esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 MFG-LEACH Protocol
### Solution Analysis  
The solution of the coupled PDEs (HJB and FPK) in MFG-LEACH is complex and often requires numerical methods particularly finite difference methods (FDM) for practical computation [51; 52]. FDM discretizes both the spatial and temporal dimensions of the equations and approximates derivatives using finite difference techniques. The resulting system of algebraic equations is then solved iteratively.  
To utilize this method effectively, the continuous variables, time, energy and \(\gamma\) are discretized into a grid with dimensions \(X\times Y\times Z\). The decision-making for the optimal control policy takes place within this discretized space and the variables are used to approximate the solutions of the PDEs which will evolve in the three-dimensional space \((0,T)\times(E_{\texttt{min}},E_{\texttt{max}})\times(0,\gamma_{\texttt{th}})\) with steps in time (\(\delta_{t}\)), energy (\(\delta_{E}\)), and signal-to-interference plus noise ratio (\(\delta_{\gamma}\)) defined as follows [51]:  
\[\delta_{t}=\frac{T}{X} \tag{15}\]  
\[\delta_{E}=\frac{E_{\texttt{max}}-E_{\texttt{min}}}{Y} \tag{16}\]  
\[\delta_{\gamma}=\frac{\gamma_{\texttt{th}}}{Z} \tag{17}\]  
For the FPK Equation (18), the Lax-Friedrichs scheme is applied to obtain (19).  
\[\delta_{t}m(t,s)+\
abla_{E}m(t,s)E(t)+\
abla_{\gamma}m(t,s)\gamma(t)=0 \tag{18}\]  
\[M(i+1,j,l) = \frac{1}{2}[M(i,j-1,l)+M(i,j+1,l)\] \[+ M(i,j,l-1)+M(i,j  
\[\underset{E_{k}(t)}{\text{min}}\mathbb{E}\bigg{[}\int_{0}^{T}c_{k}(t)dt+c_{k}(T) \bigg{]} \tag{20}\] \[\text{subject to}: \delta_{t}m(t,s)+\
abla_{E}m(t,s)E(t)\] \[+\
abla_{\gamma}m(t,s)\gamma(t)=0.\]  
In this formulation, we introduce a Lagrange multiplier \(\lambda(t,s)\) as depicted in (21), assuming \(c_{k}(T)=0\). The incorporation of \(\lambda(t,s)\) is succeeded by discretizing (21), yielding (22) [47].  
A joint finite difference algorithm is subsequently developed using the Lax-Friedrichs scheme and Lagrange relaxation. This algorithm is designed to solve the coupled HJB and FPK equations, thereby obtaining the optimal power control policy. Algorithm 1 outlines the steps to update the mean field distribution, Lagrange multipliers (27), and energy levels (26) to achieve the optimal control policy.  
\[L(m(t,s),E(t,s),\lambda(t,s)) =\mathbb{E}\bigg{[}\int_{0}^{T}c_{k}(t)dt+c_{k}(T)\bigg{]}\] \[+ \int_{0}^{  
To achieve optimality, the decision variables (\(E^{*}\) and \(M^{*}\)) must satisfy the Karush-Kuhn-Tucker (KKT) conditions. Using Algorithm 1, \(M^{*}\) is first calculated, and then \(E^{*}\) (\(E_{k}\)) is determined according to (26). This process allows the MFG-LEACH protocol to compute the optimal transmission energy \(E_{k}\).
# On the Study of Influences of Different Factors on the Rapid Topospheric Tomography
## 3 GNSS Tropospheric Tomography Methodology  
### Tomography Mathematic Model  
The GNSS signal transmitted from satellite to ground receiver can be delayed by the ionosphere and neutral atmosphere. Ionospheric delay can be minimized by combinations of observations at different frequencies. Most of the neutral atmospheric delays are induced by troposphere, so the neutral atmospheric signal delay is generally referred as tropospheric delay. In GNSS data processing, tropospheric delay along the signal path is generally mapped into the zenith direction, namely the zenith tropospheric delay (ZTD), to avoid a rank deficiency problem [25].  
