esa-sceva/satcom-chunk-collection huggingface dataset:
during closing. Dental, skeletal, respiratory, and neuromuscular factors can be recognised as possible etiological factors [2; 4; 5; 6], or FPCB may result from oral habits [7].  
Treatment of FPCB often involves the removal of occlusal interferences and slow or rapid bilateral maxillary expansion during the deciduous or early mixed dentition stages [5; 8; 9; 10].  
However, symmetrical transverse expansion of the maxilla in the mixed dentition, which is the most common treatment [11; 12], does not always fully correct midline deviations or the asymmetric sagittal molar relationship in a clinical context. This may be due to an underlying asymmetry in the maxilla or in the mandible [13; 14; 15], which can be either skeletal or dental [16].  
A 3D digital model assessment of children with unilateral posterior crossbite and controls without crossbite found that the surfaces of the two hemi-palatal parts of the vault were symmetric in both treated and untreated patients with unilateral posterior crossbite and in the control group [17]. Conversely, an analysis of transverse maxillary arch form using occlusograms of patients with unilateral functional crossbite revealed different arch morphology, with the crossbite side being either symmetric, contracted, or expanded compared to the non-crossbite side [13]. Notably, an expanded hemi-maximally arch on the crossbite side is statistically associated with skeletal mandibular asymmetry [13]. Another study, analysing palatal transverse dimensions and performing a 3D evaluation of digital casts, showed that FPCB patients exhibited symmetrical palatal vault narrowing but an asymmetrical narrowing of the alveolar bone [14].  
However, the above-mentioned studies analysed either the skeletal or alveolar asymmetry of the maxilla or the dental asymmetry of the maxillary arch but only in the transverse plane.  
Since both transverse and sagittal maxillary arch dimensions contribute to dental-alveolar morphology, both should be analysed to evaluate the presence of dental-alveolar asymmetry in FPCB patients.  
This study aimed to analyze maxillary arch asymmetry in patients with FPCB. Maximally arch was split in two halves, linear transverse and sagittal measurements of the two halves of the maxillary arch were taken in patients with FPCB and compared with those of a control group without crossbite.  
Additionally, 3D superimpositions of the digital models were performed to compare the asymmetry in the palatal morphology between the two groups.  
The null hypothesis states that there are no differences in the grade of asymmetry of the linear measurements of the maxillary arch transverse and sagittal dimensions, as well as the palatal morphology, between the FPCB and the control group.
## 5 Results and Discussion  
### Approximation Speed-Up vs. Error Percentage  
As a result of applying the loop perforation technique in the test programs, different approximate versions were obtained for each of them: 5 for the calculation of the natural logarithm of 2 (ln2), 2 for the calculation of the Euler number, and 3 versions for each one of the filters (Sobel and Emboss). With each level of approximation, the speed-up of the programs increases, as does the error in the result.  
Figure 10 shows the error rate and speed-up of the approximate versions for each test program. The horizontal axis corresponds to the percentage of error and the vertical axis to the speed-up, both axes on a logarithmic scale. The speed-up is the division between the number of cycles of the original program over the number of cycles of the approximate version. It is a dimensionless measure. Each line represents a test program. The approximate versions of each program are represented with a marker (x). It can be seen that the program that has the best results on the approximation is ln2 since it has the highest speed-ups with a lower percentage of error.  
As can be seen in Figure 10, the results differ substantially between each test program. This is due to the specific characteristics of each algorithm used. While all algorithms have an iterative nature (which is why we used loop perforation as the AC technique), the loops of each program are not the same. For example, the algorithms that show the best results (ln2 and Euler) are based on convergent series. In these cases the final iterations of the programs do not modify the results considerably. In the case of ln2, the series converges more slowly than in the case of Euler, i.e., it needs more iterations. Moreover, the image filters (Sobel and Emboss) are implemented using more 'for' statements (nested loops), but with fewer iterations. While the algorithm of the two filters is essentially the same, the matrix of weights used for the Sobel filter contains some values with zeros, so discarding a few iterations would not affect the result in some cases.
