Predicting the Effect of the Loading Rate on the Fracture Toughness of Hydraulic Asphalt Concrete Based on the Weibull Distribution.

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

Evaluation of virus removal in membrane bioreactor (MBR) and conventional activated sludge (CAS) processes based on long-term monitoring at two wastewater treatment plants.

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

An Accelerated Failure Time Model to Predict Cause-Specific Survival and Prognostic Factors of Lung and Bronchus Cancer Patients with at Least Bone or Brain Metastases: Development and Internal Validation Using a SEER-Based Study.

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

Analysis of HepG2 cell response to a wide concentration range of mitomycin C using a multichannel quartz crystal microbalance system with a microscope.

The morphological response of HepG2 cells to mitomycin C was analyzed using a multichannel quartz crystal microbalance system equipped with a home-built movable microscope that enables the simultaneous acquisition of cell images and measurements of eight-channel quartz crystal microbalance. After 24 h of cell seeding, mitomycin C was injected into the culture medium. During the attachment process, the resonant frequency decreased, and the curves fitted well with the first-order lag response. Analysis of the response to mitomycin C revealed that the resonant frequency response curves varied with mitomycin C concentration. When the mitomycin C concentration was <10 µmol L-1, the delay time was observed before the increase in resonant frequency. When the mitomycin C concentration was extremely low, an additional decrease in resonant frequency was observed in the middle of the delay time that fitted well with the cumulative log-normal distribution curve. The resonant frequency response curves after the delay time fitted well with the cumulative log-normal distribution curves. The delay time and mean cumulative log-normal distribution time for the increase in resonant frequency correlated with the mitomycin C concentration; however, the mean time for the additional decrease in the resonant frequency did not show a statistically significant difference as a function of mitomycin C concentration. For mitomycin C concentrations of >20 µmol L-1, the response to the change in resonant frequency was rapid, and the response curves fitted well with the first-order lag response. The first-order lag response indicates that the response occurred simultaneously for all cells. The results showed that the time constant was independent of the tested mitomycin C concentration between 20 and 100 µmol L-1. These results suggested that different cell death processes occurred by mitomycin C. The findings of this study suggest that the system can be used to investigate cell death in adherent cells.

Perimeter procedure to produce average equivalent area grain size.

A new method of perimeter procedure to produce average equivalent area grain size on orientation imaging microscopy (OIM) micrograph was developed. When the OIM micrograph was exported with the practical size of pixel equal to the electron backscattering diffraction (EBSD) step size, the expression for perimeter procedure in producing the average equivalent area radius is r¯p=(2AmPm+wb2Es)±wb2Es (Pm and Am are the perimeter and area of grains, respectively, which can be measured using commercial image pro plus software; wb is the pixel width of the grain boundary which is suggested to set as 1 and Es is the EBSD step size). Experiments were conducted and the four methods intercept procedure, planimetric procedure, perimeter procfedure and statistical method were adopted to measure the average grain sizes for different conditions (polygonal grains and compressed polygonal grains, different EBSD step sizes, different grain boundary widths). The results showed that the average grain size by perimeter procedure remained relatively unchanged and close to the true average grain size for all conditions. It was demonstrated that perimeter procedure has an advantage in that it can produce reliable average grain size even when the pixel step size relative to the grain size is relatively large.

Exceedance Probabilities of Log-normal Distributions for One Group, Two Groups, and Meta-analysis of Multiple Two-group Studies, With Application to Analyses of Prolonged Times to Tracheal Extubation.

Many randomized trials measure means and standard deviations of anesthesia recovery time (e.g., times to tracheal extubation). We show how to use generalized pivotal methods to compare the probabilities of exceeding a tolerance limit (e.g., > 15 min, prolonged times to tracheal extubation). The topic is important because the economic benefits of faster anesthesia emergence depend on reducing variability, not means, especially prevention of very long recovery times. Generalized pivotal methods are applied using computer simulation (e.g., using two Excel formulas for one group and three formulas for two group comparisons). The endpoint for each study with two groups is the ratio between groups of the probabilities of times exceeding a threshold or the ratio of the standard deviations. Confidence intervals and variances for the incremental risk ratio of the exceedance probabilities and for ratios of standard deviations are calculated using studies' sample sizes, sample means in the time scale of recovery times, and sample standard deviations in the time scale. Ratios are combined among studies using the DerSimonian-Laird estimate of the heterogeneity variance estimate, with Knapp-Hartung adjustment for the relatively small (N = 15) numbers of studies in the meta-analysis. We show larger absolute variability among studies' results when analyzed based on exceedance probabilities rather than standard deviations. Therefore, if an investigator's primary goal is to quantify reductions in the variability of recovery times (e.g., times until patients are ready for post-anesthesia care unit discharge), we recommend analyzing the standard deviations. When exceedance probabilities themselves are relevant, they can be analyzed from the original studies' summary measures.

