esa-sceva/satcom-chunk-collection huggingface dataset:
## 6 Performance Analysis
### Computation Cost Analysis  
In the scheme proposed by [PERSON] et al. [47], when signing a single message, the bilinear pairing scale multiplication operation is performed four times, the bilinear pairing addition operation is performed once, the bilinear pairing MapReducePoint function is performed once and the hash function is performed twice. The total time required for these operations is approximately 2.8790 ms, calculated as \(4T_{bm}+T_{hu}+T_{mfp}+2T_{h}\). And when the batch verification is implemented, the bilinear pairing addition operation is performed \(3(n-1)\) times, the bilinear pairing scalar multiplication operation is performed \(n\) times, the bilinear pairing operation is performed three times, the MapReducePoint operation is performed \(n\) times and the one-way hash function is performed \(n\) times. The total approximate time for these operations can be expressed as \(3(n-1)T_{hu}+nT_{bm}+3T_{bp}+nT_{mfp}+nT_{h}\approx 0.7996n+15.2598\) ms.  
In the scheme proposed by [PERSON] et al. [48], when signing a single message, the bilinear pairing scale multiplication operation is performed three times and the hash function operation is performed twice, resulting in approximately 2.0840 \(ms\), calculated as \(3T_{bm}+2T_{h}\). During batch verification, the bilinear pairing addition operation and the bilinear pairing scalar multiplication operation are both performed \((2n+1)\) times, the bilinear pairing operation is performed twice and the one-way hash function is performed \(n\) times, resulting in approximately \(1.3926n+10.8678\) ms, calculated as \((2n+1)T_{hu}+(2n+1)T_{hm}+2T_{bp}+nT_{h}\).  
In the scheme proposed by [PERSON] et al. [6], when signing a single message, the scale multiplication operation is performed once and the one-way hash function is performed twice, resulting in approximately 0.3238 ms, calculated as \(T_{em}+2T_{h}\). During batch verification, the scale multiplication operation is performed \((2n+2)\) times, the point addition operation is performed \(n\) times and the one-way hash function is performed \((2n)\) times, resulting in approximately \(0.648n+0.6436\) ms, calculated as \((2n+2)T_{em}+nT_{ea}+(2n)T_{h}\).  
In our scheme, when signing a single message, the scale multiplication operation is performed once and the one-way hash function is executed twice, resulting in approximately 0.3228 ms, calculated as \(T_{em}+T_{h}\). During batch verification, the scale multiplication operation is performed \(2n\) times, the point addition operation is performed \(n\) times and the one-way hash function is performed \(n\) times, resulting in approximately \(0.647n\) ms, calculated as \(2 nT_{em}+nT_{ea}+nT_{h}\).  
As Figure 4 shows, to sign a message, our scheme costs lower computation power than the other three schemes. In Figure 5, we conducted a comparison of the execution time for batch verifications and the result indicates that our scheme demonstrates superior performance.  
Figure 4: The time consumed for signing.
## 1 Introduction
Moreover, the resulting EMG percentages offer exercise-specific insights relative to maximal sprint activity, supporting their use in function-oriented assessments of plantar flexion, as supported by previous findings linking inter-limb strength asymmetries with sprint and change-of-direction performance in elite soccer players [34]. Although ankle strengthening exercises are commonly used for therapeutic and performance purposes, the literature shows low adherence to evidence-based prescription and poor reporting quality. A recent scoping review [35] found that only 2% of exercises met the American College of Sports Medicine (ACSM) recommended intensity threshold (\(\geq\)60% 1 RM) for strength gains. Moreover, the reporting completeness was critically low, averaging just 31% on the Consensus on Exercise Reporting Template (CERT) checklist. These deficiencies hinder replicability and effective implementation, limiting clinical and research outcomes. This highlights the need for research on precise triceps surae exercise prescription, given the complex compensatory muscle interactions involved. For example, individuals with Achilles tendinopathy adopt strategies that reduce tendon stress--such as lowering the peak load, the loading rate, ankle dorsiflexion, and knee flexion--during rehabilitation [36]. Additionally, muscle hardness increases with length (e.g., the MG from rest to mid-range), influencing activation and functional output [37]. This study aimed to examine the effects of ankle ROM and exercise type (bilateral vs. unilateral) on EMG activity and the MG:LG activation ratio during non-weight-bearing heel raises, using overground sprinting for EMG normalization. We hypothesized that (i) the MG and LG would show distinct activation patterns and (ii) their activation ratio would vary with the ROM and exercise type. Additionally, we explored the influence of limb dominance on gastrocnemius activation. The findings may inform exercise prescription and rehabilitation strategies targeting region-specific muscle activation.
