esa-sceva/satcom-chunk-collection huggingface dataset:
## Appendix A
\begin{array}{l}B_{21}=\Pr\left(\gamma_{SD1,k*}^{PDMA}\geq \varepsilon_{1}\right)=\Pr\left(\left|g_{1,k}\right|^{2}\geq\frac{\varepsilon_ {1}\omega\rho\left|f_{1}\right|^{2}+\varepsilon_{1}}{\alpha_{1}\rho-\varepsilon _{1}\alpha_{2}\rho}\right)\\ =\frac{1}{\lambda_{f_{1}}}\int_{0}^{\infty}\sum\limits_{k=1}^{K}\left( \begin{array}{c}K\\ k\end{array}\right)(-1)^{k-1}\exp\left(-\frac{(\varepsilon_{1}\omega\rho x+ \varepsilon_{1})k}{(\alpha_{1}\rho-\varepsilon_{1}\alpha_{2}\rho)\lambda_{1}} -\frac{x}{\lambda_{f_{1}}}\right)dx\\ =\sum\limits_{k=1}^{K}\left(\begin{array}{c}K\\ k\end{array}\right)(-1)^{k-1}\theta_{1}.\end{array} \] (A6)  
Then, \(B_{22}\) is calculated as  
\[ \begin{array}{l}B_{22}=\Pr\left(\chi_{D1}^{PDMA}\geq\varepsilon_{1}\right)= \Pr\left(\left|h_{1}\right|^{2}\geq\frac{\varepsilon_{1}\omega\rho\left|f_{1 }\right|^{2}+\varepsilon_{1}}{\rho}\right)\\ =\int_{0}^{\infty}\exp\left(-\frac{\varepsilon_{1}\omega\rho x+ \varepsilon_{1}}{\rho\lambda_{h_{1}}}\right)\frac{1}{\lambda_{f_{1}}}\exp \left(-\frac{x}{\lambda_{f_{1}}}\right)dx\\ =\frac{1}{\lambda_{f_{1}}}\exp\left(-\frac{\varepsilon_{1}}{\rho \lambda_{h_{1}}}\right)\int_{0}^{\infty}\exp\left(-\left(\frac{\varepsilon_{1} \omega\rho}{\rho\lambda_{h_{1}}}+\frac{1}{\lambda_{f_{1}}}\right)x\right)dx \\ =\frac{\rho\lambda_{h_{1}}}{\rho\lambda_{h_{1}}+\varepsilon_{1}\omega\rho \lambda_{f_{1}}}\exp\left(-\frac{\varepsilon_{1}}{\rho\lambda_{h_{1}}}\right). \end{array} \] (A7)  
Similarly, \(B_{23}\) is calculated as  
\[ \begin{array}{l}B_{23}=\Pr\left(\gamma_{SD1\gets 2,k*}^{PDMA}> \varepsilon_{1}\right)=\Pr\left(\left|g_{2,k}\right|^{2}>\frac{\varepsilon_{1 }\omega\rho\left|f_{1}\right|^{2}+\varepsilon_{1}}{\alpha_{1}\rho-\varepsilon _{1}\alpha_{2}\rho}\right)\\ =\frac{1}{\lambda_{f_{2}}}\int_{0}^{\infty}\sum\limits_{k=1}^{K}\left( \begin{array}{c}K\\ k\end{array}\right)(-1)^{k-1}\exp\left(-\frac{(\varepsilon_{1}\omega\rho y+ \varepsilon_{1})k}{(\alpha_{1}\rho-\varepsilon_{1}\alpha_{2}\rho)\lambda_{2} }-\frac{y}{\lambda_{f_{2}}}\right)dy\\ =\sum\limits_{k=1}^{K}\left(\begin{array}{c}K\\ k\end{array}\right)(-1)^{k-1}\theta_{2}.\end{array} \] (A8)From (A6), (A7) and (A8) we find the expression \(B_{2}\) to be  
\[ \begin{split}& B_{2}=\left(1-\sum\limits_{k=1}^{K}\left(\begin{array} []{c}K\\ k\end{array}\right)(-1)^{k-1}\vartheta_{1}\right)\\ &\\ &\times\left(1-\frac{\rho\lambda_{h_{1}}}{\rho\lambda_{h_{1}}+\varepsilon_{1 }\varpi\rho\lambda_{f_{1}}}\exp\left(-\frac{\varepsilon_{1}}{\rho\lambda_{h_ {1}}}\right)\right)\sum\limits_{k=1}^{K}\left(\begin{array}{c}K\\ k\end{array}\right)(-1)^{k-1}\vartheta_{2}.\end{split} \] (A9)  
This completes the proof of Proposition 1.
