esa-sceva/satcom-chunk-collection huggingface dataset:
# Research on Corrosion Damage Evolution of Aluminum Alloy for Aviation
## 3 Results and Discussion
### Depth of Corrosion Pits
#### 3.2.2 Distribution Law
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Distribution Type** & **Parameter** & **8 h** & **24 h** & **48 h** & **72 h** & **96 h** & **120 h** \\ \hline \multirow{3}{*}{Normal distribution (Y\({}_{1}\))} & \(\mu\) & 7.352 & 15.272 & 27.414 & 33.698 & 40.291 & 45.064 \\  & \(\sigma\) & 1.749 & 3.043 & 4.053 & 3.623 & 3.741 & 5.120 \\  & \(r\) & 0.957 & 0.909 & 0.990 & 0.991 & 0.994 & 0.983 \\ \hline \multirow{3}{*}{Gumbel distribution (Y\({}_{2}\))} & \(\mu\) & 6.892 & 13.991 & 26.072 & 31.891 & 38.021 & 44.123 \\  & \(\sigma\) & 2.312 & 3.221 & 4.121 & 3.458 & 3.889 & 4.451 \\  & \(r\) & \(-\)0.991 & \(-\)0.935 & \(-\)0.939 & \(-\)0.967 & \(-\)0.959 & \(-\)0.971 \\ \hline \multirow{3}{*}{Lognormal distribution (Y\({}_{3}\))} & \(\mu\) & 1.967 & 2.703 & 3.222 & 3.512 & 3.692 & 3.846 \\  & \(\sigma\) & 0.238 & 0.233 & 0.167 & 0.108 & 0.0933 & 0.108 \\  & \(r\) & 0.968 & 0.837 & 0.978 & 0.990 & 0.989 & 0.981 \\ \hline \multirow{3}{*}{Weibull distribution (Y\({}_{4}\))} & \(\beta\) & 4.362 & 5.261 & 7.556 & 10.302 & 12.120 & 9.812 \\  & \(\sigma\) & 8.036 & 16.438 & 27.105 & 35.320 & 41.990 & 49.377 \\ \cline{1-1}  & \(r\) & 0.980 & 0.939 & 0.982 & 0.960 & 0.961 & 0.959 \\ \hline \hline \end{tabular} Note: In the table, \(\mu\) is the position parameter, \(\sigma\) is the scale parameter, \(\beta\) is the shape parameter, and \(r\) is the correlation coefficient.  
\end{table} 
Table 4: Fitting results of the depth of corrosion pits’ values corresponding to three different distribution parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Corrosion Time/\(h\)** & **Distribution Form** & **Linear Regression Equation** \\ \hline
8 & Gumbel distribution & Y\({}_{2}=-4.569-0.698d\) \\
24 & Weibull distribution & Y\({}_{4}=-13.987+4.9661\)nd \\
48 & Normal distribution & Y\({}_{1}=-144.350+7.089d\) \\
72 & Normal distribution & Y\({}_{1}=-217.591+7.940d\) \\
96 & Normal distribution & Y\({}_{1}=-260.837+7.715d\) \\
120 & Normal distribution & Y\({}_{1}=-194.385+5.590d\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Combination of optimal linear regression equations for the depth of corrosion pits. Figure 9: _Cont._
## 2 Data and Methods
### SPEI Calculation  
The standardized precipitation evapotranspiration index (SPEI), proposed by [PERSON] [34], can evaluate the aridity or wetness status of a region on multiple time scales. It is calculated as:  
\[D_{i}=P_{i}-PET_{i} \tag{1}\]  
where \(P_{i}\) and \(PET_{i}\) is the precipitation and the potential evapotranspiration in month \(i\), respectively. The potential evapotranspiration is commonly estimated by the Thomthwaite and Penman-Monteith equations. The calculation is listed as follows:  
\[D_{k}^{n}=\sum_{i=0}^{k-1}(P_{n-i}+PET_{n-i})\ \ \ \ \ \ n\geq k \tag{2}\]  
where \(D\) represents cumulative water deficit, \(k\) is the time scale (month), and \(n\) is the number of calculations.  
To ensure the consistency of spatial resolution, the gridded site data (500 m spatial resolution) was generated using the ordinary Kriging interpolation method within ArcGIS. The Kriging method is more advantageous for the interpolation of climatic variables [35]in areas with a uniform distribution of meteorological stations and minimal changes in elevation [36; 37]. Most of the physical geographic data are non-linear. Considering the requirement of linear data in the subsequent model, we calculated the monthly anomaly of each variable (for example: the anomaly in April 2001 is the difference between value in April 2001 and multi-year average value in April) to partially eliminate the seasonality of original data.
