esa-sceva/satcom-chunk-collection huggingface dataset:
# A Decentralized Multi-Agent-Based Approach for Low Voltage Microgrid Restoration
## 3 Modeling of the Microgrid Components
### Converter Modeling  
There are two kinds of control mode for operating the converters: (1) grid-forming mode and (2) grid-following mode [41]. The grid-forming converters emulate the behavior of a synchronous generator and provide the voltage and frequency references for the MG. The grid-forming converter acts as a voltage source and controls its output voltage and frequency using the droop control. When the MG works in the islanded mode, at least one converter must operate as a grid-forming converter.  
DGs must meet two requirements to have the black start capability: (i) equipped with storage devices (batteries or super-capacitors) in the DC link of their inverter and (ii) operation of their inverter in the grid-forming control mode. These DGs are capable of restarting without any external power source, energize the network, supply a part of loads, and provide remote cranking power for the other DGs with the grid-following inverter control system [42]. Figure 2 shows the control structure of a droop-based grid-forming converter.  
The grid-following converters are mainly designed to deliver a pre-determined power to an energized grid. If there is no synchronous generator or grid-forming converter in the MG, the grid-following converter cannot operate. Figure 3 shows the control structure of a grid-following converter [43].
# One-Dimensional Consolidation of Multi-Layered Unsaturated Soil with Impeded Drainage Boundaries
## 2 Problem Description  
### Governing Equations  
Without a loss of generality, as schematically in Figure 1, we consider a 1D consolidation system that consists of several contiguous unsaturated soil layers. Each soil layer is indexed with \(i\) (\(i=1,2,\ldots,n\)) and its thickness is \(h_{i}\). Both the top surface and bottom base are treated as impeded drainage to the air and water phases. Assume that a time-dependent loading \(q(t)\) is uniformly acted on the top of the top soil layer. The flows and the soil settlement are assumed to only occur along the vertical direction. In each soil layer, the coefficient of air permeability and that of water permeability are denoted as \(k_{\text{a}}^{(i)}\) and \(k_{\text{w}}^{(i)}\), respectively. This study adopted all the basic assumptions of 1D consolidation theory for unsaturated soil [1,10], and employed the well known governing equations of [PERSON] and [PERSON] [10] to characterize the 1D consolidation process of each soil layer, that is:  
\[\mathbf{C}^{(i)}\mathbf{u}_{J}^{(i)}+\mathbf{K}^{(i)}\mathbf{u}_{,zz}^{(i)}= \mathbf{Q}_{J}^{(i)} \tag{1}\]  
where:  
\[\mathbf{u}^{(i)}=\left\{\begin{array}{c}u_{\text{a}}^{(i)}\\ u_{\text{w}}^{(i)}\end{array}\right\}\text{,}\quad\mathbf{C}^{(i)}=\left[ \begin{array}{cc}1&\mathbf{C}_{\text{a}}^{(i)}\\ C_{\text{a}}^{(i)}&\mathbf{C}_{\text{a}}^{(i)}/\mathbf{C}_{\text{w}}^{(i)} \end{array}\right]\text{,} \tag{2}\]  
where the superscript \((i)\) denotes the \(i\)th soil layer; \(u_{\text{a}}^{(i)}\) and \(u_{\text{w}}^{(i)}\) are the excess pore-air and pore-water pressures; \(C_{\text{a}}^{(i)}\) and \(C_{\text{w}}^{(i)}\) are two interactive constants related to the air and water phases; \(c_{\text{v}}^{\text{a}(i)}\) and \(  
suction, respectively; \(m_{1}^{a(i)}\) and \(m_{2}^{a(i)}\) are the coefficients of air volume change stemming from a variation in the net normal stress and that stemming from a variation in the matric suction, respectively; \(n_{0}^{(i)}\) and \(S_{r}^{(i)}\) are the soil porosity and the degree of saturation; \(\overline{u}_{\rm a}^{(i)}=u_{\rm a0}^{(i)}+u_{\rm atm}\) and \(u_{\rm atm}\) is the atmospheric pressure; g is the acceleration of gravity; \(R\) is the universal gas constant; \(T\) is the absolute temperature; M is the molecular mass of air; and \(\gamma_{\rm w}\) is the unit weight of water.
