esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Methodology
### Formal Problem Definition  
To apply Graph Convolutional Networks (GCNs) in noise pollution prediction, we first need to represent the data as spatiotemporal graphs. Let the graph \(G_{t}\) at a specific time \(t\) be defined as  
\[G_{t}=(V,E_{t},X_{t})\]  
where  
* \(V\) is the set of nodes, defined as \[V=\{v_{1},v_{2},\ldots,v_{|V|}\},\] where each node represents a noise measurement station in the city.
* \(E_{t}\) is the set of edges at time \(t\), which connects the nodes based on their spatial proximity. Specifically, each node is connected by edges to its \(k\) nearest neighbors according to the geodesic distance calculated using the Haversine formula. Thus, it is formally defined as \[E_{t}=\{(v_{i},v_{j})\mid v_{i},v_{j}\in V,\ v_{j}\in\mathcal{N}_{k}(v_{i})\},\] where \(\mathcal{N}_{k}(v_{i})\) is the set of the \(k\) nearest neighbors of node \(v_{i}\). The distance associated with each edge \((v_{i},v_{j})\) is defined by the Haversine distance as \[d(v_{i},v_{j})=2R\arcsin(\sqrt{\sin^{2}\left(\frac{\phi_{j}-\phi_{i}}{2} \right)+\cos(\phi_{i})\cos(\phi_{j})\sin^{2}\left(\frac{\lambda_{j}-\lambda_{ i}}{2}\right)}),\] (1) where \(\phi_{i},\lambda_{i}\) and \(\phi_{j},\lambda_{j}\) are the geographic latitudes and longitudes of stations \(v_{i}\) and \(v_{j}\), respectively, and \(R\) is the average radius of the Earth.
* \(X_{t}\in\mathbb{R}^{|V|\times F}\) is the feature matrix of the graph at time \(t\), where each row represents a node (station) and each column an acoustic or temporal feature associated with that station. Therefore, \[X_{t}=[x_{v_{1}}^{t},x_{v_{2}}^{t},\ldots,x_{v_{|V|}}^{t}]^{\top},\quad x_{v_{ i}}^{t}\in\mathbb{R}^{F}.\] Since our goal is to make future predictions based on historical sequences of graphs, we mathematically formulate the problem as follows: Given a historical sequence of graphs: \[\{G_{T-n},G_{T-(n-1)},\ldots,G_{T-1},G_{T}\},\] the goal is to learn a predictive function \(\mathcal{F}\) such that \[\mathcal{F}:\{G_{T-n},G_{T-(n-1)},\ldots,G_{T}\}\rightarrow\{G_{T+1},G_{T+2},\ldots,G_{T+N}\},\] where \(N\) is the number of future steps to predict. The prediction involves estimating the feature matrix \(X_{T+i}\) for each future graph \(G_{T+i}\), with \(i=1,2,\ldots,N\), while keeping the node structure \(V\) and edges \(E_{t}\) previously defined fixed.