## 2 Single-Patch Multi-Beam Antenna
However, increasing the antenna size to increase the size of the aperture increases the resonance length, so the effect of increasing the size of the aperture is replaced by using parasitic elements that do not significantly affect the resonance length, as shown in Figure 7. The length of the parasitic element is set to 19 mm, which is slightly shorter than the resonance length (21 mm) of the divided patch so that the parasitic element acts like a director to spread the field at the edge of the patch outward. The electric field distribution and the radiation pattern of the final single-patch multi-beam antenna structure by the excitation port are presented in Table 2 and Figure 8, respectively. Figure 6: The radiation pattern of the four-divided patch antenna with different excited ports: (**a**) single excitation and (**b**) dual excitation. Figure 7: Final antenna structure for direction finding. \begin{table}
\begin{tabular}{c c c c} \hline
**Port 1** & **Port 2** & **Port 3** & **Port 4** \\ \hline
**Ports 1** and 2 & **Ports 2** and 3 & **Ports 3** and 4 & **Ports 4** and 1 \\ \hline
**Ports 3** and 4 & **Ports 4** and 1 \\ \hline \end{tabular}
\end{table} 
Table 2: The electric field distribution of the final antenna with different port excitation. The electric field distribution of the final antenna structure exhibits a slight increase in the field distribution at the divided patch edges for both single and dual excitations. The radiation patterns show that the beamwidth of the antenna slightly decreases from 230\({}^{\circ}\) to 190\({}^{\circ}\) for single-port excitation, which reduces ambiguity between patterns. For dual excitation, the beamwidth is reduced from 180\({}^{\circ}\) to 140\({}^{\circ}\). The realized gains of the final antenna are 2.68 dB and 2.93 dB for single and dual feeding, respectively. These improved patterns contribute to the increased accuracy in direction-finding estimation by clarifying the resolution of the power values received for each pattern. The beam characteristics according to excitation by the port are summarized in Table 3.
## 4 Experimental Results and Analysis
### Random Synthesized Sparse Signals  
In this part, two kinds of randomly generated sparse signals were used as test signals: Gaussian random sparse signals and binary uniform sparse signals. Their generation method was elaborated on in Section 3. In the noiseless scenario, the performance of the measurement matrix was assessed by the ratio between the number of successful reconstructions and the total number of trials. A successful reconstruction condition is defined in (11), and number of total trials was 300.  
Figure 3 depicts the perfect recovery percentages of different measurement matrices as sparsity \(k\) varies with \(M=263\) and \(N=599\). Figure 4 illustrates the perfect recovery percentages of various measurement matrices as \(M\) changes with \(k=100\) and \(N=431\). Our proposed measurement matrix demonstrated superior performance, particularly in practical applications due to its enhanced features.  
In a noisy scenario, the process can be represented as  
\[\mathbf{y}=\mathbf{\Phi}\mathbf{x}+\mathbf{e} \tag{12}\]  
where \(\mathbf{e}\in\mathbf{R}^{M}\) represents Gaussian white noise. In this experiment, \(\left\|\mathbf{e}\right\|_{2}=0.1*\left\|\mathbf{y}\right\|_{2}\). SNR was used to evaluate the performance of different measurement matrices, which is defined as  
\[\text{SNR}=20\text{log}_{10}\bigg{(}\frac{\left\|\mathbf{x}\right\|_{2}}{ \left\|\mathbf{x}-\mathbf{\hat{x}}\right\|_{2}}\bigg{)} \tag{13}\]  
Figure 4: Exact recovery percentages of various measurement matrices for (**a**) Gaussian random sparse signals and (**b**) uniform random sparse signals with \(k=100\) and \(N=431\), against varying \(M\).  
Figure 3: Exact recovery percentages of various measurement matrices against different values of \(k\) for (**a**) Gaussian random sparse signals and (**b**) uniform random sparse signals with \(M=263\) and \(N=599\).  
where **x** is the original signal, and \(\hat{\textbf{x}}\) is the reconstructed signal.  
The SNRs of different measurement matrices for Gaussian random sparse signals and uniform random sparse signals against changes in \(M\) with \(k=100\) and \(N=431\) are shown in Table 3. It can be seen that for both Gaussian random sparse signals and uniform random sparse signals, our proposed measurement matrix exhibited a higher SNR compared to the other measurement matrices. This suggests that our proposed measurement matrix exhibits greater robustness to noise compared to the others.
