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Keywords = hybrid gray-box model

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38 pages, 2692 KB  
Article
Observability- and Identifiability-Guided Sensor-Set Design for Digital-Twin-Assisted Consolidated Bioprocessing
by Mark Korang Yeboah, Nana Yaw Asiedu and Ahmad Addo
Sensors 2026, 26(12), 3948; https://doi.org/10.3390/s26123948 (registering DOI) - 21 Jun 2026
Viewed by 146
Abstract
Consolidated bioprocessing (CBP) is difficult to monitor because enzyme production, lignocellulose degradation, sugar release, and fermentation occur simultaneously under sparse measurement, feedstock variability, and plant–model mismatch conditions. This study proposes a computational sensor-set design framework for digital-twin-assisted CBP monitoring. A five-state virtual plant, [...] Read more.
Consolidated bioprocessing (CBP) is difficult to monitor because enzyme production, lignocellulose degradation, sugar release, and fermentation occur simultaneously under sparse measurement, feedstock variability, and plant–model mismatch conditions. This study proposes a computational sensor-set design framework for digital-twin-assisted CBP monitoring. A five-state virtual plant, consisting of active biomass, cellulolytic enzyme activity, residual insoluble substrate, soluble sugar, and ethanol, was used to evaluate all 16 ethanol-mandatory measurement packages formed from ethanol, sugar, biomass, enzyme, and residual-substrate proxy channels. Candidate sensor sets were assessed using finite-difference output sensitivities, Fisher-information-based state-observability and parameter-identifiability analyses, eigenvalue and parameter-correlation diagnostics, and paired Monte Carlo unscented Kalman filter soft-sensing reconstruction. Within the tested five-state virtual-plant benchmark and with the specified excitation schedule, noise assumptions, burden indices, and scoring objective, ethanol-only sensing provided the weakest support for state-aware CBP digital-twin reconstruction. At a 6h sampling interval, the state-observability log-pseudodeterminant increased from 4.18 with ethanol-only sensing to 8.56 after adding soluble sugar and to 16.42 with full-proxy monitoring. The ethanol–sugar–biomass–substrate package also gave strong reduced state-observability performance, with log-pseudodeterminants of 15.12, 13.76, and 12.51 at 6, 12, and 24h, respectively. Biomass and enzyme proxies contributed strongly to parameter learning, and the ethanol–sugar–biomass–enzyme package gave the strongest active parameter-identifiability performance, with log-pseudodeterminants of 10.82, 9.06, and 6.67 at 6, 12, and 24h, respectively. In the paired soft-sensing analysis, full-proxy monitoring reduced the mean latent-state RMSE from 1.1899 to 0.3756, followed by ethanol–biomass–enzyme–substrate with 0.3843 and ethanol–sugar–biomass–substrate with 0.4121. The primary aggregate ranking identified ethanol–sugar–biomass–substrate as the best overall package, with a sensor-value score of 0.8432 and a burden index of 7.0, followed by full-proxy monitoring with a score of 0.8173 and a burden index of 10.0. Robustness tests showed that ethanol–sugar–biomass–substrate remained top-ranked under uniform noise scaling, full UKF missingness, delay and bias stress test conditions, most scoring-weight scenarios, and all tested sensor-specific burden workflows. Full-proxy monitoring remained a close competitor under independent sensor-specific noise variation conditions and became top-ranked for some alternative operating trajectories. The proposed framework provides a simulation-based method for prioritizing informative measurement packages before implementing CBP digital twins in laboratory and pilot-plant settings. Full article
(This article belongs to the Special Issue Soft Sensors and Sensing Techniques (2nd Edition))
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29 pages, 12987 KB  
Review
Review of Numerical Simulations for Parameter Control in Heap Bioleaching of Copper Sulfide Ore
by Rong Nie, Xinlong Yang, Bingyang Tian, Wenjuan Li, Xue Liu, Jiankang Wen and Hongying Yang
Minerals 2026, 16(6), 568; https://doi.org/10.3390/min16060568 - 25 May 2026
Viewed by 352
Abstract
Heap bioleaching is widely used to extract copper from low-grade sulfide ores thanks to its operational simplicity, low cost, and environmental sustainability. However, current control strategies rely primarily on single-factor optimization and often overlook the synergistic interactions of multiple key parameters, such as [...] Read more.
