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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]

Fractures significantly impact the elastic and hydraulic properties of geological structures, influencing fields like geothermal energy, hydrocarbon exploration, nuclear waste disposal and |$\mathrm{ \mathrm{CO}}_2$| storage. Characterizing these formations is challenging due to the scale disparity between seismic wavelengths and fracture sizes. This study leverages decades of analytical and numerical advancements to evaluate the effective mechanical properties of fractured solids at the mesoscopic scale. A novel numerical method for modelling quasi-static Biot's poroelastic equations using graphics processing units (GPUs) is introduced for simulating hydromechanically coupled systems. Capable of handling up to 133 million voxel elements on a single GPU, this method offers unprecedented spatial resolution to model complex fracture networks. The GPU-accelerated solver, FastBiot_QS, delivers exceptional performance, achieving a computational speedup of approximately 520 times compared to central processing unit-based methods. The solver's accuracy is rigorously validated in 1-D and 3-D setups. Simulations reveal that fracture clustering and spatial distribution significantly affect seismic attenuation and modulus dispersion. Clusters of interconnected fractures lead to higher attenuation at higher frequencies, while sparsely distributed fractures result in higher attenuation at lower frequencies. Simulations with log-normal and uniform distributions present intermediate behaviours between densely clustered and sparsely distributed fractures. The study can improve interpretations of seismic data and hydraulic properties in fractured media. [ABSTRACT FROM AUTHOR]

During the synthesis of tellurium (Te) crystals, the coexistence of multiple crystalline phases (α-Te, β-Te, and γ-Te) with diverse structures commonly occurs, leading to instability and complexity in the performance of Te-based optoelectronic devices. This study employs physical vapor deposition to synthesize Te crystals of various sizes and morphologies, followed by spatially and temperature-dependent evaluation using Raman mapping and infrared photoluminescence (PL) spectroscopy. Spatially resolved results reveal that the size and morphology of Te crystals significantly influence the energy and peak profiles of Raman and PL spectra. Statistical analysis of spatially random sampling indicates the PL peak energies of Te crystals follow a lognormal distribution in terms of their occurrence frequencies, reflecting the complex interplay of multiple factors during crystal growth. This results in the coexistence of α-Te and β-Te phases, forming α/β-Te heterophase homojunction (HPHJ). Meanwhile, temperature-dependent PL results, obtained for the range of 3–290 K, reveal multi-peak competitive behavior in the PL spectra, accompanied by S-shaped shifts in peak energy. These features can be rationally explained by an interface transition-recombination mechanism based on the I-type α/β-Te HPHJ model. It also confirms infrared PL spectroscopy is an effective method for identifying the crystalline phase composition of Te crystals. [ABSTRACT FROM AUTHOR]

Abstract.Motivated by the serious Type-I error issues of widely used Cox-PH method in survival analysis, this article introduces an approach one can take in deriving superior parametric tests based on distributions such as the gamma, lognormal, and Weibull. Some of the data available from such distributions are allowed to be censored, as usually the case in dealing with lifetime distributions. Since the classical approach fails to provide reasonable procedures to test the equality of means of a number of Weibull populations, beyond the two populations case, we will show how to apply the generalized inference approach to do so in a novel manner. The approach should work in other scale invariant distributions, such as the gamma and lognormal. The approach is illustrated with the Weibull distributions, taking advantage of the fact that the original data from continuous distributions can be transformed into normally distributed data leading to exact generalized test variables. [ABSTRACT FROM AUTHOR]

This study evaluates the effectiveness of advanced statistical and geospatial methods for analyzing radon concentration distributions in indoor environments, using the district of San Martín de Porres, Lima, Peru, as a case study. Radon levels were monitored using LR-115 nuclear track detectors over three distinct measurement periods between 2015 and 2016, with 86 households participating. Detectors were randomly placed in various rooms within each household. Normality tests (Shapiro–Wilk, Anderson–Darling, and Kolmogorov–Smirnov) were applied to assess the fit of radon concentrations to a log-normal distribution. Additionally, analysis of variance (ANOVA) was used to evaluate the influence of environmental and structural factors on radon variability. Non-normally distributed data were normalized using a Box–Cox transformation to improve statistical assumptions, enabling subsequent geostatistical analyses. Geospatial interpolation methods, specifically Inverse Distance Weighting (IDW) and Kriging, were employed to map radon concentrations. The results revealed significant temporal variability in radon concentrations, with geometric means of 146.4 Bq· m − 3 , 162.3 Bq· m − 3 , and 150.8 Bq· m − 3 , respectively, across the three periods. Up to 9.5% of the monitored households recorded radon levels exceeding the safety threshold of 200 Bq· m − 3 . Among the interpolation methods, Kriging provided a more accurate spatial representation of radon concentration variability compared to IDW, allowing for the precise identification of high-risk areas. This study provides a framework for using advanced statistical and geospatial techniques in environmental risk assessment. [ABSTRACT FROM AUTHOR]