ZTD can be divided into zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD) component as:  
\[ZTD=ZWD+ZHD \tag{2}\]  
ZHD can be accurately estimated by empirical models, such as the Hopfield or Saastamoinen model [26; 27]. ZWD, which is mainly caused by atmospheric water vapor, however, is hard to be accurately modeled. In GNSS meteorology, ZWD is generally obtained by subtracting ZHD from the estimated ZTD, the by-product in GNSS data processing, namely,  
\[ZWD=ZTD-ZHD. \tag{3}\]  
As mentioned previously, the ZTD or ZWD does not contain vertical distribution of humidity. In tropospheric tomography, the zenith delays need to be converted to slant delays along the GNSS signal path as inputs in tomography. The slant tropospheric delay (STD) can be calculated according to,  
\[STD=SHD+SWD=m_{h}\cdot ZHD+SWD \tag{4}\]  
where \(m_{h}\) is the hydrostatic mapping function.  
Regarding the slant wet delay (SWD), with the estimated ZWD from Equation (3), horizontal gradients and the post-fit residuals from GNSS data processing, the slant wet delays (SWD) can be retrieved according to [28],  
\[SWD=m_{w}\cdot[ZWD+cot\varepsilon(G_{N}cos\phi+G_{E}sin\phi)]+\delta \tag{5}\]  
where \(m_{w}\) is the wet mapping function, \(G_{N}\) and \(G_{E}\) are the delay gradient parameters in the north-south and east-west direction, respectively, \(\varepsilon\) denotes the elevation angle, \(\phi\) is the azimuth, and \(\delta\) is the post-fit phase residual.  
SWD is actually the integral of the wet refractivity, \(N_{w}\), along the signal path (\(S\)), as following,  
\[SWD=10^{-6}\int_{S}N_{w}d_{s} \tag{6}\]In tomography, we generally discretize the troposphere into 3D voxels and \(N_{w}\) in Equation (6) then denotes the wet refractivity in each voxel. After we get the SWD from Equation (5), Equation (6) can be discretized and written as,  
\[\textbf{SWD}=\textbf{AX} \tag{7}\]  
where **A** is the projection matrix where each element denotes the distances of the signal that passes the voxel, and the vector **X** contains the to-be-estimated wet refractivity in each voxel.
# IDSMatch: A Novel Deployment Method for IDS Chains in SDNs +
## 5 Evaluation
### Network Delay under Varying Weights and Varying Number of Flows  
The findings reported in [4] emphasize the crucial role of incoming traffic volume as a key metric in evaluating the efficacy of IDS deployment within the data plane. Additionally, the quantity of IDSs within each chain is highlighted as a significant factor influencing all recorded metrics. To delve further into these dynamics, we conducted experiments to explore the impact of both the weight of flows and the number of flows in incoming traffic on network delay. In Figure 12, the network delay is depicted when there is a fixed amount of incoming traffic and a varying weight, ranging from 10 to 300. The results, considering the flow numbers of 100, 300, and 500, indicate that a higher rate of traffic correlates with an increase in network delay. This observation underscores the direct relationship between traffic volume and delay, with larger flow rates contributing to heightened delays in network transmission and processing.  
Figure 11: Number of hops for topology 3 (Sparsity = 55%). (a) Number of hops with one chain. (b) Number of hops with fixed chain. (c) Number of hops with long chain.  
Figure 10: Number of hops for topology 2 (Sparsity = 35%). (a) Number of hops with one chain. (b) Number of hops with fixed chain. (c) Number of hops with long chain.  
Figure 9: Number of hops for topology 1 (Sparsity = 15%). (a) Number of hops with one chain. (b) Number of hops with fixed chain. (c) Number of hops with long chain.  
According to Figure 13, the network delay is illustrated for varying amounts of incoming traffic, ranging from 100 to 500, while maintaining fixed flow weights of 100, 200, and 300. Notably, the results reveal that, although a larger volume of incoming traffic does lead to an increase in network delay, the impact of the weight of flows surpasses that of the traffic volume. This suggests that the characteristics of individual flows, as represented by their weights, exert a more pronounced influence on network delay than the overall volume of traffic. As a result, optimizing the weight assignment for flows emerges as a critical consideration for mitigating network delays. These experiments contribute valuable insights into the nuanced interplay between traffic characteristics and network delay, shedding light on factors that can be strategically managed to enhance the overall efficiency of IDS deployment within the SDN data plane.