## 5 Advanced Setups
### Setups with Robotic Automation
The VAR operates with high efficiency, achieving assembly rates of up to 30 layers per hour. This robotic system allows for fully automated, operator-free fabrication of complex vdW solids, significantly improving throughput and consistency compared to traditional manual or semi-automated methods. The versatility of the VAR makes it applicable to various two-dimensional  
Figure 10: Autonomous robot searching system by [PERSON] et al. [85]. Reproduced from [85] under the Creative Commons CC BY license. (**a**) Computer-assisted design schematics showcase the presented robotic system, which includes an automated optical microscope, a stamping device, and a Si chip transfer robot. **(b)** The schematics illustrate the fabrication process of the vdW heterostructure. Initially, the automated high-speed optical microscope, equipped with a motorized XY scanning stage, scans the surfaces of SiO\({}_{2}\)/Si chips. Upon detecting 2D crystals, their locations and shape parameters are documented in a database. Using custom CAD software, the 2D crystals’ combinations, relative positions, and crystallographic orientations are planned. Subsequently, robots, guided by a computer-vision algorithm, assemble the vdW heterostructures layer by layer onto a polymer stamp utilizing vdW forces. (**c–e**) Photographs include (**c**) the entire system, (**d**) a close-up of the automated optical microscope, and (**e**) the stamping apparatus. materials, including transition metal dichalcogenides, gold thin films, and exfoliated flakes, enhancing its potential for widespread use in advanced material manufacturing. Figure 11: Automated four-dimensional pixel assembly by [PERSON] et al. [88]: (**a**) Schematic of the four-dimensional pixel assembly. (**b**) Creation of pixels through wafer-scale growth (**i**), pixel patterning (**ii**), and robotic assembly of four conceptual structures (**iii**). (**c**) Micrographs of vacuum-assembled, robot-manufactured van der Waals (vdW) solids displaying control over layer number (**i**), composition (**ii**), lateral positioning (**iii**), and interlayer twist angle (**iv**). Scale bars indicate 50 \(\upmu\)m. Reproduced from [88] with permission. Copyright 2022, Nature Publishing. Figure 12: (**a**) Diagram of the vacuum assembly robot (VAR) used for vdW heterostructure fabrication. (**b**) Schematic of the adhesive stamp structure. (**c**) Process flowchart outlining the steps for assembling (**i**) and depositing (**ii**) heterostructures onto a receiving substrate. (**d**) Schematic of the TSL process. (**e**) Stitched optical micrographs from a 1Å-13 mm\({}^{2}\) chip showing square (**i**), rectangle (**ii**), triangle (**iii**), and tiled (**iv**) WS\({}_{2}\) pixels created by TSL. Scale bar represents 1 mm. Reproduced from [88] with permission. Copyright 2022, Nature Publishing. Table 1 summarizes the transfer setups discussed so far, highlighting the transfer methods employed, the corresponding vdW heterostructures formed, and the advantages and limitations of each setup.
## 3 Performance Evaluation
### Error Probability
We can now set the \(M\) values for the test as \(M_{m}=2/\mathrm{e}\,_{2}F_{\!\left(\right)}\!\left(-m,-m;1;h_{2}^{2}\right)h_{ 1}^{2m}/m!\). Convergence of the \(\sum_{m=1}^{+\infty}M_{m}\) series can further be proven with D'Alembert criterion using \(\lim_{m\rightarrow+\infty}M_{m+1}/M_{m}\). Because of \(\lim_{m\rightarrow+\infty}2F_{\!\left(\right)}\!\left(-m-1,-m-1;1;h_{2}^{2} \right)/2F_{\!\left(\right)}\!\left(-m,-m;1;h_{2}^{2}\right)=(1+h_{2})^{2}\), which can be derived using ([21], 07.23.03.0195.01, 05.03.17.0001.01), it follows that \(\lim_{m\rightarrow+\infty}M_{m+1}/M_{m}=0\). Now, as \(\sum_{m=1}^{+\infty}M_{m}\) converges for all \(-\infty<h_{1},h_{2}<+\infty\), the \(F_{R}(r)\) series converges uniformly according to the test, which justifies interchange of integration and summation in computing \(b_{n}\) after (21). Therefore, we continue by defining  
\[a_{n}(r)=\frac{1}{n!\pi}\Gamma\Big{(}1+\frac{n}{2}\Big{)}\bigg{(}\frac{r}{ \sqrt{2}\sigma}\bigg{)}^{\!n}\exp\!\bigg{(}-\frac{r^{2}}{2\sigma^{2}}\bigg{)} _{1}\Gamma_{\!1}\!\bigg{(}\frac{n}{2}+1;n+1;\frac{r^{2}}{2\sigma^{2}}\bigg{)}. \tag{15}\]1  
The average SER is  
