esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Results and Discussion
### Clamped-Clamped Beam
The \(i\)th mode of a family \(A\) is compared to the \(j\)th mode of a family \(B\), and the resulting scalar is arranged into the MAC matrix as follows:  
\[\text{MAC}(i,j)=\frac{|\{\phi_{A}\}_{i}^{\intercal}\{\phi_{B}\}_{j}|^{2}}{\big{(} \{\phi_{A}\}_{i}^{\intercal}\{\phi_{A}\}_{i}\big{)}\big{(}\{\phi_{B}\}_{j}^{ \intercal}\{\phi_{B}\}_{j}\big{)}} \tag{17}\]  
The values of the MAC coefficients are bounded between 0 and 1, with 1 indicating fully consistent mode shapes. It can only indicate consistency and does not indicate validity or orthogonality. A value near 0 indicates that the modes are not consistent. Moreover, the MAC can be calculated between both data sets in order to compare the different mode shapes obtained. First, an auto-MAC issued from the DIC mode shapes is shown on Figure 21a. The fact that the values of the non-diagonal terms MAC(\(I\),\(A\)) and MAC(\(4\),\(I\)) are a little bit higher, but still very low (around 0.03), than for the other non-diagonal terms is due to the spurious mode perturbing the identification of the fourth mode, as previously discussed. It appears, for the zones near the nodes, that the determination of the fourth mode shapes is disturbed by another mode, whose frequency is close to the fourth mode and whose shape is similar to that of a first mode. Figure 20: Comparison of the first six mode shapes of the clamped–clamped beam for a particular test. The MAC matrix between the accelerometer and DIC data is presented in Figure 21b. One more time, this latter figure shows a good agreement between both experimental mode shape bases. As for the auto-MAC of DIC, the term MAC(_1,4_) is different (also around 0.03) due to the spurious mode observed in DIC measurements. Due to this spurious mode for the fourth mode and to the low quality of the determination of the mode shape for the sixth mode, for DIC measurements, the correlation coefficients for these modes (diagonal terms) are lower than for the other modes (0.99), respectively equal to 0.96 and to 0.94. The results obtained for this configuration are encouraging, with the first six modes quite well identified, except the sixth one. The natural frequency of the last mode is around 2192 Hz. Following the previous study carried out for clamped-clamped boundary conditions, the next section will focus on the case of the cantilever beam.
## 3 Results and Discussion
### Change in Amount of Volatile Compounds Associated with Desirable Arona Descriptors
#### 3.4.3 Aldehyde and Ketones  
Aldehydes, as volatile compounds, offer fruity and floral characteristics that enhance sensory experiences. Notably, the production of acetaldehyde and acetoin during the fermentation process, particularly at 96 and 120 h, has been closely associated with the development of fruity and creamy sensory attributes in chocolate, as shown in Figure S6. Acetaldehyde, in particular, has been recognized as a significant predictor of various sensory attributes, distinguishing itself as a critical compound during fermentation stages. Its amount notably increases with processing time, reflecting a trend consistent with other aldehydes such as 2-methylbutanal, 3-methylbutanal, and benzaldehyde, suggesting a broad impact on the aromatic profile of chocolate [16; 27].  
Ketones, similarly, are integral to the aromatic appeal of chocolate, with acetoin emerging as a key ketone due to its significant influence on aroma. The amount of acetoin has been observed to increase during fermentation, peaking at approximately 96 h. This pattern aligns with findings from previous studies, reinforcing the importance of aldehydes and ketones in defining the aromatic quality of chocolate [12; 27].
# Lifetimes of Used Nuclear Fuel Containers Affected by
## 4 Results  
### Scenario A  
Lifetimes under this scenario are above one million years in the deterministic model for both groundwater sulphate concentrations (Table 5). The flux of sulphide to the UFC eventually reaches a steady-state value of approximately 0.9 and 0.3 [mol year\({}^{-1}\) m\({}^{-2}\)] for groundwater sulphate concentrations of 1000 and 310 ppm, respectively (Figure 2).  
The steady-state concentration profile (Figure A3 in the Appendix A) shows that sulphide decreases linearly and has a slope change at the layer between the filling gap bentonite (gapfill) and the HCB. This result is expected as steady-state diffusion is linear. The concentration of sulphide at the host rock reaches a steady-state value of approximately 0.38% of the groundwater sulphate concentration, i.e., 3.8 and 1.2 ppm of sulphide for 1000 and 310 ppm of sulphate, respectively.  