Visual Monitoring Strategies of Sentinels in a Cooperative Breeder.

Vigilance is important for early detection of threats. Previous studies have focused on the allocation of time to vigilance but neglected how animals monitor their surroundings during vigilance. Where animals look and how long each look lasts can affect the quality of visual monitoring and thus the ability to detect threats during vigilance. We examined visual monitoring strategies in the Florida scrub-jay (Aphelocoma coerulescens), a cooperative breeder with sentinel behaviour. Sentinels in this species make head turns from vantage points to detect the arrival of predators and intruding neighbours. We found that sentinels initiated head turns at regular intervals and also returned their gaze to areas previously monitored at regular intervals, which is predicted when predators and intruders rely on surprise rather than stealth to approach. Sentinels made head turns in several directions, but often more frequently on one side of the body than the other, which was not predicted for regular vigilance. Average look duration during sentinel bouts was shorter in smaller groups and in juveniles. We argue that shorter looks are beneficial to increase visual coverage in more threatening situations. Our study highlights how visual monitoring strategies during vigilance reflect the risk posed by predators and intruders.

TELS: Evolution patterns of research keywords from the evidence of PNAS Social Sciences topics.

By reviewing scientific literature, researchers may obtain a comprehensive understanding of field developments, keeping abreast of the current research status and hotspot shifts. The evolution pattern of keywords is supposed to be an efficient indicator in revealing the shifting and sustainability configuration of scientific concepts, ideas, and research hotspots. Here we take an extensive investigation of the evolution of keywords among all publications in PNAS Social Sciences from 1990 to 2021. Statistical tests show the keyword mention time series always accompanied by the emergence of a log-normal distribution. Additionally, we introduce a novel schema of four patterns (TELS), which are Transient impact type, Explosive impact type, Large impact type, and Small impact type, respectively, to illustrate the evolution of keywords. The TELS schema can be used to capture the whole life circle feature of any proposed keyword, from a pool of candidates. By dividing the entire time into four periods, we also introduce the concept of elite keywords to reveal the temporal feature of social sciences focus. An explicit transition from anthropology research to neuroscience and social problems research can be observed from the evolution diagram. We argue that the proposed method is of general sense and might be applicable to other fields of science.

A family of bimodal distributions generated by distributions with positive support.

Bimodal data sets are very common in different areas of knowledge. The crude birth rates data, fish length data, egg diameter data, the eruption and interruption times of the Old Faithful geyser, are examples of this type of data. In this paper, a new class of symmetric density functions for modeling bimodal data as described above are presented. From density functions with support on [ 0 , + ∞ ) , the symmetry is getting by reflecting the density function in the negative semi-axis with their respective normalization. In this way, if the primitive density function is unimodal, then the resulting density will be bimodal. We introduce asymmetry parameters and study their behavior, in particular the values of their modes and some other statistical values of interest. The cases for densities generated by Gamma, Weibull, Log-normal, and Birnbaum-Saunders densities, among others are studied. Statistical inference is performed from a classical perspective. A small simulation study to evaluate the benefits and limitations of the new proposal. In addition, an application to a data set related to the fetal weight in grams obtained through ultrasound in a sample of 500 units is also presented; the results show the great usefulness of the model in practical situations.

Theoretical framework for the emergent floe size distribution in the marginal ice zone: the case for log-normality.