# Optimizing the Honeycomb Spoke Structure of a Non-Pneumatic Wheel to Reduce Rolling Resistance
## 2 Materials and Methods
### Geometrical Parameters  
The NPT specification was designed with reference to a 205/60 R15 pneumatic tyre. The thicknesses of the hub, shear band, reinforcement layers (inner and outer ones), and thread were 5.9, 9.36, 0.64, and 7.9 mm, and the inner radii of the hub and thread were 203 and 315 mm, respectively. The width of the NPT was 205 mm.  
Honeycomb-shaped spokes are important supporting and energy-absorbing structures for NPTs, and the structural design of honeycomb spokes has a significant impact on various  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multicolumn{2}{c}{**Density (kg/m\({}^{3}\))**} & \multicolumn{2}{c}{**Young’s Modulus (GPa)**} & \multicolumn{2}{c}{**Shear Modulus (GPa)**} & \multicolumn{2}{c}{**Poisson’s Ratio**} \\ \hline Aluminium alloy (AI 7075-T6) & 2800 & 72 & 27 & 0.33 \\ High-strength steel (ANSI 4340) & 7800 & 210 & 76 & 0.29 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material parameters of AI 7075-T6 and ANSI 4340 steel.  
Figure 1: Structural diagram of NPT.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\(i\)} & \multicolumn{4}{c}{**Polyurethane**} & \multicolumn{4}{c}{**Synthetic Ruber**} \\ \cline{2-9}  & \(\mu_{i}\) **(MPa)** & \(a_{i}\) & \(g_{i}\) & \(\tau_{i}\) & \(\mu_{i}\) **(MPa)** & \(a_{i}\) & \(g_{i}\) & \(\tau_{i}\) \\ \hline
1 & 13.546 & 1.513 & 0.125 & 0.002 & 13.356 & 1.633 & 0.200 & 0.002 \\
2 & \(-2.338\) & 2.212 & 0.125 & 0.020 & \(-6.631\) & 1.900 & 0.200 & 0.020 \\
3 & 0.093 & \(-2.471\) & 0.125 & 0.200 & 0.058 & \(-2.456\) & 0.200 & 0.200 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Polyurethane and synthetic rubber material parameters.  
performance aspects of the NPTs. The honeycomb structure of the NPT is shown in Figure 2. It shows a reference cell of a honeycomb spoke structure, which achieves the honeycomb support spoke for NPTs by uniformly distributing the reference cell at 25 equal cycles in the circumferential direction. The length of each edge of the honeycomb spokes is a crucial parameter that changes the structure of the honeycomb and affects the performance of the NPT. The length of each edge can be determined based on its radial projection length, thereby quantitatively determining the specific structure of honeycomb spokes. The specific length parameters of each structure are shown in Table 3.  
In order to facilitate the study of the effect of the spoke thickness gradient on rolling resistance, the length of each edge was a fixed constant, and the spokes were divided into four layers: Tp, Cp, Lp, and Bp, as shown in Figure 2. Moreover, the average value of the four-layer spokes' thicknesses was 5 mm, although each dimension was allowed to alter.
# Jamming Analysis between Non-Cooperative Mega-Constellations Based on Satellite Network Capacity
## 2 System Model
### Transmission Rate Calculation  
Denote the transmission rate of ISL \(L_{(i,j)}^{(i,j+1)}\) from satellite \(A(i,j)\) to satellite \(A(i,j+1)\) in \(\Psi_{A}\) at time slot \(t\) as \(R_{i,j,t}^{\times}\). When \(L_{(i,j)}^{(i,j+1)}\) is not jammed, \(R_{i,j,t}^{\times}\) is calculated as follows:  
\[R_{i,j,t}^{\
earrow}=\log_{2}(1+\frac{p_{A}G_{t}^{\max}G_{r}^{\max}\left( \frac{\lambda}{4\pi d_{i,j,t}^{\
earrow}}\right)^{2}}{KTW}) \tag{5}\]  
where \(d_{i,j,t}^{\
earrow}=\|A(i,j,t)-A(i,j+1,t)\|\).  