Figure 2: Sulphide concentration and flux to UFC for Scenario I.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Groundwater Sulphate Concentration**} \\ \hline Type of model & 1000 ppm & 310 ppm \\ \hline Deterministic lifetime & 2.24 & 7.25 \\ \hline \multirow{5}{*}{Lognormal draws} & Mean & 2.30 & 7.44 \\  & Std. dev. & 0.53 & 1.72 \\ \cline{1-1}  & Minimum & 0.98 & 3.17 \\ \cline{1-1}  & Median & 2.24 & 7.23 \\ \cline{1-1}  & Maximum & 5.33 & 17.2 \\ \cline{1-1}  & Sample & 10,000 & 10,000 \\ \hline \hline \end{tabular}
\end{table}
Table 5: UFC lifetimes under scenario A [10\({}^{6}\) years].  
Results from the stochastic model also yielded lifetimes above or around one million years. The coefficient of variation is about the same (0.23) in both sulphate concentration runs, which follows from the specification of the lognormal distribution. This result implies that larger mean lifetime values entail larger standard deviations as noticeable in Figure 3.
## 4 Lac-KHM: The Proposed Algorithm  
LAC-KHM is based on the LAC algorithm, in which each data point is equipped with a learning automaton (LA). The number of actions of each LA equals the number of clusters, and during the learning process, the LA specifies to which cluster its associated data point belongs. The action of each LA is chosen based on the action probability vector (APV). The LA's decision is compared with the output of the k-means algorithm as a reinforcement signal. However, like k-means, LAC is sensitive to the proper selection of initial points. Therefore, in this research, LAC is improved through KHM, and the distance between data points and cluster centers is calculated with regard to the harmonic distance. The proposed algorithm, LAC-KHM, is formed based on three functions: select cluster, update probability, and calculate accuracy. The LAC-KHM algorithm is shown in Algorithm 1. It is noted that the cluster centers themselves are also updated based on the harmonic distance.  
```
This algorithm has three functions with input and output parameters, and operations that follow: Select Cluster: in fact, during rounds this function specifies to which cluster the data point belongs. It is noted that initially all actions in APV have the same probability. Input parameters: Membership_cluster, probability, num_cluster, num_data Output parameter: Membership_cluster Membership_cluster = Function Select_cluster (membership_cluster, probability, num_cluster, num_data)
```  
Update probability: This function updates the APV using learning rule LRP based on the received reinforcement signal. In fact, with each execution, the probability of the selected action is either decreased or increased based on the harmonic distance between data points and cluster centers. Input parameters: membership_cluster, probability, num_cluster, position_of_data, signal, alpha, beta Output parameter: Probability Probability = Function Update_probability (membership_cluster, probability, num_cluster, position_of_data, signal, alpha, beta)  Calculate accuracy: This function evaluates the accuracy of the algorithm, demonstrating how closely it matches the expected results. Input parameters: obtained_result, expected_result, num_cluster Output parameter: Accuracy
# Model Test Research on the Propagation of Tsunamis and Their Interaction with Navigating Ships
## 3 Experimental Verification
### The Turning Test  
The maneuvering performance of the ship, in general, will be estimated in the fully loaded condition. The International Maritime Organization (IMO) has been discussing the establishment of ship maneuvering performance standards, and the recent preliminary results of this discussion have pointed out that these should consider the fully loaded condition as the first step [28]. The maneuvering characteristics are influenced considerably by effects of the loading condition, depending on ship type. For example, the turning circle when considered as the turning ability in the fully loaded condition is much larger than that in the ballast condition in some cases. Likewise, the turning circle in trim by the stern condition is larger than in the even keel condition.  
To verify the validity of the model test, the maneuverability of the ship is decided by its steering, turning, collision avoidance, and other behaviors, which are closely related to the ship's rotary performance. Therefore, the rotary performance of the ship is the only standard available to measure the maneuverability of the ship. The rotary test was performed in the laboratory of Chongqing Jiaotong University. The experimental tank is 50 m long and 30 m wide. The rotary program was written using Visual Basic language, and a Differential Global Positioning System (DGPS) was equipped within the ship to capture its position information during navigation.  
