esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Proposed Calculation Method
### Calculation of the Horizontal Displacement in an Existing Tunnel
#### 2.3.2 Derivation of Displacement Function of Existing Tunnel  
According to the energy variation method, we can assume that the horizontal displacement function of the shielded tunnel is given by  
\[\omega(y)=\sum_{n=0}^{\infty}a_{n}\cos(\frac{n\pi y}{ND_{t}})=\{T_{n}(y)\}A^{T} \tag{21}\]where \(T_{n}(y)=\left\{1,\,\cos\left(\frac{\pi y}{ND_{t}}\right),\,\cos\left(\frac{2\pi y} {ND_{t}}\right),\cdots,\,\cos\left(\frac{n\pi y}{ND_{t}}\right)\right\}\), \(A\) is the undetermined coefficient matrix in the displacement function, \(A=\left\{a_{0},\,a_{1}\cdots\,a_{n}\right\}^{T}\), and \(n\) represents the expansion order of the Fourier series.  
Taking the derivation of each undetermined coefficient on both sides of Equation (16) yields  
\[\frac{\partial W_{\sigma}}{\partial a_{i}}=\frac{\partial W_{\mathrm{R}}}{ \partial a_{i}}+\frac{\partial W_{\mathrm{S}}}{\partial a_{i}}+\frac{\partial W _{\mathrm{T}}}{\partial a_{i}} \tag{22}\]  
where \(a_{i}\) is the \(i\)th element in matrix \(A\), and \(i=1,\,2,\,3,\,\cdots,\,n\).  
Substituting Equations (17)-(20) into Equation (22) leads to  
\[\begin{array}{l}\left\{\begin{array}{l}N_{-1}\\ \sum\limits_{m=-N}^{N_{-1}}\left[\begin{array}{c}\left(k_{\mathrm{s}}(1-j)^{ 2}+\frac{k_{\mathrm{s}}\rho^{2}D^{2}}{3D_{t}^{2}}\right)\\ \frac{\partial(w((m+1)D_{t})-w(mD_{t}))}{\partial a_{i}}\\ \left(T_{n}((m+1)D_{t})-T_{n}(mD_{t})\right)\end{array}\right]+\int_{-ND_{t}}^{ ND_{t}}kD\frac{\partial w(y)}{\partial a_{i}}T_{n}(y)dy\\ =\int_{-ND_{t}}^{ND_{t}}\sigma(y)\{T_{n}(y)\}^{\mathrm{T}}dy\end{array}\right\} \times A^{\mathrm{T}}\\ \end{array} \tag{23}\]  
Simplifying Equation (23) into a matrix form results in Equation (24):  
\[([K_{r}]+[K_{\mathrm{s}}])A^{\mathrm{T}}=\{\sigma_{x}\}^{T} \tag{24}\]  
where \([K_{r}]A^{\mathrm{T}}\) is the interaction effect between the segment rings, \([K_{r}]\) stands for the matrix of the stiffness between the segment rings, \([K_{\mathrm{s}}]A^{\mathrm{T}}\) represents the effect of the resistance of the formation, \([K_{\mathrm{s}}]\) is the soil (formation) stiffness matrix, and \(\{\sigma_{x}\}^{T}\) indicates the effect of horizontal additional stress on the tunnel caused by grouting.  
From Equation (24), undetermined coefficient matrix \(A^{\mathrm{T}}\) can be obtained as follows:  
\[A^{\mathrm{T}}=([K_{r}]+[K_{\mathrm{s}}])^{-1}\{\sigma_{x}\}^{T} \tag{25}\]  
Substituting \(A^{\mathrm{T}}\) into Equation (21), the calculation function of the lateral horizontal displacement of the tunnel can be expressed by  
\[\omega(y)=\{T_{n}(y)\}A^{\mathrm{T}} \tag{26}\]  
The above calculations were programmed and calculated by MATLAB(r), and an expansion coefficient (\(n\)) of 10 could fulfill the calculation accuracy requirements.