## 2 Materials and Methods
### Data Processing and Analysis  
Data processing was carried out using MassLynx (v4.2.0, Waters; [[https://www.medicalexpo.com.cn/](https://www.medicalexpo.com.cn/)]([https://www.medicalexpo.com.cn/](https://www.medicalexpo.com.cn/))). The peaks were extracted and aligned using MSConvertGUI (v3.0; [[https://proteowizard.sourceforge.io/download.html](https://proteowizard.sourceforge.io/download.html)]([https://proteowizard.sourceforge.io/download.html](https://proteowizard.sourceforge.io/download.html))). The compounds were identified using the METLIN database ([[https://metlin.scripps.edu](https://metlin.scripps.edu)]([https://metlin.scripps.edu](https://metlin.scripps.edu))), including the identification of theoretical fragments. The deviation of mass counts was consistently within 100 ppm. After that, we used R to graph the processed data.  
To discern differences in protein expression among samples from different groups, we employed a \(t\)-test (IBM SPSS, Armonk, NY, USA, [[https://www.ibm.com/products/spss-statistics](https://www.ibm.com/products/spss-statistics)]([https://www.ibm.com/products/spss-statistics](https://www.ibm.com/products/spss-statistics))), with screening conditions set at a significance value of false discovery rate (FDR), and the log2 logarithm of the quantitative ratio, log2 FC (where FC is the fold change), between the two groups (up- or down-regulated) exceeding 2 (based on maximizing variation and data-driven approaches).  
The correlations between all genes and metabolites were computed for each difference grouping using the Pearson correlation method (IBM SPSS). Prior to correlation calculation, the data underwent Z-value transformation for preprocessing. Subsequently, the results were filtered based on the correlation coefficient (CC) and \(p\)-value [28], with screening thresholds of \(|\)CC\(|>\) 0.80 and CCP \(<\) 0.05.
## 5 Lightweight Clear Channel Assessment (LW-CCA)  
In this paper, we propose the LW-CCA, a lightweight, low-complexity programming method designed to minimize WakeUp power on ContikiMAC nodes. In this method, it attempts to reduce the time spent in Rx mode by maintaining a PDR rate similar to base ContikiMAC. By focusing on software and hardware RSSI status check time, LW-CCA reduces the percentage of duty cycles as much as possible to reduce radio power consumption. The minimum WakeUp time for a medium check would take at least one idle listening. In Section 5.1, a single idle listening is analyzed to identify the essential time factors. Furthermore, the evaluation of the minimum and maximum RSSI status check time on nodes is presented in Section 5.2. In Section 5.3, the LW-CCA node categories RSSI based on the CCA verification, whether they are predicted as a false WakeUp, idle listening, or positive WakeUp. Finally, in Section 5.4, the performance of LW-CCA for the classification and validation of RSSI and the dynamic radio check time are described. Worth mentioning that LW-CCA runs exclusively on the relay and sender node, not sink or server node. The proposed method is considered when the nodes are fixed in the network. The following sections describe the details of the proposed method.
# Perceptual Quality of Audio-Visual Content with Common Video and Audio Degradations
## 5 Immersive Audio-Visual Experiments
### Apparatus and Physical Conditions  
A recording studio from the Nucleo Multimedia e Internet (NMI) of the Department of Engineering (ENE) of the University of Brasilia (UnB) was used to conduct the perceptual experiments. This type of facility guaranteed sound isolation during each experimental session, in which only one participant was admitted. All participants were assigned the same workstation (Table 6). Lighting and viewing conditions were set following the recommendations in ITU-T BT.500.1 [8,59].  
