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15 pages, 3978 KiB  
Article
Buoyancy Characteristics of Synchronous Grouting Slurry in Shield Tunnels
by Wangjing Yao, Jianchao Sheng, Junhao Tian, Binpin Wei, Jiuchun Sun and Zhe Wang
Appl. Sci. 2025, 15(16), 8994; https://doi.org/10.3390/app15168994 - 14 Aug 2025
Abstract
Synchronous grouting slurry is widely used in shield tunnel construction to fill the gaps between stratum and shield tail segments. However, as grout is nearly liquid in the initial stages, the tunnel lining segments recently separated from the shield tail are easily affected [...] Read more.
Synchronous grouting slurry is widely used in shield tunnel construction to fill the gaps between stratum and shield tail segments. However, as grout is nearly liquid in the initial stages, the tunnel lining segments recently separated from the shield tail are easily affected by the upward buoyancy generated by grout, causing issues such as longitudinal misalignment and opening of ring joints. Therefore, studying the upward buoyancy characteristics of synchronous grout is crucial. In this study, floating characterisation parameters of grout were investigated using buoyancy model tests, orthogonal tests, and comprehensive tests. The floating characterisation parameters are affected by distribution ratio and types of each grout component. The relationship between the floating characterisation parameters of grout and buoyancy was established. The results show that density, flow index, and shear strength can be used as the floating characterisation parameters. Binder–sand and water–binder ratios have the largest impact on the density. The bentonite–water ratio exerts a primary influence on the flow index, while the water–binder ratio contributes a secondary effect. In addition, bentonite–water and binder–sand ratios have the greatest effect on the shear strength. Furthermore, the particle size of sand and type of bentonite considerably influence the flow index and shear strength. A high-shear grout using well-graded fine sand and a high mesh of sodium bentonite was considered in this study. When the content of bentonite exceeds 7% (P2.2), Archimedes’ law is not applicable for calculating the upward buoyancy of grout. Buoyancy supply rate exhibits gradual enhancement with flow index elevation, yet with diminishing growth rates. Full article
(This article belongs to the Section Civil Engineering)
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19 pages, 1035 KiB  
Article
Study on Risk Assessment and Risk Prevention of Dam Failure During the Operation Period of Tailings Pond
by Tao Gao, Zhihai Qin, Ruifang Yang, Quanming Li, Chao Geng, Jin Zhang and Zhengfa Chen
Buildings 2025, 15(16), 2833; https://doi.org/10.3390/buildings15162833 - 11 Aug 2025
Viewed by 190
Abstract
There is a huge risk of dam failure during the operation of tailings ponds. Domestic and foreign scholars have conducted extensive research on the assessment and prevention of dam failure risks during the operation of tailings ponds, but there are still many shortcomings. [...] Read more.
There is a huge risk of dam failure during the operation of tailings ponds. Domestic and foreign scholars have conducted extensive research on the assessment and prevention of dam failure risks during the operation of tailings ponds, but there are still many shortcomings. On the basis of exploring the key issues of dam failure risk assessment during the operation of tailings dams, this paper establishes a comprehensive evaluation index system for dam failure risk during the operation of tailings dams based on ten principles including scientificity, systematicity, and operability. By exploring the use of the change statistical mapping method, we can determine the weight of indicators. A risk assessment model was constructed using the fuzzy comprehensive evaluation method; compared to the traditional fuzzy comprehensive evaluation method, this model determines weights in a more extensive and scientific manner. The scientific and effective nature of the model was verified through case analysis of the Shouyun Iron Mine and Shangyu Tailings Reservoir in Beijing. Finally, in response to the risk of dam failure during the operation of tailings ponds, scientific prevention and control measures were proposed from four aspects: personnel risk prevention and control, inherent risk prevention and control of tailings ponds, environmental factor risk prevention and control, and management risk prevention and control. Full article
(This article belongs to the Section Building Structures)
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32 pages, 1187 KiB  
Article
Simple Approximations and Interpretation of Pareto Index and Gini Coefficient Using Mean Absolute Deviations and Quantile Functions
by Eugene Pinsky and Qifu Wen
Econometrics 2025, 13(3), 30; https://doi.org/10.3390/econometrics13030030 - 8 Aug 2025
Viewed by 360
Abstract
The Pareto distribution has been widely used to model income distribution and inequality. The tail index and the Gini index are typically computed by iteration using Maximum Likelihood and are usually interpreted in terms of the Lorenz curve. We derive an alternative method [...] Read more.
