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23 pages, 1608 KB  
Article
Cross-Market Risk Spillovers and Tail Dependence Between U.S. and Chinese Technology-Related Equity Markets
by Xinmiao Zhou and Huihong Liu
Int. J. Financial Stud. 2025, 13(4), 242; https://doi.org/10.3390/ijfs13040242 - 17 Dec 2025
Abstract
This study investigates risk contagion and dependence structures between U.S. and Chinese technology-related stock markets, focusing on the electronics and semiconductor sectors. We employ DCC-GARCH models to capture time-varying correlations and copula models to analyze nonlinear and tail dependencies. To highlight extreme risk [...] Read more.
This study investigates risk contagion and dependence structures between U.S. and Chinese technology-related stock markets, focusing on the electronics and semiconductor sectors. We employ DCC-GARCH models to capture time-varying correlations and copula models to analyze nonlinear and tail dependencies. To highlight extreme risk dynamics, we extend the analysis to Value-at-Risk (VaR) series derived from a GARCH(1,1)-Skewed-t model. Empirical results reveal three major findings. First, volatility clustering and negative skewness are evident across markets, with extreme downside risks concentrated during the 2015 Chinese stock market crash and the 2020 COVID-19 pandemic. Second, copula results show stronger upper-tail dependence in cross-border broad markets and more symmetric dependence within domestic Chinese markets, while U.S. sectoral linkages exhibit the highest vulnerability during downturns. Third, dynamic copula analysis indicates that downside contagion is episodic and crisis-driven, whereas rebound co-movements are structurally persistent. These findings contribute to understanding systemic vulnerability in global technology markets. They provide insights for investors, regulators, and policymakers on monitoring cross-market contagion and managing systemic risk under stress scenarios. Full article
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40 pages, 2207 KB  
Article
A Symmetric–Asymmetric Copula-Based GLMM for Energy Export and CO2 Emission Dynamics in Indonesia
by Restu Arisanti, Agus Muslim, Sri Winarni and Resa Septiani Pontoh
Symmetry 2025, 17(12), 2122; https://doi.org/10.3390/sym17122122 - 10 Dec 2025
Viewed by 205
Abstract
Indonesia’s reliance on fossil-based energy exports continuously shapes the dynamics of CO2 emission and the broader energy environment relationship across regions. This study applies a symmetric–asymmetric copula-based generalized linear mixed model (copula–GLMM) to examine the joint dependence between energy exports and CO [...] Read more.
Indonesia’s reliance on fossil-based energy exports continuously shapes the dynamics of CO2 emission and the broader energy environment relationship across regions. This study applies a symmetric–asymmetric copula-based generalized linear mixed model (copula–GLMM) to examine the joint dependence between energy exports and CO2 emissions across 34 provinces from 2010 to 2024. The proposed framework captures both balanced and tail-specific dependence structures, providing a deeper understanding of the evolving dynamics shaped by industrial concentration, policy interventions, and technological adoption. The analysis reveals a strong positive association, with the Clayton copula offering the best fit. Notably, lower-tail dependence shows that provinces with smaller export volumes face disproportionate emission risks, whereas regions with larger exports exhibit more stable outcomes due to renewable integration and improved efficiency. These findings challenge the notion that export growth inevitably leads to proportional emission increases. The study underscores the need for region-specific strategies rather than uniform national policies to advance sustainability goals and support Indonesia’s commitments to SGDs 7, 11, and 13, as well as the Paris Agreement. Full article
(This article belongs to the Section Mathematics)
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18 pages, 11718 KB  
Article
Nonstationary Spatiotemporal Projection of Drought Across Seven Climate Regions of China in the 21st Century Based on a Novel Drought Index
by Zhijie Yan, Gengxi Zhang, Huimin Wang and Baojun Zhao
Water 2025, 17(22), 3206; https://doi.org/10.3390/w17223206 - 10 Nov 2025
Viewed by 532
Abstract
Climate change is increasing the drought frequency and severity, so projecting spatiotemporal drought evolution across climate zones is critical for drought mitigation. Model biases, the choice of drought index, and neglecting CO2 effects on potential evapotranspiration (PET) add large uncertainties to future [...] Read more.
