Mixed D-vine copula-based conditional quantile model for stochastic monthly streamflow simulation

Copula functions have been widely used in stochastic simulation and prediction of streamflow.However,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months.To address this limitation,this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations.This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas.The up-to-down sequential method,which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach,was used to determine the structures of multivariate Dvine copulas.The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station,the inflow control station of the Longyangxia Reservoir in the Yellow River Basin.The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow.This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.

The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Application of the Conditional Nonlinear Local Lyapunov Exponent to Second-Kind Predictability

In order to quantify the influence of external forcings on the predictability limit using observational data,the author introduced an algorithm of the conditional nonlinear local Lyapunov exponent(CNLLE)method.The effectiveness of this algorithm is validated and compared with the nonlinear local Lyapunov exponent(NLLE)and signal-to-noise ratio methods using a coupled Lorenz model.The results show that the CNLLE method is able to capture the slow error growth constrained by external forcings,therefore,it can quantify the predictability limit induced by the external forcings.On this basis,a preliminary attempt was made to apply this method to measure the influence of ENSO on the predictability limit for both atmospheric and oceanic variable fields.The spatial distribution of the predictability limit induced by ENSO is similar to that arising from the initial conditions calculated by the NLLE method.This similarity supports ENSO as the major predictable signal for weather and climate prediction.In addition,a ratio of predictability limit(RPL)calculated by the CNLLE method to that calculated by the NLLE method was proposed.The RPL larger than 1 indicates that the external forcings can significantly benefit the long-term predictability limit.For instance,ENSO can effectively extend the predictability limit arising from the initial conditions of sea surface temperature over the tropical Indian Ocean by approximately four months,as well as the predictability limit of sea level pressure over the eastern and western Pacific Ocean.Moreover,the impact of ENSO on the geopotential height predictability limit is primarily confined to the troposphere.

Notes on Convergence and Modeling for the Extended Kalman Filter

The goal of this work is to provide an understanding of estimation technology for both linear and nonlinear dynamical systems.A critical analysis of both the Kalman filter(KF)and the extended Kalman filter(EKF)will be provided,along with examples to illustrate some important issues related to filtering convergence due to system modeling.A conceptual explanation of the topic with illustrative examples provided in the paper can help the readers capture the essential principles and avoid making mistakes while implementing the algorithms.Adding fictitious process noise to the system model assumed by the filter designers for convergence assurance is being investigated.A comparison of estimation accuracy with linear and nonlinear measurements is made.Parameter identification by the state estimation method through the augmentation of the state vector is also discussed.The intended readers of this article may include researchers,working engineers,or engineering students.This article can serve as a better understanding of the topic as well as a further connection to probability,stochastic process,and system theory.The lesson learned enables the readers to interpret the theory and algorithms appropriately and precisely implement the computer codes that nicely match the estimation algorithms related to the mathematical equations.This is especially helpful for those readers with less experience or background in optimal estimation theory,as it provides a solid foundation for further study on the theory and applications of the topic.

Strong Convergence Rates of Double Kernel Estimates of Conditional Desity Under Stationary Sequences

In the paper,we study the strong convergence rates of double kernel estimates of conditional density under stationary sequences.

GLOBAL CONVERGENCE OF A CLASS OF OPTIMALLY CONDITIONED SSVM METHODS

探讨无约束优化的一族最优条件数自调比变尺度（ＯＣＳＳＶＭ）算法的收敛性。证明了采用Ｗｏｌｆｅ线性搜索的此族算法对于一般的凸函数是整体收敛的。

Landslide susceptibility prediction using slope unit-based machine learning models considering the heterogeneity of conditioning factors

To perform landslide susceptibility prediction(LSP),it is important to select appropriate mapping unit and landslide-related conditioning factors.The efficient and automatic multi-scale segmentation(MSS)method proposed by the authors promotes the application of slope units.However,LSP modeling based on these slope units has not been performed.Moreover,the heterogeneity of conditioning factors in slope units is neglected,leading to incomplete input variables of LSP modeling.In this study,the slope units extracted by the MSS method are used to construct LSP modeling,and the heterogeneity of conditioning factors is represented by the internal variations of conditioning factors within slope unit using the descriptive statistics features of mean,standard deviation and range.Thus,slope units-based machine learning models considering internal variations of conditioning factors(variant slope-machine learning)are proposed.The Chongyi County is selected as the case study and is divided into 53,055 slope units.Fifteen original slope unit-based conditioning factors are expanded to 38 slope unit-based conditioning factors through considering their internal variations.Random forest(RF)and multi-layer perceptron(MLP)machine learning models are used to construct variant Slope-RF and Slope-MLP models.Meanwhile,the Slope-RF and Slope-MLP models without considering the internal variations of conditioning factors,and conventional grid units-based machine learning(Grid-RF and MLP)models are built for comparisons through the LSP performance assessments.Results show that the variant Slopemachine learning models have higher LSP performances than Slope-machine learning models;LSP results of variant Slope-machine learning models have stronger directivity and practical application than Grid-machine learning models.It is concluded that slope units extracted by MSS method can be appropriate for LSP modeling,and the heterogeneity of conditioning factors within slope units can more comprehensively reflect the relationships between conditioning factors and landslides.The research results have important reference significance for land use and landslide prevention.