Heap bioleaching is widely used to extract copper from low-grade sulfide ores thanks to its operational simplicity, low cost, and environmental sustainability. However, current control strategies rely primarily on single-factor optimization and often overlook the synergistic interactions of multiple key parameters, such as ore particle size, pore structure, pH, temperature, microbial activity, and oxygen transfer efficiency. As a result, issues such as low recovery rates, extended leaching periods, and high operational costs persist. Moreover, the “gray-box” nature of heap systems impedes real-time monitoring of internal physical, chemical, and biological processes. In addition, empirical multi-parameter optimization is time-consuming and inadequate for capturing complex interdependencies. This review was conducted to systematically examine the key factors influencing heap bioleaching efficiency and critically evaluate recent advances in numerical simulation and intelligent control strategies. As a result, we identified a major research gap: the existing models—including microscale shrinking core models (SCMs), mesoscale pore-network models based on CT reconstruction, and macroscale continuum models—have inherent limitations. SCMs assume idealized spherical particles with uniform mineral distribution while neglecting pore structure evolution and biofilm dynamics. Mesoscale models offer detailed pore characterization but lack robust multi-physics coupling (thermal–hydro–mechanical–chemical–biological, or THMCB). Macroscale models rely on homogenization assumptions that oversimplify spatial heterogeneity and temporal variations in permeability. This analysis covers the relevant literature from 1985 to 2025, with a focus on three methodological scales (micro, meso, and macro) and their integration with machine learning approaches. A notable finding is that hybrid neural network models (e.g., BP and RBF architectures) outperform purely physics-based models in predicting leaching kinetics under varying operational conditions. However, their accuracy depends heavily on high-quality field data—a limitation rarely addressed in prior reviews. By clearly delineating these model-specific limitations and scale-dependent trade-offs, this review makes two unique contributions: a structured framework for selecting and coupling numerical methods according to process requirements and a roadmap for integrating artificial neural networks with multi-physics simulations to achieve real-time intelligent control of heap bioleaching. The findings offer both theoretical guidance and practical references for optimizing the processing of low-grade copper sulfide ores. Full article
(This article belongs to the Special Issue Advances in the Theory and Technology of Biohydrometallurgy)
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22 pages, 2785 KB  
Article
Intelligent Optimization of Ground-Source Heat Pump Systems Based on Gray-Box Modeling
by Kui Wang, Zijian Shuai and Ye Yao
Energies 2026, 19(3), 608; https://doi.org/10.3390/en19030608 - 24 Jan 2026
Cited by 1 | Viewed by 537
Abstract
Ground-source heat pump (GSHP) systems are widely regarded as an energy-efficient solution for building heating and cooling. However, their actual performance in large commercial buildings is often limited by rigid control strategies, insufficient equipment coordination, and suboptimal load matching. In the Liuzhou Fengqing [...] Read more.
