esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Experimental Results
### X-ray Emission
A mica crystal was used in the second order of reflection (\(2d\) = 19.9419 A) to measure the spectral lines of aluminum (Ly\({}_{\alpha}\), He\({}_{\beta}\), and He\({}_{\alpha}\) with their satellites) and silicon (He\({}_{\alpha}\) with its satellites if present). The emission was recorded on a TR-type image plate. The spatial resolution of the measurement was 200 \(\upmu\)m, limited by the combined effects of the Fujifilm BAS-1800 II scanner resolution and the demagnification of the optical scheme. To protect the image plate from optical radiation, the detector holder was covered with an aluminized polypropylene foil (2 \(\upmu\)m PP + 80 nm Al). Figure 9 shows a typical X-ray spectrum averaged over seven DPM shots on 200 nm Si foils with a 50 nm Al coating (on the laser-irradiated side). By contrast, spectra without DPM exhibited strong noise, making it impossible to distinguish spectral lines. The fact that the lines in the spectrum can be distinguished from the background in the DPM case likely originates from a lower contribution from continuum emission. The latter can be attributed to both the higher laser contrast (the target being then not pre-expanded into a large volume low-density plasma, as is the case in the direct shots) and the different X-ray generation mechanisms discussed above. The spectrum shown in Figure 9 contains mostly the X-ray emission of aluminum with only a minor contribution from silicon near the Al He\({}_{\beta}\) and Li-like emission (6.4-6.9 A). Thus, the effective (i.e., temporally averaged over the plasma expansion and spatially averaged over the spectrometer's line-of-sight) electron density (\(n_{e}\)) and temperature (\(T_{e}\)) of the emitting plasma can be inferred through comparison to flychk atomic physics calculations [62] of aluminum. As shown in Figure 9, the best-fitting parameters are \(n_{e}=3\times 10^{22}\,\mathrm{cm}^{-3}\) and \(T_{e}=350\,\mathrm{eV}\). These values demonstrate the ability of the DPM to maintain the integrity of the ultrathin foils until the pulse maximum. Figure 9: X-ray spectra averaged over seven DPM shots on a 200 nm Si foils with a 50 nm Al coating (on the laser-irradiated side) (black curve). The red and blue curves represent flychk atomic physics calculations for Al emission at \(n_{e}=3\times 10^{22}\,\mathrm{cm}^{-3}\) and \(T_{e}=350\,\mathrm{eV}\), and \(n_{e}=5\times 10^{22}\,\mathrm{cm}^{-3}\) and \(T_{e}=375\,\mathrm{eV}\), respectively.
# Multi-Point Time-Synchronized Waveform Recording for the Analysis of Wide-Area Harmonic Propagation
## 3 Measurement Campaign
### Harmonic Phasor Estimation
The actual frequency (\(\omega_{h}\)) is calculated as:  
\[\omega_{h}=\omega_{k}\pm\delta f_{r}. \tag{15}\]  
From Equation (7), the ratio of magnitudes for one half of the spectrum can be written as:  
\[X_{\mathrm{w}}^{+}(\mathrm{e}^{\mathrm{i}\omega_{k}})=\sum_{h}\bigg{(}\frac{A_ {h}}{2}\mathrm{e}^{\mathrm{i}\phi_{h}}W(\mathrm{e}^{\mathrm{j}(\omega_{k}- \omega_{h})})\bigg{)} \tag{7}\]0  
Using the relationship between \(\omega_{h}\) and \(\omega_{k}\) from Equation (15), the corrected phasor magnitude is calculated using Equation (16) as:  
\[X_{\mathrm{w}}^{+}(\mathrm{e}^{\mathrm{i}\omega_{k}})=\sum_{h}\bigg{(}\frac{A_ {h}}{2}\mathrm{e}^{\mathrm{i}\phi_{h}}W(\mathrm{e}^{\mathrm{j}(\omega_{k}- \omega_{h})})\bigg{)} \tag{7}\]1  
Similarly, the phase at two frequencies are related as:  
\[X_{\mathrm{w}}^{+}(\mathrm{e}^{\mathrm{i}\omega_{k}})=\sum_{h}\bigg{(}\frac{A_ {h}}{2}\mathrm{e}^{\mathrm{i}\phi_{h}}W(\mathrm{e}^{\mathrm{j}(\omega_{k}- \omega_{h})})\bigg{)} \tag{7}\]2  
where  
\[X_{\mathrm{w}}^{+}(\mathrm{e}^{\mathrm{i}\omega_{k}})=\sum_{h}\bigg{(}\frac{A_ {h}}{2}\mathrm{e}^{\mathrm{i}\phi_{h}}W(\mathrm{e}^{\mathrm{j}(\omega_{k}- \omega_{h})})\bigg{)} \tag{7}\]3 \[X_{\mathrm{w}}^{+}(\mathrm{e}^{\mathrm{i}\omega_{k}})=\sum_{h}\bigg{(}\frac{A_ {h}}{2}\mathrm{e}^{\mathrm{i}\phi_{h}}W(\mathrm{e}^{\mathrm{j}(\omega_{k}- \omega_{h})})\bigg{)} \tag{7}\]4  
The presented interpolated-DFT method was used to estimate accurate harmonic phasors in real grid conditions. The following subsection presents the different test cases used in the study.
