esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Selection of Seismic _IMs_ for the PCA Algorithm
### Elimination of Multicollinearity IMs  
Multicollinearity was first proposed by the statistician, [PERSON], in 1934, and refers to the phenomenon of different independent variables in a model being highly correlated  
Figure 8: Bubble chart of the correlation coefficients of 14 _IMs_.  
Figure 7: Statistical diagram of the correlation coefficients between _IMs_ and sectional curvatures.  
with each other. This multicollinearity means that the different _IMs_ repeatedly describe a certain characteristic of ground motions. This will result in the overemphasis of certain characteristics of ground motions, affect the objectivity of the analysis, and compromise its accuracy and reliability. To overcome the adverse effects of overlapping information caused by multicollinearity, it is recommended to eliminate those _IMs_ that exhibit high levels of multicollinearity.  
For the remaining 14 _IMs_, after removing the weakly correlated _IMs_ in Section 4.2, if there are 15 parameters \(c_{0},c_{1},\cdots,c_{14}\), the following equation can be obtained:  
\[c_{0}+c_{1}IM_{i,1}+c_{2}IM_{i,2}+\cdots+c_{14}IM_{i,14}\approx 0(i=1,2,\cdots,100) \tag{10}\]  
There appears to be multicollinearity among the seismic _IMs_ (\(IM_{1}\), \(IM_{2},\cdots,IM_{14}\)). The vector form of the seismic _IMs_ of Equation (10) can be expressed as:  
\[c_{0}\textbf{{IM}}_{0}+c_{1}\textbf{{IM}}_{1}+c_{2}\textbf{{IM}}_{2}+\cdots+c_ {14}\textbf{{IM}}_{14}=\textbf{{IM}}^{c}_{c}\approx 0 \tag{11}\]  
where \(\textbf{{IM}}_{0}\) is a 100 \(\times\) 1 dimensional column vector where all elements are equal to 1, \(\textbf{{IM}}_{0}=\begin{bmatrix}1&1&\cdots&1\end{bmatrix}^{T}\); \(\textbf{{c}}\) is a unit eigenvector, \(\textbf{{c}}=\begin{bmatrix}c_{1}&c_{2}&\cdots&c_{14}\end{bmatrix}^{T}\); \(\textbf{{IM}}=\begin{bmatrix}\textbf{{IM}}_{0}&\textbf{{IM}}_{1}&\textbf{{IM}}_ {2}&\cdots&\textbf{{IM}}_{14}\end{bmatrix}\).  
As suggested in the literature [32], the condition number \(k_{i}\) can serve as a useful metric for determining the presence of multicollinearity among the remaining 14 _IMs_, and the condition number \(k_{i}\) can be calculated as follows:  
\[k_{i}=\sqrt{\frac{\lambda_{\max}}{\lambda_{i}}}(i=1,2,\cdots,p) \tag{12}\]  
where \(k_{i}\) is the condition number, \(\lambda_{\max}\) is the maximum eigenvalue of the matrix \(\textbf{{IM}}^{T}\textbf{{IM}}^{\prime}\), and \(\lambda_{i}\) is the \(i\)-th eigenvalue of matrix \(\textbf{{IM}}^{T}\textbf{{IM}}^{\prime}\).  
Generally, it can be considered that when \(0<k<10\), there is little multicollinearity; when \(10\leq k<100\), there is a strong multicollinearity; when \(k\geq 100\), there is a severe multicollinearity. To address the issue of multicollinearity among the remaining 14 _IMs_, this study employs Equation (12) to calculate their condition number. Any seismic _IM_ with a condition number that exceeds 100 is eliminated, as per the study's methodology.
# Metrology of Nanostructures by Tomographic Mueller-Matrix Scatterometry
## 4 Results and Discussion
### Measurement of the Grating Pitch  
We used the Littrow configuration method to measure the grating pitch by TMS. We set the incidence angle at \(\theta=0^{\circ}\), thus the zeroth-order diffracted light is overlapped with the incidence light. Then, the sample stage was rotated so that the zeroth-order diffraction light deflected from its initial direction and the first-order diffracted light coincided with the incident light. The rotating angle of the stage was 50.2\({}^{\circ}\), and the illumination wavelength used was 633 nm. Substituting the values into Equation (7), and the calculated pitch of the grating is about 412 nm, which is in good agreement with the SEM-measured pitch value of about 414 nm from Figure 4.  