The Pareto distribution has been widely used to model income distribution and inequality. The tail index and the Gini index are typically computed by iteration using Maximum Likelihood and are usually interpreted in terms of the Lorenz curve. We derive an alternative method by considering a truncated Pareto distribution and deriving a simple closed-form approximation for the tail index and the Gini coefficient in terms of the mean absolute deviation and weighted quartile differences. The obtained expressions can be used for any Pareto distribution, even without a finite mean or variance. These expressions are resistant to outliers and have a simple geometric and “economic” interpretation in terms of the quantile function and quartiles. Extensive simulations demonstrate that the proposed approximate values for the tail index and the Gini coefficient are within a few percent relative error of the exact values, even for a moderate number of data points. Our paper offers practical and computationally simple methods to analyze a class of models with Pareto distributions. The proposed methodology can be extended to many other distributions used in econometrics and related fields. Full article
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14 pages, 609 KiB  
Article
First- and Second-Trimester Uterine Artery Doppler and Hypertensive Disorders in Twin Pregnancies
by Stephanie Springer, Teresa Anzböck, Katharina Worda, Eva Karner and Christof Worda
J. Clin. Med. 2025, 14(15), 5563; https://doi.org/10.3390/jcm14155563 - 7 Aug 2025
Viewed by 330
Abstract
Objective: The objective of this study is the investigation of uterine artery Doppler studies in twin pregnancies. Methods: This retrospective cohort study included 554 twin pregnancies. All women underwent measurement using the mean uterine artery pulsatility index (UTPI) in gestational weeks 11+0 [...] Read more.
Objective: The objective of this study is the investigation of uterine artery Doppler studies in twin pregnancies. Methods: This retrospective cohort study included 554 twin pregnancies. All women underwent measurement using the mean uterine artery pulsatility index (UTPI) in gestational weeks 11+0–13+6 and 19+0–22+6 for risk assessment regarding the occurrence of preeclampsia and adverse obstetric outcomes. Results: Out of the 554 included women, a total of 51 women (9.2%) developed preeclampsia: 12 women (2.2%) developed early preeclampsia and 39 patients (7.0%) developed late preeclampsia. Adverse pregnancy outcomes occurred in 147 women (26.5%). The optimum cut-off for the mean UTPI to predict preeclampsia was calculated for gestational weeks 11+0–13+6 (UTPI > 1.682) and 19+0–22+6 (UTPI > 1.187). Between gestational weeks 11+0 and 13+6, the risk of developing preeclampsia was approximately 1.5 times higher when the mean UTPI was above the established cut-off. The risk of early preeclampsia increased 2.5-fold, and that of adverse pregnancy outcomes increased 1.5-fold. At 19+0 to 22+6 weeks, the preeclampsia risk doubled when the mean UTPI exceeded the cut-off. The risk increased 4-fold for early preeclampsia and 1.5-fold for adverse pregnancy outcomes. Regression analyses revealed that a mean UTPI above the set cut-off at both time points was significantly associated with preeclampsia, early preeclampsia, and adverse pregnancy outcomes. Conclusions: The best prediction for early preeclampsia can be achieved using a two-tailed screening approach that combines mean UTPI measurements taken at gestational weeks 11+0–13+6 and 19+0–22+6. Full article
(This article belongs to the Special Issue Clinical Challenges in High-Risk Pregnancy and Delivery)
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20 pages, 5378 KiB  
Article
Machine Learning-Based Approach for CPTu Data Processing and Stratigraphic Analysis
by Helena Paula Nierwinski, Arthur Miguel Pereira Gabardo, Ricardo José Pfitscher, Rafael Piton, Ezequias Oliveira and Marieli Biondo
Metrology 2025, 5(3), 48; https://doi.org/10.3390/metrology5030048 - 6 Aug 2025
Viewed by 224
Abstract
Cone Penetration Tests with pore pressure measurements (CPTu) are widely used in geotechnical site investigations due to their high-resolution profiling capabilities. However, traditional interpretation methods—such as the Soil Behavior Type Index (Ic)—often fail to capture the internal heterogeneity typical of [...] Read more.