\[a_{n}(r)=\frac{1}{n!\pi}\Gamma\Big{(}1+\frac{n}{2}\Big{)}\bigg{(}\frac{r}{ \sqrt{2}\sigma}\bigg{)}^{\!n}\exp\!\bigg{(}-\frac{r^{2}}{2\sigma^{2}}\bigg{)} _{1}\Gamma_{\!1}\!\bigg{(}\frac{n}{2}+1;n+1;\frac{r^{2}}{2\sigma^{2}}\bigg{)}. \tag{15}\]2  
Invoking [PERSON]'s theorem once again, the formula can be evaluated as  
\[a_{n}(r)=\frac{1}{n!\pi}\Gamma\Big{(}1+\frac{n}{2}\Big{)}\bigg{(}\frac{r}{ \sqrt{2}\sigma}\bigg{)}^{\!n}\exp\!\bigg{(}-\frac{r^{2}}{2\sigma^{2}}\bigg{)} _{1}\Gamma_{\!1}\!\bigg{(}\frac{n}{2}+1;n+1;\frac{r^{2}}{2\sigma^{2}}\bigg{)}. \tag{15}\]3  
Computing the SER using (37) requires a summation of double series, as \(b_{n}\) are themselves infinite series over \(m\). Clearly, this requires truncation after a certain number of terms in both directions. In Figure 2, we numerically analyze the precision of such truncation for typical system parameters. It can be seen that the numerical error decays quickly after the number of terms increases over a certain threshold. In this particular example, truncation to \(1\leq n\leq 22\), and \(0\leq m\leq 48\) provides precision of about two significant digits. In the case when Gray coding is used for mapping bits into symbols, the approximate error probability per bit can be calculated based on symbol error probability by using \(P_{\mathrm{eba}}=P_{e}/\log_{2}M\). In the following text, these bit error probabilities for BPSK, QPSK and 8 PSK are denoted by \(P_{\mathrm{eba}}^{\mathrm{BPSK}}\), \(P_{\mathrm{eba}}^{\mathrm{QPSK}}\) and \(P_{\mathrm{eba}}^{\mathrm{BPSK}}\), respectively. Here, the novel formula is derived for calculating coefficients \(b_{n}\). Although this formula is given in the form of an infinite sum, it enables us to evaluate SER in (37) in detecting MPSK signals over the TWDP channel taking imperfect reference signal phase recovery into account.
## 1 Introduction
Section 2 briefly reviews the SAR system to explain the origin of the autocorrelation of speckle and the ways it can be mitigated in practical application contexts. Additionally, the basics of SAR interferometry are presented, and methods for estimating SAR interferograms are discussed. Section 3 presents the quantitative results from two different datasets: one from the COSMO-SkyMed satellite constellation and one from the TerraSAR-X/Tandem-X twin satellites. Section 4 discusses the advantages of spatial decorrelation for InSAR processing and the importance of coherence analysis. Concluding remarks and possible developments are presented in Section 5.
## 3 Dependence of Geometric Placement of Antenna Array Elements in Regards to Radio Link Improvements
### Geometric Assessment of Phased Antenna Arrays
As shown in Figure 4, the scanning capacity of the planar array geometry is \(\pm\)50\({}^{\circ}\) and \(\pm\)60\({}^{\circ}\) in the 8 \(\times\) 8 and 16 \(\times\) 16 array, respectively. In this range the directivity levels are more stable and have narrower beams. It can be seen that the gain levels remain from 10 to 15 dB for 8 \(\times\) 8 array, and from 13 to 22 dB for 16 \(\times\) 16 array in the scannable range, due to the large number of antenna elements used in this array. Circular array geometry, despite it having a smaller area and less antenna elements (9.62 \(\lambda^{2}\) for 21-element-array and 44.18 \(\lambda^{2}\) for the 47 element-array), illustrates a better performance than the planar array, due to an increase of \(\pm\)55\({}^{\circ}\) of scanning with narrow beamwidths for the 21 element-array; and \(\pm\)66\({}^{\circ}\) of scanning for the 47 element-array. Although the gain levels are higher than the results of the planar array, these levels remain stable in the same scanning directions, remaining from 10 to 17 dB and from 13 to 23 dB in the 21 element-array and the 47 element-array, respectively. Considering these numerical  