A kinetic exchange model is developed to investigate wealth distribution in a market. The model incorporates a value function that captures the agents' psychological traits, governing their wealth allocation based on behavioral responses to perceived potential losses and returns. To account for the impact of transaction frequency on wealth dynamics, a non-Maxwellian collision kernel is introduced. Applying quasi-invariant limits and Boltzmann-type equations, a Fokker–Planck equation is derived. We obtain an entropy explicit stationary solution that exhibits exponential convergence to a lognormal wealth distribution. Numerical experiments support the theoretical insights and highlight the model's significance in understanding wealth distribution. [ABSTRACT FROM AUTHOR]

Understanding intra-urban travel patterns through quantitative analysis is crucial for effective urban planning and transportation management. In previous studies, a range of distribution functions were modeled to lay the groundwork for human mobility research. However, few studies have explored the nonlinear relationships between travel distance patterns and environmental factors. Using travel distance data from ride-hailing services, this research divides a study area into 1 × 1 km grid cells, modeling the best travel distance distribution and calculating the coefficients of each grid. A machine learning framework (Extreme Gradient Boosting combined with Shapley Additive Explanations) is introduced to interpret the factors influencing these distributions. Our results emphasize that the travel distance of human movement tends to follow a log-normal distribution and exhibits spatial heterogeneity. Key factors affecting travel distance distributions include the distance to the city center, bus station density, land use entropy, and the density of companies. Most environmental variables exhibit nonlinear and threshold effects on the log-normal distribution coefficients. These findings significantly advance our understanding of ride-hailing travel patterns and offer valuable insights into the spatial dynamics of human mobility. [ABSTRACT FROM AUTHOR]

The simulation is often required to assess a new model, identify problems with an existing design, and test a system under conditions that are hard to reproduce in an actual system. In this article, necessary simulations have been carried out on superparamagnetic nanoparticles considering a wide range of particle sizes and distribution widths purposefully to obtain the underlying magnetic features which cannot be envisioned easily by experimental studies. The present study demonstrates that the particle sizes and distribution widths of nanoparticle assembly have significant effect on controlling its ZFC/FC magnetization and isothermal M-H curves. The log-normal distribution function helps us to simulate the magnetic features in a reasonable fashion for distributed nanoparticles. The algorithm used for computer simulation of the present work is quite efficient as far as time is concerned. [ABSTRACT FROM AUTHOR]

To assess the preliminary therapeutic impact of a novel treatment, futility monitoring is commonly employed in Phase II clinical trials to facilitate informed decisions regarding the early termination of trials. Given the rapid evolution in cancer treatment development, particularly with new agents like immunotherapeutic agents, the focus has often shifted from objective response to time‐to‐event endpoints. In trials involving multiple time‐to‐event endpoints, existing monitoring designs typically select one as the primary endpoint or employ a composite endpoint as the time to the first occurrence of any event. However, relying on a single efficacy endpoint may not adequately evaluate an experimental treatment. Additionally, the time‐to‐first‐event endpoint treats all events equally, ignoring their differences in clinical priorities. To tackle these issues, we propose a Bayesian futility monitoring design for a two‐arm randomized Phase II trial, which incorporates the win ratio approach to account for the clinical priority of multiple time‐to‐event endpoints. A joint lognormal distribution was assumed to model the time‐to‐event variables for the estimation. We conducted simulation studies to assess the operating characteristics of the proposed monitoring design and compared them to those of conventional methods. The proposed design allows for early termination for futility if the endpoint with higher clinical priority (e.g., death) deteriorates in the treatment arm, compared to the time‐to‐first‐event approach. Meanwhile, it prevents an aggressive early termination if the endpoint with lower clinical priority (e.g., cancer recurrence) shows deterioration in the treatment arm, offering a more tailored approach to decision‐making in clinical trials with multiple time‐to‐event endpoints. [ABSTRACT FROM AUTHOR]

