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The failure behavior of rocks is complex due to the existence of random microscopic defects. This paper presents a new statistical damage model based on the modified Hoek-Brown criterion, i.e., the Pan-Hudson criterion, for predicting the mechanical characteristics of quasi-brittle rocks under compression, and demonstrated its predictive performance for medium-strong rocks. The lognormal distribution is incorporated to validate and reveal the statistical nature of internal microscopic defects. Its effectiveness in describing microscopic defects evolution is highlighted by comprehensive discussions on characteristic distribution parameters, which are rigorously derived. The degradation effects of microscopic defects on macroscopic mechanical responses are reflected by establishing the quantitative relation between damage variables and compressive strength. To validate the proposed model, a series of triaxial compression tests on sandstone are conducted. The peak strength and quasi-brittle post-peak behavior under various confining pressures are well captured. Sensitivity analyses on mechanical and characteristic distribution parameters are also carried out to develop an intuitive understanding of how the introduced modifications affect the mechanical responses. Finally, the deviatoric stress-axial strain curves were compared between our testing data of limestone and previous study. The advantages in capturing peak intensity and simulating the post-peak behavior of the proposed model is emphasized. [ABSTRACT FROM AUTHOR]

This study investigates the turbulent dispersion of pollutants in the wake of a two-dimensional square obstacle. Utilizing Laser Doppler Anemometry and Particle Image Velocimetry, we characterized the flow dynamics, identifying a recirculation zone downstream of the obstacle, marked by high shear and increased turbulent viscosity, and playing a crucial role in turbulent momentum exchange. We evaluated the turbulence kinetic energy budget, estimating its dissipation rate, and found traditional isotropy and Taylor hypothesis methods inadequate within the wake region. Furthermore, we explored pollutant dispersion from a linear source located downstream the obstacle. Analysis of mean concentration and variance revealed that the log-normal distribution is most effective for modelling concentrations within the recirculating region, while the Gamma distribution suits areas outside it. Testing various closure models for turbulent mass fluxes highlighted the limitations of the Simplified Gradient Diffusion Hypothesis model, favouring more complex closure models for longitudinal trends, though these still faced challenges with intensity estimation. The Simplified Gradient Diffusion Hypothesis model proved robust for vertical mass fluxes, with satisfactory results in turbulent diffusivity and turbulent Schmidt number calculations. The experimental results serve as a benchmark for validating numerical simulations and assessing the accuracy of closure models typically employed in pollutant dispersion modelling. [ABSTRACT FROM AUTHOR]

The enzyme-induced calcium carbonate precipitation (EICP) technique was utilized to cement calcareous sand. The mechanical properties of EICP-cemented calcareous sand at various cementation degree were investigated using consolidated drained triaxial compression tests. A statistical damage constitutive model tailored for EICP-cemented calcareous sand was also developed based on damage mechanics theory. The findings are as follows: (1) The EICP technique significantly enhances the cementation of calcareous sand. As the number of grouting operations increases, the peak deviator stress of the cemented material gradually increases, with the maximum enhancement approaching 2.5 times. Moreover, during the stress decay phase following the peak stress, the decay rate of the cemented sand accelerates, displaying a more pronounced brittle characteristic. (2) With the increased calcium carbonate content, the peak eccentric stress of the cemented body increases significantly, and there is an obvious nonlinear exponential correlation between them. (3) The statistical damage constitutive model, formulated based on Lemaitre's strain equivalence principle combined with a log-normal distribution and the Drucker–Prager strength criterion, accurately predicts the stress–strain curves, effectively simulating the complete stress–strain evolution of EICP-cemented sand under different numbers of grouting operations and varied confining pressure conditions. (4) At higher cementation levels or lower confining pressures, the internal damage process of the EICP-cemented calcareous sand specimens intensifies, indicated by the rapid increase of the damage variable D with axial strain. The research findings can provide a crucial theoretical foundation for the application of EICP technology in the treatment of island reef or roadbed foundations, aiding in the analysis and prediction of the mechanical properties of EICP-cemented calcareous sands. [ABSTRACT FROM AUTHOR]

Background: Treatment with Ra-223 dichloride is approved for the therapy of castration resistant prostate cancer (CRPC) with symptomatic bone metastases and no known visceral metastases in Europe since 2013, and Ra-223 is under discussion for labelling other molecules and nanoparticles. The direct progeny of Ra-223 is Rn-219, also known as actinon, a radioactive noble gas with a half-life of 3.98 s. This Rn-219 can be exhaled by patients while Ra-223 is present in the blood. Hence, direct measurements for assessing the exhalation of Rn-219 were performed for the first time in the context of the non-interventional multicenter study "RAPSODY", a substudy to the international early access program, which aimed at assessing the radiation exposure of relatives of patients suffering from castration resistant prostate cancer with bone metastases and treated with Ra-223 dichloride in an outpatient setting, in order to investigate if this kind of method is functional and tolerated by the patients. Methods: Rn-219 was measured directly in patients' exhalations using Alphaguard radon monitors (Saphymo, formerly Genitron, Frankfurt, Germany), originally intended for the measurement of Rn-222, and custom-made breath-test kits. Measurements were performed 20–30 min p. i. and 3–4 h p. i. In total, datasets from 21 administrations in 14 patients were obtained. Results: Although 75% of the measurement data 20–30 min p. i. and 35% of the measurement data 3–4 h p. i., respectively, were censored due to exceedance of the upper limit of the Alphaguards' measurement range in the applied measurement setup, statistical data were derived based on the assumption of lognormal distributions. For measurements 3–4 h p. i., mean activity concentrations of Rn-219 in exhaled breath of approx. 4.4 kBq/l were obtained. In measurements 20–30 min p. i., the expectation value of the activity concentration of approx. 6 kBq/l, derived by statistical methods, was higher. Conclusions: Direct measurements using Alphaguard instruments are suitable for assessing the exhalation of Rn-219 by patients treated with Ra-223. The measurement method is well tolerated by the patients. Rn-219 is present in patients' exhalations. Our results are in accordance with published data obtained using other, indirect measurement methods. [ABSTRACT FROM AUTHOR]

