esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Methodology
### Functional Analysis of Variance (Functional ANOVA)  
The functional ANOVA framework for evaluating the importance of hyperparameters was first proposed by [PERSON] et al. [22]. Since we will use this technique to obtain the importance of hyperparameters, we now go over it in more depth.  
We first introduce notation. Assuming that RF classification has n hyperparameters with domains \(\Theta_{1},\ldots,\Theta_{n}\) and configuration space \(\Theta=\Theta_{1}\times\cdots\times\Theta_{n}\). Let \(N=\{1,\ldots,n\}\) be the set of all hyperparameters of RF. An instantiation of RF is a vector \(\theta=\langle\theta_{1},\ldots,\theta_{n}\rangle\) with \(\theta_{i}\in\Theta_{i}\). A partial example of RF is a vector \(\theta_{U}=\langle\theta_{i},\ldots,\theta_{i}\rangle\) with a subset \(U\subseteq N\) of the hyperparameters.  
Functional ANOVA decomposes a function \(\hat{y}:\Theta_{1}\times\cdots\times\Theta_{n}\rightarrow\mathbb{R}\) into additive components that only depend on the subsets of the hyperparameters \(N\):  
\[\hat{y}(\theta)=\sum_{U\subseteq N}\hat{f}_{U}(\theta_{U}) \tag{1}\]  
The components \(\hat{f}_{U}(\theta_{U})\) are defined as:  
\[\hat{f}_{U}(\theta_{U})=\left\{\begin{array}{ll}\hat{f}_{\varnothing}& \text{if }U=\varnothing\\ \hat{a}_{U}(\theta_{U})-\sum_{W\subseteq U}\hat{f}_{W}(\theta_{W})&\text{ otherwise}\end{array}\right. \tag{2}\]  
where \(\hat{a}_{U}(\theta_{U})\) means the average performance of all complete instantiations \(\theta\) that agree with \(\theta_{U}\) in the instantiations of hyperparameters \(U\). The unary functions \(\hat{f}_{\{j\}}(\theta_{\{j\}})\), namely main effects, capture the effect of varying hyperparameter \(j\)[23].  
We construct an RF regression prediction model, the hyperparameter configuration space is utilized as a feature, and the performance (e.g., recall or roc_auc score) of the RF classifier is used as a label. It is equally important in the power system to correctly discriminate between normal and attack samples. The area under curve (AUC) metric, which is defined as the roc_auc score in this paper, is chosen as the hyperparameter assessment criterion because it considers the classifier's capacity to classify both positive and negative data. We then take advantage of functional ANOVA to decompose the  
Figure 2: Random forest classifier model.  
variance of each \(\hat{y}\) into contributions due to each subset of hyperparameters, as indicated by the formula:  
\[\mathbb{V}=\sum_{U\subset N}\mathbb{V}_{U}\text{, with }\mathbb{V}_{U}=\frac{1}{\| \Theta_{U}\|}\int\hat{f}_{U}(\theta_{U})^{2}d\theta_{U} \tag{3}\]  
where \(\frac{1}{\|\Theta_{U}\|}\) is the probability density of the uniform distribution across \(\Theta_{U}\).  
Functional ANOVA thus provides us with the relative variance contributions of each individual hyperparameter.
## 4 Datasets and Experimental Results
### Comparison to SOTA Methods  
In this section's final experiment, we compare our proposed method to some previously introduced SOTA spatial-spectral HSI classification methods, namely [PERSON] et al. [23], [PERSON] et al. [32], [PERSON] et al. [27], [PERSON] et al. [33], [PERSON] et al. [34], [PERSON] et al. [37], [PERSON] et al. [39], and [PERSON] et al. [25]. The comparison experiment demonstrates the innovative strength and key advantages of the proposed SF-ICNN method. The results are shown in Table 5 and represent a fair comparison as each approach takes into account the same percentage of training and testing data. This table shows that on both the IP and PU datasets, the SF-ICNN methodology showed higher overall classification accuracies than various current SOTA spatial-spectral HSI classification approaches.  