Satellites in the MJR corresponding to \(L_{(i,j)}^{(i,j+1)}\) satisfy the following conditions:  
\[\left\{\begin{array}{l}B(t)=(x_{B}(t),y_{B}(t),z_{B}(t))\\ \langle A(i,j,t)-A(i,j+1,t),B(t)-A(i,j+1,t)\rangle{<}\theta\end{array}\right. \tag{6}\]  
Assume that, at time slot \(t\), the number of satellites satisfies Equation (6) is \(J(t)\). Denote the above satellite coordinates as \(B_{j}(t),j=1,2,\cdots,J(t)\). Thus, we obtain the data transmission rate \(\tilde{R}_{i,j,t}^{\
earrow}\) of \(L_{(i,j)}^{(i,j+1)}\) under non-cooperative jamming.  
\[\tilde{R}_{i,j,t}^{\
earrow}=\log_{2}\left(1+\frac{p_{A}G_{t}^{\max}G_{r}^{ \max}\left(\frac{\lambda}{4\pi d_{i,j,t}^{\
earrow}}\right)^{2}}{\sum\limits_ {k=1}^{J(t)}p_{B}G_{t}\left(g_{i,j,t}^{\
earrow}(k)\right)\left(\frac{\lambda} {4\pi D_{i,j,t}^{\
earrow}(k)}\right)^{2}{+}KTW}\right) \tag{7}\]  
where  
\[\begin{array}{l}D_{i,j,t}^{\
earrow}(k)=\|B_{k}(t)-A(i,j+1,t)\|\\ \theta_{i,j,t}^{\
earrow}(k)=\langle A(i,j,t)-A(i,j+1,t),B_{k}(t)-A(i,j+1,t)\rangle \end{array} \tag{8}\]Similarly, we can calculate the transmission rate \(R^{\times^{\prime}}_{i,j,t},R^{\times}_{i,j,t},R^{\times}_{i,j,t}\) of \(L^{(i,j-1)}_{(i,j)}\), \(L^{(i-1,j)}_{(i,j)}\) and \(L^{(i+1,j)}_{(i,j)}\) under jamming-free conditions, as well as the transmission rate \(\bar{R}^{\times^{\prime}}_{i,j,t},\bar{R}^{\times^{\prime}}_{i,j,t},\bar{R}^{ \times}_{i,j,t}\) after jamming.  
In summary, for satellite \(A(i,j)\) in \(\Psi_{A}\), the inter-satellite link rates of \(A(i,j)\) are \((R^{\times^{\prime}}_{i,j,t},R^{\times^{\prime}}_{i,j,t},R^{\times}_{i,j,t},R^{ \times}_{i,j,t})\) and \(\left(\bar{R}^{\times^{\prime}}_{i,j,t},\bar{R}^{\times^{\prime}}_{i,j,t}, \bar{R}^{\times}_{i,j,t},\bar{R}^{\times}_{i,j,t}\right)\) under jamming-free and non-cooperative jamming conditions, respectively.
## 3 Improved Risk Coefficient  
The landing gear R/E system has a variety of failure scenarios, and the risk coefficient may be used to assess the danger level of a given system. The traditional risk priority number (\(RPN\)) refers to the product of the probability (\(P\)), severity (\(S\)), and detection difficulty (\(D\)) of the failure, \(RPN\) can be expressed as:  
\[RPN=P\times S\times D \tag{1}\]  
In aviation maintenance, the maintenance difficulty is divided into route maintenance, workshop maintenance, and base maintenance. Thus, the maintenance difficulty must be considered. Introduce the evaluation index of maintenance difficulty (\(M\)). Therefore, the improved risk coefficient is defined as:  
\[RPN-M=P\times S\times D\times M \tag{2}\]  
Utilizing the four evaluation indices described above, one can determine the danger degree of the fault model of the landing gear R/E system. Comparatively, the traditional FCE model obtains index measurements entirely through experts' questionnaires. To reduce human subjective factors as much as possible, the improved FCE model obtains index measurements from statistical data, fault simulations, and professional maintenance data. The acquisition methods of the four indicators are as follows:  
1. The probability of failure (\(P\)) is obtained from general maintenance statistics.
2. The severity (\(S\)) is obtained by the deviation degree of the fault mode in the fault simulation from the normal working condition.