# The Behavior of Tree-Width and Path-Width Under Graph Operations and Graph Transformations
## 3 Unary Graph Operations and Graph Transformations
### [PERSON] Complementation  
Limouzy [64] defined the Seidel complementation operation in order to provide a characterization for permutation graphs. For a graph \(G\) and a vertex \(v\in V(G)\), the graph resulting from the _Seidel complementation_ operation, denoted by \(SC(G,v)\), has the same vertices as \(G\), i.e., \(V(SC(G,v))=V(G)\), and edge set  
\[E(SC(G,v))=E(G)\triangle\{\{x,y\}\mid\{v,x\}\in E(G),\{v,y\}\
ot\in E(G)\}.\]  
In other words, the edge set of \(SC(G,v)\) equals the edge set of \(G\), with edges and non-edges between the neighborhood and non-neighborhood of \(v\) complemented.  
Let \(G\) be a graph that consists of two parts. The first part is a star with vertex \(v\) as the dominating vertex and \(\ell\in\mathbb{N}\) satellites \(u_{1},\ldots,u_{\ell}\), adjacent to \(v\). The second part is a set of \(\ell\) isolated vertices, \(w_{1},\ldots,w_{\ell}\). Since \(G\) has neither a \(K_{3}\) nor an \(I(K_{1,3})\) as a minor, we know that \(tw(G)=pw(G)=1\) holds. By applying the Seidel complementation operation to vertex \(v\), \(SC(G,v)\) contains a complete bipartite subgraph formed by the vertices \(u_{1},\ldots,u_{\ell},w_{1},\ldots,w_{\ell}\). By Lemma 4 (Lemma 8), it follows that \(tw(SC(G,v))\geq\ell-1\) (\(pw(SC(G,v))\geq\ell-1\)) is true. Consequently, we conclude that, given a graph \(G\) and a vertex \(v\in V(G)\), the tree-width (path-width) of \(SC(G,v)\) cannot be bounded by the tree-width (path-width) of \(G\).
# SRv6-Based Edge Service Continuity in 5G Mobile Networks +
## 2 Background on SRv6 Network Programming
### SRv6 Architecture
Finally, the payload length must be set to the SRH size plus the original IPv6 packet size. The transit node is any node that forwards a packet based on its IPv6 destination address, without processing the SRH. The packet destination address is not a node's locally configured SID. The transit node may even be non-SRv6 capable, but it must be IPv6 capable. Finally, the endpoint node is a node receiving a packet whose IPv6 destination address is a locally instantiated SID. It will process the SRH and apply the instruction coded into the received SID. The source node is the one in charge of steering packets based on a policy, i.e., a list of segments, which are instructions [20]. The policy can be identified through an IPv6 address, called Binding SID (BSID). A given policy may be executed by different source nodes. Note, however, that each source node must use a different BSID from other source nodes, to indicate that same policy. When a source node receives a packet whose destination address matches with a locally instantiated BSID, it applies the corresponding policy. In other words, the source node inserts in the packet the list of segments associated with that policy [20; 21; 22]. A source node must instantiate a different BSID for each policy it wants to implement. The BSID is a key element in the SR architecture, providing scalability and network opacity. It also allows the exploitation of the same SR policy by different entities, because setting a specific BSID as the destination address is enough to obtain the execution of a policy.
