esa-sceva/satcom-chunk-collection huggingface dataset:
## 9 Global Perturbation Bounds
### Perturbation Bounds of the Entries of \(U_{2}\)  
The main difficulty in determining global bounds of \(x\) and \(y\) is to find an appropriate approximation of the high-order term \(\Delta_{2}\) in (23). As is seen from (25), the determining of such an estimate requires knowing the perturbation \(\delta U_{2}\), which is not well determined since it contains the columns of the matrix \(\delta U_{2}=\tilde{U}_{2}-U_{2}\). This perturbation satisfies the equations  
\[(U_{1}+\delta U_{1})^{T}(U_{2}+\delta U_{2}) = 0, \tag{51}\] \[(U_{2}+\delta U_{2})^{T}(U_{2}+\delta U_{2}) = I_{m-n} \tag{52}\]  
which follow from the orthogonality of the matrix  
\[\tilde{U}=[U_{1}+\delta U_{1},U_{2}+\delta U_{2}].\]  
An estimate of \(\delta U_{2}\) can be found based on a suitable approximation of  
\[X=U^{T}\delta U_{2}:=\left[\begin{array}{c}X_{1}\\ X_{2}\end{array}\right].\]  
As shown in [26], a first-order approximation of the matrix \(X\) can be determined using the estimates  
\[X_{1}^{appr} = -(I_{n}+\delta W_{1}^{T})^{-1}\delta W_{2}^{T}\in\mathbb{R}^{n\times (m-n)}, \tag{53}\] \[X_{2}^{appr} = -X_{1}^{apprT}X_{1}^{appr}/2\in\mathbb{R}^{(m-n)\times(m-n)}, \tag{54}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \(\mathbf{c}\) & \(\|\delta A\|_{2}\) & \(|\mathbf{\Phi\max(\mathcal{U}_{r},\tilde{\mathcal{U}}_{r})}|\) & \(\mathbf{\Phi\max^{lin}(\mathcal{U}_{r},\tilde{\mathcal{U}}_{r})}\) \\ \hline \(-10\) & \(2.0819813\times 10^{-9}\) & \(\begin{array}{c}\Phi_{1}=0.0024212\times 10^{-8}\) \\ \(\Phi_{2}=0.0082136\times 10^{-8}\) \\ \(\Phi_{3}=0.0103290\times 10^{-7}\) \\ \(\Phi_{4}=0.1074643\times 10^{-7}\) \\ \hline \(-5\) & \(2.0819812\times 10^{-4}\) \\ \(\Phi_{2}=0.0082136\times 10^{-3}\) \\ \(\Phi_{3}=0.1032951\times 10^{-3}\) \\ \(\Phi_{4}=0.1073496\times 10^{-2}\) \\ \hline \(\mathbf{c}\) & \(\|\delta A\|_{2}\) & \(|\mathbf{\Theta\max(\mathcal{V}_{r},\tilde{\mathcal{V}}_{r})}|\) & \(\mathbf{\Theta\max^{lin}(\mathcal{V}_{r},\tilde{\mathcal{V}}_{r})}\) \\ \hline \(-10\) & \(2.0819813\times 10^{-9}\) & \(\begin{array}{c}\Theta_{1}=0.0425801\times 10^{-9}\) \\ \(\Theta_{2}=0.0438355\times 10^{-9}\) \\ \(\Theta_{3}=0.2782232\times 10^{-9}\) \\ \end{array}\) & \(\Theta_{1}=0.0166760\times 10^{-8}\) \\ \hline \(-5\) & \(2.0819812\times 10^{-4}\) & \(\begin{array}{c}\Theta_{1}=0.0425804\times 10^{-4}\) \\ \(\Theta_{2}=0.04383565\times 10^{-4}\) \\ \(\Theta_{2}=0.0438688\times 10^{-3}\) \\ \(\Theta_{3}=0.2782378\times 10^{-4}\) \\ \end{array}\) & \(\Theta_{1}=0.0166760\times 10^{-3}\) \\ \hline \end{tabular}
\end{table}
Table 4: Sensitivity of the singular subspaces.  