3. The detection difficulty (\(D\)) is obtained through the maintenance manual and other professional materials of the aircraft manufacturing company.
4. The maintenance difficulty (\(M\)) acquisition method is the same as (3).
# Flexible Antennas for a Sub-6 GHz 5G Band:
## 5 Challenges in Designing a Flexible Antenna
### Effect of the Human Body on the Antenna Performance  
The performance of the antenna deteriorates as it is brought into proximity to the body. The presence of lossy human tissues with varying dielectric constant values, causes the antenna's effective length to vary, which causes detuning [45]. A SAR analysis with the proper estimated distance of the antenna from the human body is another main consideration that has to be taken care of when the antenna is designed for WBAN applications. A SAR analysis has been conducted for 1 g and 10 g of tissue [83] by keeping the antenna at various distances away from the human body. It was observed that as the distance of the placement of the antenna from the human body increases, the corresponding SAR value decreases. Thus, the optimal distance measurement of the antenna should be considered so that the SAR does not cross the permissible international standards. The SAR values corresponding to different distances from the human body for 1 g and 10 g of tissue is shown in Table 9 [83].  
The flexible antenna shows a difference in its behavior on the placement to different parts of the human body, due to the variation in the dielectric values of the tissues. Therefore, the antenna characteristics should be analyzed in various positions of the human body. The change in the radiation efficiency of a wearable antenna kept in various parts of the body and the maximum possible power for a designed flexible antenna at different locations of the body at 2.4 GHz is given in [10]. A radiation efficiency of an average 50% was achieved while positioning the antenna at different body loc  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Scaled Net Input Power 100 mW** & **Maximum Mean SAR for 1 g** & **Maximum Mean SAR for 10 g** \\ \hline
**Distance (in mm)** & **Tissue (W/kg)** & **Tissue (W/kg)** \\ \hline
0.0 & 0.864 & 0.273 \\ \hline
1.0 & 0.420 & 0.199 \\ \hline
2.0 & 0.203 & 0.104 \\ \hline
3.0 & 0.134 & 0.077 \\ \hline
4.0 & 0.107 & 0.070 \\ \hline
5.0 & 0.100 & 0.069 \\ \hline
6.0 & 0.094 & 0.068 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Differences in the SAR values correspond to the changes in the distance from the human body. Reprinted with permission from ref. [83]. Copyright 2017 Taylor &Francis Ltd.  
high, leg and on the back. A maximum input power of 0.34 W/kg at the arm position and 0.267 W/kg at the leg position fulfilled the safety standards by the EU. Therefore, the positioning of an antenna at different parts of the body and its effect on the antenna performance are other main considerations that have to be addressed for the design of any flexible antenna.
## 6 Result and Discussion
### Qualitative Analysis  
Additionally, we conducted a visual comparison of segmentation results obtained from different baseline models and our proposed model. Figure 3 illustrates the segmentation outputs for five different input retinal images from the CHASEDB1 dataset. Meanwhile, Figure 4 illustrates the segmentation outputs for two different images from the ISO-STAR, HRF, and LES-AV datasets. The results from Attention U-Net, ResU-Net, DeepLabv3+, and our proposed model are compared side by side. Significant variations in vascular connection and continuity across the various baseline models can be seen upon visual evaluation of the segmentation data. For example, DeepLab has poor vessel-to-vessel connection, leading to discontinuous and fragmented vessel segments. This is explained by the DeepLab architecture's intrinsic constraints in capturing the contextual data and long-range dependencies required to keep vessels connected. Even while vessel connectedness is better than in DeepLab, as demonstrated by the segmentation results from Attention U-Net, ResU-Net, and our suggested model, there are still some vessel fractures and discontinuities. Obstacles like vessel overlap, low contrast areas, or noisy image artifacts can cause these gaps and compromise the precision of segmentation algorithms.