Figure 4: Comparison of the gain levels at different scanning directions of the planar (PA), circular (CA), and concentric ring (CR) antenna array. Figure 3: Comparison of the beamwidth at different scanning directions of the planar (PA), circular (CA), and concentric ring (CR) antenna array. results, circular antenna arrays provide better performance and compromise between beamwidth and steering features. This way, the circular antenna array is selected to analyze its effect in the TC and DPS, considering its beamwidth and gain at different frequencies. To achieve better and more accurate results in the following analysis, the full-wave simulations of the circular antenna array were implemented. To obtain the beamwidth and gain of the circular array were necessary to simulate every frequency using a circular patch. The substrate laminates were FR-4 (\(\epsilon_{r}=4.2\)) and RT/duroid 5880 (\(\epsilon_{r}=2.2\)) with a thickness of 1.6 and 0.787 mm, respectively. Moreover, the radii of the different antennas used for the simulations were 59 mm (700 MHz), 11.43 mm (3.5 GHz), 2.48 mm (26 mm), and 1.46 mm (48 GHz). Additionally, SMA and 2.4 mm connector models were included in the simulation process. Figure 5 shows the CA-21 (a) at 3.5 GHz and CA-47 (b) at 26 GHz simulated in the CST MicroWave Studio Suite. The 3D radiation pattern yielded in both antenna arrays from Figure 5 are shown in Figure 6. Due to the geometry symmetry of the antenna array design, the beamwidth and gain were similar in every simulated case (CA-21 and CA-47). Both results are listed in Table 2.
# Energy-Efficient Multicast Precoding for Massive MIMO Transmission with Statistical CSI
## 5 Conclusions  
In this paper, we have investigated energy-efficient physical-layer multicast precoding for massive MIMO transmission where the BS only has access to the statistical CSI of all UTs. We first introduced a massive MIMO beam domain channel model. Via exploiting the statistical properties of the massive MIMO beam domain channels, we then showed the optimal energy-efficient multicast signaling directions, which reduces the matrix-valued precoding design into a beam domain energy-efficient power allocation problem. We further proposed a sequential power allocation algorithm with guaranteed convergence to the global optimal solution via exploiting [PERSON]'s transform. In addition, we derived the DE of the design objective via exploiting the large-dimensional random matrix theory. Simulation results showed the near-optimal EE performance of our proposed approach for energy-efficient massive MIMO multicast precoding. The EE performance gain of the proposed approach over the conventional rate optimization approach was also demonstrated in the numerical results.  
[PERSON] perceived the idea, performed the simulations and wrote the manuscript. [PERSON] and [PERSON] revised the manuscript.  
This work was supported in part by the National Natural Science Foundation of China under Grants 61801114, 61320106003, 61761136016, 61471113, 61631018, and 61521061, the Natural Science Foundation of Jiangsu Province under Grant BK20170688, and the National Science and Technology Major Project of China under Grant 2017 ZX03001002-004.  
The authors would like to thank the Editor and the anonymous reviewers for their valuable comments and suggestions.  
The authors declare no conflict of interest.
# A Survey on Robust Video Watermarking Algorithms for Copyright Protection
## 2 Basic Models of Video Watermarking
### Watermark Embedding
#### 2.2.3 Video Watermarking Algorithms after Compression  
The video watermarking algorithm after compression searches for redundant space in the compressed bit stream and embeds watermark information into it. The advantages of this type of algorithms include (i) the algorithm is independent of the corresponding codec and has high efficiency and (ii) the computational redundancy is small and the fidelity is high. Its disadvantages include (i) the redundant space available for watermark embedding is very small, which leads to limited capacity; and (ii) the robustness of the algorithm is poor.  
To sum up, each algorithm has its own advantages and disadvantages. In practical application, different watermark types are selected according to different occasions and different requirements.
## 4 Method
### Algorithm Pseudocode  
The Algorithm 1 pseudocode used in this article is as follows:  
```
1:Initialize Actor-Critic's network parameters \(\theta^{Q}\) and \(\theta^{\mu}\).
2:Assign network parameters to the target network \(\theta^{Q^{{}^{\prime}}}\leftarrow\theta^{Q}\), \(\theta^{\mu^{{}^{\prime}}}\leftarrow\theta^{\mu}\).
3:Initialize the experience pool \(R\).