## 2 Materials and Methods
### Response Surface Methodology
#### 2.2.2 Selection of the Response Model  
Two regression adjustment models of the experimental data will be made, both polynomials, specifically first and second degree. The selection of the definitive model on which the work will be done, will be performed on the basis of the following criteria: its capacity to predict the response within the domain of the levels of the factors and especially adhering to the absence of multicollinearity. Multicollinearity is a problem that occurs when the explicative variables of the model are correlated among themselves. This gives rise to a reduction in the precision of the estimation of the coefficients of the terms of the factors, in addition to the possibility of concealing their statistical significance. An added difficulty for detecting the multi-collinearity is that it does not affect the goodness of the adjustment of the model. By means of the statistic variance inflation factor (VIF), the multicollinearity is studied. This index quantifies the severity of multicollinearity in an ordinary least squares regression analysis, since it measures how much the variance of an estimated regression coefficient is increased because of multicollinearity. It is calculated as:  
\[\text{VIF}(\hat{\beta}_{j})=\frac{1}{1-R_{j}^{2}} \tag{3}\]  
where \(\hat{\beta}_{j}\) is the value for the coefficient \(\beta_{j}\) estimated by the model and \(R_{j}^{2}\) is its determination coefficient. If multicollinearity is severe, the variance of the determination coefficients is increased, which indicates that such coefficients are unstable, which in turn gives rise to false statistical factors' significances and erroneous values/signs of their coefficients. It is commonly accepted that if VIF > 5, then the multicollinearity is high [64; 65].  
Thus, VIF \(\leq\) 5 was adopted as a limit for selecting the adjustment model, which is representative of a moderately low presence of multicollinearity, thereby deeming it very low or absent if VIF \(\simeq\) 1 [64].
## 2 Theoretical Background
### Stochastic FIR Filter  
To reduce the hardware cost of the FIR filter, a bipolar format SFIR filter is proposed in [6], where input signals and coefficients are normalized into the range [\(-1\),\(1\)] and transformed into bit streams. As a result, the multiplication and addition involved in the FIR filter are mapped into \"XNOR\" logic and multiplexer, respectively. The bipolar-based SFIR filter has an extremely low hardware costs. However, the main drawback is the degradation of accuracy.  
To overcome the accuracy degradation problem, a two-line scheme-based SFIR filter is proposed in [2], where each numerical value is represented with two stochastic bit streams: one is sign bit-stream and the other is magnitude bit-stream. The multiplication of two magnitude bit-streams and sign bit-streams are mapped into \"AND\" logic and \"XOR\" logic, respectively. The addition is implemented with a novel non-scaled two-line adder. The two-line scheme outperforms the bipolar scheme on accuracy with comparable hardware cost. However, there is still a relatively large gap with the ideal performance.
## 4 Trajectory Prediction Model Based on AIS Data and ACDE-SVM
### Results Analysis  
#### 4.3.1 Verification of De-Noising Effect  
To verify the de-noising effect, trajectory sequences with and without de-noising were used for trajectory prediction according to the above prediction steps and the errors were compared. The results are summarized in Table 4.