Cone Penetration Tests with pore pressure measurements (CPTu) are widely used in geotechnical site investigations due to their high-resolution profiling capabilities. However, traditional interpretation methods—such as the Soil Behavior Type Index (Ic)—often fail to capture the internal heterogeneity typical of mining tailings deposits. This study presents a machine learning-based approach to enhance stratigraphic interpretation from CPTu data. Four unsupervised clustering algorithms—k-means, DBSCAN, MeanShift, and Affinity Propagation—were evaluated using a dataset of 12 CPTu soundings collected over a 19-year period from an iron tailings dam in Brazil. Clustering performance was assessed through visual inspection, stratigraphic consistency, and comparison with Ic-based profiles. k-means and MeanShift produced the most consistent stratigraphic segmentation, clearly delineating depositional layers, consolidated zones, and transitions linked to dam raising. In contrast, DBSCAN and Affinity Propagation either over-fragmented or failed to identify meaningful structures. The results demonstrate that clustering methods can reveal behavioral trends not detected by Ic alone, offering a complementary perspective for understanding depositional and mechanical evolution in tailings. Integrating clustering outputs with conventional geotechnical indices improves the interpretability of CPTu profiles, supporting more informed geomechanical modeling, dam monitoring, and design. The approach provides a replicable methodology for data-rich environments with high spatial and temporal variability. Full article
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18 pages, 7363 KiB  
Article
Agronomic Evaluation of Compost Formulations Based on Mining Tailings and Microbial Mats from Geothermal Sources
by María Jesús Puy-Alquiza, Miren Yosune Miranda Puy, Raúl Miranda-Avilés, Pooja Vinod Kshirsagar and Cristina Daniela Moncada Sanchez
Recycling 2025, 10(4), 156; https://doi.org/10.3390/recycling10040156 - 5 Aug 2025
Viewed by 259
Abstract
This study, conducted in Mexico, evaluates the agricultural potential of three compost formulations BFS1, BFS2, and BFS3 produced from mining tailings and thermophilic microbial mats and collected from geothermal environments. The physicochemical characterization included pH, electrical conductivity (EC), macronutrients (N, P, K, Ca, [...] Read more.
This study, conducted in Mexico, evaluates the agricultural potential of three compost formulations BFS1, BFS2, and BFS3 produced from mining tailings and thermophilic microbial mats and collected from geothermal environments. The physicochemical characterization included pH, electrical conductivity (EC), macronutrients (N, P, K, Ca, Mg, and S), micronutrients (Fe, Zn, B, Cu, Mn, Mo, and Ni), organic matter (OM), and the carbon-to-nitrogen (C/N) ratio. All composts exhibited neutral pH values (7.38–7.52), high OM content (38.5–48.4%), and optimal C/N ratios (10.5–13.9), indicating maturity and chemical stability. Nitrogen ranged from 19 to 21 kg·t−1, while potassium and calcium were present in concentrations beneficial for crop development. However, EC values (3.43–3.66 dS/m) and boron levels (>160 ppm) were moderately high, requiring caution in saline soils or with boron-sensitive crops. A semi-quantitative Compost Quality Index (CQI) ranked BFS3 highest due to elevated OM and potassium content, followed by BFS1. BFS2, while rich in nitrogen, scored lower due to excessive boron. One-way ANOVA revealed no significant difference in nitrogen (p > 0.05), but it did reveal significant differences in potassium (p < 0.01) and boron (p < 0.001) among formulations. These results confirm the potential of mining tailings—microbial mat composts are low-cost, nutrient-rich biofertilizers. They are suitable for field crops or as components in nursery substrates, particularly when EC and boron are managed through dilution. This study promotes the circular reuse of geothermal and industrial residues and contributes to sustainable soil restoration practices in mining-affected regions through innovative composting strategies. Full article
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11 pages, 1539 KiB  
Article
An Optimum Prediction Model for the Strength Index of Unclassified Tailings Filling Body
by Jian Yao, Shenghua Yin, Dongmei Tian, Chen Yi, Jinglin Xu and Leiming Wang
Processes 2025, 13(8), 2395; https://doi.org/10.3390/pr13082395 - 28 Jul 2025
Viewed by 281
Abstract
In order to improve the poor prediction effect of current filling body strength design, a support vector machine (SVM) and Lib Toolbox were used to build an optimal match model or strength index of unclassified tailings filling body. Eight main factors were analyzed [...] Read more.