## 5 Sensitivity Analysis with Respect to Measurement Errors
### Sensitivity of the LoS Angle with Respect to Phase Measurement Errors  
By definition, the sensitivity of the LoS angles, with respect to the baseline \(R\), is as follows:  
Figure 7: Relative error of the LoS angle with respect to a baseline range of d = 0.95 m and \(1\) m, respectively, and an absolute measurement error \(\varepsilon_{R}\) of \(1\) mm and \(10\) mm, respectively.  
\[S_{\Delta\varphi}^{\alpha}=\frac{\Delta\varphi}{\alpha}\frac{d\alpha}{d\Delta \varphi}=\frac{\Delta\varphi}{\alpha}\arccos^{\prime}\bigg{(}\frac{\lambda\Delta \varphi}{d}-\frac{\lambda^{2}\Delta\varphi^{2}}{2 dR}+\frac{d}{2R}\bigg{)}. \tag{14}\]  
The impact of the range measurement error on the LoS angle is expressed as follows:  
\[\frac{\varepsilon_{\alpha}}{\alpha}S_{\Delta\varphi}^{\alpha}=\frac{ \varepsilon_{\Delta\varphi}}{\Delta\varphi} \tag{15}\]  
As seen in Equation (15), a phase difference measurement error will inherently result in an error in the LoS angle. Sources of phase difference measurement may be caused by the antenna placement (due to restrictions, the antennas are not placed at the indicated distance of 1 m) and the phase difference measurements resolution (in this case a 0.01 rad/s resolution was suggested). In Figure 8 the relative error of the LoS angle with respect to the range is depicted for the next situations: the baseline is \(d\) = 0.95 m and 1 m, respectively, and absolute measurement error of the phase difference is pi/20 rad and pi/50 rad, respectively. A shorter baseline will result in smaller LoS angle errors for large phase differences; for small phase differences the LoS angle errors are negligible.
# A Combined Elevation Angle and C/N0 Weighting Method for GNSS PPP on Xiaomi MI8 Smartphones
## 4 Experimental Results and Discussion  
In this section, the quad-constellation GPS/GLONASS/BDS/Galileo PPP processing strategy is provided in detail. Then, two kinematic smartphone-based GNSS PPP experiments are conducted to evaluate the combined elevation angle and C/N0 weighting method with comparisons to the conventional elevation-angle-only and C/N0-only weighting methods.
## 5 Experimental Results and Evaluation
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Dynamic Activities**} & \multicolumn{2}{c}{**Support Vector Machine**} & \multicolumn{2}{c}{**Genetic Algorithm**} & \multicolumn{2}{c}{**Decision Tree**} \\ \hline Activities & Precision & Recall & F-measure & Precision & Recall & F-measure & Precision & Recall & F-measure \\ \hline WLK & 0.867 & 0.907 & 0.886 & 0.858 & 0.891 & 0.874 & 0.918 & 0.960 & 0.938 \\ CLS & 0.968 & 0.873 & 0.918 & 0.836 & 0.876 & 0.855 & 0.953 & 0.925 & 0.939 \\ STS & 0.882 & 0.977 & 0.927 & 0.818 & 0.858 & 0.837 & 0.933 & 0.985 & 0.958 \\ STR & 0.874 & 0.834 & 0.853 & 0.932 & 0.892 & 0.911 & 0.905 & 0.955 & 0.929 \\ WBF & 0.843 & 0.884 & 0.863 & 0.912 & 0.872 & 0.891 & 0.949 & 0.935 & 0.942 \\ CYC & 0.890 & 0.931 & 0.910 & 0.956 & 0.816 & 0.880 & 0.963 & 0.930 & 0.946 \\ JOG & 0.876 & 0.836 & 0.855 & 0.857 & 0.814 & 0.834 & 0.928 & 0.970 & 0.948 \\ RUN & 0.962 & 0.933 & 0.947 & 0.909 & 0.869 & 0.888 & 0.965 & 0.965 & 0.965 \\ JFB & 0.877 & 0.846 & 0.861 & 0.806 & 0.848 & 0.826 & 0.919 & 0.975 & 0.946 \\ KNB & 0.947 & 0.987 & 0.966 & 0.965 & 0.925 & 0.944 & 0.966 & 0.860 & 0.910 \\ FEA & 0.855 & 0.894 & 0.874 & 0.879 & 0.839 & 0.858 & 0.936 & 0.888 & 0.911 \\ LYD & 0.943 & 0.911 & 0.926 & 0.952 & 0.915 & 0.933 & 0.954 & 0.935 & 0.944 \\ \hline \multicolumn{1}{c}{WLK = Walking, CLS = Climbing stairs, STS = Standing still, STR = Sitting & Faking, WBF = Waist bend forward, CYC = Cycling, JOG = Jogging, RUN = Running, JFB = Jump front \& back, KNB = Knees bending, FEA = Frontal} & & & \\ \multicolumn{1}{c}{YTC = Cycling, JOG = Jogging, RUN = Running, JFB = Jump front \& back, KNB = Knees bending, FEA = Frontal} & & & & \\ \end{tabular}
\end{table} 