# A Failure Risk-Aware Multi-Hop Routing Protocol in LPWANs Using Deep Q-Network
## 6 Simulation Results and Analysis
### Simulation Setup  
In this section, a comparison among FRDR, Minimum Hop Routing (MHR), and DQIR [15] is performed. MHR operates as a distributed routing algorithm that selects relays based on the minimum hop count to the GW. In DQIR, next-hop selection from candidate routers is conducted by a DQN-based routing protocol. Notably, to achieve a more equitable comparison, the learning rate and replay memory in DQIR are adjusted to \(0.01\) and \(5000\), respectively, through extensive hyperparameter tuning.  
To comprehensively evaluate the performance of FRDR, we introduce three self-contrasting algorithms detailed in Table 6.  
Additionally, to ensure fair benchmarking, all compared algorithms adopt the same pre-selection rules as FRDR and utilize the SPIN-based interaction process to determine candidate routers.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \(l_{tx}\) & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ \hline \(P_{T}\) [dBm] & 14 & 12 & 10 & 8 & 6 & 4 & 2 \\ \(l_{tx}\) [mA] & 38 & 35.1 & 32.4 & 30 & 27.5 & 24.7 & 22.3 \\ \(l_{rx}\) [mA] & & & & & 14.2 & & & \\ \(V_{\mathrm{DD}}\) [V] & & & & & 3.3 & & & \\ \hline \end{tabular}
\end{table}
Table 5: Energy consumption parameters.  
The dataset generation framework introduced in [34] is applied to deploy ENs in a stochastic and nonuniform manner across a 1 km \(\times\) 1 km area, while a GW is located at the center. The initial energy of all ENs is fixed at 0.5 mAh. During each iteration, a source EN is randomly selected from ENs, and a data packet is transmitted from this source EN to the GW under different multi-hop routing protocols. Additional network parameters are detailed in Table 7.  
During the offline training of DQN, we execute 100 training episodes, and each episode comprises 1000 complete packet transmission simulations. For each simulation, a source EN is randomly chosen from the monitoring area, which then transmits a data packet toward the GW via single-hop or multi-hop routing. Upon transmission completion (either successful delivery to the GW or failure), the simulation proceeds immediately to the next packet transmission. Other specific DQN parameters are detailed in Table 8.
## Communication protocol  
At the application level, messages are transmitted via the MQTT protocol version 3.1.1 [25]. MQTT is an established open message protocol for the transmission of telemetry data between different systems in restricted networks, e.g., in the Internet-of-Things (IoT) context, and follows the rules of indirect publish-subscribe communication. Clients can publish messages on topics (e.g., _utm/uav123/position_) within  
Figure 3: Overview of the context-dependent operation of the MMT during transit through a control zone as part of the test scenario.  
the network or subscribe to specific topics to receive relevant messages. A broker takes over the message management and distribution to the corresponding clients, so that no direct communication exists between them. The protocol also supports multiple Quality of Service (QoS) policies for the reliability of message transmissions:  
* At most once (QoS 0): reception of the message is not guaranteed, similar to UDP
* At least once (QoS 1): receiver confirms receipt of message, multiple receipt of the same message possible
* Exactly once (QoS 2): message is guaranteed to arrive at the receiver only once  
In addition, the protocol offers other useful functions for data transmission in an unreliable network. When establishing a connection with the MQTT broker, a client can place a message as a \"last will and testament\". In the event of a connection failure, this message is delivered to all clients that have subscribed to this topic. The formatting of the messages is based on the recommendation of GUTMA [30], encoded in the JavaScript Object Notation (JSON) file format [31] with the UTF-8 character set. Flight restriction areas are mapped in geojson data format [32]. In order to be able to record data packets transported via the UTM network, a MQTT2 ROS bridge [33] was integrated that subscribes to all available topics. This bridge converts MQTT messages into Robot Operating System (ROS) compatible messages and forwards them into a local ROS environment [34] so that they can be saved in a so-called BAG-file for further analysis and replay. Figure 4 depicts the implemented topics with the respective publishers and subscribers.  
