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• This study introduce extreme value theory (EVT) and Peaks Over Threshold (POT) methods into the calculation of takeover time thresholds; a methodology for calculating and verifying takeover time thresholds has been developed. • This study calculated the takeover time thresholds of drivers with different attributes, which can provide support for differentiated management of driver qualifications. • This study can also support regulatory authorities to assess the driver's takeover response ability and support the responsibility division of automated vehicle accidents. In conditional automated driving, the takeover response ability threshold is necessary for driver qualification assessment and liability division of automated vehicle accidents. The primary objective of this study is to establish a clear and quantifiable threshold for drivers' takeover response ability in conditional automated driving scenarios. This threshold aims to serve as a benchmark for evaluating drivers' readiness and developing safety regulations in automated driving. We designed 18 takeover events and invited 42 drivers to participate in the driving simulation experiment, and obtained their takeover time data. First, we analyze the differences of takeover time among drivers with different attributes (gender, age, driving year). Second, based on the Peaks Over Threshold and the generalized Pareto distribution model, we use the graphic method to calculate the range of takeover time threshold for drivers with different attributes. The result shows that the difference in the threshold range of takeover time between male and female drivers is relatively tiny. There are differences in the threshold range of takeover time for different age drivers, and the threshold is negatively correlated with age. Drivers with high driving experience within a safe range are allowed to have longer takeover times. Finally, the rationality of the takeover time threshold for drivers with different attributes has been verified. The return level curves are approximately linear (R2 > 0.77), indicating that the GPD model can capture the overall trend of the return level, which is changing with the probability level. This proves that the takeover time threshold is reasonable. This study uses TTC min to calibrate takeover safety, and the takeover time threshold has a good classification performance for takeover safety (accuracy > 85 %). The above content proves the rationality of the takeover time threshold. The contribution of this study is to calculate the takeover time threshold of drivers with different attributes, which can help regulatory authorities assess the driver's takeover response ability and support the liability division of automated vehicle accidents. [ABSTRACT FROM AUTHOR]

The Pareto distribution plays an important role in many data analysis tasks. An important aspect of this distribution is the estimation of its parameters. Several studies use classical methods, Bayes, and the neural network (NN) to evaluate Pareto parameters. Others have attempted to combine classical methods with a single NN-based. However, there isn't enough research to determine the sensitivity of the single NN to the specifics of the training data due to its stochastic training algorithm in the parameter estimation field. The current research aims to prove the efficiency of the aggregation of weighted multiple NN models and weighted ordinary least-squares regression algorithm to overcome the specifics of the training data and the sensitivity to outliers, respectively. The proposed method enables a locally less accurate model to participate to a lesser extent in the overall aggregation. The proposed method was compared with prevalent methods in the area, including the ordinary least squares, weighted ordinary least squares, maximum likelihood estimation, and the Bayes' using Monte Carlo simulations. The results verified the superiority of the proposed method in terms of regression error metrics. Moreover, it can be adapted to a variety of distributions. [ABSTRACT FROM AUTHOR]

The main goal of this article is to determine the optimally weighted coefficients (Ω 1 and Ω 2) of the balanced loss function of the form. L Κ , Ω , ξ o Ψ (σ) , ξ = Ω 1 γ σ Κ ξ o , ξ + Ω 2 γ σ Κ Ψ (σ) , ξ ; Ω 1 + Ω 2 = 1. Based on Type II Censored Data, by applying non-linear programming to estimate the shape parameter and some survival time characteristics, such as reliability and hazard functions of the Pareto distribution. Considering two balanced loss functions (BLF), including balanced square error loss function (BSELF) and balanced linear exponential loss function (BLLF), the calculation is based on the balanced loss function, including symmetric and asymmetric loss functions, as a special case. Use Monte Carlo simulation to pass Bayesian and maximum likelihood estimators through. The results of the simulation showed that the proposed model BLLF has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than the corresponding loss function. [ABSTRACT FROM AUTHOR]

This paper studies the ruin probabilities in a homogeneous continuous compound Poisson risk model which is adapted for the perturbed insurance risk model with standard Brownian motion. In such a model, we construct a martingale in terms of a differentiable exponential function based on the discounted and perturbed surplus process. We obtain the exponential upper bounds for the ruin probabilities using Martingale approach and provide a sharper exponential upper bound for the infinite time ruin probability. Moreover, we derive two asymptotic approximation formulas for the finite time ruin probability when claim size distribution belongs to some heavy-tailed families. Finally, several numerical examples are presented to show the effect of constant force of interest on the ruin probabilities and that our results are excellent and reliable. [ABSTRACT FROM AUTHOR]

• Short-term electricity generation data is used to calculate PGF for Khartoum. • Peaks over threshold method is utilized to model the highest power generation. • The obtained PGF equals 4, whereas in PV potential map equals 4.8. • This factor shall facilitate PV system sizing for local engineers. In this research, the authors used the Peaks over Threshold (POT) method alongside short-term electricity generation data belonging to a 5.5 kW p off-grid photovoltaic (PV) system installed on the premises of the National Energy Research Center in Soba district, Khartoum, to estimate the panel generation factor (PGF) of the city that rests within Sudan's capital. PGF is a fundamental technical figure primarily used in the design/sizing of solar PV systems. The addressed problem here is to calculate this coefficient with an acceptable accuracy constrained by insufficient electricity generation data from a PV system operating at its maximum capacity, relying on statistical modeling methods, which is the research novelty. Accordingly, we obtained an approximate PGF of 4 utilizing the POT technique that resulted in a threshold of 19 and Generalized Pareto distribution estimators of 2.2 × 10 - 16 and 2.3 for the shape and scale parameters, respectively. In the literature, the corresponding factor value is 4.8, illustrated in Sudan's PV potential map, based on historical long-term solar irradiance satellite records. Consequently, a 16.67% Percent Error between the two values is present due to the big difference in data amount, favoring the literature. However, in front of relatively abundant data, we believe the Extreme Value Theory methodology applied here will demonstrate robustness in approximating the target factor digits and validating Sudan's map numbers. Finally, this effort shall enable local engineers to blueprint well-assessed PV systems and support the endeavors to scientifically document Sudan's PV energy capacity, which the country lacks very much. [ABSTRACT FROM AUTHOR]

A new proportional stochastic order is defined based on the concept of quantile residual life. In addition, a new aging class of life distributions, namely, decreasing proportional failure rate distributions, was defined. Moreover, two other aging classes based on the proposed stochastic ordering are defined and investigated: decreasing proportional α-quantile residual life and its dual increasing proportional α -quantile residual life. The relationship between the proportional failure rate and proportional α -quantile residual life has been discussed. Some well-known and useful models are classified in terms of the proportional α-quantile residual life function. Finally, a new modified Pareto distribution with a decreasing proportional failure rate and an increasing proportional α-quantile residual life function was presented and studied. [ABSTRACT FROM AUTHOR]