In order to improve the poor prediction effect of current filling body strength design, a support vector machine (SVM) and Lib Toolbox were used to build an optimal match model or strength index of unclassified tailings filling body. Eight main factors were analyzed and screened as condition attributes, and backfill strength as a decision attribute. Next, we selected 72 groups of training samples and 6 groups of calibration samples. Our model adopts a radial basis function (RBF) as the kernel function and uses a grid search method to optimize parameters; it then tests the combination of optimal parameters by cross-validation. Results show that the mean error of regression prediction and verified predictions made by the SVM match model were 1.01%, which were more accurate than the BP neural network model’s predictions. On the premise that stope stability is ensured, the SVM match model may decrease cement consumption and the cost of backfill more effectively, and improve economic efficiency. Full article
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21 pages, 343 KiB  
Proceeding Paper
Detecting Financial Bubbles with Tail-Weighted Entropy
by Omid M. Ardakani
Comput. Sci. Math. Forum 2025, 11(1), 3; https://doi.org/10.3390/cmsf2025011003 - 25 Jul 2025
Viewed by 27
Abstract
This paper develops a novel entropy-based framework to quantify tail risk and detect speculative bubbles in financial markets. By integrating extreme value theory with information theory, I introduce the Tail-Weighted Entropy (TWE) measure, which captures how information scales with extremeness in asset price [...] Read more.
This paper develops a novel entropy-based framework to quantify tail risk and detect speculative bubbles in financial markets. By integrating extreme value theory with information theory, I introduce the Tail-Weighted Entropy (TWE) measure, which captures how information scales with extremeness in asset price distributions. I derive explicit bounds for TWE under heavy-tailed models and establish its connection to tail index parameters, revealing a phase transition in entropy decay rates during bubble formation. Empirically, I demonstrate that TWE-based signals detect crises in equities, commodities, and cryptocurrencies days earlier than traditional variance-ratio tests, with Bitcoin’s 2021 collapse identified weeks prior to the peak. The results show that entropy decay—not volatility explosions—serves as the primary precursor to systemic risk, offering policymakers a robust tool for preemptive crisis management. Full article
10 pages, 775 KiB  
Proceeding Paper
An Estimation of Risk Measures: Analysis of a Method
by Marta Ferreira and Liliana Monteiro
Comput. Sci. Math. Forum 2025, 11(1), 2; https://doi.org/10.3390/cmsf2025011002 - 25 Jul 2025
Viewed by 21
Abstract
Extreme value theory comprises a set of techniques for inference at the tail of distributions, where data are scarce or non-existent. The tail index is the main parameter, with risk measures such as value at risk or expected shortfall depending on it. In [...] Read more.
Extreme value theory comprises a set of techniques for inference at the tail of distributions, where data are scarce or non-existent. The tail index is the main parameter, with risk measures such as value at risk or expected shortfall depending on it. In this study, we will analyze a method for estimating the tail index through a simulation study. This will allow for an application using real data including the estimation of the mentioned risk measures. Full article
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36 pages, 1566 KiB  
Article
The Impact of Geopolitical Risk on the Connectedness Dynamics Among Sovereign Bonds
by Mustafa Almabrouk Abdalla Alfughi and Asil Azimli
Mathematics 2025, 13(15), 2379; https://doi.org/10.3390/math13152379 - 24 Jul 2025
Viewed by 498
Abstract
This study examines the impact of geopolitical risk (GPR) on the connectedness dynamics among the sovereign bonds of the emerging seven (E7) and the Group of Seven (G7) countries. Initially, a quantile-based vector-autoregressive (Q-VAR) connectedness approach is used to calculate the total connectedness [...] Read more.