**Reference Applications.** In order to simulate the interactions of the UTM participants, so-called reference applications were developed and implemented. This includes the ServerApp, which represents the core component of the UTM network and is responsible for processing flight declarations and position reports. The ATApp (Figure 5) represents the collaborative interface of the Air Navigation Service Provider (ANSP) to the UTM network and enables the air traffic controller to communicate with the UAS without a voice radio link. On the UAV's mission computer, the OnboardApp provides access to the UTM network and a UserApp allows the UAS operator to file flight plans, make system changes onboard the UAV and monitor the flight progress.  
Figure 4: MQTT based communication protocol of the experimental UTM network.
## 2 Generalized Dynamic Model
### Establishment of Global Dynamics Model
#### 2.1.1 Shaft Element  
The shaft element is simulated and connected by the lumped mass method, and the force of the shaft element is analyzed, and the dynamic model of the shaft element is established, as shown in Figure 2.  
Figure 1: Three-planet gear drive system.  
Two mass nodes are connected by one shaft element. A shaft element with two nodes and six degrees of freedom is established between two mass nodes. The generalized coordinate system of the shaft element is assumed as Equation (1).  
\[x_{s}=\{x_{1},y_{1},\theta_{1},x_{2},y_{2},\theta_{2}\}^{T} \tag{1}\]  
where \(x_{1}\), \(y_{1}\), \(x_{2}\) and \(y_{2}\) represent the transverse displacements of each node along each coordinate axis, respectively; \(\theta_{1}\) and \(\theta_{2}\), represent the torsional displacements of two mass nodes along their respective torsional directions.  
The matrix form of the motion differential equation is shown in Equation (2).  
\[M_{s}\ddot{x}_{s}+C_{s}\dot{x}_{s}+K_{s}x_{s}=0 \tag{2}\]  
where \(M_{s}\), \(C_{s}\), and \(K_{s}\) represent the element fixed mass matrix, damping matrix and stiffness matrix, respectively.
## 4 Proposed Deep Learning Based Cooperative Communication Channel Model for WUSNs  
Figure 1 depicts a proposed DL-based wireless underground sensor network infrastructure with Cooperative communication nodes. The source and sink nodes of cooperative modules have been critical components in monitoring outer communications. The component of a Cooperative communication framework to allow the WUSN and DL networks for efficient communication has been separated. Through the WUSN middleware console, various system components collaborate for computation and storage functions [27]. As a result, the virtualized distributed DL network structure is designed using the WUSN middleware management platform. In the WUSN, nodes with storage capabilities, such as source nodes, sink endpoints, and Cooperative access points, can contribute to building the DL network of WUSN Middleware. The improved process will be communicated to solve the problem of the sink node. Furthermore, the cooperating connections will be the main computational components. Moreover, the Cooperative communication node is embedded in the WUSN middleware controller.  
The Deep Learning Auto Encoder (DLAE) is built on top of a distributed DL network. The primary controller has hidden layers and output units. DLAE is responsible for estimating the underground dynamic condition through information in the approach [28]. Local storage package query information needs to be gathered and sent to the server by the sink nodes [29]. The previous information will also be examined in the input layers by the analytics system during the test process. The analytics function summarizes the existing data from many timestamp requests for the input layers in the preprocessing phase. The DLAE then makes a forecast for the known data packet [30]. Depending on the forecast, the WUSN middleware develops a storage approach. Additionally, the storage method is matched up with these storage servers so that preemptive storage can happen over time [31].  
In this work, we identify the effects of multiple factors as well as utilize DL tools in evaluating an optimal transmission strategy to decrease transmission loss and intelligent  
Figure 1: Deep learning network structure in WUSNs middleware.  
consumption of sensor power [27]. Using the DL method, the exploration of environmental conditions impacts on wireless connectivity in underground surroundings, such as transmission pathway loss, energy consumption, and system bandwidth balancing [32]. As a result, the development of a dependable and powerful data collection transmission is structured as a Cooperative and multi-constrained communication-based limitation.  
The intended solution is identified from the surroundings and articulated together for numerous limitations using DL approaches. An adaptive threshold strategy has also been established to benefit from diverse networks [33]. The proposed methodology aims to increase efficiency by means of transmission loss and energy constraints. Additionally, the proposed method can enhance transmission dependability and reduce network costs.