This paper studies the impact of the 2008 financial crisis on the distribution of firms' export sizes. Using Chinese customs data from 2003 to 2013, we first show that firms' export sizes follow a Pareto distribution. By applying a difference-in-differences method, we find that the 2008 financial crisis induced significant changes in the values of the Pareto exponents. We argue that variations in the distribution of export size signal resource reallocations in the export sector at the macro level and are associated with exporters' adjustments to their exporting behavior at the micro level. The findings suggest that the Pareto exponent is an informative indicator and offers policymakers a better understanding of firm-level adjustments to exporting behavior in the presence of external negative shocks. [Display omitted] • This study theoretically models the distribution of firm's export sizes. • This study consistently estimates the Pareto exponents for export size distribution. • The 2008 financial crisis has a significantly negative impact on the Pareto exponents. [ABSTRACT FROM AUTHOR]

The Bohai Sea off the coast of northern China plays important economic and ecological roles. No studies have been conducted on wave characteristics in the Bohai Sea nearshore area using ocean station data in the past. Observational data (1998–2022) from eight ocean-stations in the Bohai Sea were used in the present study. Overall, wave height (Hs) was small; winter seasons had higher Hs than summer seasons, and the maximum Hs occurred in the Bohai Strait. Joint distribution analysis indicated that waves with Hs ranging from 0.2 to 0.4 m, and mean wave periods (Tm) ranging from 3 to 3.5 s, were most common. Hs in the Bohai Sea nearshore area showed a weak response to climate variability and was moderately correlated with the Ocean Niño Index (ONI) and the North Pacific Index (NPI) in winter, and with the Arctic Oscillation (AO) in summer. Under extreme conditions, Hs was best described by a Generalized Pareto distribution, Tm was best described by a GEV distribution, and wave directions mainly followed a t location-scale distribution. The maximum wave height (Hmax)/ Hs was 1.51, and the ratio varied with location. Machine learning methods were used to calculate Hmax more precisely, and they yielded better results than statistical methods. • Long-term wave climate and variability characteristics are studied. • Climate response analysis of large-scale climate patterns is examined. • Wave parameters PDF distributions under extreme conditions are presented. • Extreme wave parameters in the Bohai Sea are calculated. • Correlation of maximum wave height and Hs is proposed by machine learning method. [ABSTRACT FROM AUTHOR]

• Application of partial derivative-based global sensitivity analysis. • Real-world dataset contains long-term nitrous oxide emissions. • The distribution of partial derivatives is fat-tailed. • The first moment of the distribution converged, but not the higher moments. • Convergence check of Monte Carlo simulations using MS plots. Global sensitivity analysis found a widespread use in the modeling community to study the input and output relationship of typically complex numerical models. Many sensitivity analysis studies have been published over the years across different domains, from considering simple test problems to more complex case studies involving large numerical models. However, very few studies have addressed the issue of the presence of fat-tailed distributions and its implication for the sensitivity analysis. First, we recall how the law of large numbers slowly convergences depending on the extent of tails in the distributions. Then, we present some methods to study Paretianity in the data and estimate the tail index. We then apply these concepts to a real- world global sensitivity problem using a case study of long- term measurements of N 2 O emissions dataset from WWTPs. We then propose a robust sensitivity metric based on mean absolute deviation for parameter importance ranking under fat- tailed distributions. [ABSTRACT FROM AUTHOR]

• Microgrid optimal dispatch to reduce costs, carbon emissions and power fluctuation. • The multi-objective optimization algorithm based on war strategy. • Pareto frontier sort based on membership degree. • Reasonable allocation of new energy and energy storage. This article introduces a novel metaheuristic multi-objective optimization algorithm to address the complex multi-objective optimization scheduling challenges of the microgrids for the first time. Comparing with common multi-objective optimization algorithms, the proposed Multi-Objective War Strategy Optimization (MOWSO) has the following highlights: 1) MOWSO only needs to set three parameters. The few parameters make the algorithm simple to debug and real-world implement in practical applications. 2) MOWSO avoids the local centralized distribution of Pareto frontier based on a random selection strategy. The selection range of multiple objectives is expanded properly. In addition, a comprehensive multi-objective optimization dispatch model for microgrids is established, concurrently considering operating costs, carbon emissions, and power fluctuations. Furthermore, the impact of new energy proportion and Energy Storage (ES) on microgrid optimal dispatch is thoroughly investigated. Finally, a case study about a village microgrid in North China is presented to validate the effectiveness and the superiority of proposed multi-objective optimization dispatch model and novel MOWSO algorithm. [ABSTRACT FROM AUTHOR]

The widely recognized rank-size law is being questioned as the single best rule for city size distribution by an increasing number of studies. However, these studies suffer from inconsistent findings and some deficiencies, including differing definitions of a city across countries, samples with few countries, less systematic examination of socioeconomic influencing factors and no attention being given to the dynamic changes in best-fit city size distribution types for a given country. With a larger sample of countries and a more comparable and consistent definition of cities, our empirical analysis supports two findings from the existing literature. First, there is no single, universal distribution but rather a plurality of national city sizes. Second, the main body of a country's city size distribution is generally characterized by a lognormal distribution, while the upper tail tends to follow a Pareto distribution. Furthermore, our exploratory analyses reveal that specific city size distributions are associated with nations' socioeconomic development and urbanization levels. Finally, this paper presents the changes in the best-fit city size distribution type of a country across different periods and proposes a hypothesis on the general evolutionary trend. • There is no single universal type of city size distribution at the national level. • Varied distribution types are related to the socioeconomic factors. • Evolutionary nature of the optimal city size distribution of a country • A hypothesis on the general evolutionary trend of city size distribution types [ABSTRACT FROM AUTHOR]

This paper proposes a hyper-heuristic evolutionary algorithm via proximal policy optimization, named HHEA-PPO, for solving multi-objective truss optimization problems. HHEA-PPO has a two-layer structure: a high-level strategy and low-level heuristics. The high-level strategy consists of proximal policy optimization, while the low-level heuristics consist of ten predefined heuristic operators. During the iteration process, the high-level strategy selects the most promising low-level heuristic according to the state of the individuals and the population. To maintain the convergence and distribution of the external Pareto archive, a dynamic crowding distance mechanism is employed. HHEA-PPO is applied to eight multi-objective truss optimization problems and compared with thirteen state-of-the-art optimization algorithms in terms of success rate, average computation duration, and average fitness evaluations to evaluate its performance. The results show that HHEA-PPO has higher search efficiency and greater stability, demonstrating its ability to solve large-scale engineering design problems. [ABSTRACT FROM AUTHOR]