# Effects of the Damping Parameters on the Opening and Closing Characteristics of Vent Valves
###### Abstract  
The main function of the vent valve is to release part of the air at the outlet of the axial compressor to prevent engine surges. The damping parameters have an important effect on the opening and closing characteristics of the vent valve. The control characteristics of each component were obtained by finite element analysis and testing. The overall model of a two-stage partial pressure vent valve was established, and the reliability of the model was verified by testing. The opening and closing characteristics of the damper valve with different damping parameters were obtained by parametric simulation. The results show that there was a pressure mutation point in the middle support pressure and the pressure in the control chamber during operation of the vent valve, which made the valve open and close quickly. The damping hole of the middle shell and the middle nozzle of the support had the greatest influence on the open-close pressure ratio. The damping hole and nozzle of the middle shell had the greatest influence on the opening and closing stability. The results are used to guide the structural design, and the analytical method provides a theoretical basis for research of the same type of valve.  
vent valve; two-stage partial pressure control; damping parameter; opening and closing characteristics +
Footnote †: journal: Applied
## 2 Seismic Response Calculation Method for Soil Layers Based on the Modal Superposition Method
### Approximate Calculation Method for Acceleration Time History  
The displacement, velocity, and acceleration of the generalized coordinates can be obtained by solving Equation (4). Thus, the physical coordinates of the displacement, velocity, and acceleration can be obtained by using from Equations (5)-(7). However, in the iteration process of the equivalent linearization method, the shear strain of each element is calculated by the displacement. Acceleration response is required to be output after the iteration converging. If the acceleration of each generalized coordinate is calculated during the iteration process followed by obtaining the acceleration of each degree of freedom, it will significantly increase the computational workload. At the same time, generally, only the acceleration response at a few locations needs to be output. Therefore, to improve computational efficiency, the acceleration response can be obtained by the central difference method from the discrete displacement time history.  
Assume that the displacement \(u_{j}(t)\) of the \(j\)-th degree of freedom at discrete time points \(t_{r}\), with a discrete time step of \(\Delta t\). For convenience of expression, and where it does not cause confusion, the subscript \(j\) is omitted; abbreviate \(u_{j}(t_{r})\), \(u_{j}(t_{r})\), and \(\bar{u}_{j}(t_{r})\) as \(u_{r}\), \(\bar{u}_{r}\), and \(\bar{u}_{r}\), respectively.  
For the displacement time history \(u_{r}\) at a discrete time step \(\Delta t\), the central difference approximations for velocity and acceleration are given by  
\[\dot{u}_{r}=\frac{(u_{r+1}-u_{r-1})}{2\Delta t},\ \bar{u}_{r}=\frac{(u_{r+1}-2u_{r} +u_{r-1})}{\Delta t^{2}} \tag{23}\]  
In actual sites, soil layer parameters exhibit non-uniformity, and the mechanical properties of soils cannot be determined accurately. This study mainly aims to develop a new computational method and investigate its accuracy. To avoid the influence of model errors from material parameter uncertainties, a homogeneous site and a scrap topography were systematically analyzed to study the relationship between the modal truncation index, including the error of cumulative modal participation mass and the error of cumulative modal contribution coefficient of acceleration, with displacement and acceleration response errors as the modal number changes. Then, the effect of modal truncation on the errors in displacement, velocity, and acceleration is studied. Meanwhile, the errors of velocity and acceleration calculated by using Equation (23) are further investigated.  
The \(n\)-dimensional coupled differential equation system of Equation (1) can be transformed into \(N\) decoupled motion equations by using the modal superposition method, generally \(N<<n\). Therefore, the modal superposition method can significantly simplify the computation of the motion equations. Meanwhile, since \(N<<n\), there is modal truncation error in the results of Equations (5)-(7).
# Low-Rank Approximation of Difference between Correlation Matrices Using Inner Product
###### Abstract
In this paper, we propose a new dimensional reduction clustering approach for the inner product of the difference between two correlation matrices. The problem is to estimate both the clustering structure of differences between correlation matrices and the low-rank correlation matrix, which can describe the clustering structure, given two correlation matrices. Our approach has two advantages. First, the clustering results are superior to those from methods that rely only on the difference. Second, the range of the estimated low-rank matrix is bounded within the range \(-1\) to \(1\), and thus, it is easy to interpret the relations. This approach consists of two steps. First, a low-rank matrix is estimated such that each cluster is discriminated. The novelty of the proposed approach is that the low-rank approximation model is for the inner product of the difference and not only for the difference. From the model, we can estimate the low-rank correlation matrix with features related to the clustering structure. Second, a clustering structure is calculated from the low-rank matrix using an ordinal clustering algorithm such as \(k\)-means [14]. A visualization of the proposed approach is shown in lower Figure 1. To address the problem of estimating a correlation matrix from a non-correlation matrix, previous studies have developed a variety of methods [15; 16; 17; 18; 19]. In our proposed approach, we need to estimate a low-rank correlation matrix, which indicates the difference between correlations, from the non-correlation matrix. To solve the nearest low-rank correlation matrix problem [20; 21; 22; 23], we adopted and implemented the idea of majorization [20; 21] because it eases the estimation of low-rank correlation matrices via the majorization function [24; 25]. The remainder of this paper is organized as follows. In the Methods section, the reason for using the inner product of the difference between correlation matrices is discussed, and its advantage over using only the difference is explained. In addition, the proposed model and corresponding objective function are introduced. To estimate the parameters, an algorithm based on the derived majorization function is provided. Afterward, the simulation design of our numerical study and the fMRI data for a mental arithmetic task, for a demonstration of our proposed approach, are described. The results of the simulation and real fMRI data for the mental arithmetic task are discussed. Finally, we offer our concluding remarks regarding the proposed method.