This study examined the distributions of radon and its parent radionuclides 226Ra and 238U in groundwater samples from the Singhbhum region, Jharkhand, India. Radon showed a heterogeneous spatial distribution pattern, with a lognormal distribution. A good correlation between radon bubbler-Lucas cells and liquid scintillation counting techniques was observed for radon monitoring. 222Rn and 226Ra were negatively correlated with pH, suggesting the mobilization of radionuclides at low pH. Uranium was positively correlated with common ions (e.g., Ca, Mg, and SO42−). The activity ratios among the radionuclides indicated disequilibrium, with 222Rn origin controlled by parent radionuclide activity in bedrock. The 226Ra and 238U concentrations in groundwater were lower than the limits recommended by the WHO. [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]

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]

This study explores the risk of the traditional momentum strategy in terms of its realized variance using various data frequencies. It is shown that momentum risk is infinite regardless of the data frequency, implying that (a) t-statistics for this strategy do not exist, (b) correlation-based metrics such as Sharpe ratios do not exist either, and (c) the momentum premium is not observable in reality. It is further shown that the time-honored lognormal distribution is unable to accurately model extreme events observed at various variance data frequencies. Finally, it is shown that the well-known effect of time aggregation does not work for this investment vehicle. Hence, the study is forced to conclude that momentum stories have no valid foundation for their claims. [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]

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]

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]

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

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

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

The 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]

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

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

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

Understanding the deformation and damage behaviors of soft rocks under temperatures and water–rock interactions is crucial for designing rock engineering structures and for assessing geotechnical disasters. Hence, the physical–mechanical characteristics and damage mechanisms of silty mudstone under heating and water-cooling cycles were determined by a series of laboratory tests. The results indicate that heating and water-cooling treatments prompt crack development within silty mudstone, observable through volume augmentation along with reductions in mass, density, and P-wave velocity. The interconnections between the decrease of mechanical properties such as elastic modulus, cohesion, and internal friction angle of silty mudstone and the factors including temperatures and cycle number are explicitly established. The deterioration of the physical–mechanical properties of silty mudstone primarily arises from the thermal expansion, dehydration, and hydrolysis of mineral constituents. Furthermore, a new damage constitutive model for silty mudstone considering temperature and the number of heating and water-cooling cycles is established based on lognormal distribution and the Mohr–Coulomb criterion. Additionally, the model parameters S0 and F0 characterize the homogeneity and average strength, enabling a quantitative assessment of the damage degree of rocks. [ABSTRACT FROM AUTHOR]

Studies of the mechanical response behavior of slate and the establishment of corresponding damage-ontological relationships are crucial for improving safety and avoiding disasters in construction projects. For the study reported in this paper, we first assumed that slate is a transverse isotropic body. Next, to characterize disparities in elastic characteristics between axial and radial orientations, we introduced five distinct elastic parameters for these two directions. Specifically, these parameters were Young's modulus E1, Poisson's coefficient v1 (associated with parallel bedding planes), Young's modulus E2, Poisson's coefficient v2, and shear modulus G2 (associated with perpendicular bedding planes). We then established a statistical damage-evolution equation for transverse isotropic slate based on a lognormal distribution, and we constructed a statistical damage-constitutive model for laminated slate under three-way stress by considering the shear–slip deformation and closure deformation of the laminated surface. Finally, we demonstrated the effectiveness of our model by comparing its output data with results obtained in triaxial compression tests on slate. We found that the differential stress–strain curves obtained from the model and the tests were in good agreement in the peak front. Average relative errors of 15.62% and 16.19% were recorded for cases of 5 Mpa and 10 Mpa of enclosing pressure, respectively. The rationality of the established transverse isotropic slate damage-constitutive relationship was therefore proved. [ABSTRACT FROM AUTHOR]

Rainstorm is one of the global meteorological disasters that threaten the safety of transportation infrastructure and the connectivity of transportation system. Aiming to support the resilience assessment of transportation infrastructure in three representative regions: Sichuan–Chongqing, Yangtze River Delta, and Beijing-Tianjin-Hebei-Shandong, rainfall data over 40 years in the three regions are collected, and the temporal distribution of rainfall are analyzed. Prediction equations of rainfall are established. For the purpose of this, the probabilistic density function (PDF) is assigned to the rainfall by fitting the frequency distribution histogram. Using the assigned PDF, the rainfall data are transformed into standard normal space where regression of prediction equations is performed and the prediction accuracy is tested. The results show that: (1) The frequency of rainfall in the three regions follows a lognormal distribution based on which the prediction equations of rainfall can be established in standard normal space. The error of regression shows no remarkable dependence on self-variables, and the significance analysis indicates that the equations proposed in this paper are plausible for predicting rainfalls for the three regions. (2) The Yangtze River Delta region has a higher risk of rainstorm disaster compared to the other two regions according to the frequency of rainfall and the return period of precipitation concentration. (3) Over the period of 1980–2021, the Sichuan–Chongqing region witnessed an increase in yearly rainfall but a decrease in rainstorm disasters, whereas the other two regions experienced a consistent rise in both metrics. [ABSTRACT FROM AUTHOR]