Ground-source heat pump (GSHP) systems are widely regarded as an energy-efficient solution for building heating and cooling. However, their actual performance in large commercial buildings is often limited by rigid control strategies, insufficient equipment coordination, and suboptimal load matching. In the Liuzhou Fengqing Port commercial complex, the seasonal coefficient of performance (SCOP) of the GSHP system remains at a relatively low level of 3.0–3.5 under conventional operation. To address these challenges, this study proposes a gray-box-model-based cooperative optimization and group control strategy for GSHP systems. A hybrid gray-box modeling approach (YFU model), integrating physical-mechanism modeling with data-driven parameter identification, is developed to characterize the energy consumption behavior of GSHP units and variable-frequency pumps. On this basis, a multi-equipment cooperative optimization framework is established to coordinate GSHP unit on/off scheduling, load allocation, and pump staging. In addition, continuous operational variables (e.g., chilled-water supply temperature and circulation flow rate) are globally optimized within a hierarchical control structure. The proposed strategy is validated through both simulation analysis and on-site field implementation, demonstrating significant improvements in system energy efficiency, with annual electricity savings of no less than 3.6 × 105 kWh and an increase in SCOP from approximately 3.2 to above 4.0. The results indicate that the proposed framework offers strong interpretability, robustness, and engineering applicability. It also provides a reusable technical paradigm for intelligent energy-saving retrofits of GSHP systems in large commercial buildings. Full article
(This article belongs to the Special Issue Energy Efficiency and Energy Saving in Buildings)
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28 pages, 6707 KB  
Article
Depth-Specific Prediction of Coastal Soil Salinization Using Multi-Source Environmental Data and an Optimized GWO–RF–XGBoost Ensemble Model
by Yuanbo Wang, Xiao Yang, Xingjun Lv, Wei He, Ming Shao, Hongmei Liu and Chao Jia
Remote Sens. 2025, 17(24), 4043; https://doi.org/10.3390/rs17244043 - 16 Dec 2025
Cited by 2 | Viewed by 1093
Abstract
Soil salinization is an escalating global concern threatening agricultural productivity and ecological sustainability, particularly in coastal regions where complex interactions among hydrological, climatic, and anthropogenic factors govern salt accumulation. The vertical differentiation and spatial heterogeneity of salinity drivers remain poorly resolved. We present [...] Read more.
Soil salinization is an escalating global concern threatening agricultural productivity and ecological sustainability, particularly in coastal regions where complex interactions among hydrological, climatic, and anthropogenic factors govern salt accumulation. The vertical differentiation and spatial heterogeneity of salinity drivers remain poorly resolved. We present an integrated modeling framework combining ensemble machine learning and spatial statistics to investigate the depth-specific dynamics of soil salinity in the Yellow River Delta, a vulnerable coastal agroecosystem. Using multi-source environmental predictors and 220 field samples harmonized to 30 m resolution, the hybrid Gray Wolf Optimizer–Random Forest–XGBoost model achieved high predictive accuracy for surface salinity (R2 = 0.91, RMSE = 0.03 g/kg, MAE = 0.02 g/kg). Spatial autocorrelation analysis (Global Moran’s I = 0.25, p < 0.01) revealed pronounced clustering of high-salinity hotspots associated with seawater intrusion pathways and capillary rise. The results reveal distinct vertical control mechanisms: vegetation indices and soil water content dominate surface salinity, while total dissolved solids (TDS), pH, and groundwater depth increasingly influence middle and deep layers. By applying SHAP (SHapley Additive Explanations), we quantified nonlinear feature contributions and ranked key predictors across layers, offering mechanistic insights beyond conventional correlation. Our findings highlight the importance of depth-specific monitoring and intervention strategies and demonstrate how explainable machine learning can bridge the gap between black-box prediction and process understanding. This framework offers a generalizable framework that can be adapted to other coastal agroecosystems with similar hydro-environmental conditions. Full article
(This article belongs to the Topic Water Management in the Age of Climate Change)
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25 pages, 1859 KB  
Review
Artificial Intelligence in Anaerobic Digestion: A Review of Sensors, Modeling Approaches, and Optimization Strategies
by Milena Marycz, Izabela Turowska, Szymon Glazik and Piotr Jasiński
Sensors 2025, 25(22), 6961; https://doi.org/10.3390/s25226961 - 14 Nov 2025
Cited by 12 | Viewed by 4133
Abstract
Anaerobic digestion (AD) is increasingly recognized as a key technology for renewable energy generation and sustainable waste management within the circular economy. However, its performance is highly sensitive to feedstock variability and environmental fluctuations, making stable operation and high methane yields difficult to [...] Read more.