4:for episode = (1, 1000)do
5: Go back to the initial point \(s_{1}\);
6:for step = (1, 30)do
7: Select Action \(a_{i}=\mu(s_{i}|\theta^{\mu})\) from the actor network and send it to the robot
8: After processing
9: The Fuzzy Rewards system calculates the reward value based on \(F_{y},F_{z},\Delta_{z},d_{z}\)
10: The program executes \(a_{i}\) and returns the bonus value \(r_{i}\) and the new status
11:\(s_{i+1}\)
12: The state transition process: \((s_{i},a_{i},r_{i},s_{i+1})\) is stored in the experience pool \(R\)
13: As a dataset for the training network
14: Randomly sample N \((s_{i},a_{i},r_{i},s_{i+1})\) data from Experience Pool \(R\) as a mini-
15: Batch training data for the policy network and Q network
16: Set up \(y_{i}=r_{i}+\gamma Q^{{}^{\prime}}(s_{i+1},\mu^{{}^{\prime}}(s_{i+1}|\theta^{ {}^{\prime}})|\theta^{Q^{{}^{\prime}}})\)
17: Define the loss function: \(Loss=\frac{1}{N}\sum_{i}(y_{i}-Q(s_{i},a_{i}|\theta^{Q}))^{2}\), update the Critic
18: Network with the loss function
19: Policy gradient for computing policy networks:
20:\(\
abla_{\theta^{\mu}}J=\frac{1}{N}\sum_{i}\
abla_{a}Q(s,a|\theta^{Q})|_{s=s_ {i},a=\mu(s_{i})}\
abla_{\theta^{\mu}}\mu(s|\theta^{\mu})|_{s_{i}}\)
21: Update the target network parameters:
22:\(\theta^{\mu^{{}^{\prime}}}=\tau\theta^{\mu}+(1-\tau)\theta^{\mu^{{}^{\prime}}}\)
23:\(\theta^{Q^{{}^{\prime}}}=\tau\theta^{Q}+(1-\tau)\theta^{Q^{{}^{\prime}}}\)
24:endfor
25:endfor
```  
**Algorithm 1** Fuzzy Rewards--DDPG Algorithm
## 2 Investigations Focusing on Overall Accumulated-Bed Characteristics
### Investigations with Mixed Solid Particles
#### 2.2.2 Experimental Results and Discussion  
Figure 9 shows two typical measured results for mixed-sized and mixed-density cases. As shown in Figure 9, it was observed that, regardless of the mode adopted for mixing particles (namely mixed-sized or mixed-density), heavier particles tended to accumulate in the bed center while lighter particles (such as particles with smaller size or smaller density) would be pushed aside by collisions with heavier ones and, generally, disperse laterally during bed formation. Therefore, in such cases, particle beds with larger concavity and lower mound height were more likely to be formed. Furthermore, possibly due to the larger particle-particle friction, which may increase the difficulty for the accumulated bed to collapse under the impact of falling particles, the mixed-size particle mound heights were found to be higher than the single-size ones [28]. On the other hand, it was confirmed that at the mixed-sized bed summit, a larger number of smaller particles accumulated compared to the larger ones (see Figure 9a), especially in cases using a larger nozzle size or particles with larger size differences [64]. Meanwhile, for the bed summit in cases of mixed-density particles, a larger contribution was made by lighter particles (see Figure 9b), particularly when a larger nozzle size was employed [64]. This is possibly because, due to the larger particle-jet velocity, the heavier particles pushed the lighter particles aside as a result of the impact of the heavier particles on the lighter particles at the bed summit during the DBF process. Additionally, the effect of nozzle size (i.e., shorter and more concave/flat particle beds would form with larger nozzle size) was validated again in cases of mixed particles.  
Figure 8: Positions of measured apparent surface areas of beds (Position 1: particle bed top; Position 2: middle of particle mound; Position 3: bottom of particle mound; Position 4: bottom of particle bed) [64].  