# Histogram-Based Descriptor Subset Selection for Visual Recognition of Industrial Parts
## 3 Proposed Approach
### Feature Selection Techniques  
The feature selection techniques are used to chose the descriptors for the classification. An exhaustive search of best combination of descriptors is computationally inefficient, while it guarantees that the optimal solution is achieved. Nevertheless, a suboptimal solution can be achieved using a sequential search. This is an iterative search that once a stage of the search is reached, is impossible to go back. The complexity of the exhaustive search is exponential (\(O(2^{n})\)), while the sequential search remains polynomial (\(O(n^{k+1})\)), where \(k\) is the number of evaluated subsets in each stage. This last one does not guarantee an optimal solution.  
Figure 3: Classification of a new image given a descriptor and a classifier.  
Another important consideration in the feature selection techniques is the generation of the successors, i.e., how to select the next candidates for the following stage. The simplest and most used methods are Forward and Backward generation [36]. In forward generation, on each stage the element which makes \(J\) (the evaluation measure) greater is selected and added to the selected subset. For example, the first descriptor added to the subset would be the one with the best individual score. The next stage would add to the subset the one that concatenated with the previous one makes the score greater. We refer to this method as Sequential Forward Subset Selection (SFSS) [36], and its pseudocode is described in Algorithm 1. The backwards is the opposite behavior. The subset is initialized with all the elements and on each stage the element that that makes \(J\) greater when removed is done so. The stopping criteria in both cases can be that \(J\) is not increased in \(j\) steps or the subset achieves a desired length. We refer to this method as Sequential Backward Subset Selection (SBSS) [36], and its pseudocode is described in Algorithm 2.  
```
Input : \(X\)--Set of elements \(J\)--evaluation metric Output : \(X^{\prime}\)--solution found \(X^{\prime}=\emptyset\) repeat \(x^{\prime}:=argmax\{J(X^{\prime}\cup x)|x\in(X\setminus X^{\prime})\}\) \(X^{\prime}:=X^{\prime}\cup\{x^{\prime}\}\) untilnot improvement in \(J\) OR\(X^{\prime}=X\);
```  
**Algorithm 1**Sequential Forward Subset Selection
## Appendix A Link-Budget Analysis  
Table 1 summarizes link-budget analysis for GNSS signals on geostationary orbit for the main lobe signal used in this study. In accordance with \(\theta_{\text{sv}}\), data such as antenna gain, received power, and \(C/N_{0}\) are calculated for main lobe and side lobe signals. As the \(\theta_{\text{sv}}\) increases in the main lobe, the gain of the satellite antenna decreases, but the gain increases in the peak of the side lobe and subsequently decreases again. From the received power and \(C/N_{0}\), it is noted that the gain reduction of the transmitter antenna pattern is affected more seriously than the free space loss.
## 3 Results and Discussion
### Durability Analysis  
#### 3.5.1 Freeze-Thaw Tensile Strength Test Results Analysis  
The ITS of the mixtures before and after the freeze-thaw and TSR of them is listed in Table 4. The PADG mixtures had the highest ITS of 0.5 MPa after freeze-thaw, followed by DG mixtures of 0.37 MPa and OG mixtures of 0.25 MPa. This indicates that the PADG mixtures still can approach the high level to bear traffic loads, even during adverse weather of low temperature and wet. The TSR of the PADG mixtures was larger than 80%, verifying that it provides satisfactory patching materials with insusceptibility to water and superior cohesion. However, the DG mixtures and the OG mixtures become fairly weak patching materials after a freeze-thaw, with a TSR of 62.7 and 58.1%, respectively.
## 2 Basic Theory and Principle  
### Acquisition Process  
The acquisition process of the L-ISL is designed to accurately determine the position of the counter laser terminal. This process is facilitated by a pointing, acquisition, and tracking (PAT) system, as illustrated in Figure 1. The PAT system consists of a coarse pointing assembly (CPA), fine pointing assembly (FPA), pointing ahead assembly (PAA), dichroic mirror (DM), fast steering mirror (FSM), and polarizing beam splitter (PBS). The CPA and FPA work together to track the position of the counter laser terminal in real time, while the PAA predicts its position in advance. The azimuth and elevation angles for the PAA are typically calculated based on the relative velocity of the counter satellite.  
