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18 pages, 1332 KB  
Article
Optimization of Anthocyanin Extraction from Purple Sweet Potato Peel (Ipomea batata) Using Sonotrode Ultrasound-Assisted Extraction
by Raquel Lucas-González, Mirian Pateiro, Rubén Domínguez-Valencia, Celia Carrillo and José M. Lorenzo
Foods 2025, 14(15), 2686; https://doi.org/10.3390/foods14152686 - 30 Jul 2025
Viewed by 660
Abstract
Sweet potato is a valuable root due to its nutritional benefits, health-promoting properties, and technological applications. The peel, often discarded during food processing, can be employed in the food industry, supporting a circular economy. Purple sweet potato peel (PSPP) is rich in anthocyanins, [...] Read more.
Sweet potato is a valuable root due to its nutritional benefits, health-promoting properties, and technological applications. The peel, often discarded during food processing, can be employed in the food industry, supporting a circular economy. Purple sweet potato peel (PSPP) is rich in anthocyanins, which can be used as natural colourants and antioxidants. Optimising their extraction can enhance yield and reduce costs. The current work aimed to optimize anthocyanin and antioxidant recovery from PSPP using a Box-Behnken design and sonotrode ultrasound-assisted extraction (sonotrode-UAE). Three independent variables were analysed: extraction time (2–6 min), ethanol concentration (35–85%), and liquid-to-solid ratio (10–30 mL/g). The dependent variables included total monomeric anthocyanin content (TMAC), individual anthocyanins, and antioxidant activity. TMAC in 15 extracts ranged from 0.16 to 2.66 mg/g PSPP. Peonidin-3-caffeoyl-p-hydroxybenzoyl sophoroside-5-glucoside was the predominant anthocyanin. Among four antioxidant assays, Ferric-reducing antioxidant power (FRAP) showed the highest value. Ethanol concentration significantly influenced anthocyanin and antioxidant recovery (p < 0.05). The model demonstrated adequacy based on the coefficient of determination and variation. Optimal extraction conditions were 6 min with 60% ethanol at a 30 mL/g ratio. Predicted values were validated experimentally (coefficient of variation <10%). In conclusion, PSPP is a promising matrix for obtaining anthocyanin-rich extracts with antioxidant activity, offering potential applications in the food industry. Full article
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21 pages, 8395 KB  
Article
Deep Artificial Neural Network Modeling of the Ablation Performance of Ceramic Matrix Composites in the Hydrogen Torch Test
by Jayanta Bhusan Deb, Christopher Varela, Fahim Faysal, Yiting Wang, Chiranjit Maiti and Jihua Gou
J. Compos. Sci. 2025, 9(5), 239; https://doi.org/10.3390/jcs9050239 - 13 May 2025
Viewed by 919
Abstract
In recent years, there has been increasing interest in new materials such as ceramic matrix composites (CMCs) for power generation and aerospace propulsion applications through hydrogen combustion. This study employed a deep artificial neural network (DANN) model to predict the ablation performance of [...] Read more.
In recent years, there has been increasing interest in new materials such as ceramic matrix composites (CMCs) for power generation and aerospace propulsion applications through hydrogen combustion. This study employed a deep artificial neural network (DANN) model to predict the ablation performance of CMCs in the hydrogen torch test (HTT). The study was conducted in three phases to increase the accuracy of the model’s predictions. Initially, to predict the thermal behavior of ceramic composites, two linear machine learning models were used known as Lasso and Ridge regression. In the second step, four decision tree-based ensemble machine learning models, namely random forest, gradient boosting regression, extreme gradient boosting regression, and extra tree regression, were used to improve the prediction accuracy metrics, including root mean square error (RMSE), mean absolute error (MAE), correlation coefficient (R2 score), and mean absolute percentage error (MAPE), relative to the previously introduced linear models. Finally, to forecast the thermal stability of CMCs with time, an optimized DANN model with two hidden layers having rectified linear unit activation function was developed. The data collection procedure involved preparing CMCs with continuous Yttria-Stabilized Zirconia (YSZ) fibers and silicon carbide (SiC) matrix using a polymer infiltration and pyrolysis (PIP) technique. The samples were exposed to a hydrogen flame at a high heat flux of 183 W/cm2 for a duration of 10 min. A good agreement between the DANN model’s predictions and experimental data with an R2 score of 0.9671, RMSE of 16.45, an MAE of 14.07, and an MAPE of 3.92% confirmed the acceptability of the developed neural network model in this study. Full article
(This article belongs to the Special Issue Feature Papers in Journal of Composites Science in 2025)
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24 pages, 3493 KB  
Article
Research on the Root Cause Tracing Method of the Change in Access to Electricity Index Based on Data Mining
by Hongshan Luo, Xu Zhou, Weiqi Zheng and Yuling He
Energies 2025, 18(9), 2275; https://doi.org/10.3390/en18092275 - 29 Apr 2025
Viewed by 356
Abstract
Superior electricity-optimized business ecosystems (EOBEs) have evolved into pivotal determinants in catalyzing industrial–commercial prosperity. The access to electricity index (AEI) constitutes a valid instrument for assessing the EOBE. To realize the accurate evaluation of EOBE and the root cause tracing of its changes, [...] Read more.