The main innovative point of the SF-ICNN method lies in its iterative integration of spectral-fractal features and the CNN's PMs. By using spatial information in different stages of the classification, SF-ICNN can extract more discriminating features and refine the classification results iteratively. This is a significant improvement over previous SOTA methods, which only use spectral features, without considering the information contained in the FFs and PMs resulting from the CNN for HSI classification.  
In respect of the computational time, the proposed SF-ICNN offers a processing time of around 100 s on the IP dataset, which may not be as fast as traditional non-deep approaches such as [23] or [32], which need a few seconds, but still better than some other non-deep approaches such as [27] by more than 300 s and deep-learning based techniques such as [34] that need more than 900 s for HSI classification. Our computation times can be improved by using advanced hardware such as GPU and parallel-processing techniques, improving its performance for larger-scale HSI classification tasks.  
The proposed SF-ICNN method combines fractal-spectral features and CNNs with iterative loops to achieve high classification accuracy while maintaining computational efficiency. These results show the innovative nature and advantages of the SF-ICNN method and highlight its potential as a powerful and straightforward deep-learning framework for HSI classification.
## 4 Experimental Results
### Displacement Ductility  
The structural ductility can describe the relative deformation capacity under seismic loads. The displacement ductility factor (\(\mu\)) is the ratio of the ultimate displacement to the yield displacement, which can be calculated using Equation (2) [52; 53].  
\[\mu=d_{u}/d_{y} \tag{2}\]  
By substituting the values of \(d_{u}\) and \(d_{y}\) for the IAP and GIAP specimens listed in Table 2 into Equation (2), the \(\mu\) for the GIAP specimen (2.14) is 1.67 times larger than that for the IAP specimen (1.28). The IAP specimen is classified as having moderate ductility with an average deformation capacity during earthquakes [54]. The GIAP specimen has a greater deformation capacity and better seismic performance than the IAP specimen.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Specimen** & \(F_{y}\) **(kN)** & \(F_{u}\) **(kN)** & **Elastic Range (0\(-\)\(d_{A}\)) (mm)** & **Elastic Range (\(d_{A}\)\(-\)\(d_{y}\)) (mm)** & \(d_{u}\) **(mm)** \\ \hline IAP [36] & 46.6 & 52.5 & 0–12 & 12–19.4 & 24.8 \\ \hline GIAP & 56.1 & 56.6 & 0–37.7 & 37.7–50.5 & 108.1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the skeleton curve parameters.  
Figure 14: Skeleton curve and parameters: (**a**) skeleton curve; (**b**) parameters of the skeleton curve determined using the Park method.  
Therefore, the relative deformation capacity of the GIAP specimen is underestimated if the girder is not considered.
# Deformation Analysis of Large Diameter Monopiles of Offshore Wind Turbines under Scour
## 5 Sensitivity of Pile Head Displacement under Scour
### Pile Length  
Figure 17 shows the normalized horizontal displacement and scour sensitivity of pile head under different pile lengths. The length of pile increases from 40 m to 60 m; the normalized horizontal displacement of pile head decreases from \(11.925\times 10^{-3}\) (47.7 mm) to \(4.55\times 10^{-3}\) (18.2 mm), becoming 38% of the original; and the scour sensitivity decreases from 2.35 to 1.34. It can be seen that increasing the pile length can significantly reduce the horizontal displacement of the pile body, and at the same time, the scouring sensitivity is also greatly reduced, which means the displacements are affected by scour to a lesser extent.  
When the pile length reaches 50 m, the pile head displacement is \(4.675\times 10^{-3}\), and the scour sensitivity \(S\) is 1.37. After that, increasing the pile length will not lead to an obvious change of horizontal displacement and scour sensitivity, so it could be considered as a critical value.