At the beginning of the model test, the angle of the rudder was controlled at zero, the ship was maintained in a straight line, and a signal was sent to change the rudder angle. Next, the ship model started to enter rotational motion, and the position information was recorded by DGPS during the model test. When the ship entered a stable state of rotation, the diameter of rotation was recorded. The data of the turning test in the state of 35\({}^{\circ}\), at speeds of 0.4 m/s and 0.7 m/s, is shown in Figure 8. The ship model enters the steady state for a moment, at which time the trajectories of the left and right are symmetrical. The difference from the different navigable speeds is apparent.  
The turning test results from different rudder angles are shown in Table 2. It can be seen from the trajectory that indices such as the forward speed, the rudder angle, vertical intercept, horizontal intercept, and turning radius, which represent the turning characteristics of the model ship, should be analyzed on the basis of the turning trajectory measured [29].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Real Ship** & **Ship Model** \\ \hline Aspect ratio & 1.72 & 1.72 \\ number of blades \(Z\) & 4 & 4 \\ propeller diameter (m/cm) & 3.1 & 4.4 \\ Screw pitch (m/cm) & 2.6 & 3.7 \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._
# Hypergraph-Clustering Method Based on an Improved Apriori Algorithm
## 1 Introduction
However, the efficiency of the Apriori algorithm [22] is relatively low due to its iterative method of searching frequent itemsets in a bottom-up manner, making it unable to analyze rare information. Lately, many fruits related to intelligent clustering technology have emerged. [PERSON] et al. [23] combined machine learning with geospatial technology by studying landslides using nonlinear clustering t-SNE and Apriori association rule mining. [PERSON] et al. [24] proposed a combination method based on the fuzzy firefly algorithm and random forest and applied it to clustering in wireless sensor networks (WSNs). [PERSON] et al. [25] proposed several higher-order centralities in high-order complex networks to reflect the impact of ranking on clustering and propagation. [PERSON] et al. [26] proposed a DPC algorithm based on Chebyshev inequality and differential privacy and discussed the data privacy protection function. These studies have expanded our research ideas on clustering. Based on these studies, we propose a new clustering method based on improved Apriori and hypergraph partitioning. This method first uses t-SNE to reduce the dimensionality of the dataset and combines the improved Apriori algorithm with the hypergraph construction method to construct a hypergraph for model clustering. Then, it employs the dense subgraph partition algorithm based on multi-level hypergraph partitioning to divide the hypergraph into numerous sub-clusters. After merging the sub-clusters, the final clustering results are obtained. Finally, various methods are compared on multiple datasets through clustering evaluation indicators, and the operating efficiency of all methods is analyzed, which demonstrates the effectiveness of the proposed method from many aspects. The specific contributions of this paper are as follows:  
1. This paper extends association rules to hypergraphs, then proposes a hypergraph-partitioning high-dimensional data-clustering method based on the improved Apriori algorithm (HDHPA), providing a solution for identifying clustering results of high-dimensional data. 2. In order to avoid the generation of redundant rules and improve the mining efficiency, the parallel mining of different frequent itemsets is used to obtain hyperedges with corresponding ranks. 3. The HDHPA method improves clustering accuracy by constructing a hypergraph structure of high-dimensional data. In order to demonstrate the superiority of the method, this paper conducted numerous experiments on multiple datasets. The remaining sections of this paper are organized as follows. Section 2 affords some theoretical foundations correlated to the proposed methods. Section 3 conducts the HDHPA method and its three stages. Section 4 analyzes the experiments from different perspectives to validate the feasibility and superiority of the method. Section 5 summarizes the findings and prospects for future research directions.
## 4 Experiments
### Results and Discussion
#### 4.3.1 Results on Clustering Movements of 41 Markers (C3D Dataset)  
In Table 3, we compare the performance of the 11 Grassmann clustering methods using the C3D dataset. As discussed in Section 3, our experimental results reveal significant differences among the Grassmann approaches. The results show that the four intrinsic methods achieved the best performance, followed by two extrinsic SC methods, and three semi-intrinsic methods. In contrast, the two Grassmann kernel-based extrinsic methods yielded lower performance compared to the other approaches.  