Table 2: The classification results of three classifiers on the MHEALTH dataset. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Dynamic Activities**} & \multicolumn{2}{c}{**Support Vector Machine**} & \multicolumn{2}{c}{**Genetic Algorithm**} & \multicolumn{2}{c}{**Decision Tree**} \\ \hline Activities & Precision & Recall & F-measure & Precision & Recall & F-measure & Precision & Recall & F-measure \\ \hline STU & 0.907 & 0.900 & 0.903 & 0.906 & 0.913 & 0.909 & 0.945 & 0.955 & 0.950 \\ WLK & 0.921 & 0.928 & 0.924 & 0.911 & 0.904 & 0.907 & 0.970 & 0.970 & 0.970 \\ CLP & 0.917 & 0.910 & 0.913 & 0.919 & 0.912 & 0.915 & 0.980 & 0.985 & 0.982 \\ BOX & 0.912 & 0.905 & 0.908 & 0.916 & 0.923 & 0.919 & 0.989 & 0.945 & 0.966 \\ RUN & 0.915 & 0.922 & 0.918 & 0.908 & 0.902 & 0.904 & 0.970 & 0.990 & 0.980 \\ STD & 0.913 & 0.906 & 0.909 & 0.921 & 0.914 & 0.917 & 0.955 & 0.965 & 0.960 \\ \hline \multicolumn{1}{c}{STU = Standing Up, WLK = Walking, CLP = Clapping, BOX = Boxing, RUN = Running, STD = Sitting Down.} & & & & & \\ \end{tabular}
\end{table} 
Table 3: The classification results of three classifiers on the IM-AccGyro dataset.
## 4 Case Study
### Calculate combined weights
#### 4.2.3 Comprehensive Evaluation
Judging by the weights of each metric in Table 10, the main factors that affect the performance of intelligent lubrication systems are the working environment temperature, lubricant viscosity, failure rate, lubricant replacement cycle, and equipment load. High temperatures can lead to \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name of the Indicator** & \(\mathbf{N_{1}}\) & \(\mathbf{N_{2}}\) & \(\mathbf{N_{3}}\) & **Evaluation Rating of Indicators** \\ \hline Equipment load & \(-0.5500\) & \(-0.0100\) & \(0.1000\) & excellent \\ Operating temperature & \(-0.4500\) & \(0.0100\) & \(-0.0833\) & good \\ Viscosity of the lubricant & \(-0.6500\) & \(-0.3000\) & \(0.3000\) & excellent \\ Anti-wear properties of lubricants & \(-0.9000\) & \(-0.8000\) & \(0.2000\) & excellent \\ Thickness of oil film & \(-0.5000\) & \(0\) & \(0\) & good \\ Failure rate & \(-0.1500\) & \(0.3000\) & \(-0.2917\) & good \\ MTBF & \(0.0125\) & \(-0.0455\) & \(-0.3437\) & pass \\ MTTR & \(0\) & \(0\) & \(-0.3333\) & pass \\ Lubricant replacement intervals & \(-0.0500\) & \(0.1000\) & \(-0.3214\) & good \\ Lubricant consumption & \(-0.9500\) & \(-0.9000\) & \(0.1000\) & excellent \\ Electricity consumption & \(-0.5000\) & \(0\) & \(0\) & good \\ Selection of friction sub-materials & \(-0.2500\) & \(0.5000\) & \(-0.2500\) & good \\ Selection of lubricants & \(0.0125\) & \(-0.0455\) & \(-0.3437\) & pass \\ Payback period & \(-0.7000\) & \(-0.4000\) & \(0.4000\) & excellent \\ Profitability & \(-0.3500\) & \(0.3000\) & \(-0.1875\) & good \\ Comprehensive correlation & \(-0.3819\) & \(-0.0460\) & \(-0.0801\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Correlation of each evaluation indicator with each level. increased wear due to the high lubricant viscosity. Too low or too high lubricant viscosity can affect the normal operation of the machine. In addition, the failure rate and length of the lubricant replacement cycle will also directly impact the service life and maintenance costs of intelligent lubrication systems. Therefore, when designing and applying an intelligent lubrication system, special attention should be paid to the impact of these factors on system performance. For example, grease sensors with higher sensitivity can be used to better monitor the grease state and reduce the impact of high or low lubricant viscosity on mechanical devices. The use of high-precision measurement devices for real-time monitoring and recording of wear and tear, in order to detect and respond to problems in a timely manner, allows the maintenance of components to be extended from passive to predictive maintenance. When choosing a lubricant, it is necessary to take into account the working environment of the construction machinery, the lubrication components and the mechanical maintenance cycle, so as to ensure the regular operation of the lubrication system of the construction machinery, extend the life of the machinery, and increase the efficiency of the work.