Sea ice is not horizontally homogeneous on large scales. Its morphology is inherently discrete and made of individual floes. In recent years, sea ice models have incorporated this horizontal heterogeneity. The modelling framework considers an evolution equation for the probability density function of the floe size distribution (FSD) with forcing terms that represent the effects of several physical processes. Despite the modelling effort, a key question remains: What is the FSD emerging from the collection of all forcing processes? Field observations have long suggested that the FSD follows a power law, but this result has not been reproduced by models or laboratory experiments. The theoretical framework for FSD dynamics in response to physical forcings is presented. Wave-induced breakup is further examined with an emphasis on how it affects the FSD. Recent modelling results suggesting the consistent emergence of a log-normal distribution as a result of that process are further discussed. Log-normality is also found in a dataset of floe sizes, which was originally analysed under the power law hypothesis. A simple stochastic process of FSD dynamics, based on random fragmentation theory, is further shown to predict log-normality. We therefore conjecture that, in some situations, the emergent FSD follows a log-normal distribution. This article is part of the theme issue 'Theory, modelling and observations of marginal ice zone dynamics: multidisciplinary perspectives and outlooks'.

Incubation period of wild type of SARS-CoV-2 infections by age, gender, and epidemic periods.

Background: The incubation period of the coronavirus disease 2019 (COVID-19) is estimated to vary by demographic factors and the COVID-19 epidemic periods. Objective: This study examined the incubation period of the wild type of SARS-CoV-2 infections by the different age groups, gender, and epidemic periods in South Korea. Methods: We collected COVID-19 patient data from the Korean public health authorities and estimated the incubation period by fitting three different distributions, including log-normal, gamma, and Weibull distributions, after stratification by gender and age groups. To identify any temporal impact on the incubation period, we divided the study period into two different epidemic periods (Period-1: 19 January-19 April 2020 and Period-2: 20 April-16 October 2020), and assessed for any differences. Results: We identified the log-normal as the best-fit model. The estimated median incubation period was 4.6 (95% CI: 3.9-4.9) days, and the 95th percentile was 11.7 (95% CI: 10.2-12.2) days. We found that the incubation period did not differ significantly between males and females (p = 0.42), age groups (p = 0.60), and the two different epidemic periods (p = 0.77). Conclusions: The incubation period of wild type of SARS-CoV-2 infection during the COVID-19 pandemic 2020, in South Korea, does not likely differ by age group, gender and epidemic period.

Effect of steady-state response versus excitatory/inhibitory balance on spiking synchronization in neural networks with log-normal synaptic weight distribution.

Synchronization of neural activity, especially at the gamma band, contributes to perceptual functions. In several psychiatric disorders, deficits of perceptual functions are reflected in synchronization abnormalities. Plausible cause of this impairment is an alteration in the balance between excitation and inhibition (E/I balance); a disruption in the E/I balance leads to abnormal neural interactions reminiscent of pathological states. Moreover, the local lateral excitatory-excitatory synaptic connections in the cortex exhibit excitatory postsynaptic potentials (EPSPs) that follow a log-normal amplitude distribution. This long-tailed distribution is considered an important factor for the emergence of spatiotemporal neural activity. In this context, we hypothesized that manipulating the EPSP distribution under abnormal E/I balance conditions would provide insights into psychiatric disorders characterized by deficits in perceptual functions, potentially revealing the mechanisms underlying pathological neural behaviors. In this study, we evaluated the synchronization of neural activity with external periodic stimuli in spiking neural networks in cases of both E/I balance and imbalance with or without a long-tailed EPSP amplitude distribution. The results showed that external stimuli of a high frequency lead to a decrease in the degree of synchronization with an increasing ratio of excitatory to inhibitory neurons in the presence, but not in the absence, of high-amplitude EPSPs. This monotonic reduction can be interpreted as an autonomous, strong-EPSP-dependent spiking activity selectively interfering with the responses to external stimuli. This observation is consistent with pathological findings. Thus, our modeling approach has potential to improve the understanding of the steady-state response in both healthy and pathological states.

Practical Basis of the Geometric Mean Fitness and its Application to Risk-Spreading Behavior.

Temporal variations in population size under unpredictable environments are of primary concern in evolutionary ecology, where time scale enters as an important factor while setting up an optimization problem. Thus, short-term optimization with traditional (arithmetic) mean fitness may give a different result from long-term optimization. In the long-term optimization, the concept of geometric mean fitness has been received well by researchers and applied to various problems in ecology and evolution. However, the limit of applicability of geometric mean has not been addressed so far. Here we investigate this problem by analyzing numerically the probability distribution of a random variable obeying stochastic multiplicative growth. According to the law of large number, the expected value (i.e., arithmetic mean) manifests itself as a proper measure of optimization as the number of random processes increases to infinity. We show that the finiteness of this number plays a crucial role in arguing for the relevance of geometric mean. The geometric mean provides a satisfactory picture of the random variation in a long term above a crossover time scale that is determined by this number and the standard deviation of the randomly varying growth rates. We thus derive the applicability condition under which the geometric mean fitness is valid. We explore this condition in some examples of risk-spreading behavior.