Superior electricity-optimized business ecosystems (EOBEs) have evolved into pivotal determinants in catalyzing industrial–commercial prosperity. The access to electricity index (AEI) constitutes a valid instrument for assessing the EOBE. To realize the accurate evaluation of EOBE and the root cause tracing of its changes, this paper constructs a new analytical model for evaluating and monitoring changes in EOBE. First, this paper constructs a new evaluation model of EOBE based on the Business Ready (B-READY) evaluation system, considering three factors: the power regulatory quality, the public service level, and the enterprises’ gain power efficiency. Then, the model uses the raw data collected to calculate a score for AEI to enable an accurate assessment of EOBE. Next, this paper uses a priori assessment to extract the coupling features of indicators and combines the time series features and policy features to construct the feature matrix. Finally, the characteristic contribution was analyzed using support vector regression (SVR) and Shapley’s additive interpretation (SHAP) value. The experiment shows that the factors affecting the change in AEI are time series features, policy features, and coupling features in decreasing order of importance. This study provides reference cases and improvement ideas for the assessment and optimization of EOBE. Full article
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29 pages, 13513 KB  
Article
A Physical-Based Electro-Thermal Model for a Prismatic LFP Lithium-Ion Cell Thermal Analysis
by Alberto Broatch, Pablo Olmeda, Xandra Margot and Luca Agizza
Energies 2025, 18(5), 1281; https://doi.org/10.3390/en18051281 - 5 Mar 2025
Viewed by 1120
Abstract
This article presents an electro-thermal model of a prismatic lithium-ion cell, integrating physics-based models for capacity and resistance estimation. A 100 Ah prismatic cell with LFP-based chemistry was selected for analysis. A comprehensive experimental campaign was conducted to determine electrical parameters and assess [...] Read more.
This article presents an electro-thermal model of a prismatic lithium-ion cell, integrating physics-based models for capacity and resistance estimation. A 100 Ah prismatic cell with LFP-based chemistry was selected for analysis. A comprehensive experimental campaign was conducted to determine electrical parameters and assess their dependencies on temperature and C-rate. Capacity tests were conducted to characterize the cell’s capacity, while an OCV test was used to evaluate its open circuit voltage. Additionally, Hybrid Pulse Power Characterization tests were performed to determine the cell’s internal resistive-capacitive parameters. To describe the temperature dependence of the cell’s capacity, a physics-based Galushkin model is proposed. An Arrhenius model is used to represent the temperature dependence of resistances. The integration of physics-based models significantly reduces the required test matrix for model calibration, as temperature-dependent behavior is effectively predicted. The electrical response is represented using a first-order equivalent circuit model, while thermal behavior is described through a nodal network thermal model. Model validation was conducted under real driving emissions cycles at various temperatures, achieving a root mean square error below 1% in all cases. Furthermore, a comparative study of different cell cooling strategies is presented to identify the most effective approach for temperature control during ultra-fast charging. The results show that side cooling achieves a 36% lower temperature at the end of the charging process compared to base cooling. Full article
(This article belongs to the Section J: Thermal Management)
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13 pages, 3805 KB  
Article
Radiomics-Driven CBCT Texture Analysis as a Novel Biosensor for Quantifying Periapical Bone Healing: A Comparative Study of Intracanal Medications
by Diana Lorena Garcia Lopes, Sérgio Lúcio Pereira de Castro Lopes, Daniela Maria de Toledo Ungaro, Ana Paula Martins Gomes, Nicole Berton de Moura, Bianca Costa Gonçalves and Andre Luiz Ferreira Costa
Biosensors 2025, 15(2), 98; https://doi.org/10.3390/bios15020098 - 9 Feb 2025
Cited by 1 | Viewed by 3550
Abstract
This study aimed to evaluate the effectiveness of two intracanal medications in promoting periapical bone healing following endodontic treatment using radiomics-enabled texture analysis of cone-beam computed tomography (CBCT) images as a novel biosensing technique. By quantifying tissue changes through advanced image analysis, this [...] Read more.