where \(\delta W_{1}=U_{1}^{T}\delta U_{1}\), \(\delta W_{2}=U_{2}^{T}\delta U_{1}\) and for sufficiently small perturbation \(\delta U_{1}\), the matrix \(I_{n}+\delta W_{1}^{T}\) is nonsingular. (Note that \(\delta W_{U}=[\delta W_{1}^{T}\delta W_{2}^{T}]^{T}\) is already estimated.) Thus, we have that  
\[\delta U_{2}^{appr}=UX^{appr}. \tag{55}\]
# Uncertainty Theory-Based Resilience Analysis for LEO Satellite Communication Systems
## 2 Preliminaries
### Uncertain Measure  
**Definition 1** (Liu [14]).: _Uncertain measure \(\mathcal{M}\) is a real-valued set-function on a \(\sigma\)-algebra \(\mathcal{L}\) over a nonempty set \(\Gamma\) that satisfies the following four axioms:_  
_Axiom 1: (**Normality Axiom)**_\(\mathcal{M}(\Gamma)=1\) _for the universal set_ \(\Gamma\)_._  
_Axiom 2: (**Duality Axiom)**_\(\mathcal{M}(\Lambda)+\mathcal{M}(\Lambda^{c})=1\) _for any event_ \(\Lambda\)_._  
_Axiom 3: (**Subadditivity Axiom) For every countable sequence of events \(\Lambda_{1},\Lambda_{2},\cdots\), we have_  
\[\mathcal{M}\left\{\bigcup_{i=1}^{\infty}\Lambda_{i}\right\}\leq\sum_{i=1}^{ \infty}\mathcal{M}\{\Lambda_{i}\}. \tag{1}\]  
_Axiom 4: (**Product Axiom)** Let \((\Gamma_{k},\mathcal{L}_{k},\mathcal{M}_{k})\) be uncertainty spaces for \(k=1,2,\cdots\). The product uncertain measure \(\mathcal{M}\) is an uncertain measure satisfying_  
\[\mathcal{M}\left\{\bigcup_{k=1}^{\infty}\Lambda_{k}\right\}=\bigwedge_{k=1}^{ \infty}\mathcal{M}\{\Lambda_{k}\}, \tag{2}\]  
_where \(\Lambda_{k}\) are arbitrarily chosen events from \(\mathcal{L}_{k}\) for \(k=1,2,\cdots\), respectively._  
**Definition 2** ([PERSON] [14]).: _An **uncertain variable** is a function \(\xi\) from an uncertainty space \((\Gamma,\mathcal{L},\mathcal{M})\) to the set of real numbers such that \(\{\xi\in B\}=\{\gamma\in\Gamma\mid\xi(\gamma)\in\beta\}\) is an event for any Borel set \(B\) of real numbers._  
**Definition 3** ([PERSON] [14]).: _The **uncertainty distribution**\(\Phi\) of an uncertain variable \(\xi\) is defined by \(\Phi(x)=\mathcal{M}\{\xi\leq x\}\) for any real number \(x\)._  
**Example 1** ([PERSON] [14]).: _An uncertain variable \(\xi\) is called a linear variable if it has a **linear uncertainty distribution**_  
\[\Phi(x)=\left\{\begin{array}{ll}0,&(\text{if }x\leq a)\\ \dfrac{x-a}{b-a},&(\text{if }a<x\leq b),\\ 1,&(\text{if }x>b)\end{array}\right. \tag{3}\]  
_denoted by \(\mathcal{L}(a,b)\), where \(a\) and \(b\) are real numbers with \(a<b\)._  
**Example 2** ([PERSON] [14]).: _An uncertain variable \(\xi\) is called a zigzag variable if it has a zigzag uncertainty distribution_  
\[\Phi(x)=\left\{\begin{array}{ll}0,&(\text{if }x\leq a)\\ \dfrac{x-a}{2(b-a)},&(\text{if }a<x\leq b),\\ \dfrac{x+c-2b}{2(c-b)},&(\text{if }b<x\leq c)\\ 1,&(\text{if }x>c)\end{array}\right. \tag{4}\]  
_denoted by \(\mathcal{Z}(a,b,c)\), where \(a\), \(b\) and \(c\) are real numbers with \(a<b<c\)._  
**Definition 4** ([PERSON] [16]).: _An uncertainty distribution \(\Phi\) is said to be regular if its inverse function \(\Phi^{-1}(\alpha)\) exists and is unique for each \(\alpha\in(0,1)\)._  
**Theorem 1** ([PERSON] [16]).: _Let \(\xi_{1},\xi_{2},\cdots,\xi_{n}\) be independent uncertain variables with regular uncertainty distributions \(\Phi_{1},\Phi_{2},\cdots,\Phi_{n}\), respectively. If \(f\) is a strictly increasing function, then \(\xi=f(\xi_{1},\xi_{2},\cdots,\xi_{n})\) has an **inverse uncertainty distribution**\(\Psi^{-1}(\alpha)=f(\Phi_{1}^{-1}(\alpha),\Phi_{2}^{-1}(\alpha),\)\(\cdots,\Phi_{n}^{-1}(\alpha))\)
## 2 Background
### Heritage Structures Inspection Protocols
In some cases, continuous monitoring systems are implemented to track changes in the structure over time, using sensors to measure humidity, temperature, vibration, and other factors that could affect the building's integrity [21]. 