This study examines the impact of geopolitical risk (GPR) on the connectedness dynamics among the sovereign bonds of the emerging seven (E7) and the Group of Seven (G7) countries. Initially, a quantile-based vector-autoregressive (Q-VAR) connectedness approach is used to calculate the total connectedness index (TCI) among sovereign bonds under different market states. Then, the impact of GPR on the TCI at the median and tails is estimated to examine if GPR affects the TCI among sovereign bonds. Using daily yields from 30 January 2012, to 17 June 2024, the findings show that the GPR is one of the significant determinants of the TCI among sovereign bonds during normal and extreme market conditions. Other determinants of the TCI include yields on Treasury bills (T-bills), the exchange rate, and the financial market volatility index. The impact of GPR on the TCI varies significantly during different GPR episodes and bond market conditions. The effect of GPR on the TCI among sovereign bonds yields is higher during war times and when bond yields are average. These findings can be utilized by investors seeking to achieve international diversification and policymakers aiming to mitigate the effects of heightened geopolitical risk on financial stability. Furthermore, GPR can be used as an early signal tool for systematic tail risk spillovers among sovereign bonds. Full article
(This article belongs to the Special Issue Modeling Multivariate Financial Time Series and Computing)
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18 pages, 1052 KiB  
Article
Assessment of Tailings Contamination Potential in One of the Most Important Gold Mining Districts of Ecuador
by Daniel Garcés, Samantha Jiménez-Oyola, Yolanda Sánchez-Palencia, Fredy Guzmán-Martínez, Raúl Villavicencio-Espinoza, Sebastián Jaramillo-Zambrano, Victoria Rosado, Bryan Salgado-Almeida and Josué Marcillo-Guillén
Minerals 2025, 15(8), 767; https://doi.org/10.3390/min15080767 - 22 Jul 2025
Viewed by 481
Abstract
Mining waste presents significant environmental and public health risks due to the potential release of toxic substances when improperly managed. In this study, four tailings samples were taken to evaluate the environmental risks in the Ponce Enríquez mining area in Ecuador. Chemical characterization [...] Read more.
Mining waste presents significant environmental and public health risks due to the potential release of toxic substances when improperly managed. In this study, four tailings samples were taken to evaluate the environmental risks in the Ponce Enríquez mining area in Ecuador. Chemical characterization and X-ray Fluorescence Spectrometry (XRF) were used to analyze the content of potentially toxic elements (PTEs) of interest (As, Cd, Cr, Cu, Ni, Pb, and Zn), and X-ray Diffraction (XRD) for mineralogical characterization. The contamination index (IC) was calculated to assess the potential hazard associated with the content of PTEs in the mining wastes. To assess environmental risks, leaching tests were carried out to evaluate the potential release of PTEs, and Acid-Base Accounting (ABA) tests were conducted to determine the likelihood of acid mine drainage formation. The results revealed that the PETs concentration exceeded the maximum permissible limits in all samples, according to Ecuadorian regulations: As, Pb, and Cd were identified as critical contaminants. Mineralogically, quartz was the dominant phase, followed by carbonates (calcite, dolomite and magnesite), phyllosilicates (chlorite and illite), and minor amounts of pyrite and talc. The IC indicated high to very high contamination risk levels, with As being the predominant contributor. Although leaching tests met the established limits for non-hazardous mining waste, the ABA test showed that all samples had a high potential for long-term acid generation. These results underscore the need for implementing management strategies to mitigate the environmental impacts and the development of plans to protect local ecosystems and communities from the adverse effects of mining activities. Full article
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19 pages, 6727 KiB  
Article
Soil Contamination and Related Ecological Risks: Complex Analysis of the Defor Petrila Tailings Dump, Romania
by Emilia-Cornelia Dunca, Mădălina-Flavia Ioniță and Sorin Mihai Radu
Land 2025, 14(7), 1492; https://doi.org/10.3390/land14071492 - 18 Jul 2025
Viewed by 276
Abstract
Assessing the risks associated with waste disposal is essential for environmental protection and sustainable development, especially given concerns about the impact of industrial activities on the environment. This study analyses soil contamination in the Defor Petrila tailings-dump area caused by the deposition of [...] Read more.