## 2 Results  
### Feedback-Resistant MvaK1  
MvaK1 is responsible for the first step of the lower MVA pathway by converting MVA to mexolonate phosphate (MVA 5-P in Figure 1) [10] and is important for the regulation of the entire MVA pathway because it is inhibited by known feedback inhibitors: C5 (IPP and DMAPP), C15 (geranyl pyrophosphate (GPP) and FPP), and longer chain terpenoids [13; 14]. FPP is a feedback inhibitor of the widely used _Staphylococcus aureus_ MvaK1 (_SaMvaK1_) for creating a heterologous MVA pathway [15]. Previously, we have also used _Sa_MvaK1 to produce (\(-\))-\(\alpha\)-bisabolol in engineered _E. coli_[16].  
To avoid feedback inhibition of MvaK1 and subsequently improve (\(-\))-\(\alpha\)-bisabolol production, we replaced the _S. aureus mvk1_ gene of the pTSN-Bisa-Sa plasmid with a feedback-resistant _mvaK1_ gene (Figure S1) from the versatile methanogen _M. mazei_, which resulted in a pTSN-Bisa-Mm plasmid. The _E. coli_ DH5\(\alpha\)-pTSN-Bisa-Mm strain produced 555 mg/L of (\(-\))-\(\alpha\)-bisabolol, which is 1.7-fold higher than that of the _E. coli_ DH5\(\alpha\)-pTSN-Bisa-Sa strain (Figure 2B). This is consistent with MVA accumulation of _MmM_vaxK1 showing 1.7-fold less than that of _Sa_MvaK1 (Figure 2B, right panel), suggesting that the feedback-resistant _MmM_MvaK1 leads to an increase the MVA utilization efficiency.  
Using the _E. coli_ DH5\(\alpha\)-pTSN-Bisa-Mm strain, we conducted a fed-batch fermentation by intermittently supplying glycerol (Figure 2C). Cells were grown exponentially for 24 h and produced 0.9 g/L of (\(-\))-\(\alpha\)-bisabolol and 4.9 g/L of MVA along with consuming initially supplied glycerol. A total of 8.2 g/L of (\(-\))-\(\alpha\)-bisabolol was yielded with a productivity of 0.06 g/L h, and 10.7 g/L of MVA was accumulated in 140 h. Overall, although feedback-resistant _Mm_MvaK1 was used for (\(-\))-\(\alpha\)-bisabolol production, a significant amount of MVA was still accumulated in the fed-batch fermentation.
## 5 Results and Experimental Discussion  
In this section, we present the results of our experimental evaluation conducted on the seven models introduced in the previous sections. As depicted in Table 3, these models include the two base models of BERT and RoBERTa, pre-trained in English (denoted as _BERT-base_ and _RoBERTa-base_, respectively), as well as their multilingual versions (_BERT-multilingual_ and _RoBERTa-multilingual_). Additionally, we consider the three models specifically pre-trained on extensive collections of texts in Spanish: _BETO_, _RoBERTa-BERTIN_, and _RoBERTa-BNE_. Notice that we have reserved 20% of the data from our dataset of 57,231 news articles for testing, employing a 5-fold cross-validation approach on the remaining 80%.  
Given the significant advantages demonstrated by DL models, particularly Transformer-based models, in capturing complex patterns and long-range dependencies within data, we chose to focus on DL methods rather than revisiting traditional ML approaches [18; 19; 20]. As highlighted in Section 2, ML models depend on manual feature engineering, which can miss complex patterns and deeper context, and often assume linear relationships, limiting their ability to capture intricate data interactions. In contrast, DL models automatically learn both simple and complex features from raw data, making them more effective for large and varied datasets. In this regard, studies conducted in various languages, such as English [23], Greek [44], and Bengali [45], consistently demonstrate the effectiveness of BERT models and their variants for fake news detection. These studies underline the ability of Transformer-based models to capture subtle language patterns and rich contextual information, leading to superior performance over traditional models in text classification tasks. By utilizing self-attention mechanisms, these models are able to understand complex relationships between words, making them particularly suited for identifying misinformation. Given these findings, we have chosen to focus our experiments on fine-tuned BERT and RoBERTa models, as these Transformer architectures have shown to be highly effective in addressing the challenges specific to this domain.  