3D modeling and scanning technologies enable the creation of accurate digital representations of the structure, which are useful for restoration planning and identifying hidden issues. Historical and documentary research is another critical aspect, providing valuable insights into the original construction methods, alterations over time, and significant events related to the structure [22]. This knowledge informs decisions about conservation. Construction pathology studies focus on identifying the underlying causes of deterioration and damage, whether from design flaws, natural aging, or human intervention. It is essential to recognize that each historical building is unique, requiring a tailored approach based on its historical context, current condition, and conservation needs [23]. Professionals specializing in historical preservation, such as architects, structural engineers, and conservators, typically use a combination of these protocols to ensure the proper conservation of these invaluable structures. Among the key procedures for inspection and subsequent conservation, monitoring and 3D scanning and modeling stand out, as these techniques contribute significantly to the digitalization of cultural heritage [23].
# Meta-Analysis of the Performance of Previous Concrete with Cement and Aggregate Replacements
## 5 Results and Discussion
### Cement Replacement in Pervious Concrete
#### 5.2.2 Performance Evaluation
This validates the potential replacement of cement in PC without undermining the mechanical properties. Similarly, the respective extreme whisker values, signifying the maximum and minimum, were 4-54, 5-28, and 7-45 MPa for compressive strength, 0.4-3.7, 0.3-3.7, and 1.0-3.3 MPa for tensile strength, and 0.9-4.6, 2.6-3.5, and 1.0-5.5 MPa for flexural strength. These values explain the performance disparities and indicate that PC made with cement or at least two replacement materials, in contrast to counterparts incorporating one replacement material, attained higher compressive strength while having higher divergence in the results. To conclude, the  
Figure 5: Mechanical and durability properties as a function of the cement replacement percentage. replacement of cement by other materials can maintain the performance of PC. However, the porous nature of PC seems to limit the enhancement potential of such materials but could offer a reduction in the carbon footprint of PC. In the case of hydraulic properties, the medians for the permeability of PC mixes made with cement only, one replacement material, and two or more replacement materials were approximately 6.0, 7.7, and 5.1 mm/s, respectively. The corresponding medians for porosity were 28.5, 25.8, and 27.4%, respectively. Despite the change in properties due to cement replacement, these values remain within the minimum acceptable requirement for hydraulic performance based on international standards and regulations [38]. The variability in hydraulic performance was likewise noted; the respective interquartile ranges of the types of mixes made with 0, 1, and 2 replacement materials were 2.7-14.8, 4.9-9.4, and 2.4-12.5 mm/s for permeability and 23.3-30.7, 24.3-28.3, and 23.1-28.6% for porosity. These ranges show more dispersed values, indicating dissimilarities in the hydraulic performance between the three types of mixes regardless of the number of replacement materials used. However, among the three types of mixes, those incorporating one replacement material had the lowest variability in the results. Similarly, the maximum and minimum whisker values were 0.1-27, 0.15-22, and 0.2-17 mm/s for permeability and 22.5-33, 23-27, and 22-28% for porosity, indicating the potentiality of exhibiting adequate hydraulic performance in PC with and without replacement. To conclude, the hydraulic properties of PC could be maintained upon the replacement of cement by one or more materials. The variability in the results of PC is generally improved upon cement replacement. Figure 6: Variation in **(a)** Compressive strength, **(b)** Tensile strength, **(c)** Flexural strength, **(d)** Permeability, and **(e)** Porosity based on number of SCMs (n = number of publications).