As described in Section 3.2, the Littrow configuration method is applicable when the grating pitch is greater than \(\lambda/2\). In our case, for a wavelength \(\lambda=633\) nm, the grating pitch cannot be less than 316.5 nm. To further extend the range of pitch measurement, a shorter wavelength is required. A bandpass filter with a 1 nm bandwidth (FL632.8-1, Thorlabs, Inc., Newton, NJ, USA) was employed in the measurement to ensure an accurate result, since the diffracted light associated with different wavelengths within the bandwidth will be undistinguished on the detector for a bandpass filter with a small bandwidth. Additionally, it should be noted that in the measurements of different rotating angles of the sample stage will lead to a minor change of spot size, which will further lead to a change in the number of grating periods covered by the illumination spot in the pitch measurement.
## 5 Rotor Temperature Modeling and Prediction
### Rotor Temperature Modeling and Prediction Under Small Samples  
Experiments under small-sample conditions not only verify the robustness of RIME-XGBoost but also highlight how limited data directly impact the accuracy of model decisions. Moreover, in practical applications, factors such as cost, space, and motor design constraints often make data collection and storage challenging. Thus, small-sample experiments simulate these real-world scenarios. This section conducts experiments based on the Group B dataset. The hybrid models still undergo 20 consecutive rounds of training and prediction to avoid randomness in the test results. The error evaluation metrics and the computer hardware used for the experiments remain unchanged. The population and iterations of each hybrid model are slightly adjusted, as shown in Table 6. The training and testing results are presented in Table 7.  
RIME-XGBoost demonstrates extremely high accuracy and stability on the training set, but its performance on the test set slightly declines, suggesting potential overfitting. However, its metrics on the test set are still superior to those of the comparison models. SMA-RF shows relatively consistent performance on both the training and test sets. Its overall error is higher, indicating weaker capability in capturing features from small \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **RIME-XGBoost** & **SMA-RF** & **SO-BiGRU** & **EO-SVR** \\ \hline Population & 20 & 50 & 10 & 30 \\ Iteration & 20 & 50 & 10 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Algorithm parameters of each hybrid model. Figure 5: Half-violin plot of MAE for these models on the medium-scale test set. sample data. SO-BiGRU has significantly longer computation times than other models, with prediction accuracy at a moderate level. EO-SVR performs well, especially on the training set, but its performance on the test set slightly declines. Despite its short modeling time, its overall performance is suboptimal.
## 3 Bispectrum Analysis of EEG Signals for an Emotion Recognition System
### Feature Extraction Based on Bispectrum Analysis and 3D Pyramid Filter
#### 3.4.1 Bispectrum
The higher order cumulants have the property invariant to the shift of the mean; therefore, it is practical to describe the cumulants under zero mean assumption, meaning that if the mean of a process is not zero, then as the first step, the mean should be subtracted from each value. The second order polyspectrum, which is the power spectrum, is defined as the Fourier transform of the second order cumulant, while the third order polyspectrum, which is the bispectrum, is defined as the Fourier transform of the third order cumulant. Figure 2: Comparison between (**a**) power spectrum which shows dominant frequencies and (**b**) bispectrum, which shows dominant frequencies and their correlation (if any). For the third order cumulant, the autocorrelation of a signal will be calculated until the distance \(t+\tau_{1}\) and \(t+\tau_{2}\), where \(\tau_{1}\) and \(\tau_{2}\) are the lag. The third order cumulant from a zero mean stationary process is defined as [48]:  
\[C_{3x}(\tau_{1},\tau_{2})=E\{x^{*}(n)\ x(n+\tau_{1})\ x(n+\tau_{2})\}. \tag{2}\]  
Thus, the bispectrum, \(B(f_{1},f_{2})\), defined as the Fourier transform of the third order cumulant, becomes:  
\[B(f_{1},f_{2})=\sum_{k=-\infty}^{\infty}\sum_{l=-\infty}^{\infty}C_{2x}(k)e^{- \
icefrac{{|2\pi f_{1}k}}{{k}}}e^{-\
icefrac{{|2\pi f_{2}l}}{{k}}}. \tag{3}\]  
The bispectrum has a specific symmetrical property that is derived from the symmetrical property of the third order cumulant [46], which results in similarity of the six regions of the bispectrum, shown as follows:  
\[ \begin{array}{ll}C_{3x}(\tau_{1},\tau_{2})&=C_{3x}(\tau_{2},\tau_{1})=C_{3x} (-\tau_{1}-\tau_{2},\tau_{2})=C_{3x}(\tau_{1},-\tau_{1}-\tau_{2})\\ &=C_{3x}(-\tau_{1}-\tau_{2},\tau_{1})=C_{3x}(-\tau_{2},-\tau_{1}-\tau_{2}) \end{array} . \tag{4}\]  
Because the bispectrum matrix has a redundant region as described in (4), it is sufficient to extract features from only one quadrant of the bispectrum matrix, and because the FFT in the calculation of bispectrum value may result in non-imaginary values, then the absolute value of the bispectrum is used. The pseudocode of the bispectrum calculation in the feature extraction process for an EEG signals, derived from (1)\(-\)(4), is summarized in Algorithm 1 as follows:  