The article discusses the refineR algorithm for estimating within-subject biological variation (CVI) using routine laboratory data, focusing on the practical applications of this method. By characterizing a central Gaussian peak from result ratios, refineR can estimate CVI values and reference change values (RCV). The study validates the refineR algorithm through Monte Carlo simulations and comparisons with a biological variation study, highlighting its accuracy in estimating CVI from ratio distributions. Despite some limitations, refineR offers a cost-effective tool for laboratories to estimate CVI, especially for subgroups with limited direct studies. [Extracted from the article]

We explore the relative percentages of binary systems and higher-order multiples that are formed by pure stellar dynamics, within a small subcluster of N stars. The subcluster is intended to represent the fragmentation products of a single isolated core, after most of the residual gas of the natal core has dispersed. Initially, the stars have random positions, and masses drawn from a lognormal distribution. For low-mass cores spawning multiple systems with Sun-like primaries, the best fit to the observed percentages of singles, binaries, triples, and higher-order systems is obtained if a typical core spawns on average between |$N=$| 4.3 and 5.2 stars, specifically a distribution of N with mean |$\mu _{_{N}}\sim 4.8$| and standard deviation |$\sigma _{_N}\sim 2.4$|⁠. This fit is obtained when |$\sim 50~{{\ \rm per\ cent}}$| of the subcluster's internal kinetic energy is invested in ordered rotation and |$\sim 50~{{\ \rm per\ cent}}$| in isotropic Maxwellian velocities. There is little dependence on other factors, for example mass segregation or the rotation law. While such high values of N are at variance with the lower values often quoted (i.e. |$N\!=\!1\,\,{\rm or}\,\,2$|⁠), very similar values (⁠|$N\!=\!4.3\pm 0.4$| and |$N\!=\!4.5\pm 1.9$|⁠) have been derived previously by completely independent routes, and seem inescapable when the observed distribution of multiplicities is taken into account. [ABSTRACT FROM AUTHOR]

During a flood, the geometry of a river channel constrains the flows of water and sediment, however, over many floods, bankfull channel geometry evolves to reflect the longer‐term fluxes of water and sediment supplied by the catchment. Physics‐based models predict the average relationship between bankfull geometry and discharge to within an order of magnitude, however, observed variability about the prediction remains unaccounted for. We used high‐resolution topography to extract continuous measurements of bankfull width from 67 sites spanning the continental United States, yielding a reach‐scale probabilistic description of river width for each site. Within an individual reach, bankfull river width is well‐described by a lognormal distribution. Rivers that spend a greater proportion of time above bankfull are wider for the same bankfull discharge, revealing an unrecognized pathway through which climatic or engineered changes in flow frequency could alter river geometry and therefore impact aquatic habitat and flooding risk. Plain Language Summary: Rivers adjust their shape to transport the water and sediment supplied from their watersheds. Predicting flooding throughout river networks depends on understanding how rivers grow downstream as they accumulate water from larger areas. This relationship between river size and the water discharge that just fills the channel (bankfull) underpins flood routing and hazard models and is remarkably consistent for creeks in the headwaters and throughout a watershed as rivers reach their terminus in lakes and oceans. However, for shorter sections of a river we find that the size can be highly variable, and it remains unclear how to incorporate this reach‐scale variability into watershed and basin scale models. Here we demonstrate that reach‐scale variation has a well‐defined average value and predictable variability. By accounting for the reach‐scale variability, we find that for the same amount of discharge rivers which experience more flooding are wider while those where floods are rarer are narrower. These findings may hold particular relevance for understanding how snowmelt systems which produce long duration floods may adjust to diminishing snowpacks and how to manage river systems below dams where flow durations and magnitudes may be closely regulated. Key Points: Reach‐scale bankfull river width is lognormally distributed with a constant geometric standard deviationVariation in bankfull river width across sites depends on the flow duration where rivers that spend more time above flood stage are widerBankfull flow intermittency, runoff, and basin aridity are correlated, representing an imprint of climate on river geometry [ABSTRACT FROM AUTHOR]