Climate change is increasing the drought frequency and severity, so projecting spatiotemporal drought evolution across climate zones is critical for drought mitigation. Model biases, the choice of drought index, and neglecting CO2 effects on potential evapotranspiration (PET) add large uncertainties to future drought projections. We selected 10 global climate models (GCMs) that participated in the Coupled Model Intercomparison Project Phase 6 and downscaled model outputs using the bias correction and spatial downscaling (BCSD) method. We then developed a CO2-aware standardized moisture anomaly index (SZI[CO2]) and used a three-dimensional drought identification method to extract the duration, area, and severity; we then analyzed their spatiotemporal dynamics. To account for nonstationarity, Copula-based approaches were used to estimate joint drought probabilities with time-varying parameters. Projections indicate wetting in Southern Northwest China, Inner Mongolia, and the Western Tibetan Plateau (reduced drought frequency, duration, intensity), while Central and Southern China show a drying trend in the 21st century. Three-dimensional drought metrics exhibit strong nonstationarity; nonstationary log-normal and generalized extreme value distributions fit most regions best. Under equal drought characteristic values, co-occurrence probabilities are higher under SSP5-8.5 scenarios than SSP2-4.5 scenarios, with the largest scenario differences over the Tibetan Plateau and Central and Southern China. Full article
(This article belongs to the Section Hydrology)
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51 pages, 56694 KB  
Article
Spatial Flows of Information Entropy as Indicators of Climate Variability and Extremes
by Bernard Twaróg
Entropy 2025, 27(11), 1132; https://doi.org/10.3390/e27111132 - 31 Oct 2025
Viewed by 682
Abstract
The objective of this study is to analyze spatial entropy flows that reveal the directional dynamics of climate change—patterns that remain obscured in traditional statistical analyses. This approach enables the identification of pathways for “climate information transport”, highlights associations with atmospheric circulation types, [...] Read more.
The objective of this study is to analyze spatial entropy flows that reveal the directional dynamics of climate change—patterns that remain obscured in traditional statistical analyses. This approach enables the identification of pathways for “climate information transport”, highlights associations with atmospheric circulation types, and allows for the localization of both sources and “informational voids”—regions where entropy is dissipated. The analytical framework is grounded in a quantitative assessment of long-term climate variability across Europe over the period 1901–2010, utilizing Shannon entropy as a measure of atmospheric system uncertainty and variability. The underlying assumption is that the variability of temperature and precipitation reflects the inherently dynamic character of climate as a nonlinear system prone to fluctuations. The study focuses on calculating entropy estimated within a 70-year moving window for each calendar month, using bivariate distributions of temperature and precipitation modeled with copula functions. Marginal distributions were selected based on the Akaike Information Criterion (AIC). To improve the accuracy of the estimation, a block bootstrap resampling technique was applied, along with numerical integration to compute the Shannon entropy values at each of the 4165 grid points with a spatial resolution of 0.5° × 0.5°. The results indicate that entropy and its derivative are complementary indicators of atmospheric system instability—entropy proving effective in long-term diagnostics, while its derivative provides insight into the short-term forecasting of abrupt changes. A lag analysis and Spearman rank correlation between entropy values and their potential supported the investigation of how circulation variability influences the occurrence of extreme precipitation events. Particularly noteworthy is the temporal derivative of entropy, which revealed strong nonlinear relationships between local dynamic conditions and climatic extremes. A spatial analysis of the information entropy field was also conducted, revealing distinct structures with varying degrees of climatic complexity on a continental scale. This field appears to be clearly structured, reflecting not only the directional patterns of change but also the potential sources of meteorological fluctuations. A field-theory-based spatial classification allows for the identification of transitional regions—areas with heightened susceptibility to shifts in local dynamics—as well as entropy source and sink regions. The study is embedded within the Fokker–Planck formalism, wherein the change in the stochastic distribution characterizes the rate of entropy production. In this context, regions of positive divergence are interpreted as active generators of variability, while sink regions function as stabilizing zones that dampen fluctuations. Full article
(This article belongs to the Special Issue 25 Years of Sample Entropy)
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18 pages, 2705 KB  
Article
Real-Time Risk Rate Quantification Model and Early Warning Method for Earth–Rock Dams Under Sudden Changes in Reservoir Water Levels
by Xiang Luo, Fuheng Ma, Wei Ye, Benxing Lou, Qiang Li and Hanman Li
Water 2025, 17(21), 3046; https://doi.org/10.3390/w17213046 - 23 Oct 2025
Viewed by 513
Abstract
Under the influence of global climate change, extreme weather events have become more frequent, and earth and rockfill dams often encounter unconventional working conditions such as sudden changes in reservoir water levels during operation. These abrupt changes are characterized by their strong suddenness [...] Read more.