```
1. Define: lag
2. For channel = 1 to C
3. Calculate autocorrelation signal \(X\) to the defined lag as (2)
4. Construct symmetrical matrix \(C_{3x}\) for the first quadrant
5. Construct cumulant matrix \(C_{3x}\) at other quadrant as (4)
6. Calculate bispectrum as (3)
7. Take only 1 quadrant of bispectrum matrix
8. Take the absolute value of the bispectrum matrix
9. End For
```  
**Algorithm 1**Bispectrum calculation in feature extraction algorithm.
## 4 Results and Discussion
### Station Performance Analysis
#### 4.3.2 Bottleneck Characteristics  
The five identified bottleneck stations (202-205) share common characteristics:  
* Extended operational durations (\(>\)9900 h each)
* Moderate cycle times (10.6-13.6 min/event)
* Critical position in the process flow (early to mid-process)
* High transition counts with neighboring stations  
These findings suggest that bottlenecks arise from their sequential positioning and the cumulative effect of processing delays rather than the inefficiency of the individual station.
# Path Planning for Laser Cladding Robot on Artificial Joint Surface Based on Topology Reconstruction
###### Abstract  
Artificial joint surface coating is a hot issue in the interdisciplinary fields of manufacturing, materials and biomedicine. Due to the complex surface characteristics of artificial joints, there are some problems with efficiency and precision in automatic cladding path planning for coating fabrication. In this study, a path planning method for a laser cladding robot for artificial joints surface was proposed. The key of this method was the topological reconstruction of the artificial joint surface. On the basis of the topological relation, a set of parallel planes were used to intersect the CAD model to generate a set of continuous, directed and equidistant surface transversals on the artificial joint surface. The arch height error method was used to extract robot interpolation points from surface transversal lines according to machining accuracy requirements. The coordinates and normal vectors of interpolation points were used to calculate the position and pose of the robot tool center point (TCP). To ensure that the laser beam was always perpendicular to the artificial joint surface, a novel laser cladding set-up with a robot was designed, of which the joint part clamped by a six-axis robot moved while the laser head was fixed on the workbench. The proposed methodology was validated with the planned path on the surface of an artificial acetabular cup using simulation and experimentation via an industrial NACHI robot. The results indicated that the path planning method based on topological reconstruction was feasible and more efficient than the traditional robot teaching method.  
laser cladding robot; path planning; topological relation; artificial joint Article
## 3 Research Design
### Recommendation Model  
We created a recommendation model based on item-item collaborative filtering. The collaborative filtering method is usually involves gathering and analyzing information about a user's behavior, activities, or preferences and predicting what they will like based on their similarity to other users. Collaborative filtering is based on the assumption that different individuals who have had similar preferences in the past will make the same choices in the future. For example; if a user named [PERSON] prefers A, B, and C products, and a user named [PERSON] prefers B, C, and D products, it is likely that [PERSON] will also prefer product D and [PERSON] will prefer product A. Item-item logic can thus recommend similar items to a user who consumes any item.  
Constructing a recommendation model for GitHub is different from classic (movie) principles. When recommending a movie to a user, the ratings of movies are known. However, this is not the case on GitHub, where developers do not rate projects. In this context, it is thus necessary to determine a metric that can be used as a rating. In addition, the model should recommend projects with which a developer is unfamiliar (just as a movie recommender should suggest movies that the user has not watched). We constructed a model taking into account these conditions.  
A project recommender system for software collaboration development platforms includes stages as generating a project-developer rating matrix according to a certain metric, finding similarities between projects, generating recommendations, and evaluating results. First, we generated a project-developer rating matrix (Table 3) using specific metrics. As seen the Table 3, columns represent the users, rows represent the projects (repos). We selected a metric, then, input the metric's values (quantity, ratio, or binary) into the cells. For example, as shown in Table 3(a), _User-1_ opened seven issues in _Project-2_.  