Anaerobic digestion (AD) is increasingly recognized as a key technology for renewable energy generation and sustainable waste management within the circular economy. However, its performance is highly sensitive to feedstock variability and environmental fluctuations, making stable operation and high methane yields difficult to sustain. Conventional monitoring and control systems, based on limited sensors and mechanistic models, often fail to anticipate disturbances or optimize process performance. This review discusses recent progress in electrochemical, optical, spectroscopic, microbial, and hybrid sensors, highlighting their advantages and limitations in artificial intelligence (AI)-assisted monitoring. The role of soft sensors, data preprocessing, feature engineering, and explainable AI is emphasized to enable predictive and adaptive process control. Various machine learning (ML) techniques, including neural networks, support vector machines, ensemble methods, and hybrid gray-box models, are evaluated for yield forecasting, anomaly detection, and operational optimization. Persistent challenges include sensor fouling, calibration drift, and the lack of standardized open datasets. Emerging strategies such as digital twins, data augmentation, and automated optimization frameworks are proposed to address these issues. Future progress will rely on more robust sensors, shared datasets, and interpretable AI tools to achieve predictive, transparent, and efficient biogas production supporting the energy transition. Full article
(This article belongs to the Section Biosensors)
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24 pages, 6461 KB  
Article
An AI Hybrid Building Energy Benchmarking Framework Across Two Time Scales
by Yi Lu and Tian Li
Information 2025, 16(11), 964; https://doi.org/10.3390/info16110964 - 7 Nov 2025
Cited by 1 | Viewed by 1820
Abstract
Buildings account for approximately one-third of global energy usage and associated carbon emissions, making energy benchmarking a crucial tool for advancing decarbonization. Current benchmarking studies have often been limited to mainly the annual scale, relied heavily on simulation-based approaches, or employed regression methods [...] Read more.
Buildings account for approximately one-third of global energy usage and associated carbon emissions, making energy benchmarking a crucial tool for advancing decarbonization. Current benchmarking studies have often been limited to mainly the annual scale, relied heavily on simulation-based approaches, or employed regression methods that fail to capture the complexity of diverse building stock. These limitations hinder the interpretability, generalizability, and actionable value of existing models. This study introduces a hybrid AI framework for building energy benchmarking across two time scales—annual and monthly. The framework integrates supervised learning models, including white- and gray-box models, to predict annual and monthly energy consumption, combined with unsupervised learning through neural network-based Self-Organizing Maps (SOM), to classify heterogeneous building stocks. The supervised models provide interpretable and accurate predictions at both aggregated annual and fine-grained monthly levels. The model is trained using a six-year dataset from Washington, D.C., incorporating multiple building attributes and high-resolution weather data. Additionally, the generalizability and robustness have been validated via the real-world dataset from a different climate zone in Pittsburgh, PA. Followed by unsupervised learning models, the SOM clustering preserves topological relationships in high-dimensional data, enabling more nuanced classification compared to centroid-based methods. Results demonstrate that the hybrid approach significantly improves predictive accuracy compared to conventional regression methods, with the proposed model achieving over 80% R2 at the annual scale and robust performance across seasonal monthly predictions. White-box sensitivity highlights that building type and energy use patterns are the most influential variables, while the gray-box analysis using SHAP values further reveals that Energy Star® rating, Natural Gas (%), and Electricity Use (%) are the three most influential predictors, contributing mean SHAP values of 8.69, 8.46, and 6.47, respectively. SOM results reveal that categorized buildings within the same cluster often share similar energy-use patterns—underscoring the value of data-driven classification. The proposed hybrid framework provides policymakers, building managers, and designers with a scalable, transparent, and transferable tool for identifying energy-saving opportunities, prioritizing retrofit strategies, and accelerating progress toward net-zero carbon buildings. Full article
(This article belongs to the Special Issue Carbon Emissions Analysis by AI Techniques)
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23 pages, 2604 KB  
Article
Multi-Criteria Model Predictive Controller for Hybrid Heating Systems in Buildings
by Ali Soleimani, Paul Davidsson, Reza Malekian and Romina Spalazzese
Energies 2025, 18(21), 5839; https://doi.org/10.3390/en18215839 - 5 Nov 2025
Viewed by 1100
Abstract
With more hybrid heating systems available, there is a need to optimize energy use intelligently from the end-consumer perspective. This paper focuses on a multi-criteria heating system optimization to optimize cost, carbon emission, and comfort level of building occupants. A discrete Multi-Objective Model [...] Read more.