This study aimed to evaluate the effectiveness of two intracanal medications in promoting periapical bone healing following endodontic treatment using radiomics-enabled texture analysis of cone-beam computed tomography (CBCT) images as a novel biosensing technique. By quantifying tissue changes through advanced image analysis, this approach seeks to enhance the monitoring and assessment of endodontic treatment outcomes. Thirty-four single-rooted teeth with pulp necrosis and periapical lesions were allocated to two groups (17 each): calcium hydroxide +2% chlorhexidine gel (CHX) and Ultracal XS®. CBCT scans were obtained immediately after treatment and three months later. Texture analysis performed using MaZda software extracted 11 parameters based on the gray level co-occurrence matrix (GLCM) across two inter-pixel distances and four directions. Statistical analysis revealed significant differences between medications for S [0,1] inverse difference moment (p = 0.043), S [0,2] difference of variance (p = 0.014), and S [0,2] difference of entropy (p = 0.004). CHX treatment resulted in a more organized bone tissue structure post-treatment, evidenced by reduced entropy and variance parameters, while Ultracal exhibited less homogeneity, indicative of fibrous or immature tissue formation. These findings demonstrate the superior efficacy of CHX in promoting bone healing and underscore the potential of texture analysis as a powerful tool for assessing CBCT images in endodontic research. Full article
(This article belongs to the Special Issue Biosensors for Biomedical Diagnostics)
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14 pages, 11343 KB  
Article
Study of the Shear Strength Model of Unsaturated Soil in the Benggang Area of Southern China
by Maojin Yang, Nanbo Cen, Zumei Wang, Bifei Huang, Jinshi Lin, Fangshi Jiang, Yanhe Huang and Yue Zhang
Water 2024, 16(23), 3528; https://doi.org/10.3390/w16233528 - 7 Dec 2024
Cited by 4 | Viewed by 1455
Abstract
Benggangs are a unique type of soil erosion commonly found in southern China, with the gully wall being the most dynamic component of the Benggang system and is crucial for assessing its overall progression. The unsaturated shear strength of soil in Benggang areas [...] Read more.
Benggangs are a unique type of soil erosion commonly found in southern China, with the gully wall being the most dynamic component of the Benggang system and is crucial for assessing its overall progression. The unsaturated shear strength of soil in Benggang areas is a key factor influencing the stability of the gully wall. However, quantitative analyses of the unsaturated shear strength in the gully walls of Benggangs remain limited. In this study, the soil–water characteristic curves (SWCC) and shear strengths of undisturbed soil samples from four different soil layers in the gully wall of Benggang were measured using a pressure membrane meter and a quadruple direct shear apparatus. The results revealed that the water holding capacity of the soil decreased gradually with increasing matrix suction, and the order of the water holding capacity was the sandy soil layer > transition layer > laterite layer > clastic layer. With an increasing soil water content (SWC), the shear strength, cohesion (c), and internal friction angle (φ) of the four soil layers decreased significantly, and the φ showed a power function decreasing curve (p < 0.05), whereas c in the laterite layer and transition layer exhibited a power function decreasing curve (p < 0.01). The c of the sandy soil layer and clastic layer decreased linearly and logarithmically (p < 0.01) with increasing SWC, respectively. The unsaturated shear strength model for the four soil layers was developed based on the Vanapalli model. The root mean square error (RMSE) of the simulated and measured values was less than 29.349, while the Nash–Sutcliffe efficiency (NSE) and R2 values were greater than 0.638 and 0.788, respectively. The model can be used to analyze and predict the unsaturated shear strength in different layers of Benggang gully walls, providing a theoretical foundation for studying the erosion mechanisms of Benggangs. Full article
(This article belongs to the Section Soil and Water)
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26 pages, 406 KB  
Article
On Matrices of Generalized Octonions (Cayley Numbers)
by Seda Yamaç Akbıyık
Symmetry 2024, 16(12), 1567; https://doi.org/10.3390/sym16121567 - 22 Nov 2024
Viewed by 903
Abstract
This article focuses on generalized octonions which include real octonions, split octonions, semi octonions, split semi octonions, quasi octonions, split quasi octonions and para octonions in special cases. We make a classification according to the inner product and vector parts and give the [...] Read more.