## 4 Discussion
Additionally, the height difference of the two scatterers in layover areas is lower than 50 m, which is not restricted by the theoretical resolution of the height direction. Thus, this method can break the limits of theoretical resolution and has a high resolution of scatterers in layover areas. Likewise, the normalized amplitude diagram of separable approximate sparse reconstruction is more sparse than traditional compressive sensing method which can be seen form Figures 5a and 8, and is comparably sparse compared with multi-look compressive sensing. Furthermore, the separation of scatterers and height continuity is better than in the traditional compressive sensing method, as seen in Figures 5a and 8b. Comparing processing times, the processing time of the separable approximate sparse reconstruction method is nearly one-fifth that of the multi-look compressive sensing method, and is comparable with the traditional compressive sensing method (112.9 s). Thus, layover separation method by means of separable approximate sparse reconstruction can reduce the computation time while retaining the stability of layover separation. Based on the above analysis, aiming at solving the problem of long computation time in the multi-view L1 norm compressed sensing method for airborne multi-baseline SAR systems to solve the layover separation problem, this paper uses the compressed sensing method based on separable approximate sparse reconstruction to improve the speed of iterative processing. Moreover, this method constructs differential operation and soft function, transforms the L1-L2 norm optimization into an iterative soft threshold shrinkage processing mode, and improves the processing speed by means of the threshold iteration method. Furthermore, the proposed method can effectively reduce the operation time while maintaining the scattering point resolution ability and height direction estimation accuracy in layover areas. The simulation and measured data verify the effectiveness of the method.
## 1 Introduction
However, attempts to eradicate the effect of NT by iterating through domains and discarding a single less-beneficial domain in each iteration from a pool of domains possessing significant individual differences was demonstrated to drastically deteriorate classification performance. As such, removing a single low-beneficial domain can still pose severe implications for classification performance in the next iteration, since each domain responds differently to another domain. In this study, we investigate the impact of less-beneficial and highly beneficial source domains on transfer learning performance and also address the challenge of NT in multi-class inter-session and inter-subject classification scenarios. As such, four domain selection algorithms are introduced and compared mainly to evaluate the impact of both highly and less-beneficial source domains on classification performance across individual TDs. Moreover, the effect of multi-class TL on classification performance is further evaluated across individual TDs, mainly to address the challenge of negative transfer emerging from the transfer of features from non-related sources. Therefore, all four domain selection algorithms (EMC-MMFT, DTE-MMFT, LSA-MMFT, and ROD-MMFT) are firstly implemented based on a two-class problem and further extended to a three-class and four-class inter-session and inter-subject classification scenarios [12]. The main contributions of this study are listed below:Investigate the impact of highly beneficial and less-beneficial sources contributing to negative transfer. 2. Evaluate the performance of domain selection methods based on two-class, three-class, and four-class cross-subject EEG classification problems. 3. A comparative performance analysis is carried out among EMC-MMFT, DTE-MMFT, LSA-MMFT, and ROD-MMFT. The experiment's results show that EMC-MMFT outperforms all the other domain selection algorithms for all the two-class, three-class, four-class, inter-session, and inter-subject classification problems. The remainder of this paper is organized as follows: Section 2 introduces related work on domain selection algorithms. Section 3 introduces the materials and methods. Section 4 presents the experimental results. Section 5 discusses and analyzes the results. And, finally, Section 6 is the conclusion.