With more hybrid heating systems available, there is a need to optimize energy use intelligently from the end-consumer perspective. This paper focuses on a multi-criteria heating system optimization to optimize cost, carbon emission, and comfort level of building occupants. A discrete Multi-Objective Model Predictive Controller (MO-MPC) algorithm is proposed to optimally utilize two heating sources connected to a building, namely district heating (DH) and a building-integrated electrical heat pump (HP). The model is tested on a real-world building case simulated with a gray box building model. The results are compared to a conventional PID controller as well as the MPC scheme, each with a single heating input, and eight different cases are constructed to make this comparison more visible. The results indicate that, using MO-MPC, a cost saving of up to 10% and emission saving of up to 13% can be reached without additional thermal discomfort, while the potential savings on cost and emission with the hybrid system can be up to 25% and 77%, respectively. Further, a sensitivity analysis on price and emission parameters is conducted to investigate the changes in the provided solution. Full article
(This article belongs to the Special Issue Novel and Emerging Energy Systems)
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49 pages, 3594 KB  
Review
Model Predictive Control for Smart Buildings: Applications and Innovations in Energy Management
by Panagiotis Michailidis, Iakovos Michailidis, Federico Minelli, Hasan Huseyin Coban and Elias Kosmatopoulos
Buildings 2025, 15(18), 3298; https://doi.org/10.3390/buildings15183298 - 12 Sep 2025
Cited by 23 | Viewed by 9790
Abstract
The integration of advanced control strategies into building energy management systems (BEMS) is essential for achieving energy efficiency and sustaining thermal comfort. Model predictive control (MPC) has gained significant traction as a model-based approach capable of optimizing control actions by predicting future system [...] Read more.
The integration of advanced control strategies into building energy management systems (BEMS) is essential for achieving energy efficiency and sustaining thermal comfort. Model predictive control (MPC) has gained significant traction as a model-based approach capable of optimizing control actions by predicting future system behavior under dynamic conditions. The current review offers an in-depth analysis of MPC, combining its core theoretical foundations with a broad survey of impactful applications in buildings, for extracting key breakthroughs and trends that have defined the field over the past decade. Emphasis is placed on multiverse MPC configurations and their application across various BEMS frameworks integrating HVACs, energy storage, renewable energy, domestic hot water, electric vehicle charging, and lighting systems. A detailed evaluation of MPC key attributes is then conducted, based on essential aspects of MPC, such as algorithms, optimization solvers, baselines, performance indexes, and building types, as well as simulation tools that support system modeling and real-time validation. The study concludes by outlining key research trends and proposing future directions, with a strong emphasis on addressing real-world deployment challenges and advancing scalable, interoperable solutions on smart building ecosystems. According to the evaluation, MPC research is shifting from simple white-box setups to gray- and black-box models paired with metaheuristic or hybrid solvers, leveraging machine learning for forecasting and multi-objective optimization, but still lacking robustness, benchmarks, and real-world validation. Consequently, next-generation MPC is anticipated to evolve into adaptive, hybrid, and multi-agent frameworks that integrate forecasting and control, embed occupant behavior, enable grid-interactive flexibility, and support lightweight, explainable deployment in real building environments. Full article
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48 pages, 2344 KB  
Article
Neural Network and Hybrid Methods in Aircraft Modeling, Identification, and Control Problems
by Gaurav Dhiman, Andrew Yu. Tiumentsev and Yury V. Tiumentsev
Aerospace 2025, 12(1), 30; https://doi.org/10.3390/aerospace12010030 - 3 Jan 2025
Cited by 4 | Viewed by 2983
Abstract
Motion control of modern and advanced aircraft has to be provided under conditions of incomplete and inaccurate knowledge of their parameters and characteristics, possible flight modes, and environmental influences. In addition, various abnormal situations may occur during flight, in particular, equipment failures and [...] Read more.