The stochastic rupture risk assessment of an abdominal aortic aneurysm (AAA) critically depends on sufficient data set size that would allow for the proper distribution estimate. However, in most published cases, the data sets comprise no more than 100 samples, which is deemed insufficient to describe the tails of AAA wall thickness distribution correctly. In this study, we propose a stochastic Bayesian model to merge thickness data from various groups. The thickness data adapted from the literature were supplemented by additional data from 81 patients. The wall thickness was measured at two different contact pressures for 34 cases, which allowed us to estimate the radial stiffness. Herein, the proposed stochastic model is formulated to predict the undeformed wall thickness. Furthermore, the model is able to handle data published solely as summary statistics. After accounting for the different contact pressures, the differences in the medians reported by individual groups decreased by 45%. Combined data can be fitted with a lognormal distribution with parameters μ = 0.85 and σ = 0.32 which can be further used in stochastic analyses. [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]

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]

As an extension of the (univariate) Birnbaum–Saunders distribution, the Type-II generalized crack (GCR2) distribution, built on an appropriate base density, provides a sufficient level of flexibility to fit various distributional shapes, including heavy-tailed ones. In this paper, we develop a bivariate extension of the Type-II generalized crack distribution and study its dependency structure. For practical applications, three specific distributions, GCR2-Generalized Gaussian, GCR2-Student's t, and GCR2-Logistic, are considered for marginals. The expectation-maximization algorithm is implemented to estimate the parameters in the bivariate GCR2 models. The model fitting results on a catastrophic loss dataset show that the bivariate GCR2 distribution based on the generalized Gaussian density fits the data significantly better than other alternative models, such as the bivariate lognormal distribution and some Archimedean copula models with lognormal or Pareto marginals. [ABSTRACT FROM AUTHOR]

It is shown here that if the PDF (Probability Distribution Function) of wind speed is a Rayleigh distribution with parameter $s$ s , then the PDF of wind power is a Weibull distribution with parameters $a = \sqrt 2 \rho s^3\comma \; \; b = \displaystyle{2 \over {3\; }}$ a = 2 ρ s 3 , b = 2 3 , where $\rho$ ρ is the air density; if the wind speed PDF is a Weibull distribution with parameters $a\comma \; b$ a , b , then the wind power PDF is also a Weibull distribution with parameters $\; \displaystyle{{a^3\rho } \over 2}\comma \; \displaystyle{b \over 3}$ a 3 ρ 2 , b 3 ; if the PDF of wind speed is a log-normal distribution with parameters $\mu \comma \; \sigma$ μ , σ , then the PDF of wind power is also a log-normal distribution with parameters $\ln \displaystyle{\rho \over 2} + 3\mu \comma \; 3\sigma$ ln ρ 2 + 3 μ , 3 σ . The derived relationships allow us to quickly estimate parameters that indicate the wind power potential of the considered site, and the amount of wind energy generated by the turbine. [ABSTRACT FROM AUTHOR]

This study offers a comprehensive forecast of conditional earthquake recurrence probabilities in the North Anatolian Fault Zone (NAFZ), utilizing advanced statistical models and temporal analyses, aiming to discern the likelihood of future earthquakes. We sought to contribute insights into seismic hazard assessment by analyzing earthquakes (MW ≥ 4.0) from 1900–2022, employing Inverse Gaussian (aka Brownian Passage Time) and Lognormal distribution models, categorizing the NAFZ into ten seismic zones. Rigorous model fitness assessments were conducted, including Akaike and Bayesian information criteria, Kolmogorov–Smirnov, and Anderson–Darling tests. Conditional probabilities were calculated across eleven temporal intervals (0–50 years) and eleven residual periods (1–50 years), starting on January 1, 2023, and extending into the future. Results reveal nuanced earthquake probabilities, highlighting a heterogeneous seismic hazard landscape. Probability forecasts surge within the initial five years and continue to rise for another five years, underscoring the spatiotemporal sensitivity and widespread earthquake hazard. The findings enhance the understanding of seismic hazard assessment, extending the future applicability potential to global seismic regions. Acknowledging uncertainties and relying on instrumental data, future research could explore more extensive areas and refined data sources, along with new modeling techniques, to enhance forecasting accuracy. The findings stress the need for earthquake preparedness throughout the study area, not only for the anticipated large earthquakes but especially for medium-magnitude earthquakes. This remark manifestly underscores the necessity to develop strategies to reduce possible damage and loss of life stemming from the collapse of non-engineered and rural building stock unevenly scattered along the NAFZ that remain vulnerable to moderate-magnitude earthquakes. [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]