This article focuses on generalized octonions which include real octonions, split octonions, semi octonions, split semi octonions, quasi octonions, split quasi octonions and para octonions in special cases. We make a classification according to the inner product and vector parts and give the polar forms for lightlike generalized octonions. Furthermore, the matrix representations of the generalized octonions are given and some properties of these representations are achieved. Also, powers and roots of the matrix representations are presented. All calculations in the article are achieved by using MATLAB R2023a and these codes are presented with an illustrative example. Full article
(This article belongs to the Special Issue Symmetry in Geometric Mechanics and Mathematical Physics)
17 pages, 4352 KB  
Article
Dynamical Embedding of Single-Channel Electroencephalogram for Artifact Subspace Reconstruction
by Doli Hazarika, K. N. Vishnu, Ramdas Ransing and Cota Navin Gupta
Sensors 2024, 24(20), 6734; https://doi.org/10.3390/s24206734 - 19 Oct 2024
Viewed by 2432
Abstract
This study introduces a novel framework to apply the artifact subspace reconstruction (ASR) algorithm on single-channel electroencephalogram (EEG) data. ASR is known for its ability to remove artifacts like eye-blinks and movement but traditionally relies on multiple channels. Embedded ASR (E-ASR) addresses this [...] Read more.
This study introduces a novel framework to apply the artifact subspace reconstruction (ASR) algorithm on single-channel electroencephalogram (EEG) data. ASR is known for its ability to remove artifacts like eye-blinks and movement but traditionally relies on multiple channels. Embedded ASR (E-ASR) addresses this by incorporating a dynamical embedding approach. In this method, an embedded matrix is created from single-channel EEG data using delay vectors, followed by ASR application and reconstruction of the cleaned signal. Data from four subjects with eyes open were collected using Fp1 and Fp2 electrodes via the CameraEEG android app. The E-ASR algorithm was evaluated using metrics like relative root mean square error (RRMSE), correlation coefficient (CC), and average power ratio. The number of eye-blinks with and without the E-ASR approach was also estimated. E-ASR achieved an RRMSE of 43.87% and had a CC of 0.91 on semi-simulated data and effectively reduced artifacts in real EEG data, with eye-blink counts validated against ground truth video data. This framework shows potential for smartphone-based EEG applications in natural environments with minimal electrodes. Full article
(This article belongs to the Special Issue EEG Signal Processing Techniques and Applications—2nd Edition)
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19 pages, 691 KB  
Article
A Bayesian Approach for Modeling and Forecasting Solar Photovoltaic Power Generation
by Mariana Villela Flesch, Carlos Alberto de Bragança Pereira and Erlandson Ferreira Saraiva
Entropy 2024, 26(10), 824; https://doi.org/10.3390/e26100824 - 27 Sep 2024
Cited by 2 | Viewed by 1500
Abstract
In this paper, we propose a Bayesian approach to estimate the curve of a function f(·) that models the solar power generated at k moments per day for n days and to forecast the curve for the [...] Read more.