## 5 Discussion
According to the MAPE measure, the research estimation of PCIs outperforms the previous results in 12 samples out of 16 samples. In particular, from eight samples of gamma distribution, the research estimation perform better in six samples, whereas PCI estimations of Beta distribution samples using this research approach are always better. Regarding the Weibull distribution samples, the approach of this research performs well with large samples. The variations among the estimated multivariate PCIs are due to the associated randomness in the data. The randomness sources exist in different steps of the proposed methodology, starting with the data generation of the used data for evaluating the proposed methodology or for estimating the PNCs. The variations observed in multivariate \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{2}{c}{**Results**} & \multicolumn{2}{c}{**[41]**} & \multirow{2}{*}{**Actual**} \\ \cline{2-2} \cline{4-6}  & \(\mathbf{C_{p}}\) & & **MAPE** & & \(\mathbf{C_{p}}\) & **MAPE** \\ \hline
1 & 0.932 & 4.7\% & 0.864 & 2.9\% & 0.89 \\
2 & 0.895 & 0.6\% & 0.865 & 2.8\% & 0.89 \\
3 & 0.872 & 2.0\% & 0.872 & 2.0\% & 0.89 \\
4 & 0.892 & 0.2\% & 0.888 & 0.2\% & 0.89 \\
5 & 1.155 & 2.1\% & 1.208 & 2.4\% & 1.18 \\
6 & 1.2117 & 2.7\% & 1.258 & 6.6\% & 1.18 \\
7 & 1.1806 & 0.1\% & 1.148 & 2.7\% & 1.18 \\
8 & 1.205 & 2.1\% & 1.172 & 0.7\% & 1.18 \\
9 & 0.957 & 14.6\% & 0.885 & 21.0\% & 1.12 \\
10 & 1.088 & 2.9\% & 1 & 10.7\% & 1.12 \\
11 & 1.041 & 7.1\% & 0.997 & 11.0\% & 1.12 \\
12 & 1.102 & 1.6\% & 0.975 & 12.9\% & 1.12 \\
13 & 1.685 & 31.6\% & 1.411 & 10.2\% & 1.28 \\
14 & 1.125 & 12.1\% & 1.298 & 1.4\% & 1.28 \\
15 & 1.278 & 0.2\% & 1.267 & 1.0\% & 1.28 \\
16 & 1.284 & 0.3\% & 1.297 & 1.3\% & 1.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparing research results with previous results. data generation using the Monte Carlo simulation from one run to another depend on several factors, such as the number of samples drawn from the distribution. The larger the number of samples, the more accurate and representative the synthetic data will be of the true distribution. However, larger sample sizes also require more computational resources and time. Another factor is the random number generator used to draw the samples. The quality and reliability of the random number generator affect the randomness and independence of the samples. A poor random number generator may introduce bias or correlation in the synthetic data that is not present in the true distribution. Therefore, generating data from a specific random distribution with specific parameters many times will result in different data in each run. Moreover, the proposed methodology involves randomness in terms of searching for the best root transformation. Each run may result in a different root for transforming the data and will generate different sample for comparing with the transformed specification limits. Consequently, slight differences of multivariate PCIs are experienced from different replications.