Motion control of modern and advanced aircraft has to be provided under conditions of incomplete and inaccurate knowledge of their parameters and characteristics, possible flight modes, and environmental influences. In addition, various abnormal situations may occur during flight, in particular, equipment failures and structural damage. These circumstances cause the problem of a rapid adjustment of the used control laws so that the control system can adapt to the mentioned changes. However, most adaptive control schemes have a model of the control object, which plays a crucial role in adjusting the control law. That is, it is required to solve also the identification problem for dynamical systems. We propose an approach to solving the above-mentioned problems based on artificial neural networks (ANNs) and hybrid technologies. In the class of traditional neural network technologies, we use recurrent neural networks of the NARX type, which allow us to obtain black-box models for controlled dynamical systems. It is shown that in a number of cases, in particular, for control objects with complicated dynamic properties, this approach turns out to be inefficient. One of the possible alternatives to this approach, investigated in the paper, consists of the transition to hybrid neural network models of the gray box type. These are semi-empirical models that combine in the resulting network structure both empirical data on the behavior of an object and theoretical knowledge about its nature. They allow solving with high accuracy the problems inaccessible by the level of complexity for ANN models of the black-box type. However, the process of forming such models requires a very large consumption of computational resources. For this reason, the paper considers another variant of the hybrid ANN model. In it, the hybrid model consists not of the combination of empirical and theoretical elements, resulting in a recurrent network of a special kind, but of the combination of elements of feedforward networks and recurrent networks. Such a variant opens up the possibility of involving deep learning technology in the construction of motion models for controlled systems. As a result of this study, data were obtained that allow us to evaluate the effectiveness of two variants of hybrid neural networks, which can be used to solve problems of modeling, identification, and control of aircraft. The capabilities and limitations of these variants are demonstrated on several examples. Namely, on the example of the problem of aircraft longitudinal angular motion, the possibilities of modeling the motion using the NARX network as applied to a supersonic transport aircraft (SST) are first considered. It is shown that under complicated operating conditions this network does not always provide acceptable modeling accuracy. Further, the same problem, but applied to a maneuverable aircraft, as a more complex object of modeling and identification, is solved using both a NARX network (black box) and a semi-empirical model (gray box). The significant advantage of the gray box model over the black box one is shown. The capabilities of the hybrid model realizing deep learning technologies are demonstrated by forming a model of the control object (SST) and neurocontroller on the example of the MRAC adaptive control scheme. The efficiency of the obtained solution is illustrated by comparing the response of the control object with a failure situation (a decrease in the efficiency of longitudinal control by 50%) with and without adaptation. Full article
(This article belongs to the Section Aeronautics)
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17 pages, 2769 KB  
Article
Comparison of Different Approaches to Predict the Performance of Pumps As Turbines (PATs)
by Mauro Venturini, Stefano Alvisi, Silvio Simani and Lucrezia Manservigi
Energies 2018, 11(4), 1016; https://doi.org/10.3390/en11041016 - 21 Apr 2018
Cited by 16 | Viewed by 4791
Abstract
This paper deals with the comparison of different methods which can be used for the prediction of the performance curves of pumps as turbines (PATs). The considered approaches are four, i.e., one physics-based simulation model (“white box” model), two “gray box” models, which [...] Read more.
This paper deals with the comparison of different methods which can be used for the prediction of the performance curves of pumps as turbines (PATs). The considered approaches are four, i.e., one physics-based simulation model (“white box” model), two “gray box” models, which integrate theory on turbomachines with specific data correlations, and one “black box” model. More in detail, the modeling approaches are: (1) a physics-based simulation model developed by the same authors, which includes the equations for estimating head, power, and efficiency and uses loss coefficients and specific parameters; (2) a model developed by Derakhshan and Nourbakhsh, which first predicts the best efficiency point of a PAT and then reconstructs their complete characteristic curves by means of two ad hoc equations; (3) the prediction model developed by Singh and Nestmann, which predicts the complete turbine characteristics based on pump shape and size; (4) an Evolutionary Polynomial Regression model, which represents a data-driven hybrid scheme which can be used for identifying the explicit mathematical relationship between PAT and pump curves. All approaches are applied to literature data, relying on both pump and PAT performance curves of head, power, and efficiency over the entire range of operation. The experimental data were provided by Derakhshan and Nourbakhsh for four different turbomachines, working in both pump and PAT mode with specific speed values in the range 1.53–5.82. This paper provides a quantitative assessment of the predictions made by means of the considered approaches and also analyzes consistency from a physical point of view. Advantages and drawbacks of each method are also analyzed and discussed. Full article
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