This paper addresses a stochastic job shop scheduling problem with sequence-dependent setup times, aiming to minimize the expected maximum lateness. The stochastic nature is modeled by considering uncertain times between failures (TBF) and uncertain times to repair (TTR). To tackle this problem, a simheuristic approach is proposed, which combines a tabu search (TS) algorithm with Monte Carlo simulation. A total of 320 instances were used to conduct multiple experiments. Instances were generated with two distributions to study the behavior of stochastic TTR and TBF under log-normal and exponential distributions. Firstly, the performance of the simheuristic was evaluated for small instances by comparing it with the simulation of optimal solutions obtained with a mixed-integer linear programming (MILP) model. The simheuristic approach demonstrated an average improvement of around 7% compared to the simulation of MILP model solutions. Secondly, the simheuristic performance was evaluated for medium and large-size instances by comparing it with the simulation of the solutions obtained by the earliest due date (EDD) and process time plus work in the next queue plus negative slack (PT + WINQ + SL) dispatching rules. The results showed an average improvement of around 11% compared to EDD and 14% compared to PT + WINQ + SL. Furthermore, the results highlight that even when the two distributions have the same expected value and coefficient of variation, they can yield different expected maximum lateness values. This emphasizes the importance of precise distribution fitting when solving real cases to achieve effective scheduling performance. [ABSTRACT FROM AUTHOR]

Significant errors often arise when measuring streamflow during high flows and flood events. Such errors conflated by short records of observations may induce bias in the flood frequency estimates, leading to costly engineering design mistakes. This work illustrates how observational (measurement) errors affect the uncertainty of flood frequency estimation. The study used the Bulletin 17 C (US standard) method to estimate flood frequencies of historical peak flows modified to represent the measurement limitations. To perform the modifications, we explored, via Monte Carlo simulation, four hypothetical scenarios that mimic measurement errors, sample size limitations, and their combination. We used a multiplicative noise from a log-normal distribution to simulate the measurement errors and implemented a bootstrap approach to represent the sampling error. Then, we randomly selected M samples from the total N records of the observed peak flows of four gauging stations in Iowa in central USA. The observed data record ranges between 76 and 119 years for watersheds with drainage areas between 500 and 16,000 km2. According to the results, measurement errors lead to more significant differences than sampling limitations. The scenarios exhibited differences with median magnitudes of up to 50%, with some cases reaching differences up to 100% for return periods above 50 years. The results raise a red flag regarding flood frequency estimation that warrants looking for further research on observational errors. [ABSTRACT FROM AUTHOR]

This research investigates exhalation rates of radon (222Rn) and thoron (220Rn) from soil samples in the Jaunsar-Bawar region of the Indian Himalayas. Before sampling, gamma radiation rates were evaluated, ranging from 0.08 to 0.33 µSv/h. The observed 222Rn mass exhalation rates range between 3.56 and 82.08 mBq/kg/h, with an average of 25.67 mBq/kg/h. Additionally, the surface exhalation rate of 220Rn varies from 1.28 to 22.69 Bq/m2/s, averaging 7.90 Bq/m2/s. Projected 220Rn mass emission rates span 154–2356 mBq/kg/s, with a mean of 939 mBq/kg/s. The dataset analysis employs best-fit statistics, revealing the Weibull distribution as the optimal model for gamma dose rate and 220Rn mass emanation rates. Lognormal distribution suits 222Rn mass exhalation rates, and the Gamma distribution excels for 220Rn surface exhalation rates, aligning with log-likelihood estimator indications. [ABSTRACT FROM AUTHOR]

In this paper, we consider a novel reliability-based network equilibrium problem for mixed traffic flows of human-driven vehicles (HVs) and connected autonomous vehicles (CAVs) with endogenous CAV market penetration and stochastic link capacity degradations. Travelers' perception errors on travel time and their risk-aversive behaviors on mode choice and path choice are incorporated in the model with a hierarchical choice structure. Due to the differences between HVs and CAVs, the perception errors and the safety margin reserved by risk-averse travelers are assumed to be related to the vehicle type. The path travel time distribution is derived by using the moment-matching method based on the assumption that link capacity follows lognormal distribution and link travel times are correlated. Then, the underlying problem is formulated as an equivalent variational inequality problem. A path-based algorithm embedded with the Monte Carlo simulation-based method is proposed to solve the model. Numerical experiments are conducted to illustrate the features of the model and the computational performance of the solution algorithm. [ABSTRACT FROM AUTHOR]

The log-normal and the log-logistic distributions are two of the most commonly used distributions for studying positively skewed lifetime data. Both the distributions share number of interesting properties, and for a certain range of parameters their cumulative and hazard functions can also be similar in nature. However, selecting a more appropriate distribution and discriminating among them for a given data to best fit is an important issue. Further, when the data are observed in the presence of some censoring scheme the problem becomes more challenging. In this paper, we address the problem of selecting a more appropriate distribution by discriminating based on the random samples drawn in the presence of type-II censoring. We consider the difference of the maximized log-likelihood functions, and compute the asymptotic distribution of the discrimination statistic. We further propose a modified discriminating approach, and compute the probabilities of correct selection to check the performance of the discrimination procedure. Finally, simulation study is conducted, and two real data sets are analysed for the illustration purpose. [ABSTRACT FROM AUTHOR]

The efficiency of estimating the numerical characteristics of the family of the lognormal law of distribution of a one-dimensional random variable with large amounts of statistical data is considered. To circumvent the problem of large samples, methods for discretizing the range of values of a random variable based on the Sturgess, Brooks-Carruther, Heinhold-Gaede formulas and the formula proposed by the authors of this article are used. Data arrays have been formed that make it possible to estimate the numerical characteristics of the distribution laws of random variables, taking into account their discrete values. Based on the transformed data sets, estimates of mathematical expectation, standard deviation, asymmetry and kurtosis coefficients were calculated. Estimates of the numerical characteristics of the considered distribution laws for a continuous and discrete random variable with different volumes of initial statistical data are compared. The effectiveness of methods for estimating the numerical characteristics of the family of the lognormal distribution law from the initial statistical data and from the results of transformations of these data using known discretization formulas has been established. The reliability of the comparison of the effectiveness indicators of the studied methods was confirmed using the Kolmogorov-Smirnov criterion. It is shown that the discretization formula proposed by the authors of this article is more efficient in comparison with the traditional Sturgess, Brooks-Carruther, and Heinhold-Gaede discretization formulas. [ABSTRACT FROM AUTHOR]