We present our results as follows: firstly, we compare the performance of fine-tuned BERT and RoBERTa models during training (Section 5.1) and on unseen data (Section 5.2). Additionally, beyond testing on 20% synthetic Spanish political fake news, we experimented with a smaller, independent dataset of manually curated real and non-synthetic fake news (Section 5.2.1). This aimed to assess the models' ability to detect authentic political fake news in Spanish, expanding beyond the synthetic dataset used for fine-tuning. Finally, in Section 5.2.2, we benchmark our approach against related methods in general text classification and specific fake news detection across multiple languages.
## 4 Method
### EIT Inverse Model
#### 4.1.1 Improved Levenberg-Marquardt Method
Graph convolutions, specifically designed for graph data, offer similar advantages as regular CNNs, such as translation variation, localization, and shared weights. We employ the ILM algorithm to optimize the objective function (7). When the regularization is not explicitly incorporated into the objective function, Equation (8) illustrates the Taylor expansion of the quadratic term of \(Reg\). \[F(\sigma_{0}+\phi\sigma)=F(\sigma)+F^{\prime}(\sigma)(\phi\sigma)+\frac{1}{2} F^{\prime\prime}(\sigma)(\phi\sigma)^{2} \tag{15}\]  
We can find the minimum value by setting the \(\phi\sigma\) gradient to 0. We then obtain the updated equation  
\[\phi\sigma=-F^{\prime\prime}(\sigma)^{-1}F^{\prime}(\sigma) \tag{16}\]  
Figure 4: Iterations for each parameter value obtained by running the three algorithms simultaneously once. (**a**) Number of iterations for each algorithm. (**b**) Average computation times for each algorithm. The gradient and Hessian matrix of the objective function \(F\) are denoted by \(F^{\prime}(\sigma)\) and \(F^{\prime\prime}(\sigma)\), respectively. It is defined as \(Reg(\sigma)=0\) when the following two equations hold. \[F^{\prime}(\sigma)=J(\sigma)^{T}(\Lambda(\sigma)-\mathbf{V_{meas}}) \tag{17}\] \[F^{\prime\prime}(\sigma)=J(\sigma)^{T}J(\sigma)+\sum_{i}\Lambda ^{\prime\prime}_{i}(\sigma)(\Lambda_{i}(\sigma)-V_{i}) \tag{18}\]  
The Jacobian matrix of the analog voltage \(\Lambda(\sigma)\) is denoted by \(J(\sigma)\). The Hessian matrix is computed precisely by the Newton technique as Equation (12). However, because of its significant processing cost, the second component in the GN method--which involves calculating the second derivative \(\Lambda^{\prime\prime}_{i}(\sigma)\)--is disregarded. Rather than using this term, the LM algorithm substitutes it with a scaled identity matrix \(\lambda_{\text{ILM}}I\), where the regularization term for ill-posed problems is \(\lambda_{\text{ILM}}\in\mathcal{R}^{+}\). In cases where the rank of the Jacobian matrix is inadequate, this regularization helps increase the condition number of the matrix, which can be found in Equation (16). This method is able to determine the approximate answer to Equation (7). \[\delta\sigma_{ILM}=-\Big{(}J(\sigma)^{T}J(\sigma)+\lambda_{ILM}I\Big{)}^{-1}J (\sigma)^{T}(\lambda(\sigma)-\mathbf{V_{meas}}) \tag{19}\]  
The ILM optimization method obtains an iterative reconstruction algorithm by the update rule (16) and an appropriate stopping criterion.
## 4 Theoretical Analysis and Field Distribution
### Analysis of the Field Distribution and Verifications  
According to the parameters of the signal generator, the stimulation voltage is set at 680 A, and the pulsed current frequency is set at 13 kHz. A comparison between the measurements and the numerical calculations of the magnetic flux density is shown in Figure 8. During the experiment, the measurement coil was placed on a measurement platform with the scale line.  