Fog computing has emerged as a promising paradigm for distributed data processing, but managing numerous devices in fog domains is complex due to the scale of the infrastructure. To address this challenge, organizing fog devices into fog colonies allows independent management on a smaller scale. We present a genetic algorithm (GA) approach that utilizes hierarchical clustering to define the fog colony layout. The GA selects a subset of colony candidates from the dendrogram obtained with hierarchical clustering and optimizes the network communication time between users and applications and the execution time of algorithms that manage application placement in each colony. We deployed an NSGA-II, a multi-objective approach for GAs, to evaluate our proposal. Our experimental results demonstrate that combining a GA with hierarchical clustering improves both optimization objectives. We conducted nine experiment scenarios, varying the number of applications and fog devices. Our results show that even in the worst-case scenario, the GA's results dominated the solutions obtained by two control algorithms after only 137 generations. Additionally, the number of genetic solutions and their homogeneous distribution in the Pareto front were satisfactory. • Definition of a genetic algorithm for optimization of the fog colony layout. • Solution space design based on the hierarchical clustering of the infrastructure. • Adaptation of genetic operators for solutions represented as labeled dendrograms. • Hybrid fitness evaluation with a greedy algorithm for service placement. • Results support the coordinated optimization of service placement and colony layout. [ABSTRACT FROM AUTHOR]

• A hybrid gamma-GPD model for POT threshold determination is proposed. • A uniform model function was proposed where traffic conflicts exceeding the threshold were fitted with a gamma distribution while traffic conflict extremes below the threshold were modeled using GPD. • Discontinued gamma-GPD model is superior to the continued and differentiable gamma-GPD models for determining the POT threshold in terms of crash estimation accuracy and model fit. • The crash estimates using the threshold determined by the hybrid gamma-GPD model outperform those estimated based on the traditional quantile plots method. Extreme value theory (EVT) models have been frequently utilized to estimate crash risk from traffic conflicts with the peak over threshold commonly used to identify conflict extremes. However, a common problem for the peak over threshold method is the selection of a suitable threshold to distinguish general and extreme conflicts. Subjective and arbitrary selection of the threshold in peak over threshold method can result in bias and unstable estimation results. The primary objective of the study is to propose a hybrid modelling approach for the threshold determination in peak over threshold method. The hybrid model consists of a joint gamma distribution and generalized Pareto distribution (GPD). The gamma distribution is used to fit general conflicts while the GPD is used to fit extreme conflicts. Specially, discontinued, continued and differentiable gamma-GPD models are developed with the threshold being treated as a model parameter. Traffic conflict data collected from three signalized intersections in the city of Surrey, British Columbia were used for the study. The modified time to collision (MTTC) was employed as conflict indicator. The Bayesian approach was employed to estimate the threshold as well as other hybrid gamma-GPD model parameters. The results show that the discontinued gamma-GPD model is superior to the continued and differentiable gamma-GPD models for determining the threshold in terms of crash estimation accuracy and model fit. The crash estimates using the threshold determined by the hybrid gamma-GPD model outperform those estimated based on the traditional quantile plots method, indicating that the superiority of the proposed threshold determination approach based on gamma-GPD hybrid model. The proposed hybrid gamma-GPD model could determine the threshold parameter in peak over threshold method for traffic conflicts extremes automatically in an objective and quantitative way. It contributes to existing peak over threshold method for producing reliable crash estimation. [ABSTRACT FROM AUTHOR]

[Display omitted] • Current intensity, current density and resistance voltage under thermal equilibrium are considered. • Studied the influence of various electrode structural parameters on the performance of the electrolysis cell. • Compared multiple optimization algorithms to verify the reliability of the obtained Pareto frontier distribution. • Utilized NSGA-II for multi-objective optimization of the Multipolar electrolysis cell. • Reduced electrolysis cell resistance voltage, enhanced current density. In the operation of industrial multipolar magnesium electrolysis cell, cell voltage and current density are important indicators of the production performance of the cell, while thermal balance is a key factor for normal operation. This paper utilizes the finite element method to establish a three-dimensional full cell thermal-electric model, studying the thermal field distribution and current density distribution in a 165kA multipolar magnesium electrolysis cell. Based on the heat balance of the multipolar cell, the influence of structural parameters on current intensity, average current density at the anode surface and resistance voltage is assessed. Dimensionless analysis yielded optimization criteria, and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was employed for multi-objective optimization problems. When stringent optimization is executed, significant performance improvements can be achieved in terms of the electrolysis cell's resistance voltage and current density. Moreover, under the optimization criteria, the relative error of the 265kA multipolar magnesium electrolysis cell model is less than 1 %. The results indicate that the workflow combining the finite element method with multi-objective optimization algorithms can be applied to the optimization and scale-up design of high-current multipolar magnesium electrolysis cell. [ABSTRACT FROM AUTHOR]

[Display omitted] • The H2018 function fits the FDC and PDC better than other 2 functions in 7 watersheds on northern China. • The variations of parameters in PDC and FDC in the 7 watersheds have been analyzed by Mann-Kendall test. • The parameters of FDC are derived from the measured precipitation and climate factors through Random Forest model. Obtaining reliable hydrological data for ungauged watersheds has always been a significant challenge in the water resources management. The flow duration curve (FDC) and precipitation duration curve (PDC) are classical methods to address this challenge. However, traditional FDC and PDC methods mostly rely on pre-assumed probability distribution function form, which may result in sub-optimal model parameters and consequently sub-optimal simulation results of hydrological data, and the common function forms are not applicable to deal with the data including zero-values, which often occurs in the discharge data of arid region and daily rainfall data. To address the issues in FDC and PDC , this study firstly determines the most suitable function form to describe FDC and PDC from various distribution functions, i.e., Log Normal, Generalized Pareto Distribution and H2018 function, from 1960 to 2010 in 7 watersheds in the north of China. The multiple methods including Random Forest, polynomial, Multilayer Perceptron and K-Nearest Neighbor are employed to simulate the parameters of the functions, aiming to deduce the optimal parameters of FDC functions. The results show that, H2018 function form has the best performance in simulating the PDC and FDC and in general, parameter a and b of H2018 function indicate an opposite trend, and parameter k declines in mostly condition at the annual scale from 1960 to 2010. The results of different methods indicate that the Random Forest method is the most efficient and accurate approach to deduce FDC parameters from measured precipitation and climate factors, compared with polynomial, Multilayer Perceptron and K-Nearest Neighbor. Based on the relationship between PDC parameters and FDC parameters, the FDC of ungauged basins can be deduced from the observed precipitation data. The research findings provide a new method to estimate FDC for the water resources management in the ungauged basins. [ABSTRACT FROM AUTHOR]