Under the influence of global climate change, extreme weather events have become more frequent, and earth and rockfill dams often encounter unconventional working conditions such as sudden changes in reservoir water levels during operation. These abrupt changes are characterized by their strong suddenness and rapid rate of change, which can be challenging for traditional numerical analysis methods due to slow modeling and time-consuming calculations, presenting certain limitations. Therefore, an approach has been developed that integrates seepage monitoring data into the failure probability analysis and early warning methods for earth and rockfill dams. Based on the model’s prediction results, dynamic safety warning indicators for the effect of single measurement points on earth and rockfill dams under sudden reservoir water level changes have been quantitatively designed. A risk probability function reflecting the relationship between the residuals of seepage monitoring effects and the risk rate has been constructed to calculate the risk rate of single measurement points for dam seepage effects. By employing the Copula function, which considers the differences and correlations in monitoring effect amounts across different parts of the dam, the single-point seepage risk rates are elevated to a multi-point seepage risk rate analysis. This enables the quantification of the overall seepage risk rate of dams under sudden reservoir water level changes. Case study results show that the safety model has high prediction accuracy. The joint risk rate of the dam based on the Copula function can simultaneously consider spatial correlations and individual differences among multiple measurement points, effectively reducing the interference of randomness in the calculation of single-point risk rates. This method successfully achieves the dynamic transformation of actual seepage effect measurements into risk rates, providing a theoretical basis and technical support for the operational management and safety monitoring of earth and rockfill dams during emergency events. Full article
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26 pages, 5202 KB  
Article
Time-Varying Bivariate Modeling for Predicting Hydrometeorological Trends in Jakarta Using Rainfall and Air Temperature Data
by Suci Nur Setyawati, Sri Nurdiati, I Wayan Mangku, Ionel Haidu and Mohamad Khoirun Najib
Hydrology 2025, 12(10), 252; https://doi.org/10.3390/hydrology12100252 - 26 Sep 2025
Viewed by 1030
Abstract
Changes in rainfall patterns and irregular air temperature have become essential issues in analyzing hydrometeorological trends in Jakarta. This study aims to select the best copula of the stationary and non-stationary copula models and visualize and explore the relationship between rainfall and air [...] Read more.
Changes in rainfall patterns and irregular air temperature have become essential issues in analyzing hydrometeorological trends in Jakarta. This study aims to select the best copula of the stationary and non-stationary copula models and visualize and explore the relationship between rainfall and air temperature to predict hydrometeorological trends. The methods used include combining univariate Lognormal and Generalized Extreme Value (GEV) distributions with Clayton, Gumbel, and Frank copulas, as well as parameter estimation using the fminsearch algorithm, Markov Chain Monte Carlo (MCMC) simulation, and a combination of both. The results show that the best model is the non-stationary Clayton copula estimated using MCMC simulation, which has the lowest Akaike Information Criterion (AIC) value. This model effectively captures extreme dependence in the lower tail of the distribution, indicating a potential increase in extreme low events such as cold droughts. Visualization of the best model through contour plots shows a shifting center of the distribution over time. This study contributes to developing dynamic hydrometeorological models for adaptation planning of changing hydrometeorological trends in Indonesia. Full article
(This article belongs to the Special Issue Trends and Variations in Hydroclimatic Variables: 2nd Edition)
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29 pages, 3573 KB  
Article
Joint Seismic Risk Assessment and Economic Loss Estimation of Coastal RC Frames Subjected to Combined Wind and Offshore Ground Motions
by Zheng Zhang, Yunmu Jiang and Long Yan
Buildings 2025, 15(18), 3309; https://doi.org/10.3390/buildings15183309 - 12 Sep 2025
Viewed by 471
Abstract
The dynamic environment of coastal regions subjects infrastructure to multiple interacting natural hazards, with the simultaneous occurrence of windstorms and earthquakes posing a particularly critical challenge. Unlike inland hazards, these coastal threats frequently exhibit irregular statistical behavior and terrain-induced anomalies. This study proposes [...] Read more.