# Analysis of Optimal Loading Angle in Dynamic Flattened Brazilian Disc Splitting Test for Concrete
## 6 Conclusions  
Based on the numerical simulation and theoretical analysis, the influence of the introduction of the platform loading angle on the stress field of the Brazilian disc is obtained. Under the known relationship between the platform angle and the stress field, the Brazilian disc test under the dynamic splitting platform is designed to obtain the platform Angle range suitable for concrete and other similar materials. The following conclusions can be obtained through comprehensive analysis:  
1. The numerical simulation results show that the starting point of the traditional Brazilian disc is affected by the loading speed. When the loading speed is relatively small, the crack propagation direction is from the transmission bar end to the incident bar end. When the loading speed is increased, the crack growth direction is changed. It is essentially related to stress wave propagation.
2. The Griffith equivalent stress theory well explained the optimal loading angle range in flattened BD tests on concrete from a theoretical view. With the increase in the loading angle, the maximum stress transferred from the loading end to the center of the specimen.
3. The optimal loading angle in dynamic flattened Brazilian disc splitting test for concrete is between 28\({}^{\circ}\) and 30\({}^{\circ}\). For different loading rates, this loading angle can still effectively ensure the central cracking of the specimen.
4. At the same loading rate, the dynamic tensile strength with non-center crack initiation obtained from the loading angle less than 28\({}^{\circ}\) underestimates the inherent tensile strength.
# A Wideband Digital Pre-Distortion Algorithm Based on Edge Signal Correction
## 4 Experimental Validation and Analysis  
### Experimental Setup  
This section further validates the feasibility of the proposed improved scheme through hardware experiments. The experimental block diagram is shown in Figure 3, and the physical setup is depicted in Figure 4. The system mainly consists of two 32-bit microcontrollers, one FPGA, two DAC modules, one ADC module, and a spectrum analyzer. As shown in Figure 4, the left 32-bit microcontroller modulates the data stream to generate an OFDM signal, which is considered the source signal. The middle 32-bit microcontroller acts as the pre-distorter, internally storing the proposed model algorithm with default parameters. Upon receiving the source signal, it applies the pre-distortion model to convert it into a pre-distorted signal, which is then converted to an analog signal via the DAC module. The FPGA acts as the power amplifier, receiving the pre-distorted signal and amplifying it before sending it through the DAC module to the spectrum analyzer. Subsequently, the spectrum analyzer captures the amplified signal and analyzes the frequency spectrum of the power amplifier's output signal.  
In the operational workflow, a 32-bit microcontroller first generates the source signal and transmits it to the pre-distorter via the RS-485 protocol. Upon receiving this signal,  
Figure 4: Hardware wiring setup.  
Figure 3: Experimental design block diagram.  
the pre-distorter down-samples the source signal and applies pre-distortion processing to the sampled signal, thereby producing the pre-distorted signal. Additionally, it retains the remaining band-edge sampled signals for model calibration. Subsequently, the FPGA performs power amplification with analog non-linear distortion on the pre-distorted signal, splitting the amplified signal into two paths: one path is sent back to the pre-distorter for analysis and calculation of pre-distortion model parameters, while the other path is transmitted to the spectrum analyzer to monitor the frequency spectrum of the amplified signal.
## 7 Simulations and Results
### Comparison of the Execution Time  
To compare the execution time of the GA, GWO, and HGWGA, each of them was run 50 times to find the solution of the scheduling problem, as discussed in Section 4. Different statistics of execution time for different cases using the RTP tariff scheme are shown in Table 8. For all cases, it can be observed that the proposed HGWGA technique required the lowest average execution time for 50 runs to attain the optimal solution compared to the GA and GWO. In addition, as the complexity of the case study increased due to the addition of more system elements, such as PV and an ESS, the execution time required for the simulation also increased irrespective of the algorithm used. From Table 8, it is also evident that the proposed HGWGA was the more time-efficient technique among those used in this study.  