The calculated maximum magnetic flux density at the target nerve location (8 cm beyond the coil plane) was 26.1 mT, and the measured magnetic flux density by the measurement coil was 27.2 mT. The experimental results showed that the measured values agreed well with the calculated results from the simulations as illustrated in Figure 9.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Conductivity** & **Permititivity** & **Permeability** & **Depth** \\  & **(S/m)** & **(F/m)** & **(H/m)** & **(mm)** \\ \hline Skin & 0.465 & \(1.2\times 10^{4}\) & 1 & 3 \\ Skull & 0.01 & \(0.8\times 10^{4}\) & 1 & 10 \\ Cerebrospinal & 1.654 & \(0.6\times 10^{4}\) & 1 & 2 \\ Fluid & 0.126 & \(1.2\times 10^{4}\) & 1 & 30 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Electromagnetic properties of the human head model.  
Figure 8: Structures of the human head with multilayers.
# A Distributed Approach to the Evasion Problem
## 2 Materials and Methods
### Distributing the Algorithm
#### 2.2.8 Routing Protocol  
In a distributed algorithm, messages are required to be exchanged among Delaunay neighbors which are possibly laying out of communication ranges of the sensors. In this case, the message needs to be routed through the network. As discussed in [18], the GPSR protocol [19] is able to route the message given location information of the sensors. It is also particularly useful to compute the Voronoi diagram distributively. Since location information of sensors is available in our system, we are adopting the same approach into our protocol. To apply the GPSR protocol, a planar communication graph is used. Since the sensor coverage graph \(\mathcal{A}\) is planar, this graph can be used--otherwise the Relative Neighbor Graph [20] is a common choice. A message will first attempt to be delivered to the neighbor closest to the destination. If no such neighbor exists, there is a \"void\" region in the communication graph that needs to be circumnavigated. The GPSR protocol specifies to forward the message to the first neighbor in \(\mathcal{A}\) in counterclockwise order, adopting a right-hand rule.
# Crop Yield Prediction Based on Agrometeorological Indexes and Remote Sensing Data
## 4 Results
### Comparision of Two Variable Selection Methods  
The modeling variables selected by the two variable selection methods were obviously different. In Jilin Province, the number of input variables of models 1 to 4 were 24, 24, 8, and 7, respectively. In Liaoning Province, the number of input variables of models 1 to 4 were 16, 17, 8, and 7, respectively. The difference in the input variables were caused the accuracy differences among the different yield estimation models built by the random forest method. In general, the second method had the highest modeling accuracy and used the least input variables. A possible reason is that the second method reduced the correlation between the selected variables, thus reducing information redundancy. There was a strong correlation between input variables (Figure 9). The first methods did not consider correlations between the input variables. Therefore, the selected variables were redundant to some extent. For example, the correlation coefficient between EDD7 and SPI2-7 is -0.5410, which is significant at the 0.01 level. Both were selected by method 1 and used as the input variables of Model 1 and Model 2 in Jilin Province (Table 2). In the second method, we used a two-stage variable selection method. In the first stage, 31 candidate independent variables were divided into four groups (temperature group, SPI group, GPPa group, and NDVIa group), and then the variables constituting the top 50% importance from each group were selected. In addition, GPPa and NDVIa were often highly correlated, and the selected GPPa and NDVIa variables were used in different models (Yield Model 3 and 4). The above processing reduced the number of selected variables and the correlations among them.  
Figure 8: The modeling accuracy in three severe disaster years in Jilin (**a**) and Liaoning (**b**) Provinces.  
Figure 7: Area of cultivated land suffering agricultural disasters in Jilin (**a**) and Liaoning (**b**) Provinces.
## 5 Conclusions  
In this research, a bridge vibration reduction technology was proposed using a joint simulation method and energy harvesting. The main results are as follows:  
1. Through the theoretical analysis, the calculation formulas of the electromotive force, output power and maximum electromagnetic damping force of the energy acquisition circuit were obtained.
2. By programming MATLAB, based on the study of the composition of the energy acquisition circuit, the corresponding array energy acquisition circuit was designed according to the structure of the array coil permanent magnet. By calculating the instantaneous power of the energy collection of the design circuit, the average instantaneous power collected by the design method was 1.093 \(\times\) 10\({}^{-9}\) W.