## 3 Results and Discussion
### Modeling of Static Deformations and Manipulator Errors under Elastic Pliability of Robot Links
\begin{bmatrix}0.5&0&0&0&-1\\ 0&0.72&-1.8&-1.2&0&0\\ 0&-1.8&8.5&3&0&0\\ 0&-1.2&3\,2&0&0\\ 0&0&0&0&0&0\\ -1&0&0&0&2\end{bmatrix} \cdot 10^{-6}. \tag{61}\]  
The matrix \(E\) has the property of symmetry and the main diagonal of the elements is positive. Calculation of the vector of errors of the gripper position. We assume that the gripper holds a longitudinal object weighing \(\mathrm{G}=200\;\mathrm{N}\), the center of gravity of the object is locatedat a distance of \(b=0.5\) m in the horizontal direction from the pole M of the gripper (Figure 2). We bring the gravitational forces G to the pole M. There will be a concentrated load of F\({}_{\rm z}=\) G =\(-200\) N and moment M\({}_{\rm x}=-G\cdot b=-200\cdot 0.5=-100\) N\(\cdot\)m. So, the column vector of loads (8) in this case has the form:  
\[\rm Q=[0;\ 0;-200;-100;\ 0;\ 0\ ]^{\rm T}. \tag{62}\]  
Applying (11), we determine the vector of position errors of the gripper  
\[\rm\delta_{M}=E\cdot Q= \begin{bmatrix}0\\ 0.48\\ -2\\ -0.8\\ 0\\ 0\end{bmatrix} \cdot 10^{-3}= \begin{bmatrix}\Delta x_{M}^{(0)}\\ \Delta y_{M}^{(0)}\\ \Delta z_{M}^{(0)}\\ \phi_{x}^{(0)}\\ \phi_{y}^{(0)}\\ \phi_{z}^{(0)}\end{bmatrix} . \tag{63}\]  
The results of the calculation (26) show that the pole M of the gripper as a result of the loads shifted to the right by \(0.48\cdot 10^{-3}\) m and down by \(2\cdot 10^{-3}\) m. At the same time, the gripper tilted at an angle of \(0.8\cdot 10^{-3}\) rad clockwise around the \(x_{0}\) axis.
# Gas-Liquid Mixability Study in a Jet-Stirred Tank for Mineral Flotation
## 3 Results and Discussion
### Influence of Nozzle Radius Ratio on Mixing Uniformity  
For the purpose of investigating the influence of the positional relationship between the nozzle and vessel body on the mixing homogeneity, the key parameter of nozzle radius ratio, the ratio of the position of the nozzle, r, to the radius of the vessel body, R, was introduced. Five representative working conditions are selected in this study: r: R = 0.45, r: R = 0.50, r: R = 0.55, r: R = 0.60, and r: R = 0.65. r: R = 0.65 represents the maximum ratio ensuring that the nozzle does not contact the wall. The nozzle direction for all five models is circumferential, with a nozzle radius of 5 mm and a nozzle height of 80 mm from the bottom surface. Figure 20 is the contour of gas volume fraction distribution for different radius ratios.  
Figure 21 depicts the gas volume fraction profile as a function of height, elucidating the relationship between the gas volume fraction and the radius ratio. Below the height z = 0.19 m, the gas volume fraction exhibits a decreasing trend with increasing radius ratio at identical spatial heights. However, beyond this threshold, a reversal in the trend is observed, where the gas volume fraction gradually increases with higher radius. Upon comprehensive analysis of the entire curve, it becomes evident that the slope is minimized at r: R = 0.55, indicating a smoother variation in the gas volume fraction with height and thereby enhancing the homogeneity of the reaction process under these conditions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **12.5 mm** & **8.4 mm** & **6.3 mm** & **5.0 mm** & **4.2 mm** \\ \hline Average & \(1.31\times 10^{-2}\) & \(1.48\times 10^{-2}\) & \(1.81\times 10^{-2}\) & \(1.82\times 10^{-2}\) & \(1.93\times 10^{-2}\) \\ Variance & \(1.49\times 10^{-4}\) & \(8.85\times 10^{-5}\) & \(5.22\times 10^{-5}\) & \(4.08\times 10^{-5}\) & \(6.13\times 10^{-5}\) \\ DV & \(5.76\times 10^{-15}\) & \(7.57\times 10^{-16}\) & \(7.93\times 10^{-16}\) & \(1.54\times 10^{-16}\) & \(2.10\times 10^{-16}\) \\ \hline \hline \end{tabular}
\end{table}
Table 11: Average and variance of different nozzle inner diameters.  
Figure 19: Gas volume fraction curve with height for different nozzle diameters; **(a)** all working conditions; **(b)** local zoom in grey area.  