The dynamic environment of coastal regions subjects infrastructure to multiple interacting natural hazards, with the simultaneous occurrence of windstorms and earthquakes posing a particularly critical challenge. Unlike inland hazards, these coastal threats frequently exhibit irregular statistical behavior and terrain-induced anomalies. This study proposes a novel probabilistic framework to assess compound hazard effects, advancing beyond traditional single-hazard analyses. By integrating maximum entropy theory with bivariate Copula models, a unified return period analysis is developed to capture the joint probability structure of seismic and wind events. The model is calibrated using long-term observational data collected from a representative coastal zone since 2000. For the PGA marginal distribution, our sixth-moment maximum-entropy model achieved an R2 of 0.90, compared with 0.57 for a conventional GEV fit—reflecting a 58% increase in explained variance. Analysis shows the progressive evolution of damage from slight damaged through moderate damaged and severe damaged to collapse for an 18-story reinforced concrete frame structure, and shows that the combined effect of seismic and wind loads results in risk probabilities of aforementioned damage state of approximately 2 × 10−3, 6 × 10−4, 2 × 10−4, and 3 × 10−5, respectively, under a 0.4 g ground motion and a concurrent wind speed of 15 m/s. Furthermore, when both the uncertainty of loss ratios and structural parameters are incorporated, the standard deviation of the economic loss ratio reaches up to 0.015 in the transition region (PGA 0.2–0.4 g), highlighting considerable variability in economic loss assessment, whereas the mean economic loss ratio rapidly saturates above 0.8 with increasing PGA. These findings demonstrate that uncertainty in economic loss is most pronounced within the transition region, while remaining much lower outside this zone. Overall, this study provides a robust framework and quantitative basis for comprehensive risk assessment and resilient design of coastal infrastructure under compound wind and seismic hazards. Full article
(This article belongs to the Special Issue Dynamic Response Analysis of Structures Under Wind and Seismic Loads)
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60 pages, 5577 KB  
Article
Performance of Pairs Trading Strategies Based on Various Copula Methods
by Yufei Sun
J. Risk Financial Manag. 2025, 18(9), 506; https://doi.org/10.3390/jrfm18090506 - 12 Sep 2025
Viewed by 2654
Abstract
This study evaluates three pairs trading strategies—the distance method (DM), mispricing index (MPI) copula, and mixed copula—across the Chinese equity market from 2005 to 2024, incorporating time-varying transaction costs. To enhance computational efficiency, a novel two-step methodology is proposed that first selects candidate [...] Read more.
This study evaluates three pairs trading strategies—the distance method (DM), mispricing index (MPI) copula, and mixed copula—across the Chinese equity market from 2005 to 2024, incorporating time-varying transaction costs. To enhance computational efficiency, a novel two-step methodology is proposed that first selects candidate pairs based on the sum of squared differences and then applies copula models to capture nonlinear and asymmetric dependence structures between stocks. Pre-cost monthly excess returns are 84, 30, and 25 basis points, respectively, dropping to 81, 23, and 15 basis points post-costs. While the DM consistently delivers higher returns, copula strategies offer advantages in stability and resilience, especially in volatile markets. The Student-t copula proves particularly effective in capturing dependence structures with fat tails and asymmetric correlations. Although copula methods face challenges such as unconverged trades—instances where spreads fail to revert within the trading horizon—they nonetheless highlight the diversification and risk mitigation potential of advanced dependence-based approaches. Enhancing trade convergence and controlling downside risk could further improve copula strategy performance. Overall, the results highlight the diversification and risk mitigation potential of advanced copula-based pairs trading models under dynamic market conditions. Full article
(This article belongs to the Special Issue Financial Funds, Risk and Investment Strategies)
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24 pages, 685 KB  
Article
Global Market Shocks and Tail Risk Spillovers: Evidence from a Copula-Based Contagion Framework
by Sundusit Saekow, Phisanu Chiawkhun, Woraphon Yamaka, Nawapon Nakharutai and Parkpoom Phetpradap
J. Risk Financial Manag. 2025, 18(9), 498; https://doi.org/10.3390/jrfm18090498 - 5 Sep 2025
Cited by 1 | Viewed by 1091
Abstract
This study investigates the dynamics of financial contagion using a flexible mixture copula framework, specifically a combination of the Survival Clayton and Survival Gumbel copulas, to estimate the lower tail dependence coefficient, interpreted as a measure of extreme downside co-movement or contagion. The [...] Read more.