Influence of longwall gateroad convergence on the process of mine ventilation network-model tests

Hard coal mines are required to constantly ventilate mine workings to ensure that the air composition is at a certain humidity and temperature level that is comfortable for underground mine workers,especially in deep deposits.All underground workings,which are part of the mine ventilation network,should be ventilated in a way that allows maintaining proper oxygen concentration not lower than 19%(by volume),and limits concentration of gases in the air such as methane,carbon monoxide or carbon dioxide.The air flow in the mine ventilation network may be disturbed due to the natural convergence(deformation)and lead to change in its original cross-section.Reducing the cross-sectional area of the mining excavation causes local resistances in the air flow and changes in aerodynamic potentials,which leads to emergency states in the mine ventilation network.This paper presents the results of numerical simulations of the influence of gateroad convergence on the ventilation process of a selected part of the mine ventilation network.The gateroad convergence was modelled with the finite element software PHASE 2.The influence of changes in the cross-sectional area of the gateroad on the ventilation process was carried out using the computational fluid dynamics software Ansys-Fluent.

Assessing the Performance of CMIP6 Models in Simulating Droughts across Global Drylands

Both the attribution of historical change and future projections of droughts rely heavily on climate modeling. However,reasonable drought simulations have remained a challenge, and the related performances of the current state-of-the-art Coupled Model Intercomparison Project phase 6(CMIP6) models remain unknown. Here, both the strengths and weaknesses of CMIP6 models in simulating droughts and corresponding hydrothermal conditions in drylands are assessed.While the general patterns of simulated meteorological elements in drylands resemble the observations, the annual precipitation is overestimated by ~33%(with a model spread of 2.3%–77.2%), along with an underestimation of potential evapotranspiration(PET) by ~32%(17.5%–47.2%). The water deficit condition, measured by the difference between precipitation and PET, is 50%(29.1%–71.7%) weaker than observations. The CMIP6 models show weaknesses in capturing the climate mean drought characteristics in drylands, particularly with the occurrence and duration largely underestimated in the hyperarid Afro-Asian areas. Nonetheless, the drought-associated meteorological anomalies, including reduced precipitation, warmer temperatures, higher evaporative demand, and increased water deficit conditions, are reasonably reproduced. The simulated magnitude of precipitation(water deficit) associated with dryland droughts is overestimated by 28%(24%) compared to observations. The observed increasing trends in drought fractional area,occurrence, and corresponding meteorological anomalies during 1980–2014 are reasonably reproduced. Still, the increase in drought characteristics, associated precipitation and water deficit are obviously underestimated after the late 1990s,especially for mild and moderate droughts, indicative of a weaker response of dryland drought changes to global warming in CMIP6 models. Our results suggest that it is imperative to employ bias correction approaches in drought-related studies over drylands by using CMIP6 outputs.

Fully asynchronous distributed optimization with linear convergence over directed networks

We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it for synchronized or randomly activated implementation,which may create deadlocks in practice.In sharp contrast,we propose a fully asynchronous push-pull gradient(APPG) algorithm,where each node updates without waiting for any other node by using possibly delayed information from neighbors.Then,we construct two novel augmented networks to analyze asynchrony and delays,and quantify its convergence rate from the worst-case point of view.Particularly,all nodes of APPG converge to the same optimal solution at a linear rate of O(λ^(k)) if local functions have Lipschitz-continuous gradients and their sum satisfies the Polyak-?ojasiewicz condition(convexity is not required),where λ ∈(0,1) is explicitly given and the virtual counter k increases by one when any node updates.Finally,the advantage of APPG over the synchronous counterpart and its linear speedup efficiency are numerically validated via a logistic regression problem.

STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS

This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.