The movements of the CPA and FPA were controlled using a coarse-fine composite control (CFCC) system, as shown in Figure 2. In this system, the movements of the CPA and FPA are simulated using the transfer function and decoupled with a decoupling function, which is usually established based on the system error. Measurement and vibration errors were introduced into the CPA module to ensure the accuracy of the simulation.  
Figure 1: Schematic of the PAT system.  
The azimuth and elevation were analyzed by introducing measurement and vibration errors into the CFCC system, as shown in Figure 3. We observed a slight difference before and after the transfer function in the CFCC system.  
In the acquisition process, the computation of azimuth and elevation in the CFCC system includes a counterposition calculation step, scanning in the uncertainty cone step, and a coordinate transformation step. The counterposition calculation is typically performed using an orbital recursive algorithm. The scanning step was based on an equal linear velocity spiral scanning function. The coordinate transformation step shown in Figure 4 was used to transform the pointing vector of the counter laser terminal in J2000 coordinates to the coordinate system with the laser terminal as the origin. The coordinate system with the laser terminal as its origin is referred to as the laser terminal coordinate system.
# Facial Expression Recognition Based on Discrete Separable Shearlet Transform and Feature Selection
## 3 The Proposed Algorithm
### Discrete Separable Shearlet Transform  
Given an \(N\times N\) image, the DSST procedure described in Section 2 as a fixed decomposition scale, \(j\), can be summarized as follows, and the procedure is shown in Figure 2.  
1. \(f_{j}\) is up-sampled by \(2^{j/2}\) to obtain \(f_{j\uparrow 2^{j/2}}\).
2. Compute the 1D convolution of \(f_{j\uparrow 2^{j/2}}\) and \(h^{0}_{j/2}\), where \(h^{0}_{j/2}\) is a 1D low-pass filter to obtain \(\widetilde{f}_{j}\).
3. \(\widetilde{f}_{j}\) is up-sampled by the shear matrix \(S_{k}\) to obtain \(\widetilde{f}_{j}(S_{k}(n))\).
4. \(\overline{h^{0}_{j/2}}\) is down-sampled by \(2^{j/2}\) to obtain \(\overline{h^{0}_{\lfloor j/2\rfloor}}\). The 1D convolution of \(\overline{h^{0}_{\lfloor j/2\rfloor}}\) and \(\widetilde{f}_{j}(S_{k}(n))\) is then computed.
5. Use the separable wavelet transform call and proceed through all the scales, \(j,j=0,1,\cdots,J-1\).  
DSST has no limitation on the number of directions. If we define the direction number as \(L\), the feature vectors will still have \(\left[\left(N/2^{j}\right)^{2}+N^{2}/2^{j}\right]\times L\) elements, where \(N\) is the size of the input image  
Figure 1: The framework of the proposed method.  
Figure 2: (**a**) Two computation steps for discrete separable shearlet transform (DSST) coefficients: refinement along the horizontal axis (top) and resampling associated with shear matrix (middle), followed by the separable wavelet transform along the vertical axis (bottom); (**b**) refinement along the horizontal axis to obtain the coefficients when \(j=4\) and \(k=1\).  
(e.g., \(N=64\), \(j=2\), \(L=6\)). The number of feature elements is \(\left(\left(64/2^{2}\right)^{2}+64^{2}/2^{2}\right)\times 6=7680\), which is still a high dimension for subsequent processing and recognition. Therefore, in this paper, we propose an improved method for normalized mutual information feature selection to find the optimal feature subset of the original feature set. Moreover, the feature subset not only retains the key classification information of the original set, but also reduces the amount of data.
# Efficient SMC Protocol Based on Multi-Bit Fully Homomorphic Encryption
## 5 Secure Multi-Party Computation Protocol Based on NFHE Scheme
### Security  
#### 5.3.1 In Semi-Honest Model  
In the CRS model, the security of the protocol is based on the following issues.  
* Under the above settings, the security of the NFHE solution can be attributed to the DLWE problem.