Table 12 summarizes the mean, variance, and dimensionless variance for different nozzle radius ratios. Based on the distribution curves and data analysis, a nozzle radius ratio of r: R = 0.55 was determined to be the optimal operational condition. This finding underscores the importance of nozzle radius ratio in achieving effective gas-liquid mixing and uniform distribution.
# FAmesh: Generating Frequency Adaptive Meshes from Single Images under 2D Hole Constraints
## 1 Introduction
First, a structure that incorporates multilayer perceptron (MLP) and graph convolutional neural networks (GCN) can reduce the number of graph neural network (GNN) layers by restoring the global shape of the mesh using cascaded MLP deformation blocks, thereby reducing memory consumption and over-smoothing issues [26]. At the same time,  
Figure 1: The first challenge for single-view reconstruction. Figure 2: The second challenge for single-view reconstruction. we believe that the 2D image contains the whole information in the corresponding view. On the basis of this assumption, we employ a novel mesh pruning strategy constrained by 2D holes to restore the correct mesh topology during the global shape recovery stage. Another key idea of this paper is to use an extended patch extract module to make the framework transition naturally from global to local, and then design a dual-branch refinement block composed of FAGCN [27] to fine-tune the high-frequency and low-frequency parts. The dual-branch local refinement structure can adaptively utilize features of different frequencies so that the high-curvature branch can utilize maximally high-frequency information while the low-curvature branch suppresses high-frequency features. To ensure the visual effect of the local mesh, we simultaneously design a local loss suitable for optimization on the local patch. Finally, quantitative and qualitative experiments demonstrate that the proposed method outperforms existing methods. The contributions of this paper can be summarized as follows:  
1. We propose a framework for single-view mesh reconstruction that transitions from global to local, combining the advantages of MLP and GNN and mitigating the over-smoothing caused by deep GNN. 2. We propose a new strategy for mesh pruning under the constraint of 2D holes that overcomes the limitation of the 0-genus template by combining hole contour information from 2D images to perform adaptive mesh topology correction. 3. We facilitate fine-tuning of parts with different curvatures by separating the high- and low-frequency parts of the mesh and learning the corresponding mapping functions on the local extension patches of the high and low frequencies. 4. We designed a series of experiments to demonstrate the superiority of the proposed method in topology correction and detail reconstruction over the existing methods.
## 3 Optical Buffering and TSI with Integrated Delay Lines  
### Concept  
The disaggregated DC paradigm imposes stringent requirements on the interconnection network, creating new challenges in terms of bandwidth and forward latency on the DC switches. Specifically, failing to meet these latency requirements will result in underutilization of the disaggregated DC resources that cancels out the performance advantages disaggregation targets to. Considering that most of this latency is coming from o-e-o conversion, keeping the data in the optical domain is expected to significantly lower the end-to-end latency. However, contention resolution at the switching matrix, arises as a significant problem due to the lack of practical optical RAM, despite recent promising demonstrations [46]. A solution to mitigate this burden is limited-size optical buffering using optical delay lines, already proven advantageous in IP networks [47], in conjunction with the right protocol that can ensure reduced latency values in Disaggregated DC Interconnect (DCI) environments. In this direction feed-forward buffering schemes and TSIs might eventually have a new opportunity for turning into practical elements for real applications towards latency- and energy savings coming from power hungry electronic circuitry employed so far in DC routers.  
Demonstrating such an optical based packet router in an integrated form mandates that the photonics platform should be capable both for switching the optical packets and also buffering them in suitable delay lines. This technology would then allow, the migration of fiber-based delaying and TSI deployments demonstrated so far [48; 49; 50] towards ultra-compact and highly-functional modules suitable for cooperation with integrated switch matrix designs, such as the one presented in Section 2.  