A new test on the conditional capital asset pricing model

Testing the validity of the conditional capital asset pricing model （CAPM） is a puzzle in the finance literature. Lewellen and Nagel[14] find that the variation in betas and in the equity premium would have to be implausibly large to explain important asset-pricing anomalies. Unfortunately, they do not provide a rigorous test statistic. Based on a simulation study, the method proposed in Lewellen and Nagel[14] tends to reject the null too frequently. We develop a new test procedure and derive its limiting distribution under the null hypothesis. Also, we provide a Bootstrap approach to the testing procedure to gain a good finite sample performance. Both simulations and empirical studies show that our test is necessary for making correct inferences with the conditional CAPM.

Is there regional convergence between Morocco and its OECD partner countries in terms of well-being?

Morocco wants its 12 regions to play the role as the main lever of its public policies to initiate harmonized spatial multidimensional development. In the context of this goal and Morocco’s openness over the past two decades to bilateral and multilateral cooperation in an effort toward regional integration, this article studies the convergence of 389 regions in 36 countries(Morocco and 35 of its partner member countries in the Organization for Economic Co-operation and Development(OECD)) between 2000 and 2019 in terms of well-being. To this end, we considered the territorial dimension of β-convergence models for well-being and its four domains(economic, social, environmental, and governance). Then, we adapted the absolute β-convergence model by taking into account the existence of spatial heterogeneity according to five specifications of spatial models. Thus, apart from environmental domain, we found that β-convergence of regions is significant for well-being and three of its domains(economic, social, and governance). These convergences are made by a spatially autocorrelated error model(SEM). However, the speed and period of convergence are relatively low for social domain, partly explaining the very exacerbated tensions at the territorial level. The fastest convergence was achieved in governance domain, followed by economic domain. This suggests that emerging countries must pay particular attention to national public action in favor of social cohesion at the territorial level. The lack of convergence in environmental domain calls for common actions for all countries at the supranational level to protect the commons at the territorial level.

Multivariate Generalized Autoregressive Conditional Heteroscedastic Model

In this paper, by making use of the Hadamard product of matrices, a natural and reasonable generalization of the univariate GARCH (Generalized Autoregressive Conditional heteroscedastic) process introduced by Bollerslev (J. Econometrics 31(1986), 307-327) to the multivariate case is proposed. The conditions for the existence of strictly stationary and ergodic solutions and the existence of higher-order moments for this class of parametric models are derived.

A novel conditional cell transmission model for oversaturated arterials

The objective of this work is to develop a novel feature for traffic flow models,when traffic queues on two-way arterials periodically extend until then they block an upstream signal in oversaturated conditions.The new model,proposed as conditional cell transmission model(CCTM) has been developed with two improvements.First,cell transmission model(CTM) is expanded for two-way arterials by taking account of all diverging and merging activities at intersections.Second,a conditional cell is added to simulate periodic spillback and blockages at an intersection.The results of experiments for a multilane,two-way,three-signal sample network demonstrate that CCTM can accommodate various traffic demands and accurate representation of blockages at intersections.The delay of left turns is underestimated by 40 % in moderate conditions and by 58% in oversaturated condition when using the CTM rather than CCTM.Finally,the consistency between HCS 2000 and CCTM shows that CCTM is a reliable methodology of modeling traffic flow in oversaturated condition.

Effects of Initial and Boundary Conditions on Heavy Rainfall Simulation over the Yellow Sea and the Korean Peninsula:Comparison of ECMWF and NCEP Analysis Data Effects and Verification with Dropsonde Observation

This study evaluated the simulation performance of mesoscale convective system(MCS)-induced precipitation,focusing on three selected cases that originated from the Yellow Sea and propagated toward the Korean Peninsula.The evaluation was conducted for the European Centre for Medium-Range Weather Forecasts(ECMWF)and National Centers for Environmental Prediction(NCEP)analysis data,as well as the simulation result using them as initial and lateral boundary conditions for the Weather Research and Forecasting model.Particularly,temperature and humidity profiles from 3D dropsonde observations from the National Center for Meteorological Science of the Korea Meteorological Administration served as validation data.Results showed that the ECMWF analysis consistently had smaller errors compared to the NCEP analysis,which exhibited a cold and dry bias in the lower levels below 850 hPa.The model,in terms of the precipitation simulations,particularly for high-intensity precipitation over the Yellow Sea,demonstrated higher accuracy when applying ECMWF analysis data as the initial condition.This advantage also positively influenced the simulation of rainfall events on the Korean Peninsula by reasonably inducing convective-favorable thermodynamic features(i.e.,warm and humid lower-level atmosphere)over the Yellow Sea.In conclusion,this study provides specific information about two global analysis datasets and their impacts on MCS-induced heavy rainfall simulation by employing dropsonde observation data.Furthermore,it suggests the need to enhance the initial field for MCS-induced heavy rainfall simulation and the applicability of assimilating dropsonde data for this purpose in the future.