## 4 Simulation
### Dipole Coupling  
The coupling strength for the \(|0\rangle\rightarrow|1\rangle\) transition is given by [18; 30]  
\[g_{01}=\frac{2e\cdot d_{eff}\cdot E_{0}}{\hbar}\frac{1}{\sqrt{2}}\bigg{(} \frac{E_{j}}{8E_{c}}\bigg{)}^{\frac{1}{2}}. \tag{11}\]  
where \(e\) is the charge of the electron, \(\hbar\) is [PERSON]'s constant, \(E_{0}\) is the field amplitude of the cavity mode, \(E_{j}\) is the Josephson energy, and \(E_{c}\) is the charging energy of the transmon:  
\[E_{0}=\sqrt{\frac{\hbar\omega_{r}}{2\epsilon_{0}V_{\text{mode}}}},\qquad E_{j} =\frac{\Phi_{0}I_{c}}{2\pi},\qquad E_{c}=\frac{e^{2}}{2C}, \tag{12}\]  
with \(\omega_{r}\) being the resonance frequency of the qubit, the vacuum permittivity \(\epsilon_{0}\), the mode volume \(V_{\text{mode}}\), the magnetic flux quantum \(\Phi_{0}\), and the critical current of the junction \(I_{c}\). \(V_{\text{mode}}\) is calculated as:  
\[V_{\text{mode}}=\frac{\int_{V}\epsilon_{r}(\vec{r})|E(\vec{r})|^{2}d\vec{r}}{ max(|E(\vec{r})|^{2})} \tag{13}\]  
The effective distance is given by [30] :  
\[d_{\text{eff}}=\int_{A_{\text{up}}}\bigg{(}\frac{\rho_{up}(\vec{r})}{|q|} \bigg{)}\cdot z\,d\vec{r}+\int_{A_{\text{down}}}\bigg{(}\frac{\rho_{down}( \vec{r})}{|q|}\bigg{)}\cdot z\,d\vec{r} \tag{14}\]  
Figure 7: **(Left)**: Model in Ansys HFSS of the resonance cavity with the transmon qubit at its center. The TE110 cavity mode, which is influenced by the transmon, is also shown. **(Right)**: Zoom in on the transmon with its charge distribution and the local electric field.  
it is calculated in ANSYS-HFSS from the charge distribution \(\rho(\vec{r})=\rho_{up}(\vec{r})+\rho_{down}(\vec{r})\) on the transmon pads, as shown in Figure 8. \(A_{up}\) and \(A_{down}\) are the areas of the upper and lower pads. For the electric field, we only considered the fundamental cavity mode TE110.
# A Multiview Representation Learning Framework for Large-Scale Urban Road Networks
## 4 Experiments with a Real-World Dataset
### Efficiency Evaluation of Large-Scale Road Network Organization  
Before the performance evaluation of the downstream traffic task, we first illustrate the efficiency evaluation results of the proposed large-scale road network organization method in the multiview random walk process. With the use of a large-scale dataset, i.e., the Shenzhen dataset, as an example, the memory usage distribution of the subgraphs is shown in Figure 6a. Compared to the theoretical memory usage of 375 GB without optimal partitioning, our method significantly reduces the memory burden by optimal partitioning. Specifically, only approximately 1/60 of the theoretical memory usage is needed to perform the calculations. In addition, another advantage of our road network organization is that it is easy to parallelize the multiview random walk process via the partitioned subgraphs, thereby improving the computational time efficiency. As shown in Figure 6b, the computation speed exponentially increases with the number of processes.
# Traffic-Based Heuristics for Regenerator Placement in Translucent Dynamic Optical Networks
## 3 Definitions
### Set of Possible Regenerator Combinations (PRC)  
A regenerator combination of a route is a combination of nodes in the route that satisfies the criteria that all TSs formed with the signal regeneration in such nodes are feasible, i.e., their optical lengths are shorter than \(T_{R}\). Let \(C_{ij}\) be the set of all those regenerator combinations on route \(\pi_{i,j}\) that use the minimum number of possible regeneration points, \(K_{ij}\), i.e.,:  
\[\begin{split} C_{ij}=&[(n_{1}^{(1)},\ldots,n_{K_{ ij}}^{(1)})\ldots(n_{1}^{(M_{ij})},\ldots,n_{K_{ij}}^{(M_{ij})})]\\ =&\{c_{ij}^{(1)},\ldots,c_{ij}^{(M_{ij})}\},\end{split} \tag{1}\]  
in which \(M_{i,j}\) is the number of regenerator combinations of \(\pi_{i,j}\) and \(n_{k}^{(m)}\) is the \(k\)-th selected regeneration node along the route \(\pi_{ij}\) of the \(m\)-th regenerator combination. \(C_{ij}\) is defined as the possible regenerator combinations (PRC). It stores all regenerator combinations that segment the route \(\pi_{ij}\) into \(K_{ij}+1\) feasible transparent segments. Notice that \(M_{ij}\leq(^{H_{ij}-2}_{K_{ij}})\), since \(H_{ij}-2\) is the number of intermediate nodes where regeneration can take place and \(K_{ij}\) is the number of nodes using regeneration.