Assessing the risks associated with waste disposal is essential for environmental protection and sustainable development, especially given concerns about the impact of industrial activities on the environment. This study analyses soil contamination in the Defor Petrila tailings-dump area caused by the deposition of waste material resulting from coal exploitation. To characterise the heavy-metal contamination in detail, we applied a comprehensive methodology that includes the calculation of the geo-accumulation index (Igeo), contamination factor (Cf), and potential ecological risk index (PERI), along with an analysis of the heavy-metal concentration isolines and a statistical analysis using the Pearson correlation coefficient. The results reveal varying levels of heavy-metal concentrations, as indicated by the calculated indices. The findings underscore the need for remediation and ongoing monitoring to mitigate the environmental impacts. This study provides a scientific basis for decision making in environmental management and highlights the importance of assessing mining-waste disposal near human settlements using various contamination-assessment methods. Full article
(This article belongs to the Section Land Use, Impact Assessment and Sustainability)
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26 pages, 9572 KiB  
Article
Geochemical Characteristics and Risk Assessment of PTEs in the Supergene Environment of the Former Zoige Uranium Mine
by Na Zhang, Zeming Shi, Chengjie Zou, Yinghai Zhu and Yun Hou
Toxics 2025, 13(7), 561; https://doi.org/10.3390/toxics13070561 - 30 Jun 2025
Viewed by 309
Abstract
Carbonaceous–siliceous–argillaceous rock-type uranium deposits, a major uranium resource in China, pose significant environmental risks due to heavy metal contamination. Geochemical investigations in the former Zoige uranium mine revealed elevated As, Cd, Cr, Cu, Ni, U, and Zn concentrations in soils and sediments, particularly [...] Read more.
Carbonaceous–siliceous–argillaceous rock-type uranium deposits, a major uranium resource in China, pose significant environmental risks due to heavy metal contamination. Geochemical investigations in the former Zoige uranium mine revealed elevated As, Cd, Cr, Cu, Ni, U, and Zn concentrations in soils and sediments, particularly at river confluences and downstream regions, attributed to leachate migration from ore bodies and tailings ponds. Surface samples exhibited high Cd bioavailability. The integrated BCR and mineral analysis reveals that Acid-soluble and reducible fractions of Ni, Cu, Zn, As, and Pb are governed by carbonate dissolution and Fe-Mn oxide dynamics via silicate weathering, while residual and oxidizable fractions show weak mineral-phase dependencies. Positive Matrix Factorization identified natural lithogenic, anthropogenic–natural composite, mining-related sources. Pollution assessments using geo-accumulation index and contamination factor demonstrated severe contamination disparities: soils showed extreme Cd pollution, moderate U, As, Zn contamination, and no Cr, Pb pollution (overall moderate risk); sediments exhibited extreme Cd pollution, moderate Ni, Zn, U levels, and negligible Cr, Pb impacts (overall extreme risk). USEPA health risk models indicated notable non-carcinogenic (higher in adults) and carcinogenic risks (higher in children) for both age groups. Ecological risk assessments categorized As, Cr, Cu, Ni, Pb, and Zn as low risk, contrasting with Cd (extremely high risk) and sediment-bound U (high risk). These findings underscore mining legacy as a critical environmental stressor and highlight the necessity for multi-source pollution mitigation strategies. Full article
(This article belongs to the Special Issue Assessment and Remediation of Heavy Metal Contamination in Soil)
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36 pages, 4216 KiB  
Article
Research on the Tail Risk Spillover Effect of Cryptocurrencies and Energy Market Based on Complex Network
by Xiao-Li Gong and Xue-Ting Wang
Entropy 2025, 27(7), 704; https://doi.org/10.3390/e27070704 - 30 Jun 2025
Viewed by 580
Abstract
As the relationship between cryptocurrency mining activities and electricity consumption becomes increasingly close, the risk spillover effect is steadily drawing a lot of attention to the energy and cryptocurrency markets. For the purpose of studying the risk contagion between the cryptocurrency and energy [...] Read more.