This study investigates the dynamics of financial contagion using a flexible mixture copula framework, specifically a combination of the Survival Clayton and Survival Gumbel copulas, to estimate the lower tail dependence coefficient, interpreted as a measure of extreme downside co-movement or contagion. The model captures nonlinear and asymmetric dependencies between the global stock market and nine national markets: Australia, China, Hungary, India, New Zealand, Spain, Thailand, the United Kingdom, and the United States. The analysis spans the period from 2018 to 2024 and focuses on three major global crises: the China–U.S. trade war, the COVID-19 pandemic, and the Russia–Ukraine conflict. The results reveal substantial heterogeneity in contagion intensity across countries and crises. The COVID-19 pandemic generated the highest and most synchronized levels of contagion, with tail dependence exceeding 0.8 in the United States and above 0.6 in several developed and emerging markets. The China–U.S. trade war resulted in moderate contagion, particularly in countries with close trade links to the U.S. and China. The Russia–Ukraine conflict produced elevated contagion in European and energy-sensitive markets such as the UK and Spain. Conversely, China and New Zealand exhibited relatively lower levels of contagion across all periods Full article
(This article belongs to the Special Issue Risk Management in Capital Markets)
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13 pages, 1224 KB  
Article
Cryptocurrency Market Dynamics: Copula Analysis of Return and Volume Tails
by Giovanni De Luca and Andrea Montanino
Risks 2025, 13(9), 168; https://doi.org/10.3390/risks13090168 - 2 Sep 2025
Viewed by 2306
Abstract
This paper investigates the dependence structure between returns and trading volumes for five major cryptocurrencies: Bitcoin, Cardano, Ethereum, Litecoin, and Ripple. Using a copula-based framework, we focus on a mixture of the Joe copula and its 90-degree rotation to capture asymmetric relationships, especially [...] Read more.
This paper investigates the dependence structure between returns and trading volumes for five major cryptocurrencies: Bitcoin, Cardano, Ethereum, Litecoin, and Ripple. Using a copula-based framework, we focus on a mixture of the Joe copula and its 90-degree rotation to capture asymmetric relationships, especially in the tails of the distribution. Our findings reveal significant upper and lower–upper tail dependencies, suggesting that extreme trading volumes are associated with both positive and negative return extremes. The results confirm a nonlinear and asymmetric volume–return relationship, which traditional linear models fail to capture. Full article
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34 pages, 1917 KB  
Article
Enhancing Insurer Portfolio Resilience and Capital Efficiency with Green Bonds: A Framework Combining Dynamic R-Vine Copulas and Tail-Risk Modeling
by Thitivadee Chaiyawat and Pannarat Guayjarernpanishk
Risks 2025, 13(9), 163; https://doi.org/10.3390/risks13090163 - 27 Aug 2025
Viewed by 1231
Abstract
This study develops an integrated risk modeling framework to assess capital adequacy and optimize portfolio performance for Thai life and non-life insurers. Leveraging ARMA–GJR–GARCH models with skewed Student-t innovations, extreme value theory, and dynamic R-vine copulas, the framework effectively captures volatility, tail risks, [...] Read more.
