different dimensions through multi-method interactive validation. Firstly, a method for predicting equipment fault time targeting batch equipment is introduced. This method utilizes reliability statistics to construct a model of the remaining faultless operating time distribution considering uncertainty, thereby predicting the remaining faultless operating probability of the BTM unit. Secondly, considering the complexity of the BTM unit's fault mechanism, the small sample size of fault cases, and the potential presence of multiple fault features in fault text records, an individual-oriented fault prediction method based on Bayesian-optimized Gradient Boosting Regression Tree (Bayes-GBRT) is proposed. This method achieves better prediction results compared to linear regression algorithms and random forest regression algorithms, with an average absolute error of only 0.224 years for predicting the fault time of this type of equipment. Finally, a multi-method interactive validation approach is proposed, enabling the fusion and validation of multi-dimensional results. The results indicate that the predicted fault time and the actual fault time conform to a log-normal distribution, and the parameter estimation results are basically consistent, verifying the accuracy and effectiveness of the prediction results. The above research findings can provide technical support for the maintenance and modification of BTM units, effectively reducing maintenance costs and ensuring the safe operation of high-speed railway, thus having practical engineering value for preventive maintenance. [ABSTRACT FROM AUTHOR]

Let X be a random variable with finite second moment. We investigate the inequality: P { | X - E [ X ] | ≤ Var (X) } ≥ P { | Z | ≤ 1 } , where Z is a standard normal random variable. We prove that this inequality holds for many familiar infinitely divisible continuous distributions including the Laplace, Gumbel, Logistic, Pareto, infinitely divisible Weibull, Log-normal, Student's t and Inverse Gaussian distributions. Numerical results are given to show that the inequality with continuity correction also holds for some infinitely divisible discrete distributions. [ABSTRACT FROM AUTHOR]

Nowadays, many cities in China are facing the challenge of returning black and odorous waters during the rainy seasons. Combined sewer overflow (CSO) was one of the critical triggers. In this study, a new method for estimating frequency distribution of the excess rainfall intensity considering double thresholds (ERId in short) was proposed, which is helpful for estimating severity of CSO. For the specific interceptor well, the upper threshold is the design areal unit discharge (the equivalent rainfall intensity) of its upstream combined sewer and the lower one is the design areal unit discharge of its downstream interceptor sewers minus dry weather flow rate. First, rainfall events were divided and the minimum inter-event time (MIET) was set based on the time of concentration of the combined sewer catchment. Second, double-threshold method was used for ERId calculation and sampling for scenario of 30- minute CSO duration. Finally, the empirical frequency of the sampled ERId(30) was calculated by the mathematical expectation formula (Weibull formula) and five functions (doubly censored exponential distribution, exponential function, Gumbel distribution, Weibull distribution and lognormal distribution) were used for comparison to obtain the best theoretical frequency distribution. Results revealed that: (1) The excess rainfall intensity of double thresholds (ERId) is suitable for characterizing CSO. (2) The frequency distribution of ERId was right (positively) skewed. (3) The kurtosis of the ERId samples is not greater than 3 for all the thresholds studied, which indicates that the distribution is thin-tailed. (4) The optimal frequency distribution function for ERId is doubly censored exponential distribution. Highlights: The double-threshold method of ERI was proposed for characterizing CSO. The frequency distribution is right (positively) skewed and thin-tailed. The doubly censored exponential distribution was the optimal one of ERId. [ABSTRACT FROM AUTHOR]

Reliability analysis of mechanical strength could be used for evaluation of wood scrimber properties in this study. Normal, lognormal, and Weibull distributions were used to determine and selected the optimal model for wood scrimber for the first time. The results of reliability analysis indicated that the bending and tensile strength were well fit for normal distribution. Weibull distribution could describe the probability distribution law of compression strength, and lognormal distribution could reflect the probability distribution law of shear strength, respectively. The standard value of each mechanical strength was determined and compared in accordance with two methods. This illustrated that a significant difference between these two methods is evident in the case of modulus of elasticity (MOE), compression strength (CS), and shear strength (SS), while modulus of rupture (MOR) and tensile strength (TS) yielded similar data. The improvement in mechanical strengths was remarkably affected by the increase in density. Moreover, the microstructure of wood scrimber has a good ratio of deformation with respect to density, which can be significantly explained by compressive densification. The results suggest that the deformation ratio increased from 49.75% to 78.67%, which might reflect the variation in macroscopic mechanical strength of wood scrimber. [ABSTRACT FROM AUTHOR]

Citation rankings have emerged as a popular approach to ranking the scholarly impact of law faculties. This paper develops a statistical approach for inferring faculty quality from citation counts and determining when differences among law schools are significant. Statistical tests demonstrate that the distribution of citations within faculties closely follows the lognormal distribution, subject to small adjustments. This suggests a simple test for comparing faculties: whether they could be drawn from lognormal distributions with the same log mean. Under this approach, the geometric mean of citations is the most efficient measure for summarizing faculty quality. Using citation data collected from HeinOnline, this article provides a citation ranking for 195 law schools in the United States. Most differences between peer schools are statistically insignificant, and confidence intervals on citation ranks are extremely wide. Except for the highest‐ranked faculties, citation rankings provide little information on the relative quality of faculties. [ABSTRACT FROM AUTHOR]

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Our research paper introduces a newly developed probability distribution called the transformed MG-extended exponential (TMGEE) distribution. This distribution is derived from the exponential distribution using the modified Frechet approach, but it has a more adaptable hazard function and unique features that we have explained in detail. We conducted simulation studies using two methods: rejection sampling and inverse transform sampling, to produce summaries and show distributional properties. Moreover, we applied the TMGEE distribution to three real datasets from the health area to demonstrate its applicability. We used the maximum likelihood estimation technique to estimate the distribution's parameters. Our results indicate that the TMGEE distribution provides a better fit for the three sets of data as compared to nine other commonly used probability distributions, including Weibull, exponential, and lognormal distributions. [ABSTRACT FROM AUTHOR]