As the relationship between cryptocurrency mining activities and electricity consumption becomes increasingly close, the risk spillover effect is steadily drawing a lot of attention to the energy and cryptocurrency markets. For the purpose of studying the risk contagion between the cryptocurrency and energy market, this paper constructs a risk contagion network between cryptocurrency and China’s energy market using complex network methods. The tail risk spillover effects under various time and frequency domains were captured by the spillover index, which was assessed by the leptokurtic quantile vector autoregression (QVAR) model. Considering the spatial heterogeneity of energy companies, the spatial Durbin model was used to explore the impact mechanism of risk spillovers. The research showed that the framework of this paper more accurately reflects the tail risk spillover effect between China’s energy market and cryptocurrency market under various shock scales, with the extreme state experiencing a much higher spillover effect than the normal state. Furthermore, this study found that the tail risk contagion between cryptocurrency and China’s energy market exhibits notable dynamic variation and cyclical features, and the long-term risk spillover effect is primarily responsible for the total spillover. At the same time, the study found that the company with the most significant spillover effect does not necessarily have the largest company size, and other factors, such as geographical location and business composition, need to be considered. Moreover, there are spatial spillover effects among listed energy companies, and the connectedness between cryptocurrency and the energy market network generates an obvious impact on risk spillover effects. The research conclusions have an important role in preventing cross-contagion of risks between cryptocurrency and the energy market. Full article
(This article belongs to the Special Issue Complexity of Social Networks)
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28 pages, 2850 KiB  
Article
Quantification and Evolution of Online Public Opinion Heat Considering Interactive Behavior and Emotional Conflict
by Zhengyi Sun, Deyao Wang and Zhaohui Li
Entropy 2025, 27(7), 701; https://doi.org/10.3390/e27070701 - 29 Jun 2025
Viewed by 394
Abstract
With the rapid development of the Internet, the speed and scope of sudden public events disseminating in cyberspace have grown significantly. Current methods of quantifying public opinion heat often neglect emotion-driven factors and user interaction behaviors, making it difficult to accurately capture fluctuations [...] Read more.
With the rapid development of the Internet, the speed and scope of sudden public events disseminating in cyberspace have grown significantly. Current methods of quantifying public opinion heat often neglect emotion-driven factors and user interaction behaviors, making it difficult to accurately capture fluctuations during dissemination. To address these issues, first, this study addressed the complexity of interaction behaviors by introducing an approach that employs the information gain ratio as a weighting indicator to measure the “interaction heat” contributed by different interaction attributes during event evolution. Second, this study built on SnowNLP and expanded textual features to conduct in-depth sentiment mining of large-scale opinion texts, defining the variance of netizens’ emotional tendencies as an indicator of emotional fluctuations, thereby capturing “emotional heat”. We then integrated interactive behavior and emotional conflict assessment to achieve comprehensive heat index to quantification and dynamic evolution analysis of online public opinion heat. Subsequently, we used Hodrick–Prescott filter to separate long-term trends and short-term fluctuations, extract six key quantitative features (number of peaks, time of first peak, maximum amplitude, decay time, peak emotional conflict, and overall duration), and applied K-means clustering algorithm (K-means) to classify events into three propagation patterns, which are extreme burst, normal burst, and long-tail. Finally, this study conducted ablation experiments on critical external intervention nodes to quantify the distinct contribution of each intervention to the propagation trend by observing changes in the model’s goodness-of-fit (R2) after removing different interventions. Through an empirical analysis of six representative public opinion events from 2024, this study verified the effectiveness of the proposed framework and uncovered critical characteristics of opinion dissemination, including explosiveness versus persistence, multi-round dissemination with recurring emotional fluctuations, and the interplay of multiple driving factors. Full article
(This article belongs to the Special Issue Statistical Physics Approaches for Modeling Human Social Systems)
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