# A New Method for Evaluating the Bearing Capacity of the Bridge Pile Socketed in the Soft Rock
## 2 Research Methodology
### Fitting of the Pile Bearing Capacity Coefficient  
To obtain the bearing capacity coefficient \(\lambda\), a multiple linear regression analysis was used, and the influence of a comprehensive coefficient \(k\) with six control variables was considered. With the coefficient \(\lambda\) as the dependent variable and the length of pile \(L\), the diameter of pile \(D\), the embedded rock elastic modulus \(E_{b}\), the elastic modulus of surrounding rock \(E_{s}\), the rock socketed depth \(h\), and the pier elastic modulus \(E_{p}\) as independent variables, the mathematical regression model of the bearing capacity coefficient is obtained:  
\[\lambda=\frac{R_{a}}{K_{\text{vs}}}=k\bigg{[}c_{1}Af_{rk,b}+uc_{2}hf_{rk,b}+ \frac{1}{2}c_{s}u(L-h)d_{sk}\bigg{]}\bigg{(}\frac{L}{EA}+\frac{1}{C_{0}A}\bigg{)} \tag{29}\]  
\[k=a_{0}L^{a_{1}}D^{a_{2}}E_{b}^{a_{3}}E_{s}^{a_{4}}h_{0}{}^{a_{5}}E_{p}^{a_{6}} \tag{30}\]  
where \(a_{0}\sim a_{6}\) are the pending parameters, \(f_{rk,b}\) is the saturated uniaxial compressive strength of the bearing stratum at the pile end, \(q_{sk}\) is the lateral resistance of strongly weathered rock, and k is a comprehensive coefficient that can comprehensively reflect the influence of each variable on the bearing capacity and the constraint stiffness.  
The numerical model with 120 sample data of the above six impact factors was established. With Formula (29) used as the calculation model, a multiple nonlinear regression was carried out. A loss function was used to minimize the sum of squared residuals, and the parameter was obtained by each iteration substituted into the loss function. When the sum of squared residuals is less than \(1\times 10^{-8}\) the iteration is terminated. After 190 iterations, the optimal solution is obtained, and the prediction regression model is:  
\[\lambda=k\bigg{[}c_{1}Af_{rk,b}+uc_{2}hf_{rk,b}+\frac{1}{2}c_{s}u(L-h)q_{sk} \bigg{]}\bigg{(}\frac{L}{EA}+\frac{1}{C_{0}A}\bigg{)} \tag{31}\]  
\[k=2866.669L^{-0.507}D^{0.237}E_{b}^{-0.704}E_{s}^{-0.009}h^{-0.267}E_{p}^{0.4 99} \tag{32}\]  
The fitting results of all the sample data were evaluated with the coefficient of determination \(R^{2}\). The closer the coefficient is to 1, the better the fitting effect is. After calculation, the fit degree was 0.997, which shows that the model can explain 99.7% of the variation, and the fitting degree is accurate.