## 6 Space-Segment Optimization Aspects
### Constellation Maintenance  
#### 6.6.1 Orbital Perturbations  
The orbital elements under the influence of perturbations result in osculating elements. These perturbations are due to Earth's oblateness, atmospheric drag, solar radiation pressure, and third body effects. These time-dependent osculating elements change differently for satellites at different points in orbital planes. This results in a relative drift between each satellite changing the constellation pattern and ground coverage over time. The in-plane Sat spacing and plane-to-plane RAAN spacing vary over time, requiring maneuvers for corrections. For LEO Sat, the most significant perturbations are due to Earth oblateness, atmospheric drag, and solar radiation pressure [132].  
Earth's gravitational potential due to non-spherical earth is presented in spherical harmonics. \(J_{2}\) has the major effect; the higher order zonal, sectoral, and tesseral harmonics in order of magnitude are three times smaller than \(J_{2}\). \(J_{2}\) produces secular rates in RAAN \(\Omega\), argument of perigee \(\omega\), and mean motion \(n\). The Argument Of Latitude (AOL) \(u\), which is defined as the sum of \(\Omega\) and true anomaly \(\theta\), also experiences a secular change as a result of \(J_{2}\). The nodal precession is the rate of change of RAAN, whereas the apsidal precession refers to the precession of the line of nodes on the orbital plane. The atmospheric drag affects the semi-major axis \(a\) and eccentricity \(e\) of the orbit. \(J_{2}\) or drag does not affect the inclination. The third body effects for LEO satellites are also very small in comparison to \(J_{2}\). Deviations in \(a\), \(e\), and \(i\) will result in secular drifts in \(\Omega\), \(\omega\), and \(n\)[93].
# Navigating the Maps: Euclidean vs. Road Network Distances in Spatial Queries
## 3 Methodology
### Classification
#### 3.3.2 Classification Process  
To ensure comprehensive and accurate results, 30 query points were randomly selected from the residential address dataset in each city under study, thereby preventing clustering in a single location. This approach encourages a diverse representation of scenarios within the sample, thus enhancing result variability. The categorization of each query point into distinct groups based on the density of the surrounding POIs is a pivotal step in the methodology. This categorization employs four varying buffer sizes to calculate density, thereby assigning each point to the appropriate category.  
The density calculation involves overlaying the buffer on the mesh block, thereby incorporating weights derived from overlapping POI buffer zones at different distances. The resulting values generate a heatmap (see Figures 11-15), thus categorizing density into five distinct classes. Each class represents a unique density level, thus facilitating the observation and analysis of different scenarios. This classification process aids in evaluating the accuracy of Euclidean and road network distance methods under varying POI density conditions.  
Significantly, the characteristics of POI density varied between datasets, especially in the ambulance and hospital datasets. Despite utilizing the same query points in each dataset, the categorization may differ due to these density variations. The experiment comprised 300 samples, with 30 query points randomly selected from each city in the hospital and ambulance datasets. The cumulative count of query points in each category is as follows: Class One (73 points), Class Two (58 points), Class Three (55 points), Class Four (55 points), and Class Five (59 points). This ensures a reasonably equitable distribution, thereby minimizing the impact of data imbalance on the results.  
The balanced distribution of samples across categories enhances the reliability of experimental results, thereby allowing for a robust evaluation of the accuracy of both Euclidean and road network distance methods. This balanced approach minimizes potential biases from unequal representations of different density levels, thus enabling a fair comparison
## Challenges and Potential Solutions
### Potential Health Issues  
The massive data rate (terabit/seconds) in the THz band and available bandwidth can be exploited in fast communication networks. Although experts projected that the 6G networks and applications are still inchoate, 6G could benefit from the very high-frequency bands (100 GHz to 1 THz). Thus, considering human safety, which could be affected by the propagation of THz waves, is necessary.  
Notably, THz radiation is nonionizing because the photon energy is insufficient (0.1 to 12.4 meV). In other words, the magnitude of an ionizing photon's energy levels is three times higher than that of the nonionizing photon [83, 84]. The Federal Communications Commission (FCC) [85] and the International Commission on Non-Ionizing Radiation Protection standards [86] are utilized to protect humans from potential hazards such as those to the eyes and skin tissues, which are highly sensitive to heat due to the low level of blood flow. In addition, the biological and molecular impact of THz radiation on the environment requires careful consideration. Electromotive force transmission is another novel concept which will be presented in 6G to mitigate health issues [87].