In unsaturated soil mechanics, the soil–water characteristic curve (SWCC) is the most fundamental soil attribute. All seepage analyses require SWCC to generate the pore-water pressure and water content distribution within the soil layers. SWCC is often determined using laboratory procedures. However, the expensive cost, long testing time, and difficulty of the SWCC tests hinder the use of unsaturated soil mechanics in engineering practice. Models for predicting SWCC have been proposed in the literature; however, the equations cannot be applied to soils of a wide variety, and their parameters lack physical significance. This work used a modified lognormal distribution function to generate the equations that best suit the grain-size distribution (GSD) and the model that estimates SWCC for a wide range of soil types. The parameters of the proposed GSD equation have well-defined physical meanings. The model for estimating SWCC was established based on the link between soil pore-size distribution and dry density, void ratio, and saturated water content. The air-entry value of coarse-grained soil is a function of inflection point of SWCC and percentage of coarse particle. The air-entry value of fine-grained soil is a function of saturated water content. Experiments were carried out as part of this study to evaluate the proposed equation as well as its model. The proposed model to estimate SWCC was compared with other models. The proposed model is better than other models in the estimation of SWCC from GSD. [ABSTRACT FROM AUTHOR]

This study evaluates the joint impact of non-linearity and non-Gaussianity on predictive performance in 23 Brazilian monthly streamflow time series from 1931 to 2022. We consider point and interval forecasting, employing a PAR(p) model and comparing it with the periodic vine copula model. Results indicate that the Gaussian hypothesis assumed by PAR(p) is unsuitable; gamma and log-normal distributions prove more appropriate and crucial for constructing accurate confidence intervals. This is primarily due to the assumption of the Gaussian distribution, which can lead to the generation of confidence intervals with negative values. Analyzing the estimated copula models, we observed a prevalence of the bivariate Normal copula, indicating that linear dynamic dependence is frequent, and the Rotated Gumbel 180°, which exhibits lower tail dependence. Overall, the temporal dynamics are predominantly shaped by combining these two types of effects. In point forecasting, both models show similar behavior in the estimation set, with slight advantages for the copula model. The copula model performs better during the out-of-sample analysis, particularly for certain power plants. In interval forecasting, the copula model exhibits pronounced superiority, offering a better estimation of quantiles. Consistently demonstrating proficiency in constructing reliable and accurate intervals, the copula model reveals a notable advantage over the PAR(p) model in interval forecasting. [ABSTRACT FROM AUTHOR]

In this study, we explore the evolution of the size distribution of Ag nanoparticles produced by a spark ablation vapor source. The as-prepared Ag nanoparticles exhibit a special bimodal lognormal size distribution, containing both ultrafine (~ 1.5 nm) and larger (3 to 15 nm) particles. Such a size distribution differs from previous investigations of nanoparticles generated by spark ablation, which had larger particles with a lognormal distribution. The 1.5 nm size of the ultrafine Ag nanoparticles in this study is close to the theoretical size of the critical nucleus predicted by classic nucleation theory. By considering the simultaneous precipitation and coagulation of the particles and different coalescence dynamics at different sizes, we established a quantitative model that describes the evolution of the special size distribution of the Ag nanoparticles. The model's predictions accurately reproduce the as-measured nanoparticle size distribution. This study can provide a new experimental and theoretical basis for understanding the kinetics of the growth of ultrafine nanoparticles produced by a rapidly quenched vapor source. [ABSTRACT FROM AUTHOR]

Plasma metabolomics holds potential for precision medicine, but limited information is available to compare the performance of such methods across multiple cohorts. We compared plasma metabolite profiles after an overnight fast in 11,309 participants of five population-based Swedish cohorts (50–80 years, 52% women). Metabolite profiles were uniformly generated at a core laboratory (Metabolon Inc.) with untargeted liquid chromatography mass spectrometry and a comprehensive reference library. Analysis of a second sample obtained one year later was conducted in a subset. Of 1629 detected metabolites, 1074 (66%) were detected in all cohorts while only 10% were unique to one cohort, most of which were xenobiotics or uncharacterized. The major classes were lipids (28%), xenobiotics (22%), amino acids (14%), and uncharacterized (19%). The most abundant plasma metabolome components were the major dietary fatty acids and amino acids, glucose, lactate and creatinine. Most metabolites displayed a log-normal distribution. Temporal variability was generally similar to clinical chemistry analytes but more pronounced for xenobiotics. Extensive metabolite-metabolite correlations were observed but mainly restricted to within each class. Metabolites were broadly associated with clinical factors, particularly body mass index, sex and renal function. Collectively, our findings inform the conduct and interpretation of metabolite association and precision medicine studies. [ABSTRACT FROM AUTHOR]

The lognormal statistical distribution was used to present the reliable integrated data on the content of various physicochemical forms of tritium in air, natural water, and components of aquatic ecosystems at nuclear facility sites. Statistics of lognormal distributions took into account the left truncation, which reflects the effect of finite sensitivity of measurements. The statistics of lognormal distributions were used to obtain estimates for ecosystems of NPP sites at limited sets of data. Specific activities were estimated for various forms of tritium such as HTO (free water), TFWT (tissue free water tritium), and OBT (organically bound tritium). The measurement results show that the specific activity of tritium in the body in bound forms was, as a rule, higher than its specific activity in free water in the ambient environment. Equilibrium concentration ratios (CRs) (partition coefficients of hydrogen) ranged from 1 to about 20. The results obtained by the Radium Institute research team agree with those obtained by the researchers from Canada and France for the specific activity of tritium in different chemical forms in environmental samples. [ABSTRACT FROM AUTHOR]