Modeling Multivariate Count Time Series Data with a Vector Poisson Log-Normal Additive Model: Applications to Testing Treatment Effects in Single-Case Designs.

In education and psychology, single-case designs (SCDs) have been used to detect treatment effects using time series data in the presence or absence of intervention. One popular design variant of SCDs is a multiple-baseline design for multiple outcomes, which often collects outcomes with some form of a count. A Poisson model is a natural choice for the count outcome. However, the assumption of the Poisson model that the outcome variable's mean is equal to its variance is often violated in SCDs, as the variance is often larger than the mean (called overdispersion). In addition, when multiple outcomes are from the same participant, it is likely that they are correlated. In this paper, we present a vector Poisson log-normal additive (V-PLN-A) model to deal with (a) change processes (auto- and cross-correlations and data-driven trend) and (b) correlation and overdispersion in multivariate count time series. A multivariate normal distribution was adapted to account for correlation among multiple outcomes as well as possible overdispersion. The V-PLN-A model was applied to an educational intervention study to test treatment effects. Simulation study results showed that parameter recovery of the V-PLN-A model was satisfactory in a large number of timepoints using Bayesian analysis, and that ignoring change processes and overdispersion led to biased estimates of the treatment effects.

Average and longest expected treatment times for ultraviolet light disinfection of rooms.

BACKGROUND: Planning Ultraviolet-C (UV-C) disinfection of operating rooms (ORs) is equivalent to scheduling brief OR cases. The study purpose was evaluation of methods for predicting surgical case duration applied to treatment times for ORs and hospital rooms. METHODS: Data used were disinfection times with a 3-tower UV-C disinfection system in N=700 rooms each with ≥100 completed treatments. RESULTS: The coefficient of variation of mean treatment duration among rooms was 19.6% (99% confidence interval [CI] 18.2%-21.0%); pooled mean 18.3 minutes among the 133,927 treatments. The 50th percentile of coefficients of variation among treatments of the same room was 27.3% (CI 26.3%-28.4%), comparable to variabilities in durations of surgical procedures. The ratios of the 90th percentile to mean differed among rooms. Log-normal distributions had poor fits for 33% of rooms. Combining results, we calculated 90% upper prediction limits for treatment times by room using a distribution-free method (e.g., third longest of preceding 29 durations). This approach was suitable because, once UV-C disinfection started, the median difference between the duration estimated by the system and actual time was 1 second. CONCLUSIONS: Times for disinfection should be listed as treatment of a specific room (e.g., "UV-C main OR16"), not generically (e.g., "UV-C"). For estimating disinfection time after single surgical cases, use distribution-free upper prediction limits, because of considerable proportional variabilities in duration.

An Accelerated Life Model Analog for Discrete Survival and Count Data.

BACKGROUND AND OBJECTIVE: Our goal is to provide an overall strategy for utilizing continuous accelerated life models in the discrete setting that provides a unique and flexible modeling approach across a variety of hazard shapes. METHODS: We convert well-known continuous accelerated life distributions into their discrete counterpart and show theoretically that the existing software that currently exists to accommodate, left, right and interval censoring in the continuous case is re-usable in the discrete setting due to the structure of the likelihood equations. RESULTS: We demonstrate across a variety of simulated and real-world data that our modeling approach can accommodate discrete data that may either be approximately symmetric, left-skewed or right skewed, overcoming the limitations of more traditional modeling approaches. CONCLUSIONS: We illustrate both theoretically and through simulations that our approach for accommodating discrete failure time and count data is quite flexible. We demonstrate that the special case of the discrete Weibull model readily can accommodate truly Poisson distributed data and has a great degree of flexibility for non-Poisson distributed data.

Subjective assessment of frequency distribution histograms and consequences on reference interval accuracy for small sample sizes: A computer-simulated study.