A quality assessment web-based platform, developed by the Grupo de Processamento Digital de Sinais (GPDS), was used for displaying the test clips and collecting the responses from participants. The experiments were carried out with volunteers (mostly graduate students) from the Electrical Engineering and Computer Science Departments from the University of Brasilia. No particular expertise was needed in terms of digital video and  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Setup** & \\ \hline Monitor & Samsung SyncMaster P2370 \\  & Resolution: 1920 \(\times\) 1080; Pixel-response rate: 2 ms; \\  & Contrast ratio: 1000:1; Brightness: 250 cd/m\({}^{2}\) \\  & Sennheiser Hd 518 Headfone \\  & Impedance: 50 Ohr, Sound Mode: Stereo; \\  & Frequency response: 14–26,000 Hz; \\ Sound Card & Asus Xonar DGX 5.1 \\ \hline  & **Experiment 1** & **Experiment 2** & **Experiment 3** \\ \hline
**Stimuli** & \\ \hline Source Stimuli & 60 & 40 & 40 \\ Test Conditions (HRC) & 12 & 20 & 20 \\ Test Sequences (PVS) & 720 & 800 & 800 \\ Average length & 37 s & 35 s & 34 s \\ Scores per PVS & 5 & 2 & 2 \\ Scores per HRC & 300 & 80 & 80 \\ \hline
**Participants** & \\ \hline Total & 60 & 40 & 42 \\ Male & 18 & 15 & 16 \\ Female & 42 & 25 & 26 \\ Age Range & 19–36 & 21–36 & 20–34 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Detailed specifications of the Experiments 1–3.  
Figure 2: Source videos spatial and temporal information measures.  
audio defects. Although no vision or hearing tests were requested from participants, unimpaired hearing was a pre-requirement. In addition, any participant that wears glasses or contact lenses to watch TV was asked to use them for the experimental session. Details about the participants' genders and ages are presented in Table 6.
# An Internet of Things (IoT) Application on Volcano Monitoring
## 3 IoT Thermometers Network
### Software
#### 3.2.4 Server Software  
Since the gateway synchronizes data to the data analysis center every 10 min, is possible to display the measurements in real-time. For this purpose, a web page interface was developed. Users can check the system operation and view data in real-time. The website is built by means of join.py and LoRa_represent.py python scripts, which are executed every 10 minutes using cron of Linux.  
The join.py script joins in a single file all the files stored in the nested folders in the database. Then, the LoRa_represent.py script reads the file generated by join.py and plot data in HTML files by means of the Bokeh library [40] and P5.JS [90]. As a result, five HTML files are obtained with different time periods: 7 days.html, 30 days.html, 90 days.html, 1 year.html, and series.html. Each html file has its  
Figure 9: End devices flow chart.  
own tab in the web page (Figure 10) where users can select the desired time period. Each html file is organized in five plots as follows: temperature values recorded, battery level of each thermometer, RSSI level, measurement percentage of error for each thermometer in the last 24 h (only in 7.html file), and measurement percentage of error for each thermometer along the time period displayed (Figure 10).  
Figure 10: Webpage. (**a**) Temperature values measured by thermometers in area A; (**b**) Temperature values measured by thermometers in area B; (**c**) Battery level of each thermometer; (**d**) RSSI level of each thermometer measured in the repeater; (**e**) Percentage of error of each thermometer in the last 24 h; (**f**) Percentage error for the selected time period.
## 3 5G and TSN Integrated Prototype for Resilience and High Reliability
### Overall Architecture and Measurement Setup
#### 3.4.2 Setup 2: Redundant Transmissions Using FRER via Different 5G Mid-Band Systems  
In Setup 2, as shown in Figure 6, we investigate the use of FRER using not one mid-band system as in Setup 1 but one for each replicated data packet. This creates a redundancy not only on the UE side but also on the network side. After replication in Switch 1, one packet is sent via a non-standalone (NSA) 5G system, and one packet is sent via a standalone (SA) 5G system. As in Setup 1, in Switch 2, only the first copy of the packet will be forwarded, and any redundant copy arriving later is discarded.