We explore the thermal characteristics of fermionic fields with a nonminimal coupling in one, two, and three dimensions using the framework of superstatistics theory. We consider three distinct distributions: the gamma distribution, the lognormal distribution, and the F distribution. Each of these distributions is governed by a specific probability density function. To calculate the partition function, we use the Euler–Maclaurin formula, specifically in the low-energy asymptotic approximation of superstatistics. This calculation takes the remainder term into consideration. In each scenario, using the derived partition functions, we analyze the variations in entropy and specific heat with varying temperatures and the universal parameter denoted as . In general, we observe that increasing the value of enhances all the curves. Additionally, we note that entropy values tend to increase as the temperature decreases, and tend to decrease as the parameter increases. [ABSTRACT FROM AUTHOR]

The determination of the so-called design block is one of the central elements of the Austrian guideline for rockfall protection ONR 24810. It is specified as a certain percentile (P95–P98, depending on the event frequency) of a recorded block size distribution. Block size distributions may be determined from the detachment area (in situ block size distribution) and/or from the deposition area (rockfall block size distribution). Deposition areas, if present, are generally accessible and measurable without technical aids. However, most measuring methods are subjective, uncertain, not verifiable, or inaccurate. Also, rockfall blocks are often fragmented due to the preceding fall process. The in situ block size distribution is (also) required for meaningful rockfall modelling. The statistical method seems to be the most efficient and cost-effective method to determine in situ block size distributions with many blocks within the whole range of block sizes. In the current literature, joint properties are often described by the lognormal and exponential distribution functions. Today, we can model synthetic rock masses on the basis of discrete fracture networks. They statistically describe the geometric properties of the joint sets. This way, we can carry out exact rock mass block surveys and determine in situ block size distributions. We wanted to know whether the in situ block size distributions derived from the synthetic rock mass models can be described by probability distribution functions, and if so, how well. We fitted various distribution functions to three determined in situ block size distributions of different lithologies. We compared their correlations using the Kolmogorov–Smirnov test and the mean-squared error method. We show that the generalized exponential distribution function best describes the in situ block size distributions across various lithologies compared to 78 other distribution functions. This could lead to more certain, accurate, verifiable, holistic, and objective results. Further investigations are required. [ABSTRACT FROM AUTHOR]

Purpose: The lognormal distribution is by far the most frequent distribution type to model uncertainty in LCA data. Its parameterization is non-trivial, and there are various options for this, some of which employ confusing names and symbols. The result is that by now many different systems have emerged, including ambiguous and incorrect forms. Methods: Here, we clarify the situation by studying the approaches in textbooks on probability and statistics, LCA documents on uncertainty, LCA databases, LCA software, and often-used programming and simulation tools. Results and discussion: One of our conclusions is that the representation of the lognormal distribution in LCA is done in a very heterogeneous, confusing, and sometimes contradicting or inconsistent way. Even high-profile organizations (such as ISO) and widely used databases (such as ecoinvent) which aim to harmonize practice are unclear or ambiguous about the way they represent the parameters of the lognormal distribution. A final issue of concern is the use of units in relation to those parameters. If one source specifies a lognormally distributed variable in kilogram, how should a system working with gram process those parameters? Also here, the answer is surprisingly hard and we expect that mistakes with this may have been made in case studies and databases. Conclusions: We end by proposing a consistent and unambiguous system of parameters to communicate a lognormally distributed variable. [ABSTRACT FROM AUTHOR]

Chiggers are a group of ectoparasites and they are the vector of scrub typhus. Although the Ryukyu mouse (Mus caroli) is a common species of rodent in some outdoor habitats, few studies are about the mouse itself and its ectoparasites. To date, there has been no specific report on chiggers of M. caroli. Based on the field investigation in southwest China from 2001 to 2019, this paper reported the infestation and distribution of chiggers on M. caroli for the first time. Among the 91 sites investigated, 263 Ryukyu mice were captured at 18 sites, and 678 chiggers were collected from the mice. The collected chiggers were identified to be one family, two subfamilies, six genera, and 16 species with relatively low species diversity. The overall infestation prevalence (PM), mean abundance (MA), and mean intensity (MI) were PM = 27.38%, MA = 2.58 chiggers/per mouse, and MI = 9.42 chiggers/per mouse respectively. The dominant chigger species are Walchia ewingi and W. micropelta with a total constituent ratio of Cr = 94.10% (638/678), and they were of aggregated distribution among different individuals of the host M. caroli. The distribution of two dominant chigger species seemed to be mutually independent with the association coefficient V ≈ 0 (p < 0.001). The infestation (PM, MA, and MI) of M. caroli with chiggers greatly fluctuated in different geographical landscapes, altitudes, and latitudes with an obvious environmental heterogeneity. The male and adult M. caroli harbored much more chigger mites with significantly higher infestations (PM, MA and MI) than the female and juvenile mice. The theoretical curve of species abundance distribution of the chigger mite community on M. caroli was fitted by Preston lognormal distribution model with fitting goodness R2 = 0.77. Based on the iChao1 formula, the expected total number of chigger species on the mice was estimated to be 24 species. [ABSTRACT FROM AUTHOR]

Understanding joints is becoming increasingly important in South Korea owing to the development of plans for high-level waste disposal. This study examined drill cores to assess the morphology of joints in five areas with different rock types. The depths and dip angles of 14,169 joints were measured, and the joints were then classified based on their dip angles. Joint spacings within each set were statistically analyzed and fitted to five statistical distribution models: double Weibull, exponential, generalized log-logistic, gamma, and lognormal. Results for each given type of rock showed similar dip angles but varying depths. The observed joint spacings were most accurately fitted using the lognormal distribution. The results of this study will provide insights into the distributions of joints in South Korea and can be used in numerical modeling and stability assessments. [ABSTRACT FROM AUTHOR]