In this paper, we propose a Bayesian approach to estimate the curve of a function f(·) that models the solar power generated at k moments per day for n days and to forecast the curve for the (n+1)th day by using the history of recorded values. We assume that f(·) is an unknown function and adopt a Bayesian model with a Gaussian-process prior on the vector of values f(t)=f(1),, f(k). An advantage of this approach is that we may estimate the curves of f(·) and fn+1(·) as “smooth functions” obtained by interpolating between the points generated from a k-variate normal distribution with appropriate mean vector and covariance matrix. Since the joint posterior distribution for the parameters of interest does not have a known mathematical form, we describe how to implement a Gibbs sampling algorithm to obtain estimates for the parameters. The good performance of the proposed approach is illustrated using two simulation studies and an application to a real dataset. As performance measures, we calculate the absolute percentage error, the mean absolute percentage error (MAPE), and the root-mean-square error (RMSE). In all simulated cases and in the application to real-world data, the MAPE and RMSE values were all near 0, indicating the very good performance of the proposed approach. Full article
(This article belongs to the Special Issue Bayesianism)
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19 pages, 4664 KB  
Article
A Biomechanical Study of Potential Plants for Erosion Control and Slope Stabilization of Highland in Thailand
by Warakorn Mairaing, Apiniti Jotisankasa, Nisa Leksungnoen, Monir Hossain, Chatchai Ngernsaengsaruay, Prem Rangsiwanichpong, Jarunee Pilumwong, Sony Pramusandi, Surat Semmad and Abu Noman Faruq Ahmmed
Sustainability 2024, 16(15), 6374; https://doi.org/10.3390/su16156374 - 25 Jul 2024
Cited by 3 | Viewed by 2969
Abstract
Soil bioengineering provides a sustainable method for erosion control and soil slope stabilization using vegetation with multiple co-benefits. This study evaluated ten plant species in Thailand’s highland regions for their soil bioengineering potential and additional benefits. Root architecture, tensile strength, and Young’s modulus [...] Read more.
Soil bioengineering provides a sustainable method for erosion control and soil slope stabilization using vegetation with multiple co-benefits. This study evaluated ten plant species in Thailand’s highland regions for their soil bioengineering potential and additional benefits. Root architecture, tensile strength, and Young’s modulus were measured to compare biomechanical traits. G. sepium, F. griffithii, P. americana, B. asiatica, and C. arabica exhibited H-type roots with wide lateral spread, while M. denticulata and C. officinarum had VH-type roots with deep taproots and wide lateral extent. A. sutepensis showed M-type roots with most root matrix in the top 0.3 m, where C. cajan and C. sinensis had R-type roots with deep, oblique growth. Most species showed a negative power relationship between the root strength and Young’s modulus with the root diameter except C. cajan that showed a positive correlation. P. americana, F. griffithii, C. officinarum, and C. arabica showed relatively high values of 1 mm root tensile strength (exceeding 24 to 42 MPa), while M. denticulata, G. sepium, and B. asiatica exhibited intermediate root tensile strength (ranging from 8 to 19 MPa). A. sutepensis, C. cajan, and C. sinensis demonstrated the lowest root tensile strength, up to 7 MPa. It is advised to plan slope vegetation by selecting diverse plant species with varying root structures and benefits, addressing both engineering and socioeconomic needs of the sustainable nature-based solution. Full article
(This article belongs to the Topic Nature-Based Solutions-2nd Edition)
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12 pages, 2828 KB  
Article
Multidimensional Quality Characteristics of Sichuan South-Road Dark Tea and Its Chemical Prediction
by Yao Zou, Xian Li and Deyang Han
Agronomy 2024, 14(7), 1582; https://doi.org/10.3390/agronomy14071582 - 20 Jul 2024
Cited by 2 | Viewed by 1455
Abstract
The distinctive quality of Sichuan south-road dark tea (SSDT) is gradually disappearing with processing innovation. Here, near-infrared (NIR) spectroscopy (NIRS) and spectrofluorometric techniques were utilized to determine the spectral characteristics of dried SSDT and its brew, respectively. Combined with chemical analysis, the multidimensional [...] Read more.