## 3 Small Amplitude Wave Approximation
### Case 1 (\(\beta=1\))  
The next order of \(\varepsilon\) provides a set of equations that gathers between the first and second perturbed quantity, and by eliminating the second perturbed quantities, we obtain the following evolution equation:  
\[\frac{\partial}{\partial\tau}\phi_{1}+A\phi_{1}\frac{\partial}{\partial \xi}\phi_{1}+B\varepsilon^{2\alpha+1}\frac{\partial^{3}}{\partial\xi^{3}} \phi_{1}+C\varepsilon^{\alpha+\gamma+1}\frac{\partial^{2}}{\partial\xi^{2}} \phi_{1}=0 \tag{9}\]  
where  
\[A=\frac{1}{A_{0}}\left[2\alpha_{2}-\frac{3}{\lambda^{4}}+\frac{3\mu_{+}\big{(} \lambda^{2}\mu+\sigma\big{)}}{\big{(}\lambda^{2}\mu-3\sigma\big{)}^{3}}\right], \tag{10a}\] \[B=\frac{1}{A_{0}},\] (10b) \[C=\frac{1}{A_{0}}\left[\frac{\eta_{1}}{\lambda^{3}}+\frac{\mu_{+}\eta_{2} \lambda}{\big{(}\lambda^{2}\mu-3\sigma\big{)}^{2}}\right],\] (10c) \[A_{0}=\left[\frac{2}{\lambda^{3}}+\frac{2\mu_{+}\lambda\mu}{\big{(}\lambda^{2} \mu-3\sigma\big{)}^{2}}\right],\] (10d) \[\alpha_{2}=\frac{1}{2}\left[\mu_{i}\frac{4k_{i}^{2}-1}{(2k_{i}-3)^{2}}-\mu_{e} \sigma_{e}^{2}\frac{4k_{e}^{2}-1}{(2k_{e}-3)^{2}}\right] \tag{10e}\]  
Equation (9) represents the Kortweg-de Vreis Burger equation, where the second term describes the nonlinearity, while the third and fourth terms represent the dispersion and dissipation, respectively. Equation (9) shows that the dispersion and dissipation terms are mainly dependent on the two arbitrary parameters, \(\alpha\) and \(\gamma\). At \(\alpha=\frac{1}{2}\), \(\gamma>\frac{1}{2}\), Equation (9) tends to the so-called KdV evaluation equation. This means that at \(\gamma>\frac{1}{2}\) the effect of the dissipation term can be neglected in comparison with the dispersion term. Consequently, the KdV equation has a soliton solution at the balance between nonlinear and dispersion terms as  
\[\phi_{KdV}(\xi,\tau)=\phi_{0 KdV}\sec h^{2}\left(\frac{\xi-\
u\tau}{\Delta} \right),\ \phi_{0 KdV}=3\upsilon/A,\ \ \Delta=\upsilon/4B, \tag{10f}\]  
However, at \(\alpha=1\), \(\gamma=0\), Equation (9) converts to Burgers' equation, and the effect of dispersion can be neglected in comparison with the effect of the dissipation term. In this case, Equation (9) has a shock wave solution:  
\[\phi_{B}(\xi,\tau)=\phi_{0B}\left(1+\tanh\left(\frac{\xi-\
u\tau}{\Delta} \right)\right),\ \ \phi_{0B}=\upsilon/A,\ \Delta=2C/\upsilon \tag{10g}\]Conversely, the effects of both dispersion and dissipation exist, and a solitary wave appears from the interaction between nonlinearity with dispersion and dissipation at \(\alpha=\frac{1}{2}\), \(\gamma=\frac{1}{2}\). At \(\beta=1\), as is clear from (10f) and (10g), there is a possibility of two types of propagating wave (compressive and rarefactive), depending mainly on the sign of the nonlinear coefficient, but when the nonlinear coefficient equals zero, the propagated waves are undefined, so the nonlinear term must have more strength.
# A Compact Multi-Identity Fully Homomorphic Encryption Scheme Without Fresh Ciphertexts
## 2 Preliminaries
### Preimage Sampling Algorithm  
Lemma 4 ([27]): Let \(\mathbf{(A,T)}\) be a matrix approximation trapdoor pair, \(\mathbf{B}=\left[\begin{smallmatrix}\mathbf{T}\\ -\mathbf{I}_{N}\end{smallmatrix}\right]\) and \(\big{(}\mathbf{r},\mathbf{\Sigma}\big{)}\) such that \(\sqrt{\mathbf{\Sigma}_{p}\oplus\mathbf{r}^{2}\mathbf{I}_{N}}\geqslant\eta (\mathcal{L}(\mathbf{B}))\). Use \(\mathbf{A}^{-1}\) to denote \(\mathbf{ApproxPreSample}(\mathbf{A},\mathbf{T},\cdot,\mathbf{r},\mathbf{\Sigma})\). The two distributions that follow are statistically indistinguishable:  
\[\Big{\{}\big{(}\mathbf{A},\mathbf{x},\mathbf{u},\mathbf{e}\big{)}:\mathbf{u} \stackrel{{\mathcal{S}}}{{\leftarrow}}\mathbb{Z}_{Q^{\prime}}^{n }\mathbf{x}\leftarrow\mathbf{A}^{-1}(\mathbf{u})\text{, }\mathbf{e}=\mathbf{u}-\mathbf{Ax}\text{ mod }Q\big{\}}\]  
\[\Big{\{}\big{(}\mathbf{A},\mathbf{x},\mathbf{u},\mathbf{e}\big{)}:\mathbf{x} \gets D_{\mathbb{Z}^{n},\sqrt{\mathbf{\Sigma}}}\mathbf{e}\stackrel{{ \mathcal{S}}}{{\leftarrow}}\mathbb{Z}_{p}^{n}\text{, }\mathbf{u}=\mathbf{Ax}+\mathbf{e}\text{ mod }Q\big{\}}\]  
The efficiency of basic Gaussian sampling is crucial to the overall performance of the Gaussian preimage sampling algorithm. The standard deviation \(\sigma\) is a significant measure of this algorithm's effectiveness. A smaller standard deviation \(\sigma\) indicates a higher quality of the Gaussian preimage sampling algorithm. Furthermore, the quality of the trapdoor matrix \(\mathbf{R}\) also significantly influences the performance of the Gaussian preimage sampling algorithm.