To comprehend the empirical seismic vulnerability capability of various typical structures in towns and suburbs, this study considers, as the research background, the structural damage data observation from the Mw 7.1 Yushu earthquake that occurred on 2010 April 14th in China. The proposed research activity sorts out the actual investigation data (7156 buildings) of five types of typical structures in towns and villages and establishes the vulnerability and seismic fragility evaluation model of a group of buildings considering multidimensional parameters by using the Chinese macroseismic intensity standard. Using spatial modal, numerical calculation, and regression analysis methods, an updated lognormal distribution vulnerability and resilience assessment model based on multidimensional quantitative parameters is performed. Based on the principle of the conditional probability and damage quantification model, an innovative model (domain, point cloud, curve, surface, matrix, and function) is established for regional vulnerability and seismic resilience assessment of typical group buildings. A logarithmic relationship model considering both the updated Chinese macroseismic intensity and three-dimensional composite peak ground acceleration as intensity measures is proposed, and an empirical vulnerability assessment model for typical rural buildings is established. The traditional average earthquake loss index calculation model is updated, and an innovative regional domain vulnerability assessment model is conducted. Taking the samples of various typical structures surveyed in the Yushu earthquake, regional group structure vulnerability domain comparison models of various structures are performed. Ultimately, depending on the typical damage characteristics of structures, the actual damage features and mechanisms of various structures are analysed. [ABSTRACT FROM AUTHOR]

The article proposes a procedure for selecting the blur factor of kernel functions for nonparametric density estimation of a one-dimensional random variable given large amounts of statistical data, for example, obtained via the remote sensing of natural objects. The proposed procedure uses regression density estimation. A procedure is presented for synthesizing a regression density estimate. The estimate synthesis is based on the original sample compression by decomposing the range of a random variable. To this end, the Heinhold-Gaede rule and a formula for choosing the optimal number of sampling intervals are applied. The article considers two approaches to selecting the blur factor of regression density estimation using the conventional method and that proposed by the authors to optimize nonparametric density estimation. The conventional method for optimizing nonparametric density estimation is based on minimizing its standard deviation. In the proposed method, the choice of the blur factors of kernel functions relies on the conditions for the minimum approximation error of regression density estimation. The article analyzes the approximation properties of regression density estimation using two optimization methods. The conditions of their competence in estimating the probability densities of random variables following lognormal distribution are established. The results obtained for a one-dimensional random variable can be used to optimize the regression density estimation of a multi-dimensional random variable. [ABSTRACT FROM AUTHOR]

Demand side management (DSM) is widely utilized in smart grid for its reliable features, flexibility, and cost benefits that it offers to customers on reduction of the energy bill. In the smart grid, demand response aggregator, power customers, and utility operator all strive to increase their individual profits. However, it is extremely challenging to guarantee profits for all of the candidates simultaneously. In this paper, these criteria are employed to execute a problem with multiple objectives by combining the concept of DSM and dynamic economic emission dispatch considering uncertainties of renewable energy sources (RESs). The uncertainties of RESs can bring adverse effects on the grid operator. Thus, Weibull probability distribution function and lognormal probability distribution function are used to model the uncertainties of wind speed and solar irradiation, respectively, in this paper. Further, the multi-objective improved DSM scheme is optimized by Class Topper optimization algorithm. The objective here is to optimally schedule load demand and generation pattern simultaneously to improve load factor, minimize electricity bill and maximize the profits of all candidates of the day-ahead electricity market simultaneously. Error in the load forecasting model may lead to growing operational cost of energy generation. In this paper, a machine learning model using linear regression is used for short-term load forecasting (STLF) to forecast day-ahead load demand. The simulation results show the importance of the improved DSM scheme and the advantage of STLF, which further help to improve the economy and efficiency of the smart grid. [ABSTRACT FROM AUTHOR]

Since spring discharge, especially in arid and semiarid regions, varies considerably in different months of the year, a time series of spring discharge observations is needed to determine the firm yield of the spring and the amount of water allocated to different needs. Because most springs are in mountainous and inaccessible areas, long-term observational data are often unavailable. This study proposes a probabilistic method based on bivariate analysis to estimate the discharge of the Absefid spring in Iran. This method constructed the bivariate distribution of the outflows of Absefid (AS) and Gerdebisheh (GS) springs using Copula functions. For this purpose, the fit of 11 different univariate distributions to the discharge data of each spring was tested. The results revealed that the GEV and log-normal distributions best fit the discharge data of GS and AS springs, respectively. In addition, among eight different copula functions, the Joe copula function was selected to construct the bivariate distribution of the discharge data of AS and GS springs. With the help of the created bivariate distribution and assuming a certain probability level, it is possible to estimate the discharge of Absefid spring based on the discharge of Gerdebisheh spring in a particular month. The estimated values of the discharge of the Absefid spring in the period from March 1993 to August 2022 show that with a probability of 90%, the lowest discharge of this spring is 600 L per second and occurred in June 2001. Therefore, to allocate the water from this spring for drinking purposes, this discharge value can be considered as the firm yield of this source. However, the amount of allocated water from this source should be determined by considering the ecological needs of the river downstream of this spring. [ABSTRACT FROM AUTHOR]