The distinctive quality of Sichuan south-road dark tea (SSDT) is gradually disappearing with processing innovation. Here, near-infrared (NIR) spectroscopy (NIRS) and spectrofluorometric techniques were utilized to determine the spectral characteristics of dried SSDT and its brew, respectively. Combined with chemical analysis, the multidimensional quality characteristics of SSDT will be presented. Finally, the NIR spectral fingerprint of dried SSDT was observed, with Kangzhuan (KZ) and Jinjian (JJ) showing a very similar NIR spectrum. The SiPLS models effectively predicted the levels of theabrownin, caffeine, and epigallocatechin gallate, based on the NIR spectrum, with root-mean-square errors of calibration of 0.15, 0.12, and 0.02 for each chemical compound, root-mean-square errors of prediction of 0.20, 0.09, and 0.03, and both corrected and predicted correlation coefficients greater than 0.90. Meanwhile, the fluorescence characteristics of the SSDT brew were identified based on the parallel factor analysis for the fluorescence excitation–emission matrix (EEM). The KZ and JJ brews could be classified with 100% accuracy using extreme-gradient-boosting discriminant analysis. The integration of NIRS and fluorometric EEM seems to be a powerful technique for characterizing SSDTs, and the results can greatly benefit the production and quality control of SSDTs. Full article
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21 pages, 3465 KB  
Article
Total Least Squares Estimation in Hedonic House Price Models
by Wenxi Zhan, Yu Hu, Wenxian Zeng, Xing Fang, Xionghua Kang and Dawei Li
ISPRS Int. J. Geo-Inf. 2024, 13(5), 159; https://doi.org/10.3390/ijgi13050159 - 8 May 2024
Cited by 5 | Viewed by 2421
Abstract
In real estate valuation using the Hedonic Price Model (HPM) estimated via Ordinary Least Squares (OLS) regression, subjectivity and measurement errors in the independent variables violate the Gauss–Markov theorem assumption of a non-random coefficient matrix, leading to biased parameter estimates and incorrect precision [...] Read more.
In real estate valuation using the Hedonic Price Model (HPM) estimated via Ordinary Least Squares (OLS) regression, subjectivity and measurement errors in the independent variables violate the Gauss–Markov theorem assumption of a non-random coefficient matrix, leading to biased parameter estimates and incorrect precision assessments. In this contribution, the Errors-in-Variables model equipped with Total Least Squares (TLS) estimation is proposed to address these issues. It fully considers random errors in both dependent and independent variables. An iterative algorithm is provided, and posterior accuracy estimates are provided to validate its effectiveness. Monte Carlo simulations demonstrate that TLS provides more accurate solutions than OLS, significantly improving the root mean square error by over 70%. Empirical experiments on datasets from Boston and Wuhan further confirm the superior performance of TLS, which consistently yields a higher coefficient of determination and a lower posterior variance factor, which shows its more substantial explanatory power for the data. Moreover, TLS shows comparable or slightly superior performance in terms of prediction accuracy. These results make it a compelling and practical method to enhance the HPM. Full article
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18 pages, 3783 KB  
Article
Forest Canopy Height Estimation by Integrating Structural Equation Modeling and Multiple Weighted Regression
by Hongbo Zhu, Bing Zhang, Weidong Song, Qinghua Xie, Xinyue Chang and Ruishan Zhao
Forests 2024, 15(2), 369; https://doi.org/10.3390/f15020369 - 16 Feb 2024
Cited by 3 | Viewed by 2098
Abstract
As an important component of forest parameters, forest canopy height is of great significance to the study of forest carbon stocks and carbon cycle status. There is an increasing interest in obtaining large-scale forest canopy height quickly and accurately. Therefore, many studies have [...] Read more.