This study develops an integrated risk modeling framework to assess capital adequacy and optimize portfolio performance for Thai life and non-life insurers. Leveraging ARMA–GJR–GARCH models with skewed Student-t innovations, extreme value theory, and dynamic R-vine copulas, the framework effectively captures volatility, tail risks, and evolving asset interdependencies. Utilizing daily data from 2014 to 2024, the models generate value-at-risk forecasts consistent with international standards such as Basel III’s 10-day 99% VaR and rolling Sharpe ratios for portfolios integrating green bonds compared to traditional asset allocations. The results demonstrate that green bonds, fixedincome instruments funding renewable energy and other environmental projects, significantly improve risk-adjusted returns and have the potential to reduce capital requirements, particularly for life insurers with long-term sustainability mandates. These findings underscore the importance of portfolio-level capital assessment and support the proactive integration of ESG considerations into supervisory investment guidelines to enhance financial resilience and align the insurance sector with Thailand’s sustainable finance agenda. Full article
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54 pages, 22294 KB  
Article
Research on Risk Evolution Probability of Urban Lifeline Natech Events Based on MdC-MCMC
by Shifeng Li and Yu Shang
Sustainability 2025, 17(17), 7664; https://doi.org/10.3390/su17177664 - 25 Aug 2025
Viewed by 1084
Abstract
Urban lifeline Natech events are coupled systems composed of multiple risks and entities with complex dynamic transmission chains. Predicting risk evolution probabilities is the core task for achieving the safety management of urban lifeline Natech events. First, the risk evolution mechanism is analyzed, [...] Read more.
Urban lifeline Natech events are coupled systems composed of multiple risks and entities with complex dynamic transmission chains. Predicting risk evolution probabilities is the core task for achieving the safety management of urban lifeline Natech events. First, the risk evolution mechanism is analyzed, where urban lifeline Natech events exhibit spatial evolution characteristics, which involves dissecting the parallel and synergistic effects of risk evolution in spatial dimensions. Next, based on fitting marginal probability distribution functions for natural hazard and urban lifeline risk evolution, a Multi-dimensional Copula (MdC) function for the joint probability distribution of urban lifeline Natech event risk evolution is constructed. Building upon the MdC function, a Markov Chain Monte Carlo (MCMC) model for predicting risk evolution probabilities of urban lifeline Natech events is developed using the Metropolis–Hastings (M-H) algorithm and Gibbs sampling. Finally, taking the 2021 Zhengzhou ‘7·20’ catastrophic rainstorm as a case study, joint probability distribution functions for risk evolution under Rainfall-Wind speed scenarios are fitted for traffic, electric, communication, water supply, and drainage systems (including different risk transmission chains). Numerical simulations of joint probability distributions for risk evolution are conducted, and visualizations of joint probability predictions for risk evolution are generated. Full article
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24 pages, 9802 KB  
Article
Threshold Dynamics of Vegetation Carbon Sink Loss Under Multiscale Droughts in the Mongolian Plateau
by Hongguang Chen, Mulan Wang, Fanhao Meng, Chula Sa, Min Luo, Wenfeng Chi and Sonomdagva Chonokhuu
Atmosphere 2025, 16(8), 964; https://doi.org/10.3390/atmos16080964 - 14 Aug 2025
Viewed by 872
Abstract
Gross primary productivity (GPP) is a key carbon flux in the global carbon cycle, and understanding the inhibitory effects of drought on GPP and its underlying mechanisms is crucial for understanding carbon–climate feedback. However, current research has not sufficiently addressed the threshold dynamics [...] Read more.