The parallel measurements of wavelength dependent optical absorption, particle number size distribution have made by a multi wavelength photoacoustic spectrometer (4λ-PAS) and scanning mobility particle sizer (SMPS) respectively at different modes of a diesel engine using two different types of fuel. The thermal evolution of the emission was also investigated using posterior temperature treatment of emission. The bimodal size distribution of emitted particles at a set reference temperature has been observed regardless of the applied fuel at idle. However, the emitted particulate assembly had lognormal size distribution falls into the accumulation mode at all other defined engine modes and both fuel types. The total number- and volume concentration (TNC and TVC) showed retrograde tendency with the increasing torque and rpm independently of the applied fuel types. The TNC values decreased up to 50% for both fuels with engine operation changes from idle engine mode(em#1) to low engine mode(em#2). With further increase in torque and rpm of engine, the change in TNC is negligible. On the other hand, the TVC remains more or less the same for idle to low engine mode transition and increased more than 60% for high mode (em#3) transition. The Optical Absorption Coefficient (OAC) values measured at the operational wavelengths of the 4λ-PAS instrument decreased at all wavelengths with increasing rpm and torque. The wavelength dependency quantified by Aerosol Ängström Exponent (AAE) was applied here for qualitative analysis of the carbonaceous emission and showed decreased values towards the higher engine speed and torque output of the engine. The proposed technique can be used as real-time, precise and accurate measurement of light absorption by DPM aerosols, which opens up novel possibilities for the volatility and thermal evolution investigation of diesel emissions. [ABSTRACT FROM AUTHOR]

The load spectrum is an important component in the reliability testing of machining centers. The statistical characteristics of a load must be accurately estimated to evaluate the capacity of a machining center to withstand the applied load. Due to the complexity of the processing technology, diversity of the processed materials, and uncertain factors, several types of cutting loads present single or bimodal distributions for which the conventional one-component probability density function (PDF) is inappropriate. Mixture distributions are regarded as an appropriate alternative for modeling such load data. In addition, parameter estimation for these mixture models requires an advanced optimization method, which takes a substantial amount of time to process. However, machining centers typically involve a variety of processing methods, each giving rise to various load types, resulting in a significant increase in the amount of calculation in parameter estimation. Accordingly, rapid and accurate selection of the best matching hybrid model is a great challenge. To solve this problem, a method for compiling a two-component distribution function based on the linear moment ratio diagram (L-MRD) method is proposed to rapidly and accurately model multiple types of load distributions. First, the one-component and the two-component mixture models consisting of normal distribution (Norm), Gumbel or extreme value type I (E), generalized extreme value (GEV), Pearson type III (P3), and 3-parameter Lognormal (LN3) distributions are selected as candidate models, and the mean and amplitude are applied to milling total eight load sets. Thereafter, the best two-component hybrid model for each load set is determined by taking the estimated value of the load sample data in L-MRD and the relative position of the candidate distribution in L-MRD as the basis for selecting the best matching distribution. The estimation of the parameter of the mixture models is obtained with the least-squares and maximum likelihood methods. The optimization of the objective functions related to these estimation methods is carried out with a genetic algorithm (GA) that is more adapted to mixture distributions. Finally, the results obtained with the L-MRD are compared with those obtained with goodness-of-fit statistics through model selection criteria. Analysis results indicate that L-MRD quickly and effectively selects the optimal mixture distribution component type on a single graph and offers more information than a goodness-of-fit criterion because it provides knowledge about such characteristics as the skewness and kurtosis of the load data samples. In addition, the mixture models improve the modeling flexibility, minimize statistical errors, enhance the fitting accuracy, and generate load spectra that better reflect the actual load characteristics. [ABSTRACT FROM AUTHOR]

The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds. Accurately obtaining the entrainment rate (λ) is particularly important for its parameterization within the overall cumulus parameterization scheme. In this study, an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculate λ of cumulus clouds in a large-eddy simulation. The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method, because λ, as calculated from the improved method, falls within the range of λ values obtained from the traditional method using different conserved variables. The probability density functions of λ for all data, different times, and different heights can be well-fitted by a log-normal distribution, which supports the assumed stochastic entrainment process in previous studies. Further analysis demonstrate that the relationship between λ and the vertical velocity is better than other thermodynamic/dynamical properties; thus, the vertical velocity is recommended as the primary influencing factor for the parameterization of λ in the future. The results of this study enhance the theoretical understanding of λ and its influencing factors and shed new light on the development of λ parameterization. [ABSTRACT FROM AUTHOR]

Magnetic bright points (MBPs) are located in intergranular channels on the solar surface. Studying the properties and evolution process of MBPs can help us to better understand solar activity and predict solar events that have a significant impact on Earth. In this study, we performed a statistical analysis of MBPs at different latitudes and longitudes. Data from the quiet-Sun (QS) in the eastward-equator (8 June 2021) and in the southern hemisphere (31 July 2020), as well as data from the QS near the disk center (30 July 2020), are analyzed. We studied the properties of MBPs, including lifetime, intensity contrast, and velocity. Moreover, we analyzed the intensity contrast of isolated MBPs at the moments of their birth and disappearance at different latitudes and longitudes, as well as the variation in the number of MBPs that appeared and disappeared in each frame. The results show that non-isolated MBPs have longer lifetimes than isolated MBPs, and the average lifetime of non-isolated MBPs located in the southern hemisphere (SH) is significantly shorter than that of MBPs near the disk center (DC) in the eastward-equator (EE). We find that the lifetime of non-isolated MBPs in the SH is negatively correlated with the intensity contrast, with higher intensity contrast associated with a shorter lifetime. The velocities of isolated MBPs at different latitudes and longitudes follow a Rayleigh distribution, while the velocities of non-isolated MBPs follow a log-normal distribution. Non-isolated MBPs exhibit higher horizontal velocities, with the maximum horizontal velocity reaching 8 km s−1. Finally, we find that the number of isolated MBPs per square Mm at different latitudes and longitudes remains stable during consecutive periods, and the intensity contrast of isolated MBPs is similar at the moment of their birth and disappearance. [ABSTRACT FROM AUTHOR]