# Hybrid Satellite-Terrestrial Networks toward 6G: Key Technologies and Open Issues
## 5 Key Cooperative and Cognitive Technologies
### Physical-Layer Security
#### 5.4.1 Physical-Layer Security of HSTN Cooperative Networks
Motivated by the latest advances in physical-layer security and the potential of the hybrid satellite-FSO system in various scenarios, the secrecy performance of satellite-FSO cooperative systems for cases of both AF and DF relay were investigated in [205]. Addressing hardware impairment on the secrecy performance of HSTN relay networks, the authors of [206] proposed an optimal relay-selection (ORS) scheme and analyzed its secrecy outage probability in the presence of hardware impairment along with traditional round-robin scheduling (RRS) as a benchmark scheme. Most works based on the physical-layer security of UAV networks have considered the optimization problem. Very few works have analyzed the information-theoretic secrecy performance of a downlink point-to-point UAV network (e.g., [207,208]) without mobile relaying. In [209], the authors introduced novel 3D-secure mobile UAV relaying for HSTN in the presence of an eavesdropper. By considering three opportunistic UAV relay-selection strategies, namely closest UAV relay selection, uniform UAV relay selection, and maximum signal-to-noise ratio UAV relay selection strategies, the secrecy performance of the system, probability of non-zero security capacity (PNZSC), and secrecy outage probability (SOP) were analyzed. A beamforming scheme for maximizing the achievable secrecy rate (ASR) for a DF-based UAV relay equipped with multiple antennas was proposed in [210] to investigate secure transmission on an HSTN with multiple eavesdroppers. Secrecy energy efficiency (SEE) is a key performance metric for the evaluation of security and energy efficiency in networks. To address rising energy costs and security requirements of communication networks, the authors of [190] looked into the problem of SEE optimization in satellite-terrestrial integrated networks by proposing novel hybrid analog-digital beamforming.
## 9 PGB Force Coefficients vs. Excitation Frequency  
Figure 7 displays the PGB force coefficients vs. frequency ratio (\(\omega/\Omega^{\star}\)) for the bearing supplied with air at increasing pressures. In general, \(K_{XX}\) grows (hardens) as the whirl frequency increases, whereas the direct damping (\(C_{XX}\)) quickly drops. The magnitude of  
Figure 6: PGB (synchronous frequency) force coefficients vs. shaft speed: (**a,b**) stiffnesses (\(K_{XX}\), \(K_{XY}\)), (**c,d**) damping coefficients (\(C_{XX}\), \(C_{XY}\)), (**e,f**) effective stiffness (\(K_{eff}\)) and damping (\(C_{eff}\)) coefficients. Excitation frequency \(\omega=\Omega\) (synchronous with speed). Supply pressure \(p_{S}=2\) to 8 bar; MOS = 25 krpm.  
all force coefficients increases with an increase in gas supply pressure. In addition, at the cross-over frequency, \(\omega=\
icefrac{{1}}{{2}}\Omega\), half-frequency whirl, the effective stiffness (\(K_{\textit{eff}}\)) has a dip, and the effective damping turns positive, \(C_{\textit{eff}}\)\(>0\). Hence, the PGB has the identical aerodynamic stability characteristics as a plain journal bearing. The predictions reveal that the cross-coupled stiffness (\(K_{XY}\)) reverses sign for \(\omega>\
icefrac{{1}}{{2}}\Omega\), this frequency increasing as the supply pressure grows. Incidentally, for a low-pressure supply, \(p_{S}<4\) bar, the direct damping is negative, \(C_{XX}<0\), at low whirl frequencies (\(\omega<<\Omega^{*}\)). This effect is remarkable and a precursor to a pneumatic hammer; see [13].  