## 4 Materials and Methods
### Transcriptome Analysis  
Leaf samples of WT and _OsVTC1-1_ RI1-2 line were collected at 0 and 24 hpi and labelled as W0, W24, RI1-2_0, and RI1-2_24, respectively. Total RNA was extracted using the GF-1 Total RNA extraction kit (Vivantis, Shah Alam, Malaysia) according to the manufacturer'sinstructions. Pair-end sequencing using Illumina Novaseq 6000 platform (Illumina, San Diego, CA, USA) was conducted by Novogene Bioinformatics Technology Co., Ltd., Beijing, China. For data analysis, the RNA-seq data was performed as previously described [35] using apps in the CyVerse Discovery Environment (DE) [57]. The sequences were mapped using IRGSP-1.0 as the reference genome sequence. DEGs were identified using adjusted \(p\)-value < 0.05 and \(|\)log2 FC \(|>\) 1 as cutoff criterion. The Rice Annotation Project Database (RAP-DB, [[http://rapdb.dna.affrc.go.jp/](http://rapdb.dna.affrc.go.jp/)]([http://rapdb.dna.affrc.go.jp/](http://rapdb.dna.affrc.go.jp/))) was used to find gene descriptions for DEGs (accessed on 11 June 2022) [58; 59]. DEGs with up- and down-regulated genes at 0 and 24 h after rice blast inoculation between WT and _OsVTC1-1_ RI1-2 line were compared. A Venn diagram was constructed using Venny version 2.1.0. ([[https://bioinfogp.cnb.csic.es/tools/venny/index.html](https://bioinfogp.cnb.csic.es/tools/venny/index.html)]([https://bioinfogp.cnb.csic.es/tools/venny/index.html](https://bioinfogp.cnb.csic.es/tools/venny/index.html)), accessed on 8 June 2022). Gene ontology (GO, [[http://geneontology.org/](http://geneontology.org/)]([http://geneontology.org/](http://geneontology.org/))) enrichment analysis was performed to classify the function of DEGs (accessed on 11 June 2022) [60; 61; 62]. Pathway analysis was analyzed using plant reactome database ([[http://plantreactome.gramene.org/](http://plantreactome.gramene.org/)]([http://plantreactome.gramene.org/](http://plantreactome.gramene.org/)), accessed on 11 June 2022) [63]. A heatmap of up-regulated DEGs and correlation between three biological replicates was generated based on the fragments per kilobase of transcript per million mapped reads (FPKM) values transformed by log10 (FPKM+1) using GraphPad Prism version 9.0.0 for Windows (San Diego, CA, USA). Principal component analysis (PCA) was carried out with factoextra package in RStudio [64] using a log10 transformation of (FPKM+1) values to compare similarity between three biological replicates.
## 3 Proposal of Ground Station Direction Detection Method Using Color Markers
### Color Marker Detection Algorithm
#### 3.1.2. Predicting the Marker Position in an Image  
As shown in Figure 3, the camera position at a distance of position \(T:\left(T_{x},T_{y,r},T_{z_{s}}\right)^{T}\) from the origin \(\mathrm{O_{s}}\) of the space-fixed coordinate system \(\mathrm{O_{s}}-\mathrm{X_{s}Y_{s}Z_{s}}\) is set as the origin \(\mathrm{O_{c}}\). Define a camera coordinate system \(\mathrm{O_{c}}-\mathrm{X_{c}Y_{c}Z_{c}}\) that is rotated by the camera attitude angle \((\psi,\theta,\phi)\) and is expressed by using Euler angles in this spatial coordinate system. When multiple color markers are expressed in the camera coordinate system, the coordinate points of the markers on the image plane are deformed in the expansion, rotation, and  
Figure 2: Process to detect RCM.  
translation directions. We compute each point of these deformed marker coordinates. The initial coordinates \(M_{c,i}(x_{i},y_{i})\) of each marker i are determined by Equations (4) and (5).  
\[M_{c,i}=\begin{pmatrix}x_{c,i}\\ y_{c,i}\\ z_{c,i}\end{pmatrix}=R\times(M_{s,i}-T) \tag{4}\]  
where R is the rotation matrix obtained from the camera attitude angle \((\psi,\theta,\phi)\). The marker coordinates in the camera coordinate system obtained from Equation (4) can be projected to the 2-D image plane by the perspective projection transformation in Equation (5).  
\[s_{i}\begin{pmatrix}x_{i}\\ y_{i}\\ 1\end{pmatrix}=\begin{pmatrix}f_{x}&0&c_{x}\\ 0&f_{y}&c_{y}\\ 0&0&1\end{pmatrix}\begin{pmatrix}x_{c,i}\\ y_{c,i}\\ z_{c,i}\end{pmatrix}=K\times M_{c,i} \tag{5}\]  
The matrix K in Equation (5) represents the camera internal matrix, \(f_{x}\), \(f_{y}\) are the camera focal lengths, and \(c_{x}\), \(c_{y}\) are the image center coordinates. The coordinates \((x_{i},\ y_{i})\) in Equation (5) are \(M_{i}(x_{i},y_{i})\), the i-th marker coordinates predicted in the image plane.