3. The initial vibration signal of the target node was obtained through analysis. The vibration signals of the node before and after the electromagnetic damping were obtained through a joint simulation. The acceleration signal energies before and after energy harvesting were calculated to be 3.1048 \(\times\) 10\({}^{8}\) and 3.1044 \(\times\) 10\({}^{8}\), and the reduction rate of the vibration energy before and after the node was 0.01%. The velocity signal energies before and after energy harvesting were 5.9724 \(\times\) 10\({}^{2}\) and 5.9750 \(\times\) 10\({}^{2}\), and the reduction rate of the vibration energy before and after the node was 0.02%.  
Based on the array coil permanent magnet structure and the energy acquisition circuit, the system realized the distributed bridge vibration energy acquisition. At the same time, by adjusting the load of the circuit, it has the function of vibration control in different degrees,  
Figure 21: Speed comparison.  
Figure 20: Acceleration comparison.  
which provides a new idea for vibration reduction research and the energy collection of civil structures such as bridges.  
Conceptualization, H.Y.; formal analysis, Q.C.; funding acquisition, P.L. and L.W.; project administration, H.Y.; resources, H.L.; supervision, L.W.; validation, S.-H.Y.; writing--original draft, H.Y. and H.C.; writing--review and editing, H.Y., H.C., S.-H.Y. and P.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Fundamental Research Funds of the Central Universities, China (No. FRF-TP-18-048A1) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)-SFB/TRR 339, Project-ID 453596084.  
Not applicable.  
The authors would like to express their thanks to everyone who offered help in the experiments and in the creation of the paper. A special thanks to [PERSON] and [PERSON] for their help in the process of revising the manuscript.  
The authors declare no conflict of interest.
## 5 Conclusions  
A fault diagnosis method, which was based on the BA of the stator current analytical signal envelope, is proposed in our paper. The proposed method is verified on the scraper conveyor reducer model HB-kpl-75. The main conclusions are as follows:  
1. The interference of fundamental frequency and impact signal in the current will seriously weaken the gear fault characteristics. The proposed current preprocessing method, which is based on the WPMD and HT, is used to enhance the fault characteristics. When the current signal is decomposed in five layers, the best extraction of the fault frequency band can be achieved, and the  
Figure 25: Current spectrum under the different load conditions: (**a**) the 90A peak current; (**b**) the 128A peak current; (**c**) the 166A peak current; (**d**) the 204A peak current; (**e**) the 242A peak current; and (**f**) the 280A peak current.  
effect of eliminating the impact interference is optimal. The extracted best fault frequency band is processed by HT, thus the fundamental frequency of the current can be suppressed.
2. The fault characteristic frequency of the gear is extracted successfully by BA, and the quantitative analysis of the fault under time-varying load conditions is realized with BE. With the increase in the load, the BE is 10.84, 14.71, 10.65, 10.49, 10.35 and 10.15, respectively. Obviously, the BE decreases with the increase in the load. The decrease in the BE indirectly reflects that the fault signal in the current is more intense with the increase in the load.  
Conceptualization, S.Z.; formal analysis, P.W.; methodology, S.Z. and P.W.; project administration, S.Z.; resources, S.Z. and S.L.; software, P.W.; supervision, S.L.; validation, P.W.; writing--original draft, P.W.; writing--review and editing, P.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National key Research and Development Program (Project NO.2017 YFC0804310) and Shaanxi Provincial Key Research and Development Program (Project NO.S2020-YF-ZDCXL-ZDLGY-0295) and Shaanxi province special project of technological innovation guidance (fund) (Program No.2019 QYPYP-055) and Key Research and development plan of Shaanxi Province (Project NO. S2020-YF-ZDCXL-ZDLGY-0226) and the Shaanxi Province key Research and Development Program (Project NO.2019 ZDLGY03-09-02) and Shaanxi Provincial Education Department serves Local Scientific Research Plan in 2019 (Project NO.19 JC028) and Shaanxi Provincial Key Research and Development Program (Project NO.2018 ZDCXL-G-13-9).  
The authors declare no conflict of interest.