## 4 Problem Transformation and DRL-Based Solution
Since the bandwidth of SUL is usually much less than that of NR, the constraint on \(\delta\) is equivalent to 0.5 to 0.95 of the coverage radius of the BS. The TDD pattern is limited to between 0.2 and 0.8 to account for varying traffic demands. Furthermore, each slice occupies no less than 10% of the total bandwidth \(W^{nr}\). **Reward:** The reward function is the same as (11). \(\pi(s_{t}|\theta^{\pi})\) and \(\mu(s_{t},a_{t}|\theta^{\mu})\) are used to parameterize the actor network and the critic network, respectively. The corresponding policy is denoted as \(\pi\). \(Q^{\pi}(s_{t},a_{t})\) denotes the value function. The critic network is trained by minimizing the mean-squared Bellman error as follows,  
\[L(\theta^{\mu})=\frac{1}{B}\times\sum_{t}(y_{t}-Q(s_{t},a_{t}|\theta^{\pi}))^{ 2}, \tag{14}\]  
where \(B\) is the batch size, and the target value \(y_{t}\) is expressed as,  
\[y_{t}=r(s_{t},a_{t})+\gamma\times\max_{a_{t+1}}Q\Big{(}s_{t+1},\pi\Big{(}s_{t +1}|\theta^{\pi^{\prime}}\Big{)}|\theta^{\mu^{\prime}}\Big{)}, \tag{15}\]  
where \(\theta^{\mu^{\prime}}\) is the parameter of the target network. The actor network is trained by maximizing the policy objective function \(J\), which is described as:  
\[\
abla_{\theta^{\pi}}\approx\frac{1}{B}\times\sum_{t}\
abla_{a}Q(s,a|\theta^{ \mu})|_{s=s_{t},\mu=\theta(s_{t})}\
abla_{\theta^{\pi}}\pi(s|\theta^{\pi})|_{ s=s_{t}}. \tag{16}\]  
The entire algorithm of DDPG-Agent for the proposed QGJRA-SUL is shown in Algorithm 2. ```
0: The State \(s_{t}\)of the BS includes the QoS satisfaction rate Q, the load E, and the weight A of all slices. 0: An action \(a_{t}\) includes the SUL admission \(\delta\), the TDD pattern \(\lambda\), and the band slicing scheme \(\mathbf{w}\). 1: Initialize the Actor Network and the Critic Network; Initialize an empty buffer; Set the number of episode \(N_{episode}=1000\) and the number of step in one episode \(N_{step}=10\); The batch-size \(B\) is set to 64;
2:for\(index_{episode}=0\to N_{episode}-1\)do
3: state \(s_{t-1}\leftarrow\) Reset the environment;
4:for\(index_{step}=0\to N_{step}-1\)do
5: DDPG-Agent \(\leftarrow\) the state \(s_{t-1}\);
6: The initial action \(a^{\prime}_{t}\leftarrow\) DDPG-Agent;
7:\(a^{\prime\prime}_{t}\leftarrow\) Exploring the action space with \(\epsilon\)-greedy \(\leftarrow\)\(a^{\prime}_{t}\);
8:\(a_{t}\leftarrow\) Action clipping \(\leftarrow\)\(a^{\prime\prime}_{t}\);
9: The BS of the environment operates for a period \(T\);
10:\(s_{t},r_{t}\leftarrow\) environment;
11:\(s_{t},a_{t},s_{t-1},r_{t}\to\) reply buffer;
12:\(s_{t}=s_{t-1}\)
13:if The number of experiences in the reply buffer< batch-size \(B\)then
14: Pass;
15:else
16: Update the DDPG-Agent [29];
17:endif
18:endfor
```  
**Algorithm 2** DDPG-Agent for QGJRA-SUL  
Figure 3: The DDPG-Agent is trained for decision-making mechanisms by interacting with the environment. The architecture of the neural network for Actor and Critic for QGJRA-SUL is well designed.