# Bit Streaming Processing Algorithms for Intelligent Hardware Converters
## 2 Materials and Methods
### Bit-Stream Multiplication Process  
The main operation for bit stream processing algorithm implementation is streaming multiplication (SM). In order to perform this operation, the one for multiplied code should be converted into a pulse frequency modulated bit stream (PFM bit stream), while the other should be converted into a pulse width modulated signal (PWM signal) stream.  
The conversion of a binary code to a pulse frequency modulated bit stream involves representing the code as a stream of bits, in which the number of bits in period T corresponds to the processed code N\({}_{1}\). The average value (frequency) of bits in period T is defined as follows:  
\[\mathrm{F_{N_{1}}}=\frac{\mathrm{N_{1}}}{\mathrm{T}}.\]  
Conversion of the binary code to a pulse width modulated signal is achieved by generating an active signal \(\theta\), for example, equal to one. The duration of this signal for the code N\({}_{2}\) is determined as follows:  
\[\mathrm{\theta_{N_{2}}}=\frac{\mathrm{N_{2}}}{\mathrm{N_{max}}}.\]  
In this equation, N\({}_{\mathrm{max}}\) is the maximum value of the code represented in the selected bit grid n, N\({}_{\mathrm{max}}=2^{n}-1\). The process period T is defined as  
\[\mathrm{T=\frac{2^{n}}{f}},\]  
where n is the digit capacity of the codes to be processed; f stands for the clock frequency of the process quantization.  
During the bit stream multiplication of two codes, three operations are performed simultaneously. The first is multiplication of code N\({}_{1}\) by code N\({}_{2}\), the second is multiplication of code N\({}_{1}\) by inversion of code N\({}_{2}\), and the third is multiplication of code N\({}_{1}\) by one. A schematic of the parallel bit stream multiplication process is shown in Figure 1a.  
The code N\({}_{1}\) is converted into a bit stream P\({}_{1}\) (blocks 1, 3). The code N\({}_{2}\) is converted into a PWM stream (blocks 2, 4). As a result, three bit streams are formed. The PWM stream has no effect on P1; therefore, P1 is the result of the code to the bit stream sweep (block 7): N\({}_{\mathrm{out1}}=\mathrm{N_{1}}\). To obtain stream P2, it is necessary to interrupt the stream based on the code N\({}_{1}\), with the stream PWM generated from N\({}_{2}\) (block 5). This interrupt provides streams multiplication and allows us to implement the following operation: N\({}_{\mathrm{out2}}=\mathrm{N_{1}}\mathrm{N_{2}}\) (block 8). The P3 stream is the result of interrupting the stream based on the N\({}_{1}\) code by a stream of inverted PWM pulses. Such an interrupt implements the multiplication by inverted code \(\overline{\mathrm{N_{2}}}\):N\({}_{\mathrm{out3}}=\mathrm{N_{1}}\overline{\mathrm{N_{2}}}\) (block 9).
# Analysis of Injected Electron Beam Propagation in a Planar Crossed-Field Gap
## 4 Simulation Results
### Effect of Magnetic Field and Current Density
The ratio of the slope to intercept provides the variation in cycloidal orbits in terms of the height of the cycloid (\(y\)-axis) over the propagation length (z-axis) with respect to the center of the orbit of each cycloid. The calculated variation for the 1.5 mA injected current is \(\approx\)11% and for the 250 mA injected current is \(>\)300%. This much higher variation for the 250 mA injected current clearly indicates instability in the beam propagation. Figure 8: Current density from CST simulation at two different locations (center, end collector) as a function of (**a**) injected current and (**b**) actual current for \(B\) = 0.05 T, \(D\) = 20 mm. There is a sharp transition in current density at a beam current of 275 mA and an input current of 500 mA.
## 2 Inapproximability of Minimum \(k\)-Cut  
We now proceed to prove our main results. Let us start with the simplest: Minimum \(k\)-Cut.  