When a graphical representation of the cumulative percentage of total citations to articles, ordered from most cited to least cited, is plotted against the cumulative percentage of articles, we obtain a Leimkuhler curve. In this study, we noticed that standard Leimkuhler functions may not be sufficient to provide accurate fits to various empirical informetrics data. Therefore, we introduce a new approach to Leimkuhler curves by fitting a known probability density function to the initial Leimkuhler curve, taking into account the presence of a heterogeneity factor. As a significant contribution to the existing literature, we introduce a pair of mixture distributions (called PG and PIG) to bibliometrics. In addition, we present closed-form expressions for Leimkuhler curves. Some measures of citation concentration are examined empirically for the basic models (based on the Power and Pareto distributions) and the mixed models derived from these. An application to two sources of informetric data was conducted to see how the mixing models outperform the standard basic models. The different models were fitted using non-linear least squares estimation. • Introduction of mixture distributions (called PG and PIG) to bibliometrics. • Closed-form expressions for Leimkuhler curves. • Calculations with mixture distributions. • Theoretical and mathematical results in bibliometrics/informetrics. [ABSTRACT FROM AUTHOR]

We introduce an iterative discrete information production process where we can extend ordered normalised vectors by new elements based on a simple affine transformation, while preserving the predefined level of inequality, G, as measured by the Gini index. Then, we derive the family of empirical Lorenz curves of the corresponding vectors and prove that it is stochastically ordered with respect to both the sample size and G which plays the role of the uncertainty parameter. We prove that asymptotically, we obtain all, and only, Lorenz curves generated by a new, intuitive parametrisation of the finite-mean Pickands' Generalised Pareto Distribution (GPD) that unifies three other families, namely: the Pareto Type II, exponential, and scaled beta distributions. The family is not only totally ordered with respect to the parameter G, but also, thanks to our derivations, has a nice underlying interpretation. Our result may thus shed a new light on the genesis of this family of distributions. Our model fits bibliometric, informetric, socioeconomic, and environmental data reasonably well. It is quite user-friendly for it only depends on the sample size and its Gini index. • A new discrete information production process (IPP) is proposed. • The IPP preserves a predefined level of inequality as measured by the Gini index. • Its corresponding empirical Lorenz curves are stochastically ordered with respect to both the sample size and the Gini index. • Analysis of bibliometric, econometric, environmental, informetric, and other data shows a good fit of our model. • The model asymptotically leads to a new parametrisation of the Pickands generalised Pareto distribution. [ABSTRACT FROM AUTHOR]

It is important to improve the performance indexes including the net power and system efficiency for polymer electrolyte membrane fuel cell (PEMFC), especially considering the parameter uncertainty. To this end, this paper proposes a hierarchical multi-objective optimization framework including the off-line and on-line optimization. Firstly, a steadystate non-linear PEMFC system model is established as the base model. Secondly, an adaptive multi-objective particle swarm optimization (AMPSO) algorithm scheme is proposed in the off-line optimization procedure for the exact optimization of operation parameters. Meanwhile, an adaptive flight parameter strategy based on the particle dispersity (PD) information is proposed to balance the convergence and diversity of Pareto solutions. Finally, to decrease the influence caused by parameter uncertainty, the interval optimization method is proposed in the on-line optimization layer based on the results of AMPSO. The convergence condition of the proposed optimization scheme is verified by theory analysis. The proposed AMPSO is compared with different algorithms in the numerical simulation and hardware-in-loop (HIL) experiments. Meanwhile, the performance of the proposed method is tested on four representative benchmark problems. These results demonstrate that the PEMFC system with the proposed optimization scheme performs better than the base model and classical optimization algorithms in terms of the net power and system efficiency indexes, revealing the success of this hierarchical optimization approach in solving the accurate optimization and parameter uncertainty problems. By using statistical test methods, the proposed algorithm performs better hypervolume (HV) metric from the Pareto solution distribution. [ABSTRACT FROM AUTHOR]

The energy test of multivariate normality is an affine invariant test based on a characterization of equal distributions by energy distance. The test statistic is a degenerate kernel V-statistic, which asymptotically has a sampling distribution that is a Gaussian quadratic form under the null hypothesis of normality. The parameters of the limit distribution are the eigenvalues of the integral operator determined by the energy distance. Although a Monte Carlo approach provides excellent approximations to the sampling distribution of the test statistic for finite samples, in this work we develop two methods to obtain the eigenvalues and the asymptotic distribution of the energy test statistic. We derive the explicit integral equations for the eigenvalue problem for the simple and composite hypotheses of normality and solve them by a variation of Nyström's method. For the simple hypothesis, we also obtain the eigenvalues by an empirical approach which we call the sample kernel method. Numerical results are summarized in tables of derived eigenvalues for several cases. The resulting probability distribution in each case is obtained by Imhof's method. We also include simulation results that illustrate that for large samples the derived limit distribution is quite accurate in the upper tail. Software is available in the energy package for R to implement the tests by the original (Monte Carlo) approach and by applying the new methods using the derived asymptotic distribution. • The energy test of normality is an affine invariant consistent test based on energy distance. • Parameters of the limit distribution are eigenvalues of an integral operator. • Derive integral equations for simple and composite hypotheses of normality. • Solve them numerically for four cases of known or estimated parameters. • Software available in the energy package for R. [ABSTRACT FROM AUTHOR]

The probability characteristics of the heliostat support column base shear are discussed, and related methods are used to determine whether the base shear is conformed to the Gaussian distribution under all working conditions. Then, three kinds of peak estimating methods are selected to calculate the peak base shear, and results are compared. It is found that the Generalized Pareto Distribution (GPD) method is the most suitable for calculating the peak value of the heliostat support column base shear. Finally, the variation law of peak values of heliostat support column base shear is obtained and the variation law of peak and mean base shear are compared. The judgment criterion of whether the heliostat support column base shear is conformed to the Gaussian distribution is obtained, Gaussian and Non-Gaussian regions are divided. The peak value of the heliostat support column base shear which is calculated by the GPD method and met the specified guarantee rate has high accuracy. It can be met the needs of engineering application. The analysis of the variation law of peak values of heliostat support column base shear can be a reference for engineering design and scientific research. • Study of probability characteristics of heliostat base shear is provided. • The criterion of whether the base shear is conformed to the Gaussian distribution. • GPD method is the most suitable method for calculating peak base shear of heliostat. • Positive and negative maximum peak base shear should be studied in design. [ABSTRACT FROM AUTHOR]