Figure 7: PGB force coefficients vs. frequency ratio (\(\omega/\Omega\)). Mean operating speed \(\Omega^{*}\) = 25 krpm (417 Hz); (**a**,**b**) stiffnesses (\(K_{XX}\), \(K_{XY}\)), (**c**,**d**) damping coefficients (\(C_{XX}\), \(C_{XY}\)), (**e**,**f**) effective stiffness (\(K_{\textit{eff}}\)) and damping (\(C_{\textit{eff}}\)) coefficients. Supply pressure \(p_{S}\) = 2 to 8 bar.  
In sum, shaftt whirl motions at super synchronous motions (\(\omega>\
icefrac{{1}}{{2}}\)\(\Omega\)), produce stiffness hardening and a marked reduction in effective damping. On the other hand, SSVs are likely to occur at \(\
icefrac{{1}}{{2}}\) frequency whirl since \(C_{\mathit{eff}}=0\).
# Ultra-Reliable Link Adaptation for Downlink MISO Transmission in 5G Cellular Networks
## 3 Sources of SINR Variability  
There are a number of sources of SINR/interference variability that can jeopardize reliability in a wireless/cellular network. These include the following:  
1. Variations in wanted signal channel between time of measurement and time of transmission
2. Interference variability caused by the changes in channels of interferers
3. Interference variability caused by radio resource management (RRM) in interfering cells (Changing multi-antenna transmissions, channel activity, power control, uplink user scheduling)  
We consider all of these, separately as well as their joint effect. SINR/interference variations caused by RRM may be stabilized by applying persistent RRM strategies. For example, downlink precoded multi-antenna transmissions, where the precoders are not user specific but frequency resource specific and optimized for a population of users, may be considered. As a result, the SINR misprediction of the third kind partially vanishes. Not much can be done to remove the variability of the first and second kind, however, if the user and/or the channel is mobile. To mitigate the impairments caused by these sources of SINR variability, we consider robust link adaptation where the SINR statistics of the realized transmission conditioned on the measured SINR are known.
# Multi-Layer Feature Fusion-Based Community Evolution Prediction
## 3 Multi-Layer Feature Fusion-Based Community Evolution Prediction
### Global- and Local-Based Community Role Extraction
The loss function is as follows:  
\[Cost=||\ell_{C}-\Re_{C}H_{C}||_{F}^{2}+||\xi_{C}-\Re_{C}W_{C}||_{F}^  
\[H_{C}=H_{C}\frac{\Re_{C}^{T}\ell_{C}}{\Re_{C}^{T}\Re_{C}H_{C}} \tag{2}\] \[\Re_{C}=\Re_{C}\frac{\ell_{C}H_{C}^{T}+\xi_{C}W_{C}^{T}}{\Re_{C}H_{ C}H_{C}^{T}+\Re_{C}W_{C}^{T}W_{C}^{T}}\] (3) \[W_{C}=W_{C}\frac{\Re_{C}^{T}\xi_{C}}{\Re_{C}^{T}\Re_{C}W_{C}} \tag{4}\]  
After obtaining the community role attribution matrix \(\Re_{C}\), we can obtain the community role of each node. Each row in \(\Re_{C}\) represents the probability that the node belongs to each community role. The nodes in the community can be assigned roles through the elements in \(\Re_{C}\):  
\[\Re_{C,i}=argmax_{k}\Re_{C,ik} \tag{5}\]  
The process of the GLRE algorithm is shown in Algorithm 1. ```
0: network structure \(G\), community \(C\)
1: Calculate the node features of each node from the global and local, respectively
2: Construct matrices \(\xi_{C}\) and \(\ell_{C}\) according to the obtained node features
3: Get \(H_{C}\), \(W_{C}\), \(\Re_{C}\), according to Formulas (2)-(4)
4: Obtain the role distribution \(\Re_{C,i}\) of each node according to Formula (5)
5: Output division result \(\Re_{C}\)
```  
**Algorithm 1** GLRE  
After obtaining the roles of nodes in the community through GLRE, for nodes with the same role, MCEP calculates the node features and uses the average value as the features of this type of role.