* In \(\mathbf{\eta}_{i}=\bar{\mathbf{t}}_{i}\cdot\mathbf{C}+\mathbf{\gamma}_{i}\) and \(\mathbf{\eta}=\bar{\mathbf{t}}\mathbf{C}+\mathbf{\gamma}\), the first \(l\) components in \(\mathbf{\gamma}_{i}\) and \(\mathbf{\gamma}\) obey the bounded distribution of \(B_{\chi}\), which implies that these two equations constitute two some-are-errorless LWE instances discussed in Section 2. Therefore, after each party announces its own \(\mathbf{\eta}_{i}\) in Round 3, its private key and joint key will not be disclosed, and the protocol is safe under the semi-honest model.
## 2 Materials and Methods
### Research Methods
#### 2.3.5 Correlation Analysis  
Pearson's correlation analysis was employed to assess the relationship between vegetation growth and drought, using the maximum correlation coefficient to evaluate the response of vegetation in Xinjiang to climate change in terms of both response magnitude and timing. Correlation analyses were conducted between the SPEI at different timescales (SPEI-03, SPEI-06, SPEI-12, and SPEI-24) and NDVI and GOSIF. The analysis involved resampling all the raster data to a spatial resolution of 0.05\({}^{\circ}\), and the monthly NDVI and GOSIF values were correlated with each SPEI timescale on a pixel-by-pixel basis (NDVI was resampled using a spatial aggregation method based on mean values). The maximum  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Slope** &
\begin{tabular}{c} **Z** \\ **Normal Statistics** \\ \end{tabular} & **Variation Trends** \\ \hline \(\geq\)0.0005 & \(>\)1.96 & Significant improvement \\ \(\geq\)0.0005 & \(-1.96<\) Z \(<1.96\) & Slight improvement \\ \(-\)0.0005–0.0005 & \(-1.96<\) Z \(<1.96\) & Relatively stable \\ \(\leq\)\(-\)0.0005 & \(-1.96<\) Z \(<1.96\) & Slight deterioration \\ \(\leq\)\(-\)0.0005 & \(<\)\(-1.96\) & Significant deterioration \\ \hline \hline \end{tabular}
\end{table}
Table 2: Grading of SPEI variation trends.  
correlation coefficients, \(\mathrm{R_{n}}\) for NDVI and \(\mathrm{R_{S}}\) for GOSIF, were used to quantify the structural and physiological responses of vegetation to climate variability. The highest value, \(\mathrm{R_{max}}\), represents the maximum response magnitude, with the corresponding NDVI or GOSIF, indicating that the vegetation index was the most responsive to climate change. The associated timescale \(\mathrm{n}\) is considered as the response time of vegetation photosynthesis to variations in moisture conditions.
# Removal of Heavy Metal Cd Element from Paddy Soil by Geo-Electrochemical Technology
## 4 Results and Discussion
### Variation in the Content of the Seven Remaining Heavy Metal Elements of Paddy Soil  
Before the experiment, soil sampling and related analyses were performed on the paddy soil. The results showed no exceedances for all seven elements except Cd. The content of the remaining seven heavy metal elements in the three experimental groups is detailed in Table 3. As presented in the table, relative to the initial content of heavy metal elements in soil without experimental treatment, the contents of Cr, Ni, Cu, Zn, As, Hg, and Pb in the soil of the T1, T2, and T3 experimental groups all decreased, with a significant reduction (\(p\) < 0.05) of Cr, Ni, and Cu. In accordance with GB 15618-2018 [23], it can be argued that after the experimental treatment, the content of seven heavy metal elements in the soil of each experimental group also meets the national standard.  
The experimental results clearly indicate that the content of other heavy metal elements in the soil will decrease correspondingly when the GT is selected for the remediation of Cd-contaminated paddy field. Based on the above-mentioned results, it can be preliminarily speculated that under the action of a direct current electric field, some heavy metal elements in the paddy soil will also have directional migration and accumulation along with Cd, and then will be collected through the adsorbent materials around the electrodes, thus reducing the content of heavy metal elements in the soil. Therefore, the GT is anticipated to show a certain potential in the remediation and treatment of composite-contaminated soils with multiple heavy metal elements.  