Interestingly, the Procrustes distance outperformed other metrics such as Euclidean distance and principal angle. Furthermore, the combination of the principal angle and Procrustes distance for the \(k\)-means consistently yielded better performance than the tangent norm in the semi-intrinsic approach. In the extrinsic approach, SC with Euclidean distance performed comparably to the intrinsic methods, while KSC methods exhibited the worst performance among the 11 methods. This suggests that tangent space extrinsic methods generally outperformed Grassmann kernel methods on the C3D dataset.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Measure**} & **Clustering Methods** & **Euclidean Distance** & **Tangent Norm** & **Principal Angle** & **Procrustes Distance** \\ \hline \multirow{8}{*}{NMI} & \(k\)-means & - & 0.738 & 0.752 & 0.787 \\ \cline{2-6}  & FC-SC 1 & 0.820 (\(\sigma\) = 100) & - & 0.822 (\(\sigma\) = 10) & **0.844** (\(\sigma\) = 2) \\ \cline{2-6}  & \(m\)NN-SC 2 & 0.792 (\(\sigma\) = 3, \(m\) = 7) & - & 0.799 (\(\sigma\) = 5, \(m\) = 8) & **0.844** (\(\sigma\) = 0.5, \(m\) = 5) \\ \cline{2-6}  & PK-KSC 3 & & & 0.731 \\ \cline{2-6}  & CCK-KSC 4 & & & 0.690 \\ \hline \multirow{8}{*}{Accuracy} & \(k\)-means & - & 66.975 & 68.364 & 70.972 \\ \cline{2-6}  & FC-SC & 71.482 (\(\sigma\) = 100) & - & 72.053 (\(\sigma\) = 100) & 73.596 (\(\sigma\) = 5) \\ \cline{1-1} \cline{2-6}  & \(m\)NN-SC & 75.170 (\(\sigma\) = 100, \(m\) = 8) & - & 78.750 (\(\sigma\) = 0.1, \(m\) = 8) & **84.228** (\(\sigma\) = 0.5, \(m\) = 5) \\ \cline{1-1} \cline{2-6}  & PK-KSC & & & 64.198 \\ \cline{1-1} \cline{2-6}  & CCK-KSC & & & 66.049 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Clustering performances of 11 Grassmann clustering methods combinations for C3D dataset.
## 1 Introduction
By incorporating these thickness variations, the NOXI aligner is better able to address specific biomechanical needs, reducing the necessity for additional attachments or auxiliary devices. However, further research is required to determine the impact of stress relaxation on the efficacy of NOXI aligners compared to traditional thermoformed alternatives. Previous studies have indicated that stress relaxation is a major limiting factor in aligner therapy, as it influences both the duration and the predictability of force application. For instance, materials such as PET-G and polyurethane have been found to exhibit different rates of stress decay, with PET-G showing a faster decline in force retention [16]. Previous studies have shown that stress relaxation occurs primarily within the first 8 h, reaching a plateau thereafter [16]. As a result, this study concentrated on the early phase of force decay, which is critical for assessing aligner performance. The objective of this study was to compare the initial and final force values exerted on the upper central incisor and the upper first molar at three specific points using three types of NOXI aligners, differentiated by gingival margin cut and thickness. These results were compared with those from thermoformed aligners with different gingival margins. Additionally, the percentage of stress relaxation over time was analyzed for each type of aligner, aiming to identify which material and configuration may optimize force application for specific areas.
# Monitoring and Analysis of Slope Geological Hazards Based on UAV Images
## 5 Geographic Information Interpretation and Analysis
### Slope Stability Analysis  
Slope Gradient Analysis: The slope information of the two DEM phases was extracted using the Spatial Analyst--Surface--Slope module of the ArcMap 10.8 software, and the slopes were classified into 9 categories and set in degrees. The slope maps for both phases were then obtained (Figure 10). The maximum slope value in Phase I of the study area is 87.93\({}^{\circ}\), while the maximum value in Phase II is 87.74\({}^{\circ}\). The change in slope between the two phases is minimal. The topography of this area is steep, with Areas 1 and 3 containing numerous slopes exceeding 50\({}^{\circ}\). Data analysis indicates that soil landslides are likely to occur when the slope gradient exceeds 20\({}^{\circ}\), rocky landslides when the gradient is greater than 30\({}^{\circ}\), and rock avalanches when the gradient exceeds 45\({}^{\circ}\). This suggests that the area is in an unstable state, with a higher likelihood of landslides and rock avalanches as geological hazards.  
Slope Curvature Analysis: Slope shapes are generally classified into three basic types: convex, straight, and concave slopes [42]. A commonly used algorithm for calculating  
Figure 10: Slope map: (**a**) Phase I slope map; (**b**) Phase II slope map.  