The Thick-Silicon photonics platform holds the credentials for such an undertaking allowing the integration of long spiral waveguides, inducing delays of up to a few tens of nanoseconds, while maintaining a reasonable total power budget due to their extremely low-loss (<0.15 dB/cm). This buffering time can either be extended through the use of cascaded stages of feed-forward buffers, as demonstrated in [49], or it can be utilized more efficiently by a sophisticated optical switch architecture, as proposed in [51]. By employing this approach, throughput values higher than 80% can be achieved [51], even using ns inducing waveguides, showing the way for integrated functional sub-systems.
## 2 Materials and Methods
### Preparation of Self-Healing Coatings for Corrosion and Mechanical Tests  
Epoxy resin was mixed with reactive diluent with a 3:1 weight ratio to reduce its viscosity. The produced nanocapsules were dispersed into diluted epoxy resin using mechanical stirring with a speed of 200 rpm for 5 min. Then, the curing agent was added with a proportion of 100:50 (mass ratio of epoxy to polyaminoamide). The nanocapsules' content inside the prepared mixture was set at 1, 2, and 4 wt.%. Before applying the coating on the steel panels, their surface was polished with sandpaper and washed by acetone to eliminate any contaminants on the surfaces. The panels were coated by epoxy mixtures using a film applicator (Zehtner Zau 2000.80, Zurich, Switzerland) and the thickness of the coatings was controlled to 100 \(\upmu\)m. The coatings were allowed to cure for seven days at room temperature. For the self-healing evaluations, the cured coatings were scratched using a scalpel blade. The scratched coatings were then kept at room temperature for seven days to enable the healing process of the coating. The control panels were prepared by the same procedure but without embedding any nanocapsules into the resin.
## 3 Results and Discussion
### Comparison with Other Recently Proposed Algorithms  
#### 3.4.1 Experimental Results on 10D, 20D, and 30D Test Problems  
Four recently proposed SAEAs were first selected as comparison algorithms, i.e., HSAOA, DSP-SAEA, BiS-SAHA, and FSAPSO, and they were compared with the proposed MSAMT on 10D, 20D, and 30D 14 test functions to evaluate the performance of the MSAMT. The HSAOA is a hierarchical surrogate-assisted optimization algorithm that alternately uses DE and TLBO. During the local search phase, the HSAOA selects the samples that are closest to the optimal solution or have the best fitness value to construct a novel dynamic ensemble of surrogates. The DSP-SAEA is a two-stage search algorithm that integrates the global search phase based on decision space partition strategy with the local search phase using an adaptive surrogate within the trust region. The BiS-SAHA performs the global and local search stages in turn using the SL-PSO assisted by a surrogate ensemble and  
Figure 5: Convergence curves of the MSAMT with/without decision space partition on 20D F2, F3, F5, and F9 (From **(a)** to **(d)** are the convergence curves of F1, F3, F5, and F9, respectively).  
RBF-assisted DE. The FSAPSO is a fast optimization technique using global RBF-assisted PSO that suggests a novel evaluation criterion to select particles for real function evaluation.  
Table 14 demonstrates that the suggested MSAMT had a superior performance compared to the other SAEAs, with the best results on 26 functions and the second-best results on 3 functions. Compared with the HSAOA, the MSAMT had a better performance on 28 test problems. Both algorithms used a dynamic ensemble of surrogates developed from the same ensemble. However, the dynamic ensemble of surrogates proposed by the MSAMT had a better fitting performance, which is helpful for the algorithms to converge better. The MSAMT significantly outperformed the DSP-SAEA on 66.7% of the test functions. Despite the introduction of the decision space partition strategy from the DSP-SAEA into the global search, the MSAMT utilizes the G-MFEA to seek the optimal solution, thus facilitating information exchange between different decision space regions and preventing premature convergence to local optima. The MSAMT had a better performance than the BiS-SAHA on 31 out of 42 functions. Both use a surrogate ensemble, but the G-MFEA employed by the MSAMT enables the algorithm to converge better. The MSAMT had a better performance than FSAPSO on 73.8% of the test functions. The FSAPSO uses only the global RBF model, while the MSAMT simultaneously utilizes the RBF model and dynamic ensemble of surrogates, which makes the MSAMT perform better than the FSAPSO.  