Currently, reinforcement learning, the interpretability of the algorithm is a challenge. The lack of interpretability limits the use of reinforcement learning limited when facing agents in the physical world. To improve the interpretability of reinforcement learning, this study proposes a Levy-Brown hybrid strategy to improve the working of the traditional Actor-Critic algorithm. The proposed strategy is bioinspired from the Brown motion and Levy motion in nature; therefore, it can explain the process of data acquisition in the learning process from biological principles. The main idea of this new strategy is to map the Gaussian strategy to the biological Brown motion, and introduce the biological Levy strategy to improve the exploration efficiency. By combining the two strategies, it effectively takes advantage of the Levy strategy to improve exploration speed and the Brown strategy to improve exploration stability. The experiments demonstrate the advantages of the proposed Levy-Brown hybrid strategy, which effectively make best use of the advantages and overcomes the disadvantages of the two strategies. The code is available at https://www.researchgate.net/publication/377014427_LevyBrown_Hyribd_strategy. [ABSTRACT FROM AUTHOR]

Contemporary patent analytics employs a holistic approach whose purpose is to extract insights from aggregate analysis of patent landscapes. For the fruits of this endeavour to be accessible to executives, public servants and other individuals who value their time, the insights must be graphical in nature. In this paper, time evolved ranked Pareto distribution of patent family counts per assignee are analyzed by power law analysis. A graphical representation is presented which provides instantaneous insights into comparative scale and consolidation of technology landscapes. A number of specific data-analytical issues have been investigated and their impact on the validity of the results have been bounded and best-known methods proposed. [ABSTRACT FROM AUTHOR]

Due to the growing proportion of wind energy in Great Britain's energy mix, prolonged periods of low wind power generation have become a significant challenge for decarbonising the electricity system. As such, characterising drought severity and duration is important for ensuring the reliability of the electricity system. Employing concepts derived from hydrology, an extreme value analysis was carried out on wind drought events in Great Britain based on 72 years of ERA5 reanalysis data. The application of pooling procedures was found to be beneficial in robustly identifying wind droughts in cases where the capacity factor is not constantly below an arbitrary threshold. The sequent peak algorithm pooling was found to have particular relevance for electricity systems where energy storage technologies are used to compensate for low wind power generation. The Pearson-III distribution was identified as a suitable model to represent extreme wind droughts, while the Lognormal and Generalised Pareto distributions are also viable alternatives. Sustained periods of low wind power generation with a duration of 14 days were estimated to have a return period of five years and the longest event on record of approximately 26 days is expected to occur once every 100 years. The investigation of these wind droughts from a hydrological perspective has thus shown that they may not be particularly rare occurrences. • Pooling methods can characterise wind droughts as periods of overall low energy generation. • Sequent Peak Algorithm is able to identify the longest wind droughts. • Pearson-III distribution is a suitable model for representing extreme wind droughts. • Wind droughts lasting two weeks are estimated to have a return period of five years. [ABSTRACT FROM AUTHOR]

Windward walls, which are critical for setting the base shear loads, have been observed to follow non-Gaussian features due to the upstream horseshoe vortex, which nature is more prominent for low-rise buildings. Regarding the non-Gaussian process, a translation framework from a Gaussian to a non-Gaussian process has been widely used to approximate the non-Gaussian peak pressures. However, there is a lack of knowledge regarding the connection between the fluid mechanism (i.e., horseshoe vortex around buildings) and the translation framework. To address this, the paper uses two aerodynamic databases to identify the key parameters affecting the upstream horseshoe vortex, by examining the dependence of statistics of windward wall pressures on the potential parameters influencing the physical characteristics of horseshoe vortex. Aside from the height-to-breadth ratio, the turbulence intensity strongly affects the skewness and kurtosis of area-averaged windward wall pressures. The results suggest that turbulence intensity also affects the structure of the horseshoe vortex and subsequently amplifies the peak pressures, especially for lower height-to-breadth ratios. The statistical trend based on the height-to-breadth ratio and the turbulence intensity are then used with existing translation frameworks to approximate the peak factors of the windward wall pressures. The translation framework using cumulative distribution function mapping with a generalized Pareto distribution shows a good performance. An empirical model with parameters of height-to-breadth ratio and turbulence intensity is then developed for the generalized Pareto distribution parameters and up-crossing rate. This model is able to predict peak factors based on the height-to-breadth ratio and turbulence intensity alone. The results show that the non-Gaussian peak factors may range from 1.4 to 1.7 times its Gaussian counterpart for high turbulence intensity, particularly for low-rise buildings. • Horseshoe vortices cause the non-Gaussian distribution of wind loads especially for low-rise buildings. • Turbulence intensity and H/B are key parameters influencing the characteristics of pressures on windward walls. • A peak factor model considering the horseshoe vortex effects was established based on the translation framework. • The proposed peak factor model relies on H/B and turbulence intensity alone. [ABSTRACT FROM AUTHOR]

• A framework for assessing corridor-wide pedestrian safety is developed. • Autonomous vehicle sensor data was utilized to extract pedestrian-vehicle conflicts. • Extreme value theory models with block maxima and peak over threshold sampling approaches have been tested. • The proposed framework provides reliable estimates of pedestrian crash risks. Pedestrians are a vulnerable road user group, and their crashes are generally spread across the network rather than in a concentrated location. As such, understanding and modelling pedestrian crash risk at a corridor level becomes paramount. Studies on pedestrian crash risks, particularly with the traffic conflict data, are limited to single or multiple but scattered intersections. A lack of proper modelling techniques and the difficulties in capturing pedestrian interaction at the network or corridor level are two main challenges in this regard. With autonomous vehicles trialled on public roads generating massive (and unprecedented) datasets, utilising such rich information for corridor-wide safety analysis is somewhat limited where it appears to be most relevant. This study proposes an extreme value theory modelling framework to estimate corridor-wide pedestrian crash risk using autonomous vehicle sensor/probe data. Two types of models were developed in the Bayesian framework, including the block maxima sampling-based model corresponding to Generalised Extreme Value distribution and the peak over threshold sampling-based model corresponding to Generalised Pareto distribution. The proposed framework was applied to autonomous vehicle data from Argoverse—a Ford Motors subsidiary. This autonomous vehicle fleet of Agro AI (owner of Argoverse dataset) is equipped with two 64 beams synchronised LiDAR sensors, a cluster of seven high-resolution cameras, and a pair of stereo-vison high-resolution cameras to capture surrounding road users' information within a range of 200 meters. A subset of the Argoverse dataset, focussing on an arterial corridor in Miami, USA, was used to extract pedestrian and vehicle trajectories. From these trajectories, vehicle–pedestrian conflicts were identified and measured using post encroachment time. The non-stationarity of extremes was captured by vehicle volume, pedestrian volume, average vehicle speed, and average pedestrian speed in the extreme value model. Both block maxima and peak over threshold sampling-based models were found to provide a reasonable estimate of historical pedestrian crash frequencies. Notably, the block maxima sampling-based model was more accurate than the peak over threshold sampling-based model based on mean crash estimates and confidence intervals. This study demonstrates the potential of using autonomous vehicle sensor data for network-level safety, enabling an efficient identification of pedestrian crash risk zones in a transport network. [ABSTRACT FROM AUTHOR]