## 3 Proposed Approach
### Scale Adjustment  
Buildings can appear different in size even if they are photographed from the same camera distance, due to true size differences, partial occlusions, or variability in vantage points. Scale augmentation simulates these changes by resizing images along the horizontal (\(x\)) and vertical (\(y\)) axes, as captured in Equation (3):  
\[\begin{pmatrix}x^{\prime}\\ y^{\prime}\end{pmatrix}=\begin{pmatrix}S_{x}&0\\ 0&S_{y}\end{pmatrix}\begin{pmatrix}x\\ y\end{pmatrix} \tag{3}\]  
where \(S_{x}\) and \(S_{y}\) are the scaling factors controlling how much the image is enlarged or reduced [16]. Scaling factors above 1 magnify the image, while factors below 1 shrink it. Because the transformed coordinates (\(x^{\prime}\), \(y^{\prime}\)) typically do not align with the pixel grid, an interpolation step determines the intensity values in the resized image. In this  
Figure 3: Examples of images with contrast augmentation.  
Figure 2: Examples of images with brightness augmentation.  
research, nearest neighbor interpolation was used, which assigns each new pixel the value of its closest original pixel. This method runs quickly but can produce less smooth results compared to more sophisticated approaches, such as those based on Generative Adversarial Networks (GANs) [13]. Figure 4 illustrates a baseline image alongside two scaled outcomes: the left one is reduced using \(S_{x}=1.8\) and \(S_{y}=2.2\), and the right one is enlarged with \(S_{x}=0.7\) and \(S_{y}=0.8\).
## 4 Distributed Clustering Algorithm for the UAV Swarm
### Selection of the Best Switch Operation  
Transferring UAVs from one coalition to another can update the coalition structure of the clustering problem. Next, we review the definition of switch operation in [12]. **Definition 3**. : _A switch operation \(\sigma_{k,l}(\mathcal{P})\) is defined as transferring players \(\mathcal{P}\) from the current coalition \(C_{k}\in\Pi\) to \(C_{l}\in\Pi\cup\{\varnothing\},C_{k}\
eq C_{l}\). Hence, \(\sigma_{k,l}(\mathcal{P}):C_{k}\mapsto C_{k}\backslash\mathcal{P},C_{l}\mapsto C _{l}\cup\mathcal{P}\)._  
According to the coalition revenue, we can define the gain of the switch operations as follows:  
\[\mathcal{R}(\sigma_{k,l}(\mathcal{P}))=u(C_{k}\backslash\mathcal{P})+u(C_{l} \cup\mathcal{P})-u(C_{k})+u(C_{l}) \tag{12}\]  
In order to facilitate the evaluation of switch operations, the preference relation is introduced. **Definition 4**. : _The preference relation \(\succ\) over switch operations \(\sigma_{k,l}(\mathcal{P}_{i})\) and \(\sigma_{k^{\prime},l^{\prime}}(\mathcal{P}_{j})\) can be expressed as:_  
\[\sigma_{k,l}(\mathcal{P}_{i})\succ\sigma_{k^{\prime},l^{\prime}}\big{(} \mathcal{P}_{j}\big{)}\Longleftrightarrow\mathcal{R}(\sigma_{k,l}(\mathcal{ P}_{i}))>\mathcal{R}(\sigma_{k^{\prime},l^{\prime}}(\mathcal{P}_{j})) \tag{13}\]  
It indicates that when the gain of switch operation \(\sigma_{k,l}(\mathcal{P}_{i})\) is greater than \(\sigma_{k^{\prime},l^{\prime}}(\mathcal{P}_{j})\), the game participants prefer to choose the switch operation \(\sigma_{k,l}(\mathcal{P}_{i})\). Then, based on the concept of switch operation and the corresponding switch gain, the definition of Nash-stable partition is given below. **Definition 5**. : _The coalition partition \(\Pi=\{C_{1},C_{2},\cdots,C_{K}\}\) is Nash stable, if \(\forall k\in\mathcal{K},\forall i\in C_{k},\forall C_{l}\in\Pi\cup\emptyset\), \(\mathcal{R}(\sigma_{k,l}(\{i\}))\leqslant 0\)._  
Nash stable partition means that no UAV wants to deviate from the current coalition unilaterally. When no switch operations can increase the total revenue of all coalitions, the partition is stable, which is the corresponding suboptimal solution to the clustering problem. **Theorem 3**. : _For a static network, starting from any initial coalition partition \(\Pi_{0}\) in which all clusters satisfy the clustering constraints, the clustering structure can converge to a final coalition partition \(\widetilde{\Pi}\) in a finite number of iterations when UAVs periodically select the switch operations with positive gains._Proof. : See Appendix C.  
For a fixed network topology, Theorem 3 indicates that a stable coalition partition can be constructed in a finite number of iterations when UAVs periodically select the switch operations with positive gains. We detail the specific process of selecting the best switch operation in Algorithm 1.