Figure 9: Distribution of mixed particles for particle beds (\(d_{\text{n}}\) = 40 mm). (**a**) Al\({}_{2}\)O\({}_{3}\) mixed-sized particles (\(d_{\text{p}}\) = 2 and 6 mm, mixing ratio = 1:1), and (**b**) Al\({}_{2}\)O\({}_{3}\) and SS mixed-density particles (\(d_{\text{p}}\) = 2 mm, mixing ratio = 1:1) [64].
# Quad-Band Uniformly Spaced Array Antenna Using Diverse Patch and Fractal Antennas
## 2 Materials and Methods
### Patch and Fractal Element Antennas
Figure 3: Different kinds of element antennas: (**a**) basic square patch; (**b**) fat bow tie patch; (**c**) bow tie patch; (**d**) bow tie Sierpinski fractal antenna; (**e**) fat bow tie Sierpinski fractal patch. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Antenna Type** & **Center Frequency** & **Wireless Comm. Services** \\ \hline Square & 5.08 GHz & Wi-Fi \\ Fat bow tie & 4.40 GHz & Wi-Fi \\ Fat bow tie fractal & 3.72 GHz & 5G \\ Bow tie & 2.80 GHz & None \\ Bow tie fractal (Iteration 2) & 2.60 GHz & None \\ Bow tie fractal (Iteration 3) & 2.47 GHz & Wi-Fi \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Types of antenna elements, their resonant frequencies, and corresponding wireless communication services. Figure 2: (**a**) Quad-band uniformly spaced array displacement with four elements for each band on top layer; (**b**) four-port feed network to evenly distribute signals in terms of magnitude and phase.
## 3 Multi-Time Scale Dispatching Framework of Active Power and Reactive Power Based on MPC  
To achieve safe and economical operation of the distribution network, considering that the forecast accuracy of wind, PV, and load improves as the time scale shortens, this paper divides the optimal dispatch of the distribution network into day-ahead and intra-day rolling stages. Additionally, model predictive control is introduced in the intra-day rolling optimization stage. Figure 1 illustrates the multi-time scale active and reactive power coordinated dispatch based on the MPC framework proposed in this paper. The controllable resources include wind, PV, SVG, On-Load Tap Changers (OLTCs), Capacitor Banks (CBs), Gas Turbine (GT), Battery Energy Storage (BES) and VPSSH.
###### Abstract  
In the era of sustainable development goals (SDGs), energy efficient heat transfer systems are a must. Convective heat transfer within circular pipes is an important field of research on a rarely addressed limitation of fluid flows. Vacuum solar tubes is one of many applications that could benefit from the existence of nanoparticles, Al\({}_{2}\)O\({}_{3}\), for example, to enhance the heating of air or water steam. The current research investigates the impacts of the Reynolds number (Re), Prandtl number (Pr), Knudsen number (Kn), aspect ratio (x/D\({}_{\rm h}\)), and volume fraction of Al\({}_{2}\)O\({}_{3}\) nanoparticles (\(\phi\)) on the Nusselt number (Nu) under constant wall heat flux conditions. An axisymmetric computational fluid dynamics (CFD) analysis of the nanofluid flowing at the entrance region of a circular pipe was conducted under a slip flow at steady-state developing laminar conditions using the Ansys-Fluent 2018 software package. A mesh sensitivity analysis was conducted, and a proper number of mesh elements was selected. The results showed that an increasing Re and/or \(\phi\) would result in an increasing Nu. The dependance of Nu on Kn was strong due to the high slip values and temperature jump. An increasing x/D\({}_{\rm h}\) ratio resulted in reduced Nu values. The major impact was due to Kn, which caused a reduction of up to 40% in the Nu value due to slip conditions. However, there was an enhancement of 2.5% in the heat transfer due to the addition of nanoparticles, which was found at Re = 250, Kn = 0.1, and \(\phi\) = 0.1 (Pr = 0.729). Finally, Nu\({}_{\rm avg}\), Nu\({}_{\rm x}\), U/U\({}_{\rm m}\), and Re\({}_{\rm f}\) were corelated with Kn, Pr, Re, and x/D\({}_{\rm h}\) with proper coefficient of determination (R\({}^{2}\)) values.  
slip flow; CFD; nano particles; Nusselt number; entrance region; energy efficiency