A single-degree-of-freedom oscillator with a nonlinear restoring force and stochastic external forcing is studied with the goal of understanding the distributions of certain response rates. Motivated by applications to ship motions, the response rates concern the minimum response rate leading to capsizing (the critical response rate) and a measurement comparing an observed response rate to the critical response rate (the split-time metric), whose distributions are investigated both analytically and numerically. Three nonlinear restoring forces are considered: piecewise linear (experiencing linearly softening stiffness above a "knuckle" point), doubly piecewise linear (experiencing piecewise linearly softening stiffness above a "knuckle" point), and the cubic softening restoring force of the Duffing oscillator. In the first two cases, an efficient numerical simulation of the critical response rate and split-time metric is proposed from a derived distribution; in the latter case, the density of the critical response rate is approximated assuming white noise excitation. A key interest is in the nature of the right tail of the split-time metric, specifically as it relates to its extrapolation through extreme value analysis in estimating the probability of capsizing. The distribution is found to have a "light" tail, which motivates the use of exponential rather than the generalized Pareto distribution for exceedances above threshold in extreme value analysis. Finally, threshold selection through a prediction error criterion for the exponential distribution is examined, and the Weibull distribution tail is suggested as a useful means for a more refined examination of the distribution tail. • First analytic treatment of a split-time method for capsizing in nonlinear oscillators. • Distributions of critical response rate and split-time metric for capsizing are studied. • The main finding is the exponential character of the distribution tails of interest. • Connections to extreme value theory and peaks-over-threshold analysis are made. • This complements similar earlier work on the response in nonlinear oscillators. [ABSTRACT FROM AUTHOR]

The weapon-target assignment problem is a challenging optimization issue, but reliability is seldom considered in the majority of existing literature. To address the high-reliability weapon-target assignment problem, this paper integrates weapon reliability and mission reliability into a multi-objective optimization model (MOD) and presents an improved algorithm termed MOEA/D-iAM2M to the problem. This algorithm effectively combines the strengths of adaptive search space decomposition-based MOEA (MOEA/D-AM2M) and two-stage hybrid learning-based MOEA (HLMEA), resulting in a faster convergence rate and a more extensive distribution of the Pareto solution set. Furthermore, a reference point is incorporated into MOEA/D-iAM2M to facilitate the adaptive weight adjustment. Numerical experiments are carried out to confirm the effectiveness of the proposed MOEA/D-iAM2M. This research is significant in the field of optimization and has practical value in the defense industry. [ABSTRACT FROM AUTHOR]

This study presents a comprehensive experimental assessment of three hybrid mooring systems for a heaving-buoy wave energy converter. Free decay model tests are conducted to study the natural periods in heave, pitch and surge modes of the buoy when it is moored with different mooring configurations. A series of regular and irregular wave model tests are carried out to investigate the hydrodynamic responses of the point absorber as well as mooring dynamics. The effects of wave period, incident wave height and mooring configuration are evaluated. Besides, the influence of mooring configuration on buoy motion is discussed. To study the short term extreme dynamic tension, the traditional Weibull distribution, Weibull distribution based on tail data and peaks-over-threshold method are applied. The results showed that the Weibull distribution failed to present accurate extreme dynamic tension prediction when the snap events occur frequently, while the other two methods showed good performance despite of number of snap events. Based on the results of energy production performance and extreme dynamic tension, a novel mooring line design is suggested, which helps to reduce mooring dynamic tension. • A slack mooring and two hybrid mooring systems are experimentally studied. • The snap load can frequently occur in the slack mooring system. • The hybrid mooring shows good performance to prevent snap events. • Two methods are proposed to estimate extreme mooring tension when snap events occur. [ABSTRACT FROM AUTHOR]

Based on geographical location, Indonesia is crossed by the equator which has a tropical climate with a high diversity of rainfall. This can lead to an increase or decrease in extreme rainfall that has the potential to cause hydrometeorological disasters such as floods, winds and landslides. Estimation of rainfall is not only influenced by the local topography in each region, but there are also spatial and temporal influences. Therefore, this study aims to estimate the pattern of extreme rainfall and map the rain observer station based on the status of extreme rainfall on spatio-temporal data in the West Java province, Indonesia. Estimator of extreme rainfall patterns uses the generalized linear mixed model (GLMM) which consists of spatial and temporal random components with INLA (integrated nested Laplace approximation) inference. Response data in the form of daily rainfall in 73 observer stations, within 2 years period of observation. Average rainfall data is assumed to have gamma distribution, rainfall above the average is identified using the Bernoulli distribution then identified (extreme) rainfall above average is assumed to have generalized pareto distribution. From the rainfall patterns produced there are a number of conclusions, including that the average rainfall in West Java experiences a consistent downward trend in 13-th week to 32-nd week, which indicates that there is a decrease in rainfall intensity at the beginning of dry season in early April until the end of dry season at the end of August. While in the case of extreme rainfall, the decrease in rainfall intensity consistently occurs from the first week in January to 32-nd week at the end of August. The resulting extreme rainfall mapping states that more extreme rainfall occurs in the north to southeast region of West Java. [ABSTRACT FROM AUTHOR]