Proof of Theorem 2.: The reduction from SSE\((\delta,\eta)\) to Minimum \(k\)-Cut is simple; the graph \(G\) remains the input graph for Minimum \(k\)-Cut and we let \(k=\delta n+1\) where \(n=|V|\).  
**Completeness.** If there is \(S\subseteq V\) of size \(\delta n\) such that \(\Phi(S)\leqslant\eta\), then we partition the graph into \(k\) groups where the first group is \(V\setminus S\) and each of the other groups contains one vertex from \(S\). The edges cut are the edges across the cut \((S,V\setminus S)\) and the edges within the set \(S\) itself. The total weight of edges of the former type is \(d|S|\Phi(S)\leqslant\eta d|S|\) and that of the latter type is at most \(d|S|/2\). Hence, the total weight of edges cut in this partition is at most \((1/2+\eta)d|S|=(1/2+\eta)\delta dn\).  
**Soundness.** Suppose that, for every \(S\subseteq V\) of size \(\delta n\), \(\Phi(S)\geqslant 1-\eta\). Let \(T_{1},\ldots,T_{k}\subseteq V\) be any \(k\)-partition of the graph. Assume without loss of generality that \(|T_{1}|\leqslant\cdots\leqslant|T_{k}|\). Let \(A=T_{1}\cup\cdots\cup T_{i}\) where \(i\) is the maximum index such that \(|T_{1}\cup\cdots\cup T_{i}|\leqslant\delta n\).  
We claim that \(|A|\geqslant\delta n-\sqrt{n}\). To see that this is the case, suppose for the sake of contradiction that \(|A|<\delta n-\sqrt{n}\). Since \(|A\cup T_{i+1}|>\delta n\), we have \(T_{i+1}>\sqrt{n}\). Moreover, since \(A=T_{1}\cup\cdots\cup T_{i}\), we have \(i\leqslant|A|<\delta n-\sqrt{n}\). As a result, we have \(n=|T_{1}\cup\cdots\cup T_{k}|\geqslant|T_{i+1}\cup\cdots\cup T_{k}|\geqslant (k-i)|T_{i+1}|>\sqrt{n}\cdot\sqrt{n}=n\), which is a contradiction. Hence, \(|A|\geqslant\delta n-\sqrt{n}\).  
Now, note that, for every \(S\subseteq V\) of size \(\delta n\), \(\Phi(S)\geqslant 1-\eta\) implies that \(E(S)\leqslant\eta d\delta n/2\) where \(E(S)\) denotes the total weight of all edges within \(S\). Since \(|A|\leqslant\delta n\), we also have \(E(A)\leqslant\eta d\delta n/2\). As a result, the total weight of edges across the cut \((A,V\setminus A)\), all of which are cut by the partition, is at least  
\[d|A|-\eta d\delta n\geqslant(1-\eta)d\delta n-d\sqrt{n}=\left(1-\eta-\frac{1}{ \delta\sqrt{n}}\right)\delta dn.\]  
For every sufficiently small constant \(\varepsilon>0\), by setting \(\eta=\varepsilon/20\) and \(n\geqslant 100/(\varepsilon^{2}\delta^{2})\), the ratio between the two cases is at least \((2-\varepsilon)\), which concludes the proof of Theorem 2.