BACKGROUND: Inaccuracy in estimating reference intervals (RIs) is a problem with small sample sizes. OBJECTIVES: This study aimed to identify the most accurate statistical methods to estimate RIs based on sample size and population distribution shape. We also studied the accuracy of sample frequency distribution histograms to retrieve the original population distribution and compared strategies based on the histogram and goodness-of-fit test. METHODS: The statistical methods that best enhanced accuracy were determined for various sample sizes (n = 20-60) and population distributions (Gaussian, log-normal, and left-skewed) were determined by repeated-measures ANOVA and posthoc analyses. Frequency distribution histograms were built from 900 samples of five different sizes randomly extracted from six simulated populations. Three reviewers classified the population distributions from visual assessments of a sample histogram, and the classification error rate was calculated. RI accuracy was compared among the strategies based on the histograms and goodness-of-fit tests. RESULTS: The parametric, nonparametric, and robust methods enhanced lower reference limit estimation accuracy for Gaussian, log-normal, and left-skewed distributions, respectively. The parametric, nonparametric bootstrap, and nonparametric methods enhanced the upper limit estimation accuracy for Gaussian, log-normal, and left-skewed distributions, respectively. Regardless of sample size, sample histogram assessments properly classified the original population distribution 71% to 93.9% of the time, depending on the reviewers. In this study, the strategy based on histograms assessed by the statistician was significantly more precise and accurate than the strategy based on the goodness-of-fit test (P < 0.001). CONCLUSIONS: A strategy based on histograms might enhance the accuracy of RI estimations. However, relevant inter-reviewer variations in histogram interpretation were detected. Factors affecting inter-reviewer variations should be further explored.

[The modelling of productivity level and the comparability of sport evaluation depending on the athlete age.]

Throughout the life, a person's working capacity is variable. It is influenced by a wide range of factors, both external and internal, which are difficult to take into account in various studies. An approximation of the density function of the given distribution, based on the assumption of the random nature of the physical condition, depending on a number of different reasons, among competitors and the hypothesis of the asymmetric distribution of athletes' achievements, shown at different ages, is formed. Optimum parameters of a log-normal distribution describing the working capacity of a person according to his or her age are determined by using the least squares method. This is a comparative analysis of the received model and the previously known methods, which were created by Litvinov and Spiridonov. The study has showed the validity of the method for determining age coefficients and the possibility of its practical application.

A simple method to determine the sampling numbers in decision-making units with unknown variations of soil cadmium.

Sampling number is one critical issue to achieve credible results when surveying soil contamination and making remediation decisions. Traditional methods based on a normal distribution for determining numbers of samples are not always optimal because most distributions of soil heavy metal concentrations followed a log-normal distribution. Moreover, the variation of soil heavy metal concentrations is a prerequisite for previous methods to determine sampling numbers. Unfortunately, the variation is often unknown before soil sampling. Therefore, a simple method under the log-normal distribution without relying on variation to determine quickly the sampling number (QSN) was developed for soil cadmium and compared with other methods based on classical statistics and Chebyshev inequality. Results showed that an equation as a function of sampling areas could be used to determine QSN (QSN = 18.44 × A0.54 + 8.69, A is sampling areas, km2), with acceptable errors ranging from 13 to 33% at the sampling areas of 0.03-10 km2. The developed simple method for QSN was easy to use and cost-effective without prerequisite on the estimation of variation. Moreover, when the sampling cost was enough and the improved accuracy was requested, the increased sampling numbers were recommended as 1.53 times as the number calculated by the simple method. Therefore, the proposed method is believed as a simple and cost-effective method to determine the sampling numbers of soil Cd in decision-making units with unknown variations.

Quasi-Static Variation of Power-Law and Log-Normal Distributions of Urban Population.

We analytically derived and confirmed by empirical data the following three relations from the quasi-time-reversal symmetry, Gibrat's law, and the non-Gibrat's property observed in the urban population data of France. The first is the relation between the time variation of the power law and the quasi-time-reversal symmetry in the large-scale range of a system that changes quasi-statically. The second is the relation between the time variation of the log-normal distribution and the quasi-time-reversal symmetry in the mid-scale range. The third is the relation among the parameters of log-normal distribution, non-Gibrat's property, and quasi-time-reversal symmetry.