The convergence curves of the MSAMT and the four comparison algorithms on 10-, 20-, and 30-dimensional test functions are given in Figures 15-16, respectively. According to the figures, the MSAMT outperformed the competing algorithms overall, with better convergence on most of the test functions. The preceding analysis indicates that MSAMT is competitive for low- and medium-dimensional problems.
# Satellite Attitude Determination and Map Projection Based on Robust Image Matching
## 2 Datasets  
This section describes the satellite images used for attitude determination and map projection, and the images used as the base map.
## 4 Results and Discussion
### Pile-Wall Spacing Factor Analysis
#### 4.3.1 Influence of Pile-Wall Spacing on the Bearing Characteristics of the USCSP  
(1) Horizontal displacement of the USCSP  
Figure 13 shows the comparative analysis of pile displacement for different pile-wall spacing, and the pile displacement gradually decreases with the increase in pile-wall spacing. This is because the increase in pile-wall spacing leads to a weakened interaction effect between the supporting structure and the retaining wall caused by excavation unloading. At 1 m excavation, when the pile-wall gap increases from 1.0 m to 4.0 m, the pile top displacement reduces from 7.2 mm to 6.2 mm, decreasing by 13.9%; at 2 m excavation, when the pile-wall gap increases from 1.0 m to 4.0 m, the pile top displacement reduces from 14.4 mm to 11.7 mm, decreasing by 18.6%.  
(2) Internal force of the USCSP  
Figure 14 shows the variation rule of pile section stress at different pile-wall spacing values, and the pile stress gradually decreases as the pile-wall spacing increases, and the interaction influence between the supporting structure and the retaining wall gradually weakens as the pile-wall gap expanding. The maximum stress of the pile section appears at about 7.5 m from the pile's top. When the pile-wall gap grows from 1.0 m to 4.0 m at 1 m excavation, the maximum tensile stress reduces from 526.1 kPa to 400.9 kPa, decreasing by 23.8% and the maximum compressive stress reduces from 743.3 kPa to 569.0 kPa, decreasing by 23.4%; when the pile-wall gap expands from 1.0 m to 4.0 m at 2 m excavation, the maximum tensile stress decreases from 998.3 kPa to 784.5 kPa, decreasing by 21.4%, and the maximum compressive stress decreases from 1323.5 kPa to 1067.2 kPa, decreasing by 19.4%.
Similarly, in [22], a high gain of 7 dBi is achieved for the mmWave band antenna. However, the proposed work has several flaws, including no information for gain and radiation efficiency for the lower band and with no solution for MIMO applications mentioned. On other hand, in [23], researchers proposed a 2-element MIMO antenna for 4G applications integrated with a-4 element MIMO array antenna for 5G mmWave applications. Although high gain and wideband is achieved at a high-frequency band, the design still has several limitations, i.e., the non-inclusion of the entire LTE and lower 5G bands, low isolation between the antenna elements and larger footprint. Concluding the above literature overview, it can be inferred that the designing of wideband, high gain, low mutual coupling and the compact design-based integrated antenna is still a challenge for the research community. Therefore, this article reports an integrated prototype for the sub-6 GHz (mid-band) and 5G mmWave spectrums, for the 4G LTE and 5G handheld applications. For the two bands, the reported design includes two separate MIMO configurations. In the sub 6 GHz spectrum, the proposed design effectively operates in the lower 5G/4G LTE, i.e., 3.3-4.2, 4.4-5.0, 4.8-5.0 and IMT 2.5-2.690 GHz bands. In addition, the design also operates effectively in the 5G mmWave band, i.e., 24.25-27.5 GHz. Aside from the wide bandwidth coverage, the proposed architecture was meticulously examined in terms of both single and MIMO antenna performance. Owing to the high-performance parameters of the antenna and proper MIMO characteristics, the proposed design may be considered as a potential candidate for mid- and high-band handheld applications.