esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 An Architecture for IoT and Multimedia Data Handling
### Downstream Data Flow Management
#### 4.1.1 Content Popularity Measurements  
In ICN, content is transferred as chunks. Every chunk requires a content request packet and content are replied as a sequence of chunks. This content chunk is cached into the CS and cache replacement policy is required when the memory is full. We already mentioned the pros and cons of several cache replacement mechanisms in the related work section. Our proposed mechanism uses a unique content popularity mechanism to replace the contents in the cache memory. Initially, the popularity of a content (\(P_{C}\)) is zero. If any content request packet is served from a node, then a small impact, \(\alpha\), is added with \(P_{C}\) and; therefore, the increased popularity of that content becomes \(P_{C}=P_{C}+\alpha\). The value of \(\alpha\) is 0.01 and it is continuously increased after a successful content hit in the cache memory of the node. Similarly, we calculate the content popularity for each content in the cache memory of a node. The contents are cached into the cache memory of a node with the highest \(P_{C}\) values. If the cache memory size of node \(n\) is \(\mathcal{E}_{n}\), the existing cached content size of a node is \(\lambda\), incoming content size is \(\beta\) with content popularity, \(P_{Ci}\), then the Algorithm 2 is used to take the decision of content caching.  
**Input**: \(\beta\), \(P_{Ci}\)  
**Output**: Whether the cache memory is updated or not.  
1 Definition of used variables:  
2\(\mathcal{E}_{n}\) = The cache memory size of node \(n\)  
3\(\lambda\) = Existing cached content size of a node  
4\(\beta\) = Incoming content size  
5\(P_{Ci}\) = Incoming content popularity  
6\(P_{Ci}\) = The lowest content popularity among the cached content  
6 Initialization:  
7 For each content in the network \(P_{C}\) = 0;  
8
9 Begin;  
10 Calculate the free cache memory (FCM) = \(\mathcal{E}_{n}\) - \(\lambda\)  
11 if FCM \(\geq\beta\)  
12 Cache the incoming content  
13 else if FCM < \(\beta\)  
14 if \(P_{Ci}\) > \(P_{Ci}\)  
15 Do not cache the incoming content  
16 else if \(P_{Ci}\) < \(P_{Ci}\)  
17 Find the lowest content with \(P_{Ci}\)  
18 Select those contents where the summation of content size with lowest \(P_{C}\) \(\geq\beta\)  
19 Replace those contents by incoming contents  
20 End;  
21 return output;
## 1 Introduction  
Given the increasing importance of a globally interconnected world, driven by modern digital services and the need for fast and reliable access to digital resources, communications networks are one of the key infrastructures in today's society. Telecom operators strive to make networks increasingly efficient and low-cost at every step of the technology's development. In this scenario, fiber optics and optical devices play a leading role, as they allow for an unprecedent growth in our capacity to cope with the ever-increasing traffic demand.  
Currently, most worldwide communications rely on optical technologies [1], and most research and industrial efforts focus on achieving the optimum trade-off between transmission speed and cost per bit. This goal is usually pursued by acting on three main aspects: the manufacture of low-cost devices [2], the introduction of digital solutions to help overcome some of the physical limitations of optical communications systems [3] and the optimization of network design [4].
# Adaptive Compensation for Robotic Joint Failures Using Partially Observable Reinforcement Learning
## 5 Results and Discussion
### Kinematics Results  
This section also demonstrates that when a joint malfunctions, the robot's end effector is unable to follow the programmed trajectory with a traditional inverse kinematic controller. The details of the experimental setup are discussed in Section 4.2, and intuitive results are presented in Figure 4. Figure 4a shows that the robot followed the trajectory from the initial position to the drawer position and opened it, which went through the three points \(p_{i}\), \(p_{d}\), and \(p_{p}\). However, as shown in Figure 4b, when one joint was faulty (its angle was fixed)--typically joint 3--the robot was unable to reach the desired end-effector trajectory, hence failing to open the drawer.  
Figure 4: Comparison of the trajectories of the end effector when one of the joints of the robot is broken and when all the joints work properly. The robot body is illustrated in blue color, and the orientation of the end-effector is indicated at \(p_{i}\) with the red color being the \(x\) direction, the green color being the \(y\) direction, and the dark blue color being the \(z\) direction. When the robot operates properly, it must follow the desired trajectory light blue color in (**a**) or orange lines in (**b**) constructed by three joints: the initial position (\(p_{i}\)), the drawer position (\(p_{d}\)), and the pulled-out position (\(p_{p}\)). (**a**) The end effector followed the desired trajectory when all joints of the robot worked properly. (**b**) The end effector failed to follow the expected trajectory when one of the joints was broken as illustrated in light blue color.  