We normalized the values of the project-developer matrix using min-max normalization. The values of the metrics were scaled from 0 to 10. As in the movie-user model, we assumed that each developer gave a rating (0-10) to each project (Table 3(b)). First, we calculated similarity scores between projects using two methods (cosine and TF-IDF similarity). We then recommended the top-\(n\) projects to each developers. Finally, we evaluated the correct recommendations using two evaluation methods (community relation and language experience).  
\begin{table}  
\end{table}
Table 3: A sample project-developer matrix belongs to the metric _issue_opened_.
## 3 Results
### Histological Analysis  
Further, the evaluation was carried out in the histological slices. In untreated control wounds, the mean neoepidermal thickness was 22.50 \(\upmu\)m with a range of 12.52-39.5 \(\upmu\)m. Epidermal thickness had increased from treatment with the non-crosslinked biomatrix at a mean thickness of 31.01 \(\upmu\)m (range 23.03-61.45 \(\upmu\)m; \(p=0.0015\)) and from the crosslinked biomatrix at a mean of 43.12 \(\upmu\)m (range of 25.78-173.09 \(\upmu\)m; \(p<0.0001\)), as shown in Figure 3. Thus, the histological examination revealed higher epidermal thickness in the crosslinked biomatrix-derived neoepidermis. Rete ridge-like formations were visible in both treatment groups (Figure 1).  
Figure 3: Epidermal thickness of untreated wounds versus crosslinked and non-crosslinked biomatrices-derived neoepidermis in three different sections per sample with an interval of 100 \(\upmu\)m in micrometers. Histologic examination verified highest epidermal thickness in the crosslinked biomatrix-treated wounds. * Statistically significant results.  
Figure 2: Time in days to complete epithelialization of control wounds and treated wounds with the crosslinked and non-crosslinked biomatrices. The wound closure was significantly increased in the treatment groups. * Statistically significant results.  
In comparison, the mean epidermal cell count for untreated controls amounted to 41,00 cells/5 mm\({}^{2}\) (range of 22.00-68.00 cells/5 mm\({}^{2}\)). Higher values of cell density were seen in the crosslinked biomatrix-treated groups with 69.50 cells/5 mm\({}^{2}\) (range of 57.00-107.00 cells/5 mm\({}^{2}\), \(p=0.0089\)), whereas in the non-crosslinked biomatrix-treated wounds the highest values for mean neepidermal cell count with an average of 84.50 cells/5 mm\({}^{2}\) (range of 79.00-106.00 cells/5 mm\({}^{2}\), \(p=0.0002\)) could be observed. The templates were fully integrated into the host tissue with the colonization of epidermal minipig cells within all sections at statistically significant levels (Figure 4).  
To sum up, treatment groups showed overall improved wound healing with accelerated wound closure, thicker neoepidermal tissue and increased epidermal cell density in comparison to untreated wounds.
# Pose Estimation of Primitive-Shaped Objects from a Depth Image Using Superquadric Representation
## 6 Quantitative Evaluation
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**3D Error [cm] \(\downarrow\)**} \\ \hline
**Method** & **S1** & **S2** & **S3** & **S4** & **S5** & **S6** & **S7** & **S8** & **S9** & **S10** & **Ave.** \\ \hline ICP [7] & 0.080 & 5.012 & 1.723 & 1.409 & 1.382 & 5.887 & 5.964 & 1.392 & 6.935 & 6.919 & 3.670 \\ NDT [38] & 37.52 & 70.77 & 52.23 & 62.04 & 73.35 & 64.01 & 60.28 & 112.4 & 97.52 & 95.24 & 72.53 \\ RANSAC [37] & 0.714 & 2.145 & 3.077 & 0.184 & 0.785 & 4.335 & 0.362 & 1.201 & 1.720 & 1.524 & 1.604 \\ Baseline & 0.096 & **0.230** & 5.800 & **0.197** & **0.245** & 4.232 & 1.113 & 0.015 & 0.064 & 0.010 & 1.200 \\ Ours & **0.052** & 0.695 & **1.135** & 1.342 & 0.268 & **0.995** & **0.007** & **0.003** & **0.015** & **0.010** & **0.452** \\ \hline \multicolumn{7}{c}{**2D Error [px] \(\downarrow\)**} \\ \hline
**Method** & **S1** & **S2** & **S3** & **S4** & **S5** & **S6** & **S7** & **S8** & **S9** & **S10** & **Ave.** \\ \hline ICP [7] & 3.378 & 67.10 & 8.973 & 5.301 & **1.204** & 33.25 & 33.25 & 1.562 & 21.32 & 24.53 & 19.98 \\ NDT [38] & 149.8 & 19.12 & 56.44 & 18.10 & 34.57 & 65.65 & 133.1 & 32.42 & 25.31 & 53.21 & 58.78 \\ RANSAC [37] & 9.816 & 27.54 & 19.60 & 18.72 & 15.23 & 28.42 & 11.48 & 21.53 & 23.52 & 12.52 & 18.83 \\ Baseline & 3.280 & 3.447 & 43.26 & **5.724** & 4.678 & 23.62 & 15.76 & 1.780 & **3.594** & 2.130 & 10.73 \\ Ours & **2.152** & **2.803** & **4.609** & 17.23 & 6.452 & **13.63** & **1.670** & **1.381** & 16.10 & **2.059** & **6.809** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Error of primitive shape pose estimation (per scene) using our dataset. S1 to S10 denotes the indices of the scene in the dataset. The rightmost column shows the average of entire scenes. Figure 8: The failure of the proposed method. The upper row shows the results of the baseline method and the bottom row shows the results of the proposed method. The column shows the five successive frames in the scene.