Gross primary productivity (GPP) is a key carbon flux in the global carbon cycle, and understanding the inhibitory effects of drought on GPP and its underlying mechanisms is crucial for understanding carbon–climate feedback. However, current research has not sufficiently addressed the threshold dynamics and regional differentiation of GPP responses to the synergistic effects of meteorological drought (MD) and soil moisture drought (SD), particularly in the drought-sensitive Mongolian Plateau. This study focuses on the Mongolian Plateau from 1982 to 2021, using the standardized precipitation index (SPI) and standardized soil moisture index (SSI) to characterize MD and SD, respectively. The study combines the three-threshold run theory, cross-wavelet analysis, Spearman correlation analysis, and copula models to systematically investigate the variation characteristics, propagation patterns, and the probability and thresholds for triggering GPP loss under different time scales (monthly, seasonal, semi-annual, and annual). The results show that (1) both types of droughts exhibited significant intensification trends, with SD intensifying at a faster rate (annual scale SSI12 trend: −0.34/10a). The intensification trend strengthened with increasing time scales. MD exhibited high frequency, short duration, and low intensity, while SD showed the opposite characteristics. The most significant aridification occurred in the central region. (2) The average propagation time from MD to SD was 11.22 months. The average response time of GPP to MD was 10.46 months, while the response time to SD was significantly shorter (approximately 2 months on average); the correlation between SSI and GPP was significantly higher than that between SPI and GPP. (3) The conditional probability of triggering mild GPP loss (e.g., <40th percentile) was relatively high for both drought types, and the probability of loss increased as the time scales extended. Compared to MD, SD was more likely to induce severe GPP loss. Additionally, the drought intensity threshold for triggering mild loss was lower (i.e., mild drought could trigger it), while higher drought intensity was required to trigger severe and extreme losses. Therefore, this study provides practical guidance for regional drought early-warning systems and ecosystem adaptive management, while laying an important theoretical foundation for a deeper understanding of drought response mechanisms. Full article
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29 pages, 10185 KB  
Article
Multiple Correlation Analysis of Operational Safety of Long-Distance Water Diversion Project Based on Copula Bayesian Network
by Pengyuan Li, Fudong Dong, Guibin Lv, Yuansen Wang, Yongguo Sheng, Feng Cheng and Bo Wang
Water 2025, 17(16), 2389; https://doi.org/10.3390/w17162389 - 12 Aug 2025
Cited by 1 | Viewed by 604
Abstract
Based on the Copula theory, a multiple correlation analysis model for the operation safety risks of long-distance water diversion projects was established. Combined with Bayesian network reasoning, a polynomial regression analysis, and other techniques, a dynamic analysis method for the operation safety of [...] Read more.
Based on the Copula theory, a multiple correlation analysis model for the operation safety risks of long-distance water diversion projects was established. Combined with Bayesian network reasoning, a polynomial regression analysis, and other techniques, a dynamic analysis method for the operation safety of long-distance water diversion projects based on a Copula Bayesian network model was proposed, providing decision support for the operation safety risk management of long-distance water diversion projects. We took the Middle Route Project of the South-to-North Water Diversion Project as an example to verify the validity and practicability of the model. The results show that this method can capture the nonlinear mapping relationship when the probability of risk occurrence changes dynamically on the basis of considering the risk correlation, and realize the dynamic analysis of risk correlation. Full article
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18 pages, 484 KB  
Article
LLM-Guided Ensemble Learning for Contextual Bandits with Copula and Gaussian Process Models
by Jong-Min Kim
Mathematics 2025, 13(15), 2523; https://doi.org/10.3390/math13152523 - 6 Aug 2025
Viewed by 2460
Abstract
Contextual multi-armed bandits (CMABs) are vital for sequential decision-making in areas such as recommendation systems, clinical trials, and finance. We propose a simulation framework integrating Gaussian Process (GP)-based CMABs with vine copulas to model dependent contexts and GARCH processes to capture reward volatility. [...] Read more.
Contextual multi-armed bandits (CMABs) are vital for sequential decision-making in areas such as recommendation systems, clinical trials, and finance. We propose a simulation framework integrating Gaussian Process (GP)-based CMABs with vine copulas to model dependent contexts and GARCH processes to capture reward volatility. Rewards are generated via copula-transformed Beta distributions to reflect complex joint dependencies and skewness. We evaluate four policies—ensemble, Epsilon-greedy, Thompson, and Upper Confidence Bound (UCB)—over 10,000 replications, assessing cumulative regret, observed reward, and cumulative reward. While Thompson sampling and LLM-guided policies consistently minimize regret and maximize rewards under varied reward distributions, Epsilon-greedy shows instability, and UCB exhibits moderate performance. Enhancing the ensemble with copula features, GP models, and dynamic policy selection driven by a large language model (LLM) yields superior adaptability and performance. Our results highlight the effectiveness of combining structured probabilistic models with LLM-based guidance for robust, adaptive decision-making in skewed, high-variance environments. Full article
(This article belongs to the Special Issue Privacy-Preserving Machine Learning in Large Language Models (LLMs))
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