In this paper, the insurance company considers venture capital and risk-free investment in a constant proportion. The surplus process is perturbed by diffusion. At first, the integro-differential equations satisfied by the expected discounted dividend payments and the Gerber-Shiu function are derived. Then, the approximate solutions of the integro-differential equations are obtained through the sinc method. Finally, the numerical examples are given when the claim sizes follow different distributions. Furthermore, the errors between the explicit solution and the numerical solution are discussed in a special case. [ABSTRACT FROM AUTHOR]

Many experiments suggest that long-term information associated with neuronal memory resides collectively in dendritic spines. However, spines can have a limited size due to metabolic and neuroanatomical constraints, which should effectively limit the amount of encoded information in excitatory synapses. This study investigates how much information can be stored in the population of sizes of dendritic spines, and whether it is optimal in any sense. It is shown here, using empirical data for several mammalian brains across different regions and physiological conditions, that dendritic spines nearly maximize entropy contained in their volumes and surface areas for a given mean size in cortical and hippocampal regions. Although both short- and heavy-tailed fitting distributions approach 90 - 100 % of maximal entropy in the majority of cases, the best maximization is obtained primarily for short-tailed gamma distribution. We find that most empirical ratios of standard deviation to mean for spine volumes and areas are in the range 1.0 ± 0.3 , which is close to the theoretical optimal ratios coming from entropy maximization for gamma and lognormal distributions. On average, the highest entropy is contained in spine length ( 4 - 5 bits per spine), and the lowest in spine volume and area ( 2 - 3 bits), although the latter two are closer to optimality. In contrast, we find that entropy density (entropy per spine size) is always suboptimal. Our results suggest that spine sizes are almost as random as possible given the constraint on their size, and moreover the general principle of entropy maximization is applicable and potentially useful to information and memory storing in the population of cortical and hippocampal excitatory synapses, and to predicting their morphological properties. [ABSTRACT FROM AUTHOR]

Polymodal particle size distributions are generally analyzed by separating them into lognormal distributions, but estimating the precise number of lognormal components required remains a considerable problem. In the present study, appropriate evaluation criteria for the estimation of the number of components were examined by using artificial data for which the true number of components was known. The characteristics of estimations of the number of components by four evaluation criteria, the mean square error (MSE), Akaike information criterion (AIC), Bayesian information criterion (BIC), and adjusted R-squared (ARS), were investigated. The results showed that the MSE and ARS were less sensitive to the true number of components and tended to overestimate the number of components. By contrast, the AIC and BIC tended to underestimate the number of components, and their correct answer rates decreased as the true number of components increased. The BIC tended to include the true number of components among its higher ranked models. The present evaluation results suggest that the MSE, although frequently used, is not necessarily the most appropriate evaluation criterion, and that the AIC and ARS may be more appropriate criteria. Furthermore, checking whether the number of components estimated by the AIC or ARS is included among higher ranked BIC models might prevent overestimation and thereby allow for more valid estimation of the number of components. When the criteria were applied to grain-size distributions of lacustrine sediments, it was possible to estimate the number of components that reflected differences in grain-size distribution characteristics. [ABSTRACT FROM AUTHOR]

The heat transfer characteristics and particle size distribution (PSD) characteristics of ice slurry in double-tube heat exchanger (DTHE) are experimentally investigated. An experimental microscopic observation device is used to characterize the PSD of ice slurry. Experimental ice slurry PSDs are compared to classical normal, log-normal, Weibull and Gamma distributions, and the results match basically to log-normal distribution. The effects of flow rate, ice mass fraction and water temperature on the PSD and heat transfer coefficient of ice slurry are analyzed. The results showed that the heat transfer coefficient of ice slurry hc increases linearly with the increase of flow rate. The higher the water temperature and ice mass fraction, the larger hc, especially in the high flow rate region. After heat exchange, the peaks of PSD curves shift to the left and the range of PSD is significantly narrowed. The water temperature rises from 25℃ to 40℃, the differences in Sauter diameter (∆d32) can be increased by approximately 2 times. In addition, increasing the ice mass fraction can cause the increase of the Sauter diameter (d32) and decrease of ∆d32. The increase of flow rate leads to the decrease of ∆d32, which is caused by the insufficient heat exchange of ice slurry. These studies can give some help to further improve the heat transfer mechanism of ice slurry. [ABSTRACT FROM AUTHOR]

Neural circuits with multiple discrete attractor states could support a variety of cognitive tasks according to both empirical data and model simulations. We assess the conditions for such multistability in neural systems using a firing rate model framework, in which clusters of similarly responsive neurons are represented as single units, which interact with each other through independent random connections. We explore the range of conditions in which multistability arises via recurrent input from other units while individual units, typically with some degree of self-excitation, lack sufficient self-excitation to become bistable on their own. We find many cases of multistability—defined as the system possessing more than one stable fixed point—in which stable states arise via a network effect, allowing subsets of units to maintain each others' activity because their net input to each other when active is sufficiently positive. In terms of the strength of within-unit self-excitation and standard deviation of random cross-connections, the region of multistability depends on the response function of units. Indeed, multistability can arise with zero self-excitation, purely through zero-mean random cross-connections, if the response function rises supralinearly at low inputs from a value near zero at zero input. We simulate and analyze finite systems, showing that the probability of multistability can peak at intermediate system size, and connect with other literature analyzing similar systems in the infinite-size limit. We find regions of multistability with a bimodal distribution for the number of active units in a stable state. Finally, we find evidence for a log-normal distribution of sizes of attractor basins, which produces Zipf's Law when enumerating the proportion of trials within which random initial conditions lead to a particular stable state of the system. [ABSTRACT FROM AUTHOR]