The Pareto game for the model-free continuous-time stochastic system is studied through approximate/adaptive dynamic programming (ADP) in this paper. Firstly, the model-based online iterative algorithm is proposed, and it is proved that the control iterative sequence converges to the Pareto efficient solution, but the algorithm requires complete system parameters. Then, we derive the model-free iterative equation and develop the ADP algorithm to calculate the equation by collecting updated states and input information online. From the derivation of the ADP algorithm, the model-free iterative equation and the model-based iterative equation have the same solution, which means that the ADP algorithm can approximate the Pareto optimal solution. Next, the convergence analysis shows that the Pareto optimal strategy is uniquely determined by the ADP algorithm. Finally, two simulation examples confirm the feasibility of the ADP algorithm. • Solving the Pareto optimal control problem usually needs full system information. • The Pareto game problem is studied for model-free mean-field system. • Firstly, the Pareto optimal control is given by an iterative algorithm. • Next, an adaptive dynamic programming (ADP) method is used to get the Pareto game. • Lastly, the effectiveness of the ADP method is verified by two examples. [ABSTRACT FROM AUTHOR]

The paper presents a new multiple scenario multi-objective salp swarm optimization (MS-MOSS) algorithm to optimally size a standalone PV system. An accurate estimation of the number of PV modules and storage battery is crucial as it affects the system reliability and cost. Three scenarios have been presented focusing on Pareto optimal solutions by minimizing two conflicting objectives. Loss of load probability (LLP) and life-cycle cost (LLC) are considered to obtain the Pareto front. The iterative method is employed for validation of the superiority results of the proposed MS-MOSS algorithm. The results show that the scenarios are able to find Pareto optimal configuration at a high level of accuracy and at a very low cost. The proposed three scenarios are faster than iterative approach approximately by 158, 194.2, and 141.6 times, respectively. The third scenario outperforms other scenarios in terms of coverage and convergence of the distribution of solution to the Pareto front. As a conclusion, The MS-MOSS algorithm is found to be very effective in sizing of SAPV system. • A new multiple scenario multi-objective salp swarm optimization (MS-MOSS) is proposed. • An optimal size for a standalone PV system is found using MS-MOSS. • Three scenarios have been presented to obtain on Pareto optimal solutions. • The results demonstrate the efficiency of MS-MOSS for sizing of SAPV system. [ABSTRACT FROM AUTHOR]

The number-weighted particle size distributions are difficult to be estimated experimentally. This study offers a simple conversion method to convert mass-weighted distributions to their number-weighted equivalents. Besides, the number-weighted equivalents of the Gates-Gaudin-Schuhmann, Gaudin-Meloy, Pareto, and Rosin-Rammler distributions were determined by the conversion method. The accuracy of the method was successfully confirmed on the artificial populations generated from the Gates-Gaudin-Schuhmann, Rosin-Rammler (Weibull), and Pareto distributions. However, the number-weighted equivalent of the Gaudin-Meloy distribution was found to be trivial. The results also indicate that the conversion method may be applied to a wide range of sieve size distributions that are truncated with upper and lower bounds. Unlabelled Image • A method to estimate number-weighted size distributions from sieve analyses. • The method assumes constant density and shape factor for all particles. • The method was successful on artificial populations of the common distributions. • The method may be widely applied to the truncated sieve size distributions. • The number-weighted equivalent of the Gaudin-Meloy distribution is trivial. [ABSTRACT FROM AUTHOR]

In this paper, we focus on multiobjective two-level simple recourse programming problems with discrete-type LR fuzzy random variables, in which each of the decision makers called the leader and the follower optimizes his/her multiple objective functions independently, shortages and excesses arising from the violation of the constraints with discrete-type LR fuzzy random variables are penalized, and the sum of the objective function and the expectation of the amount of the penalties is minimized. To deal with such problems, we introduce a new solution concept called an estimated Pareto Stackelberg solution for the leader. To obtain a candidate of a satisfactory solution for the leader from among an estimated Pareto Stackelberg solution set, using the Kuhn-Tucker approach and the transformation technique for complementarity conditions, an original problem is transformed into a mixed integer programming problem. Then, we propose an interactive algorithm to obtain a satisfactory solution of the leader from among an estimated Pareto Stackelberg solution set. A numerical example illustrates the proposed algorithm for a multiobjective two-level fuzzy random simple recourse programming problem under the hypothetical leader. [ABSTRACT FROM AUTHOR]

Causal inference aims to estimate the treatment effect of an intervention on the target outcome variable and has received great attention across fields ranging from economics and statistics to machine learning. Observational causal inference is challenging because the pre-treatment variables may influence both the treatment and the outcome, resulting in confounding bias. The classic inverse propensity weighting (IPW) estimator is theoretically able to eliminate the confounding bias. However, in observational studies, the propensity scores used in the IPW estimator must be estimated from finite observational data and may be subject to extreme values, leading to the problem of highly variable importance weights, which consequently makes the estimated causal effect unstable or even misleading. In this paper, by reframing the IPW estimator in the importance sampling framework, we propose a Pareto-smoothing method to tackle this problem. The generalized Pareto distribution (GPD) from extreme value theory is used to fit the upper tail of the estimated importance weights and to replace them using the order statistics of the fitted GPD. To validate the performance of the new method, we conducted extensive experiments on simulated and semi-simulated datasets. Compared with two existing methods for importance weight stabilization, i.e., weight truncation and self-normalization, the proposed method generally achieves better performance in settings with a small sample size and high-dimensional covariates. Its application on a real-world heath dataset indicates its utility in estimating causal effects for program evaluation. [ABSTRACT FROM AUTHOR]

• A new uncertain risk measure is defined for the modeling of investment risk. • An uncertain portfolio optimization model is formulated. • A method is presented for finding the set of analytic Pareto optimal solutions. Portfolio optimization problem is concerned with choosing an optimal portfolio strategy that can strike a balance between maximizing investment return and minimizing investment risk. In many cases, the return rate of risky asset is neither a random variable nor a fuzzy variable. Then, it can be described as an uncertain variable. But, the existing works on uncertain portfolio optimization problem fail to find an analytic solution of optimal portfolio strategy. In this paper, we define a new uncertain risk measure for the modeling of investment risk. Then, an uncertain portfolio optimization model is formulated. By introducing a new variable, we transform it into an equivalent bi-criteria optimization model. Then, we derive a method for the construction of the set of analytic Pareto optimal solutions. Finally, a numerical simulation is carried out to show the applicability of the proposed model and the convenience of finding the analytic solution. [ABSTRACT FROM AUTHOR]

Pareto distributions are the most popular models in economics and finance. Hence, it is essential to have a wide spectrum of tools for checking their goodness of fit to a given data set. This paper provides the first review of known goodness of fit tests for Pareto distributions. Over twenty tests are reviewed. Their powers are compared by simulation. [ABSTRACT FROM AUTHOR]