# A Mayfly-Based Approach for CMOS Inverter Design with Symmetrical Switching
## 4 Problem Formulation
### Case II  
To obtain an optimal symmetrical switching response, the fall time must equal the rise time of the output voltage. The main objective, in this case, is to find the inverter design parameters, \(C_{L}\), (\(W/L\))\({}_{p}\), and (\(W/L\))\({}_{n}\) that minimize the cost function given in Equation (15) [25; 26; 27; 28; 29; 30; 32]. This cost function measures the difference between the fall time and rise times of the CMOS inverter.  
\[\text{CF}=\left|(t_{f}(C_{L}\left(\frac{W}{L}\right)n))-(t_{r}(C_{L}\left( \frac{W}{L}\right)p))\right| \tag{15}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Set Number** & \(C_{L}\) **(pF)** & **W/L** & **T\({}_{f}\) (ns)** \\ \hline
1.0 & 0.10–2.40 & 0.30–3.30 & 0.50–6.70 \\ \hline
2.0 & 0.20–5.60 & 0.40–2.30 & 0.30–6.00 \\ \hline
3.0 & 0.60–3.40 & 0.90–5.00 & 0.60–8.60 \\ \hline
4.0 & 0.50–3.60 & 1.20–4.10 & 0.90–11.00 \\ \hline
5.0 & 0.70–1.80 & 0.70–4.90 & 1.20–15.00 \\ \hline
6.0 & 0.30–2.40 & 2.20–3.20 & 1.40–12.00 \\ \hline
7.0 & 0.70–2.30 & 0.70–3.00 & 1.60–5.70 \\ \hline
8.0 & 0.60–1.90 & 1.50–3.50 & 1.00–8.150 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Lower and upper bounds for the eight design sets of Case I [25; 26; 27; 28; 29; 30; 32].  
Subject to the following constraints as in Equations (16)-(20) [25; 26; 27; 28; 29; 30; 32].  
\[\left(\mathrm{t_{f}}\right)_{\mathrm{min}}\leq\mathrm{t_{f}}\leq\left(\mathrm{t_ {f}}\right)_{\mathrm{max}} \tag{16}\]  
\[\left(\mathrm{t_{r}}\right)_{\mathrm{min}}\leq\mathrm{t_{r}}\leq\left(\mathrm{t _{r}}\right)_{\mathrm{max}} \tag{17}\]  
\[\left(\mathrm{C_{L}}\right)_{\mathrm{min}}\leq\mathrm{C_{L}}\leq\left(\mathrm{C _{L}}\right)_{\mathrm{max}} \tag{18}\]  
\[\left(\left(\frac{\mathrm{W}}{\mathrm{L}}\right)_{\mathrm{n}}\right)_{ \mathrm{min}}\leq\left(\frac{\mathrm{W}}{\mathrm{L}}\right)_{\mathrm{n}}\leq \left(\left(\frac{\mathrm{W}}{\mathrm{L}}\right)_{\mathrm{n}}\right)_{ \mathrm{max}} \tag{19}\]  
\[\left(\left(\frac{\mathrm{W}}{\mathrm{L}}\right)_{\mathrm{P}}\right)_{ \mathrm{min}}\leq\left(\frac{\mathrm{W}}{\mathrm{L}}\right)_{\mathrm{P}}\leq \left(\left(\frac{\mathrm{W}}{\mathrm{L}}\right)_{\mathrm{P}}\right)_{ \mathrm{max}} \tag{20}\]  
Table 2 shows the eight different design sets considered with the corresponding bound constraints. In this case, the evaluation of the fall time (\(\mathrm{t_{f}}\)), and the rise time (\(\mathrm{t_{r}}\)) of the output voltage is implemented for the eight different design sets of the parameters \(\mathrm{C_{L}}\), (\(\mathrm{W/L}\))\({}_{\mathrm{P}}\) and (\(\mathrm{W/L}\))\({}_{\mathrm{n}}\).