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]

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]

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]

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]

Allometric length-weight relationships are traditionally analyzed using the Huxley model, which assumes a lognormal distribution of errors. Still, other models have been successfully evaluated to describe these relationships, and it has been found that the distribution of errors is not necessarily lognormal. Two data sets of carapace width and weight, composed of 1,554 females and 2,531 males of Callinectes bellicosus (Stimpson, 1859), were fitted to five models to address this problem, which included: Huxley model, quadratic, cubic, breakpoint and two-segment. Lognormal distribution of the residuals was first assumed, but the goodness-of-fit test did not confirm this assumption, and the QQ plots revealed heavy tails. As an alternative, logistic distribution of the residuals was assumed, and the goodness-of-fit test and the QQ plots supported this. The Akaike information criterion (AIC) was used to select the best models. When a lognormal distribution of the residuals was assumed, the best model for females was the two-segment model and the cubic model for males. In contrast, with the logistic distribution, the best model was the two-segment model for both sexes. Furthermore, AIC was smaller in models with error loglogistic distribution than lognormal distribution. The two-segment model is associated with size at maturity in both sexes, and each segment represents juvenile and adult crabs. It is concluded that it is important to confirm the assumptions of the distribution of the residuals when fitting models to data because a wrong assumption can result in an erroneous model selection. [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]

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]

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]

Integral geometry uses four geometric invariants—the Minkowski functionals—to characterize certain subsets of three-dimensional (3D) space. The question was, how is the fluid flow in a 3D porous system related to these invariants? In this work, we systematically study the dependency of permeability on the geometrical characteristics of two categories of 3D porous systems generated: (i) stochastic and (ii) deterministic. For the stochastic systems, we investigated both normal and lognormal size distribution of grains. For the deterministic porous systems, we checked for a cubic arrangement and a hexagonal arrangement of grains of equal size. Our studies reveal that for any three-dimensional porous system, ordered or disordered, permeability k follows a unique scaling relation with the Minkowski functionals: (a) volume of the pore space, (b) integral mean curvature, (c) Euler characteristic, and (d) critical cross-sectional area of the pore space. The cubic and the hexagonal symmetrical systems formed the upper and lower bounds of the scaling relations, respectively. The disordered systems lay between these bounds. Moreover, we propose a combinatoric F that weaves together the four Minkowski functionals and follows a power-law scaling with permeability. The scaling exponent is independent of particle size and distribution and has a universal value of 0.428 for 3D porous systems built of spherical grains. [ABSTRACT FROM AUTHOR]

The size of drops generated by the capillary-driven disintegration of liquid ligaments plays a fundamental role in several important natural phenomena, ranging from heat and mass transfer at the ocean-atmosphere interface to pathogen transmission. The inherent nonlinearity of the equations governing the ligament destabilization leads to significant differences in the resulting drop sizes, owing to small fluctuations in the myriad initial conditions. Previous experiments and simulations reveal a variety of drop size distributions, corresponding to competing underlying physical interpretations. Here, we perform numerical simulations of individual ligaments, the deterministic breakup of which is triggered by random initial surface corrugations. The simulations are grouped in a large ensemble, each corresponding to a random initial configuration. The resulting probability distributions reveal three stable drop sizes, generated via a sequence of two distinct stages of breakup. Four different distributions are tested, volume-based Poisson, Gaussian, Gamma, and Log-Normal. Depending on the time, range of droplet sizes and criteria for success, each distribution has successes and failures. However, the Log-Normal distribution roughly describes the data when fitting both the primary peak and the tail of the distribution while the number of droplets generated is the highest, while the Gamma and Log-Normal distributions perform equally well when fitting the tail. The study demonstrates a precisely controllable and reproducible framework, which can be employed to investigate the mechanisms responsible for the polydispersity of drop sizes found in complex fluid fragmentation scenarios. [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]

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]

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]

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]

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]

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]

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]

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]

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 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]

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]

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]

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]

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]

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]