# Robust Estimators in Geodetic Networks Based on a New Metaheuristic: Independent Vortices Search
## 3 Independent Vortices Search
### A New Search Space Definition  
For the definition of the search space in the adjustment of geodetic networks, we defined the limits of each parameter \(j\) by \(x_{min,j}\) and \(x_{max,j}\). By using the parameter vector \(\boldsymbol{x}\) obtained from conventional LS computation, we set the exploration area according to Equation (27):  
\[\begin{cases}x_{min,j}=x_{j}-\max_{i}|\boldsymbol{v}_{i}|\times\left[1-\max_{i }\operatorname{diag}\left(\boldsymbol{R_{e}}\right)_{i}\right]\times 1.15,\\ x_{max,j}=x_{j}+\max_{i}|\boldsymbol{v}_{i}|\times\left[1-\max_{i} \operatorname{diag}\left(\boldsymbol{R_{e}}\right)_{i}\right]\times 1.15, \end{cases} \tag{27}\]  
where \(\max_{i}|\boldsymbol{v}_{i}|\) is the greatest absolute residual from the LS solution, \(\max_{i}\operatorname{diag}\left(\boldsymbol{R_{e}}\right)_{i}\) is the greatest absorption fraction of an error and \(1.15\) indicates a \(15\%\) safety margin. Additionally, \(\boldsymbol{R_{e}}\) is defined by Equation (28) [44]:  
\[\boldsymbol{R_{e}}=\frac{1}{\sigma^{2}}\boldsymbol{\Sigma}_{\vartheta} \boldsymbol{W}, \tag{28}\]  
where \(\boldsymbol{\Sigma}_{\vartheta}\) is the covariance matrix of adjusted residuals from the LS solution.  
Equation (27) presents a novel method to define the search space. It can be applied to any problem susceptible to outliers that use the Gauss-Markov model to generate residuals and MH to explore the solution. It is not limited to geodetic networks and can be used along with REs or other techniques--for example, in hyperspectral image data [45; 46] or 3D Point Clouds [47]. Applying this strategy to 900 scenarios, it did not omit any solution in the IVS exploration limit.
## 6 Conclusions  
1. Based on on-site geological surveys, drone images, and multiple remote sensing images, 9 debris flow risk assessment indicators were selected from 14 debris flows in Longmenshan Town, Pengzhou, China. Each indicator's subjective and objective weights were calculated using hierarchical analysis and CRITIC methods, and the two weights were coupled to obtain the synthetic weights of the evaluation indicators. Based on this, the synthetic evaluation score \(D_{i}\) was calculated for each debris flow so that the obtained synthetic evaluation score could scientifically reflect the risk level of each debris flow gully.
2. This study conducted cluster analysis of 14 debris flows, established the classification model, and classified the debris flows in the study area into four categories. By combining the classification results with synthetic evaluation scores, it was ultimately determined that, among the 14 debris flows in the study area, 3 were extremely dangerous (\(0.6718\leq D_{i}\leq 0.8301\)), 4 were highly dangerous (\(0.3963\leq D_{i}\leq 0.5359\)), 3 were moderately dangerous (\(0.2716\leq D_{i}\leq 0.3064\)), and 4 were low-risk (\(0.2113\leq D_{i}\leq 0.2692\)).  
Y.L.: Investigation, Methodology, Data curation, Visualization, Writing--original draft. J.S.: Funding acquisition, Data curation. M.H.: Investigation. Z.P.: Investigation. All authors have read and agreed to the published version of the manuscript.  
This research was funded by The National Natural Science Foundation of China (No. 41572308).  
Not applicable.  
The data presented in this study are available on request from the corresponding authors.  
The authors declare no conflict of interest.