## 4 Salinity Origin and Its Impacts on Plants
### Seed Germination  
Plants exhibit great variability toward salinity resistance [55; 56]. Many seeds, including those of _L. cossonianuum_, present their highest germination rate in distillated water and are extremely sensitive to salinity [57; 58]. Salinity delays the germination process in a process that is dependent on abiotic and biotic factors such as light, temperature [59; 60], and plant microbiome [61]. Overall, salt stress adversely influenced seed germination; both osmotically via decreased water absorption or ionically via the accumulation of Cl\({}^{-}\) and Na\({}^{+}\) causing toxicity impact and an imbalance in nutrient uptake [61]. It affects the sowing increase of plants by less or slow mobilization of preserve foods, suspending the division of cells, injuring and enlarging hypocotyls [62]. For instance, germination percentage in Lettuce (_Lactuca sativa_) showed substantial reduction with cumulative salinity up to 14.1 dS m\({}^{-1}\) NaCl. The essential time for germination likewise increased with increasing salinity levels. The seedling growth was meaningfully repressed [63]. Furthermore, the study conducted by [PERSON] et al. [64], showed that salinity influenced seed germination of different wheat and barley cultivars. Although, all cultivars showed a reduction in total germination percentage, with increasing salinity levels from EC 0 to EC 20 dS m\({}^{-1}\). Wheat cultivars outperformed barley cultivars at EC levels 0, 4, 8, 12, and 16 dS m\({}^{-1}\).
# Fast Screening Algorithm for Satellites Based on Multi-Constellation System
## 3 Fast Satellite Screening Algorithm Based on Multi-Threshold Optimization
### Fast Satellite Selection Algorithm Based on Spatial Zoning
The above satellite selection strategy takes into account both high- and low-elevation-angle satellites and achieves the basic unchanged spatial configuration of the original satellites. The selection of satellites with high-elevation-angles can supplement the altitude direction positioning information, and the selection of satellites with low-elevation-angles can supplement the horizontal plane direction information. The strategy flowchart of the algorithm is shown in Figure 1.  
Figure 1: Flowchart of star selection algorithm.
## 5 Conclusions  
This study investigated various combinations of deep learning (DL) models, sEMG features, and muscle selections to identify effective intrasubject models for estimating ankle moments during natural walking. The best-performing models and features were then transferred to train intersubject models. To mitigate overfitting and reduce computational costs, the models were trained with a limited number of parameters.  
It was found that signal energy features were sufficient for intrasubject ankle moment estimation. However, frequency-based features (such as zero crossing count), predictive models, and signal differentiation posed challenges for small models due to the difficulty in learning such features. The top-performing sEMG and DEMG models utilized all the proposed muscles introduced in this study.  
Finally, this study offers valuable insights into feature selection, muscle selection, and model architecture for intersubject DL models in ankle moment estimation. The proposed RCNN model, which employed waveform length (WL) features from all four shank muscles, demonstrated significant potential for practical applications, with only 757 parameters.  
Conceptualization, A.E.A.A., D.O. and M.H.; methodology, A.E.A.A.; software, A.E.A.A.; validation, A.E.A.A., D.O. and M.H.; formal analysis, A.E.A.A.; investigation, A.E.A.A.; resources, A.E.A.A. and M.H.; data curation, M.H.; writing--original draft preparation, A.E.A.A.; writing--review and editing, D.O. and M.H.; visualization, A.E.A.A.; supervision, M.H.; project administration, M.H.; funding acquisition, M.H. All authors have read and agreed to the published version of the manuscript.  
This work was supported by JSPS KAKENHI Grant Number JP24K00841.  
The study was conducted in accordance with the Declaration of Helsinki, and approved by the ethical committee of Tohoku University (protocol code 22A-3).  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.  
Data Availability Statement: Data can be downloaded from 16 August 2024 on [[https://drive.google.com/drive/folders/1g4-s1](https://drive.google.com/drive/folders/1g4-s1) zmAk3 aFg4 ilhfw60 EnuLbNIdT6Z]([https://drive.google.com/drive/folders/1g4-s1](https://drive.google.com/drive/folders/1g4-s1) zmAk3 aFg4 ilhfw60 EnuLbNIdT6Z).  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
Autoregressive model AR  
Biceps femoris BF  
Convolutional neural network CNN  
Deep learning DL  
Differentiated electromyography DEMG  
Extensor digitorum longus EDL  
Flexor hallucis longus FHL  
Gastrocnemius lateral GL  
Gastrocnemius medialis GM  
Inertial measurement unit IMU  
Inverse Dynamic ID  
Long short-term memory LSTM  
Machine learning ML  
Mean absolute value  
Mean squared error MSE  
Multi-layer perception MLP  
Neuromusculoskeletal NM  
Normalized root square error NRMSE  
Ordinary differential equations ODE  
Peroneus brevis