We investigate a variant of the parabolic Anderson model, introduced in previous work, in which an i.i.d. potential is partially duplicated in a symmetric way about the origin, with each potential value duplicated independently with a certain probability. In previous work we established a phase transition for this model on the integers in the case of Pareto distributed potential with parameter α > 1 and fixed duplication probability p ∈ (0 , 1) : if α ≥ 2 the model completely localises, whereas if α ∈ (1 , 2) the model may localise on two sites. In this paper we prove a new phase transition in the case that α ≥ 2 is fixed but the duplication probability p (n) varies with the distance from the origin. We identify a critical scale p (n) → 1 , depending on α , below which the model completely localises and above which the model localises on exactly two sites. We further establish the behaviour of the model in the critical regime. [ABSTRACT FROM AUTHOR]

• Hyperbolic geometry describes multiple aspects of human perception. • Hyperbolic geometry describes multiple aspects of signals from natural environments. • Correspondence between Zipf's law and hyperbolic geometry. • Maximally informative representations lead to hyperbolic geometry. This review connects several lines of research to argue that hyperbolic geometry should be broadly applicable to neural circuits as well as other biological circuits. The reason for this is that networks that conform to hyperbolic geometry are maximally responsive to external and internal perturbations. These networks also allow for efficient communication under conditions where nodes are added or removed. We will argue that one of the signatures of hyperbolic geometry is the celebrated Zipf's law (also sometimes known as the Pareto distribution) that states that the probability to observe a given pattern is inversely related to its rank. Zipf's law is observed in a variety of biological systems — from protein sequences, neural networks to economics. These observations provide further evidence for the ubiquity of networks with an underlying hyperbolic metric structure. Recent studies in neuroscience specifically point to the relevance of a three-dimensional hyperbolic space for neural signaling. The three-dimensional hyperbolic space may confer additional robustness compared to other dimensions. We illustrate how the use of hyperbolic coordinates revealed a novel topographic organization within the olfactory system. The use of such coordinates may facilitate representation of relevant signals elsewhere in the brain. [ABSTRACT FROM AUTHOR]

The development and application of the Envelope Peak-over-Threshold (EPOT) method is summarized for the roll motion of a ship in irregular waves. The method is based on the conventional Peak-over-Threshold (POT) method, but uses an envelope of the peaks for declustering the data. As suggested by a reduced-order model, a power-law tail should be applicable for the peaks of roll motions, which allows the introduction of physical considerations into the statistical model. A data-driven Generalized Pareto distribution (GPD) is applied to study the behavior of the shape parameter on large-volume samples in order to confirm the theoretical prediction of the tail structure. The physics-informed statistical model approximates data above a suitable threshold with a Pareto distribution, while the threshold is determined with a prediction error criterion. An example is included, where extrapolations with GPD are compared to the physics-informed model. • Application of Peak-over-Threshold method is considered where a time history envelope is used for declustering the data. • The study of behavior of distribution tails of roll motion peaks. • A physics-informed model with power-law, Pareto tail was formulated and applied to amplitudes of roll motions. [ABSTRACT FROM AUTHOR]

In the absence of wave measuring buoys operating over extended periods, wave hindcast data or satellite observations are indispensable for estimating global extreme wave heights. However, the results may depend on the analysed wind wave sources and the period's length. The sensitivity of the estimated extreme significant wave heights (SWH) to the analysed data sources and periods is investigated in this study. Global extreme wave heights are estimated using ECMWF Reanalysis v5 data (ERA5), global wave hindcast developed based on Simulating WAves Nearshore forced by the Japanese 55-year Reanalysis (SWAN-JRA55), satellite altimeter observations, and long-term wave buoy measurements. Both Annual Maximum fitting to the Generalized Extreme Value Distribution (AM-GEV) and Peaks Over Threshold fitted to the Generalized Pareto Distribution (POT-GPD) models are used. The results show that the global extreme SWH estimates considerably depend on the analysed data sources. The relative differences observed between the analysed data sources are >20% in large parts of the world. Thus, the relative differences in extreme SWH are mainly lower by increasing the analysed data periods. However, they can reach 30% and are more critical using AM-GEV. Besides, by comparing the extreme values from reanalysis and hindcast wave data to those from long-term wave measurements, underestimations of up to 2 m are observed for a return period of 100 years in the North-West Atlantic and North-East Pacific. • Extreme waves estimates are highly dependent on wave sources in the global ocean. • Changes extreme wave estimates are up to ±30% among different analysed periods. • Satellite observations are more appropriate for an EVA using AM-GEV. • POT-GEV is more recommended for EVA in tropical cyclone areas. • The accuracy of wave storm peaks should be considered for extreme wave estimates. [ABSTRACT FROM AUTHOR]

The Matthew effect qualitatively describes the social phenomenon that the impact and recognition of well-known scientists for their new accomplishments are relatively overpriced by the scientific community when compared to the similar output of researchers without fame or status. We quantify the manifestation of this phenomenon in scientific research careers. For this purpose, using a mixed survey-plus-bibliometrics method, we assembled a dataset containing detailed career information on scientists in the field of chemistry. The mathematical model of the Matthew effect in scientific research careers proposed in this paper identifies career distribution as the generalized extreme value distribution with the shape parameter q = 0.5. This result is in good agreement with the obtained data: the empirical distribution of scientific careers can be approximated by the generalized extreme value distribution with q = 0.423. We also find that the distribution of starting positions of social trajectories of scientists fits by the Pareto distribution. Our analysis deepens scientific insight into the emergence of the Matthew effect in scientific careers and its relationship to the distribution of citations and citation entropy. • Using a survey-plus-bibliometrics method, the dataset on 1067 researchers is assembled. • The scientific research careers fit by the generalized extreme-value distribution. • The stochastic model of the scientific research career distribution is proposed. [ABSTRACT FROM AUTHOR]

The opposition in some countries to including nuclear power in future sustainable energy portfolios—in part due to "nuclear dread"—often has limited quantitative scientific foundation of the real benefits and risks. This has been amplified by the lack of sound estimates of operational risk due to the scarcity of the relevant empirical data. In order to address this gap, we use the largest open database on accident precursors along with our in-house generic probabilistic safety assessment models to conduct a comprehensive statistical study of operational risks in the civil nuclear sector. We find that the distribution of precursor severities follows a Pareto distribution, and we observe a runaway Dragon Kings regime for the most significant events. Based on our findings, we have determined that exogenous factors account for 95% of the risk associated with nuclear power. By addressing these factors in new reactor designs, we estimate that the frequency of accidents similar to the Fukushima Daiichi level can be reduced to about one every 300 years for the global fleet. Finally, our study highlights the importance and need for international cooperation focused on constructing comprehensive blockchains of accident precursors. [ABSTRACT FROM AUTHOR]