Figure 5: Variation in Cd bioconcentration factor in various tissues and organs of rice. The T3 group was the control group, and the T2 group used the geo-electrochemical technology. Different letters above the error lines indicate significant differences (\(p\) < 0.05).
## 3 Methodology
### Scene Tensor Modeling Based on Spatial Features  
Within integrated transportation hubs, the movement of pedestrians from an origin to a destination is influenced by static spatial layouts and dynamic spatial elements such as other pedestrians and service robots. Consequently, in order to provide precise forecasts about future paths, it is crucial to consider how pedestrians interact with each other and how the surrounding spatial environment affects their movement. To consider the influence of the physical surroundings on the future movement paths of pedestrians, we propose a Scene Potential Module-Scene Tensor, designed to represent pedestrians' past empirical observations to reflect information about obstacles within the scene. Inspired by the collective behavior theory that pedestrians prefer the paths taken by previous pedestrians, especially in complex environments, and refer to other people's trajectories to make decisions, the Scene Potential Module provides a data-driven method to quantify the guidance effect of the environment on pedestrians by counting the probability that all pedestrians have passed through each location in the past time. As shown in Figure 3, the heat map reflects the frequency of pedestrians passing through each area in the entire scene. Specifically, we segment the entire scene into a grid to determine the probability of each grid being traversed. This module allows us to capture information about obstacles in the environment and the paths preferred by pedestrians.  
The Scene Tensor encapsulates the probability of each grid in the scene being traversed. Its calculation method is shown in Equation (1). We partition the scene into grid cells of size \(m\times n\) and compute the likelihood of people passing through each cell. After that, the values corresponding to the pedestrian coordinates are spliced with the pedestrian trajectory data that we performed embedding on before to represent the pedestrian's interaction with nearby obstacles.  
Additionally, we introduce a hyperparameter \(g_{size}\) to simulate the range of pedestrian gaze in real-life scenarios. The definition of the Scene Tensor \(M^{i}_{scene}\in R^{4}\) is as follows:  
\[M^{i}_{scene}(m,n,:)=\frac{1}{|M_{mm}|}\sum_{j\in M_{mm}}v_{j} \tag{1}\]  
The variables \(m\) and \(n\) serve as the dimensions of the scene, where \(M_{mm}\) represents the location of the \(i\)-th pedestrian in cell \((m,n)\). The term \(v_{j}\) refers to the number of people passing through location \(j\), and \(|M_{mm}|\) indicates the total number of positions within the cell \((m,n)\).
## 2 Methodology
### Prototype Design  
The alternator prototype has been developed featuring a single-wound stator and an H-shaped core, with two concentric rings of permanent magnets having vertically ascending magnetic field lines. The design aims to achieve radial symmetry, ensuring that regardless of the wind direction, the oscillation of the machine similarly affects its interaction with the alternator. This contrasts with the vertically descending magnetic field of the central magnet ring of the \"oscillator\" (equivalent to the rotor in conventional alternators). The detailed components of the developed alternator prototype are illustrated in Figure 2.  
The operating principle for the design of the alternator prototype is based on altering the magnetic field in its core, induced by the oscillation of the wind turbine. This shift in the core's magnetic field is crucial for the fluctuation of the magnetic flux that passes through the stator winding, a fundamental principle in generating electrical energy through alternators. The oscillatory motion causes the magnetic field lines of the \"oscillator\" (moving part) to approach and move away from the magnetic field lines of the stator's magnetic rings (fixed part). Since the field lines are opposite, the magnetic field traversing the alternator's core is reversed. This change in the magnetic field induces an electromotive force in the stator winding. In Figure 3, the positions and directions of the aforementioned field lines are described within a section of the alternator's central plane.  
In the development of the circular alternator prototype described herein, an innovative approach was employed involving the placement of magnets within the stator. This design not only aims to alternate the polarity of the field lines in the alternator's core but also ingeniously utilizes the physical properties of magnetostatic interactions to produce dynamically variable repulsion forces with the oscillator. This design principle enhances the aerodynamic and structural tuning of the system, thereby optimizing the interaction between the mechanical oscillation and electromagnetic responses.