As an important component of forest parameters, forest canopy height is of great significance to the study of forest carbon stocks and carbon cycle status. There is an increasing interest in obtaining large-scale forest canopy height quickly and accurately. Therefore, many studies have aimed to address this issue by proposing machine learning models that accurately invert forest canopy height. However, most of the these approaches feature PolSAR observations from a data-driven viewpoint in the feature selection part of the machine learning model, without taking into account the intrinsic mechanisms of PolSAR polarization observation variables. In this work, we evaluated the correlations between eight polarization observation variables, namely, T11, T22, T33, total backscattered power (SPAN), radar vegetation index (RVI), the surface scattering component (Ps), dihedral angle scattering component (Pd), and body scattering component (Pv) of Freeman-Durden three-component decomposition, and the height of the forest canopy. On this basis, a weighted inversion method for determining forest canopy height under the view of structural equation modeling was proposed. In this study, the direct and indirect contributions of the above eight polarization observation variables to the forest canopy height inversion task were estimated based on structural equation modeling. Among them, the indirect contributions were generated by the interactions between the variables and ultimately had an impact on the forest canopy height inversion. In this study, the covariance matrix between polarization variables and forest canopy height was calculated based on structural equation modeling, the weights of the variables were calculated by combining with the Mahalanobis distance, and the weighted inversion of forest canopy height was carried out using PSO-SVR. In this study, some experiments were carried out using three Gaofen-3 satellite (GF-3) images and ICESat-2 forest canopy height data for some forest areas of Gaofeng Ridge, Baisha Lizu Autonomous County, Hainan Province, China. The results showed that T11, T33, and total backscattered power (SPAN) are highly correlated with forest canopy height. In addition, this study showed that determining the weights of different polarization observation variables contributes positively to the accurate estimation of forest canopy height. The forest canopy height-weighted inversion method proposed in this paper was shown to be superior to the multiple regression model, with a 26% improvement in r and a 0.88 m reduction in the root-mean-square error (RMSE). Full article
(This article belongs to the Section Forest Inventory, Modeling and Remote Sensing)
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15 pages, 303 KB  
Article
Solving the Matrix Exponential Function for Special Orthogonal Groups SO(n) up to n = 9 and the Exceptional Lie Group G2
by Norbert Kaiser
Mathematics 2024, 12(1), 97; https://doi.org/10.3390/math12010097 - 27 Dec 2023
Viewed by 1414
Abstract
In this work the matrix exponential function is solved analytically for the special orthogonal groups SO(n) up to n=9. The number of occurring k-th matrix powers gets limited to [...] Read more.
In this work the matrix exponential function is solved analytically for the special orthogonal groups SO(n) up to n=9. The number of occurring k-th matrix powers gets limited to 0kn1 by exploiting the Cayley–Hamilton relation. The corresponding expansion coefficients can be expressed as cosine and sine functions of a vector-norm V and the roots of a polynomial equation that depends on a few specific invariants. Besides the well-known case of SO(3), a quadratic equation needs to be solved for n=4,5, a cubic equation for n=6,7, and a quartic equation for n=8,9. As an interesting subgroup of SO(7), the exceptional Lie group G2 of dimension 14 is constructed via the matrix exponential function through a remarkably simple constraint on an invariant, ξ=1. The traces of the SO(n)-matrices arising from the exponential function are sums of cosines of several angles. This feature confirms that the employed method is equivalent to exponentiation after diagonalization, but avoids complex eigenvalues and eigenvectors and operates only with real-valued quantities. Full article
(This article belongs to the Section A: Algebra and Logic)
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20 pages, 2302 KB  
Article
Personalized E-Learning Recommender System Based on Autoencoders
by Lamyae El Youbi El Idrissi, Ismail Akharraz and Abdelaziz Ahaitouf
Appl. Syst. Innov. 2023, 6(6), 102; https://doi.org/10.3390/asi6060102 - 27 Oct 2023
Cited by 18 | Viewed by 6482
Abstract
Through the Internet, learners can access available information on e-learning platforms to facilitate their studies or to acquire new skills. However, finding the right information for their specific needs among the numerous available choices is a tedious task due to information overload. Recommender [...] Read more.
Through the Internet, learners can access available information on e-learning platforms to facilitate their studies or to acquire new skills. However, finding the right information for their specific needs among the numerous available choices is a tedious task due to information overload. Recommender systems are a good solution to personalize e-learning by proposing useful and relevant information adapted to each learner using a set of techniques and algorithms. Collaborative filtering (CF) is one of the techniques widely used in such systems. However, the high dimensions and sparsity of the data are major problems. Since the concept of deep learning has grown in popularity, various studies have emerged to improve this form of filtering. In this work, we used an autoencoder, which is a powerful model in data dimension reduction, feature extraction and data reconstruction, to learn and predict student preferences in an e-learning recommendation system based on collaborative filtering. Experimental results obtained using the database created by Kulkarni et al. show that this model is more accurate and outperforms models based on K-nearest neighbor (KNN), singular value decomposition (SVD), singular value decomposition plus plus (SVD++) and non-negative matrix factorization (NMF) in terms of the root-mean-square error (RMSE) and mean absolute error (MAE). Full article
(This article belongs to the Special Issue Advancements in Deep Learning and Its Applications)
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