The standard deviation can be a good indicator to assess the performance of an optimization algorithm for its consistent optimal solutions. In terms of execution time, the standard deviation was calculated along with its maximum and minimum values, and the results are presented in Table 8. It can be noted that the standard deviation in execution time of the proposed HGWGA was better for all cases in comparison with the GA and GWO, which validates the performance of the proposed technique.  
Figure 21: AWT with an ESS and PV.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Technique (Case)**} & **Maximum** & **Minimum** & **Average Execution** & **Standard Deviation** & **Variance** \\  & **Execution Time (s)** & **Execution Time (s)** & **Time (s)** & **Standard Deviation** & **Variance** \\ \hline
**GA (Scheduled)** & 23.73 & 20.09 & 21.87 & 0.425 & 0.180 \\ \hline
**GWO (Scheduled)** & 21.69 & 16.97 & 18.16 & 0.373 & 0.139 \\ \hline
**Proposed HGWGA (Scheduled)** & 17.46 & 12.53 & 13.99 & 0.221 & 0.049 \\ \hline
**GA (Scheduled + ESS)** & 25.57 & 21.37 & 23.43 & 0.498 & 0.248 \\ \hline
**GWO (Scheduled + ESS)** & 23.19 & 18.29 & 20.65 & 0.407 & 0.165 \\ \hline
**Proposed HGWGA (Scheduled + ESS)** & 18.93 & 13.74 & 15.25 & 0.369 & 0.136 \\ \hline
**GA (Scheduled + ESS + PV)** & 28.15 & 22.07 & 23.65 & 0.596 & 0.355 \\ \hline
**GWO (Scheduled + ESS + PV)** & 26.27 & 18.47 & 20.42 & 0.515 & 0.265 \\ \hline
**Proposed HGWGA (Scheduled + ESS + PV)** & 20.59 & 14.83 & 16.09 & 0.493 & 0.241 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of the execution time of different algorithms for 50 runs.
## 2 Problem Definition
### Quantum-Based Pheromone Initialization and Update  
The QACO algorithm by [43] is based on initializing the pheromone values \(\phi_{t=(d,s,\ell)}\) referring to the theory of quantum computing (we direct the reader to the survey [49] for an exhaustive introduction to quantum technology and computation). Specifically, QACO employs a qubit (quantum bit-the basic unit of quantum information) with probabilities of states 0 and 1 represented by \(\alpha^{2}\) and \(\beta^{2}\), respectively, (thus it holds \(\alpha^{2}+\beta^{2}=1\)).  
As in [43], the value of \(\alpha\) is computed for each possible move (in our case representing the rental of triple \(t=(d,s,\ell)\)) on the basis of the objective function coefficients and we set:  
\[\alpha_{d,s,\ell} =\mu\cdot\frac{v_{ds\ell}}{\sum_{s\in S(d)}\sum_{\ell\in L(d,s)}v _{ds\ell}} \forall t =(d,s,\ell)\in T \tag{7}\] \[\beta_{d,s,\ell} =\sqrt{1-\alpha_{d,s,\ell}^{2}} \forall t =(d,s,\ell)\in T \tag{8}\]  
in which \(\mu=rand[0,1]\) and \(v_{ds\ell}\) is the value associated with renting lot \(\ell\).  
The initial pheromone value \(\phi_{d,s,\ell}\) of each triple \((d,s,\ell)\) is then set equal to \(\alpha_{d,s,\ell}\), taking into account that the higher the value of \(\alpha\), the higher the attractiveness of the move since it is higher than the value \(v_{ds\ell}\) of renting the lot (i.e., we initially set \(\phi_{d,s,\ell}=\alpha_{d,s,\ell}\)).  
At the end of a cycle of solution construction of the set of ants, the pheromone values are updated in order to learn from the quality of solutions built and to model the natural fact that the ant pheromone fades away with time. We follow the approach proposed by [43] consisting of involving the quantum values in the update formula and we set:  
\[\phi_{d,s,\ell}[i]=(1-\epsilon)\cdot\phi_{d,s,\ell}[i-1]+\frac{1}{(\beta_{ds \ell}^{\text{best}})^{\lambda}} \tag{9}\]  
in which \(\epsilon\in(0,1)\) is the evaporation rate, \([i]\) and \([i-1]\) are the index representing the cycle execution count, \(\beta_{ds\ell}^{\text{best}}\) is the best value of \(\beta_{ds\ell}\) found until iteration \([i]\) and \(\lambda\) is a parameter such that \(\lambda\geq 2\).