A Hybrid SIR-Fuzzy Model for Epidemic Dynamics:A Numerical Study

This study focuses on the urgent requirement for improved accuracy in diseasemodeling by introducing a newcomputational framework called the Hybrid SIR-Fuzzy Model.By integrating the traditional Susceptible-Infectious-Recovered(SIR)modelwith fuzzy logic,ourmethod effectively addresses the complex nature of epidemic dynamics by accurately accounting for uncertainties and imprecisions in both data and model parameters.The main aim of this research is to provide a model for disease transmission using fuzzy theory,which can successfully address uncertainty in mathematical modeling.Our main emphasis is on the imprecise transmission rate parameter,utilizing a three-part description of its membership level.This enhances the representation of disease processes with greater complexity and tackles the difficulties related to quantifying uncertainty in mathematical models.We investigate equilibrium points for three separate scenarios and perform a comprehensive sensitivity analysis,providing insight into the complex correlation betweenmodel parameters and epidemic results.In order to facilitate a quantitative analysis of the fuzzy model,we propose the implementation of a resilient numerical scheme.The convergence study of the scheme demonstrates its trustworthiness,providing a conditionally positive solution,which represents a significant improvement compared to current forward Euler schemes.The numerical findings demonstrate themodel’s effectiveness in accurately representing the dynamics of disease transmission.Significantly,when the mortality coefficient rises,both the susceptible and infected populations decrease,highlighting the model’s sensitivity to important epidemiological factors.Moreover,there is a direct relationship between higher Holling type rate values and a decrease in the number of individuals who are infected,as well as an increase in the number of susceptible individuals.This correlation offers a significant understanding of how many elements affect the consequences of an epidemic.Our objective is to enhance decision-making in public health by providing a thorough quantitative analysis of the Hybrid SIR-Fuzzy Model.Our approach not only tackles the existing constraints in disease modeling,but also paves the way for additional investigation,providing a vital instrument for researchers and policymakers alike.

A SUFFICIENT CONDITION OF CONVERGENCE FOR CLIFFORD CONTINUED FRACTIONS

In this article, a sufficient condition for a Clifford continued fraction to be convergent is established, and some applications are given.

Uncertainties of landslide susceptibility prediction: Influences of random errors in landslide conditioning factors and errors reduction by low pass filter method

In the existing landslide susceptibility prediction(LSP)models,the influences of random errors in landslide conditioning factors on LSP are not considered,instead the original conditioning factors are directly taken as the model inputs,which brings uncertainties to LSP results.This study aims to reveal the influence rules of the different proportional random errors in conditioning factors on the LSP un-certainties,and further explore a method which can effectively reduce the random errors in conditioning factors.The original conditioning factors are firstly used to construct original factors-based LSP models,and then different random errors of 5%,10%,15% and 20%are added to these original factors for con-structing relevant errors-based LSP models.Secondly,low-pass filter-based LSP models are constructed by eliminating the random errors using low-pass filter method.Thirdly,the Ruijin County of China with 370 landslides and 16 conditioning factors are used as study case.Three typical machine learning models,i.e.multilayer perceptron(MLP),support vector machine(SVM)and random forest(RF),are selected as LSP models.Finally,the LSP uncertainties are discussed and results show that:(1)The low-pass filter can effectively reduce the random errors in conditioning factors to decrease the LSP uncertainties.(2)With the proportions of random errors increasing from 5%to 20%,the LSP uncertainty increases continuously.(3)The original factors-based models are feasible for LSP in the absence of more accurate conditioning factors.(4)The influence degrees of two uncertainty issues,machine learning models and different proportions of random errors,on the LSP modeling are large and basically the same.(5)The Shapley values effectively explain the internal mechanism of machine learning model predicting landslide sus-ceptibility.In conclusion,greater proportion of random errors in conditioning factors results in higher LSP uncertainty,and low-pass filter can effectively reduce these random errors.

Analysis of convergence for initial condition estimation of coupled map lattices based on symbolic dynamics

A novel approach to the inverse problem of diffusively coupled map lattices is systematically investigated by utilizing the symbolic vector dynamics. The relationship between the performance of initial condition estimation and the structural feature of dynamical system is proved theoretically. It is found that any point in a spatiotemporal coupled system is not necessary to converge to its initial value with respect to sufficient backward iteration, which is directly relevant to the coupling strength and local mapping function. When the convergence is met, the error bound in estimating the initial condition is proposed in a noiseless environment, which is determined by the dimension of attractors and metric entropy of the system. Simulation results further confirm the theoretic analysis, and prove that the presented method provides the important theory and experimental results for better analysing and characterizing the spatiotemporal complex behaviours in an actual system.