## 4 Soil-Tank Coupling Model
\begin{array}{l}E_{P}=\frac{1}{2}\sum\limits_{n=1}^{N}k_{1n}^{*}(q_{n}^{*})^ {2}+\frac{1}{2}k_{0}^{h}(u_{0})^{2}+\frac{1}{2}\sum\limits_{j_{1}=1}^{N_{h}}k _{j_{1}}^{h}(u_{j_{1}-1}-u_{j_{1}})^{2}+\frac{1}{2}k_{0}^{r}(\varphi_{0})^{2} +\frac{1}{2}\sum\limits_{j_{2}=1}^{N_{r}}k_{j_{2}}^{r}(\varphi_{j_{2}-1}- \varphi_{j_{2}})^{2}\end{array}  \tag{42}\]  
where \(M_{\rm t}\), \(y_{\rm t}\) and \(J_{\rm t}\) are the mass, barycenter and moment of inertia for the cylindrical tank with the base, respectively. \(N_{h}\) and \(N_{r}\) denote orders for horizontal and rocking nested LPMs, respectively. The variation of the energy dissipation \(\delta W_{c}\) is expressed as  
\[\delta W_{c}=-c_{0}^{h}\dot{u}_{0}\delta u_{0}-\sum\limits_{j_{1}=1}^{N_{h}}c _{j_{1}}^{h}\dot{u}_{j_{1}}\delta u_{j_{1}}-c_{0}^{r}\dot{\varphi}_{0}\delta \varphi_{0}-\sum\limits_{j_{2}=1}^{N_{r}}c_{j_{2}}^{r}\dot{\varphi}_{j_{2}} \delta\varphi_{j_{2}} \tag{43}\]  
Introducing Equations (41)-(43) into Equation (40) can obtain the movement equation for the soil-tank-liquid system  
\[\mathbf{M}\Big{\{}\tilde{U}\Big{\}}+\mathbf{C}\Big{\{}\dot{U}\Big{\}}+\mathbf{ K}\{U\}=-\mathbf{M}\{\tilde{\xi}\}\ddot{u}_{g} \tag{44}\]  
in which \(\{U\}=\big{\{}\{q_{n}^{*}\}\ u_{0}\ \big{\{}u_{j_{1}}\ \big{\}}\ \varphi_{0}\ \big{\{}\varphi_{j_{2}}\}\big{\}}^{\rm T}\) represents the displacement vector. \(u_{j_{1}}\) and \(\varphi_{j_{2}}\) are the horizontal displacement and rotation angle of each degree of freedom relative to those at bedrock in LPMs, respectively. \(u_{0}\) and \(\varphi_{0}\) represent the horizontal displacement and rotation angle at the circular base relative to those at bedrock, respectively. \(\mathbf{M}\), \(\mathbf{C}\) and \(\mathbf{K}\) are the mass, damping and stiffness matrices, respectively. Detailed expressions are  
Figure 4: Nested lumped parameter model for soil foundation. presented in Appendix A. The coefficient vector \(\{\xi\}=\left\{\underbrace{0,\ \cdots\ 0}_{N}1,\ \underbrace{0,\ \cdots\ 0}_{N_{b}+N_{r}+1}\right\}^{\rm T}\) describes impacts of the excitation direction on loads. \(\tilde{u}_{g}(t)\) is the horizontal acceleration at bedrock along the direction \(\theta=0\). The Newmark-\(\beta\) approach with the constant average acceleration can be employed to obtain sloshing responses of the soil-tank coupling system. The control parameters for the Newmark-\(\beta\) approach are considered as \(\gamma=1/2\) and \(\beta=1/4\) which can unconditionally guarantee the convergence and stability for the method.
## 5 Current Solutions for HO and Mobility Management Challenges in 5G HetNet
The mobility prediction model is designed to predict traffic patterns and various attributes of user mobility, such as future cell load, time, and the next candidate cell for HOs. A novel approach based on intuitionistic fuzzy sets is proposed for the QoS estimation of service compositions, which is appropriate for all kinds of networks and is particularly advantageous in the 5G and B5G network paradigm [117]. To achieve the promising QoE and empower the mobility management paradigms for future HetNets, the OPERA framework is proposed in [118]. This technique predicts the next cell load and optimizes CIOs and antenna parameters. The presented technique also investigated coverage, capacity constraints, and load-aware strategies to ensure seamless operations. Additionally, other latest ML-, D-HCP-, FLC-, and SDN-based schemes for improving HO and mobility performance in 4G/5G cellular systems are listed in Tables 6, 7, 8, and 9, respectively. The tables highlight the various HODPs and KPIs achieved and the limitations of these techniques in achieving excellent HO performance in high-speed scenarios.