Figure 9: Distribution map of hazardous areas.  
curvature involves fitting a surface, consisting of a 3 \(\times\) 3 window, to a second-order polynomial equation [43], as given by:  
\[Z=Ax^{2}y^{2}+Bx^{2}y+Cxy^{2}+Dx^{2}+Ey^{2}+Fxy+Gx+Hy+I, \tag{2}\]  
where \(Z\) represents the topographic surface function, \(x\) and \(y\) are the spatial positions, and coefficients \(A-I\) are calculated from the image elevation values and their respective sizes in the 3 \(\times\) 3 window. Convex slopes are more likely to generate inertial forces, which can lead to landslides under external forces. Concave slope topography facilitates the convergence of rainfall and reduces the strength of geotechnical bodies, while rectilinear slopes are relatively more stable. The curvature values of the DEM were extracted, with standard curvature greater than 0 for convex slopes, less than 0 for concave slopes, and equal to 0 for straight slopes. The curvature maps of the study area were then generated (Figure 11). The curvature maps of the two phases are similar, with convex and concave slopes interspersed in Areas 1 and 3, exhibiting complex and variable slope shapes. This indicates that the slopes in these areas are unstable and prone to geological hazards such as landslides and rockfalls. Areas 1 and 3 are susceptible to slope hazards, particularly under conditions such as heavy rainfall and freeze-thaw cycles. Preventive reinforcement is recommended to mitigate potential risks to nearby pedestrians and road infrastructure.
## 4 Nonlinear Analyses
### Analysis of the Regular Bridge (RB)  
The RB was analyzed at several seismic intensity levels: from PGA = 0.175 g to PGA = 0.7 g, with PGA = 0.35 g being the design value.  
Since the response of this bridge was governed by one dominant mode (Mode 2), with Mode 2 and Mode 4 being the modes considered in the multimodal approach, and since the mode shape was not changing significantly (it was not considerably influenced by the occurrence of new hinges), the estimated response was practically the same, regardless of the method used (MPA, SPA or UPA) in the analysis (Figures 14-17). The estimated response has a good agreement with the results of NRHA for PGA = 0.175 g (SF = 0.5) and PGA = 0.35 g (SF = 1.0).  
Figure 12: Regular bridge—deck displacements derived by performing pushover analysis (ag = 0.7 g), with a load pattern proportional to the main mode shapes, with respect to different monitoring points (M.P.). Pushover with Mode 2 (a) or Mode 4 (b).  
Figure 13: Irregular bridge—deck displacements derived by performing pushover analysis (ag = 0.7 g), with a load pattern proportional to the main mode shapes, with respect to different monitoring points (M.P.). Pushover with Mode 1 (a), Mode 3 (b) or Mode 4 (c).  
Figure 16: Regular bridge—pier drift (transversal top displacement/height) derived by performing nonlinear dynamic analysis and pushover analysis according to the approaches considered (PGA from 0.175 to 0.7 g).  
Figure 14: Regular bridge—deck displacements derived by performing nonlinear dynamic analysis and pushover analysis according to the approaches considered (PGA from 0.175 to 0.7 g).  
Figure 15: Regular bridge—deck displacements derived by performing nonlinear dynamic analysis and pushover analysis according to the approaches considered (PGA from 0.175 to 0.7 g).  
Analyzing in Figure 18 the capacity curves obtained by applying the IMPA\(\beta\) and comparing them with IDA results, it was confirmed that the use of the incremental modal pushover analysis allowed to describe the structural response with excellent accuracy, and without relevant estimation errors, inside the intensity range for which the bridge was designed. Indeed, the use of the second pushover approach (UPA) brought us to conservative results in terms of deck displacements related to the seismic intensity considered, but it underestimated the base shear if the capacity curve was considered. The u\({}_{r}\)-Sa curve showed how, for an intensity level (Sa) beyond the design value (0.35 g), the displacement estimate with IMPA\(\beta\) differs from IDA, but it is conservative, whereas the u\({}_{r}\)-V\({}_{b,x}\) curve (V\({}_{b,x}\) is the base shear evaluated for all the piers) better matched the curve derived from IDA since, beyond the design intensity (V\({}_{b,x}\)\(\sim\) 9200 kN), the higher displacements derived with IMPA\(\beta\) are related to a base shear value that are very similar, since the bridge (hinges of the piers) is in a plastic stage.