Figure 3: Example of successful task completion and failed task completion. (**a**) The robot successfully opened the cabinet. (**b**) The robot failed to open the cabinet.  
The results demonstrate that the traditional inverse kinematics controller required all joints to be operational properly in order to complete a task. The kinematic analysis using DH parameters and inverse kinematics highlights the critical role of each joint in the Franka robot's ability to perform complex tasks. The demonstrated impact of a joint malfunction underscores the importance of developing robust control algorithms that can compensate for such failures [21]. By developing a DRL algorithm based on our proposed framework as described in the previous sections, we demonstrate that joint failures can be effectively handled for robotic manipulators.
# A Routing Protocol for Multisink Wireless Sensor Networks in Underground Coalmine Tunnels
## 3 Network and Power Control Model
### Power Control Model  
The working power of each sink is negotiated to ensure network coverage and connectivity.  
Generally, the propagation range of the electric wave in the tunnel is divided into two areas: the propagation near zone and the propagation far zone. When the distance between the transponders is less than the maximum communication radius of the sink, it belongs to the near zone. In this area, the guided communication is not established, radio waves are mainly conducted in multi-mode propagation mode, and most of them belong to high-order mode. This propagation is similar to the free space model, so we use the propagation model. Furthermore, the process of confirming the appropriate transmission power in the power control mechanism was described by [30; 31; 32]. Thus, we use the propagation model and base on the following assumptions: First, the physical layer can transmit a frame at one of the discrete power levels notified by the MAC layer. Second, the physical layer notifies the MAC layer about RSSI of a received frame.  
The receiving power of the node is obtained as follows based on the Friis formula of propagation loss of the electric wave in free space:  
\[P_{r}=P_{t}g_{t}g_{r}\left(\frac{\lambda}{4\pi d}\right)^{n}, \tag{1}\]  
where \(P_{r}\) is the receiving power of the node; \(P_{t}\) is the transmission power of the node; \(g_{t}\) and \(g_{r}\) are the gains of the transmitting and receiving antennas, respectively; \(d\) is the distance between the transmitting and receiving nodes; and \(\lambda\) is the carrier wavelength decided by the carrier frequency. \(\lambda\) is usually 0.1 in the commonly used 2.4-GHz wireless sensor; \(n\) refers to the channel fading coefficient, which is usually 2; and \(g_{t}\), \(g_{r}\), and \(\lambda\) are the parameters of the sensor network. The values of these parameters are determined for a confirmed network and are expressed by \(\varphi\) as follows:  
\[\varphi=g_{t}g_{r}\left(\frac{\lambda}{4\pi}\right)^{2}. \tag{2}\]  
The formula of the node receiving power is then rewritten as  
\[P_{r}=P_{t}\frac{\varphi}{d^{2}}. \tag{3}\]  
Furthermore, based on the preceding formula, the transmission power from the sink to the node in its coverage is written as  
\[P_{t}=\frac{P_{r}d^{2}}{\varphi}. \tag{4}\]  
The receiving power is calculated on the basis of the intensity of the receiving signal, as shown by [32]. The optimal transmission power is calculated using Equation (4), where \(d\) is equal to the best communication radius of the sink. Therefore, the control problem of the transmission power is converted to the control problem of the communication radius.
## 5 Field Test Configuration and Results
### Results of Geometric Similarity Evaluation  
We analyzed the testing efficiency and scenario representativeness based on the geo metric similarity indicators presented in Section 4. For the scenarios that were deemed credible based on the three evaluation criteria discussed earlier, we calculated the geometric similarity between the shapes by visualizing the credibility-assessment results across the three representative speed ranges\(-\)low, medium, and high\(-\)through spider charts. The aim of this process was to quantify the consistency of shape changes across speed conditions and verify whether the results for a specific speed condition can represent the characteristics across the entire speed range.  
The primary objective of this study was to establish objective criteria for determining whether testing under a single representative speed condition can replace individual tests under multiple speed conditions when the speed condition is not a dominant factor in the credibility assessment. This approach can significantly enhance testing efficiency and resource optimization if the geometric similarity between velocity conditions exceeds a certain threshold. Sections 5.3.1 and 5.3.2 present the results of the geometric similarity assessment and the scenario representativeness assessment, respectively. Through a multifaceted interpretation and in-depth examination of these results, we discuss the efficiency and validity of the geometry-based verification methodology.
## 5 Thrust Distribution Layout
### Thrust Coupling Projection Analysis of the Propulsor  
#### 5.2.1.  
Thrust Projection of the Vertical Thruster  
The new ROV is affected by four vertical thrusters at the front and rear. They can provide force and torque in all directions for the ROV. As shown in Figures 14 and 15,  
Figure 12: Vertical thruster vector layout views in various orientations. (**a**) Top view of 4 thrusters. (**b**) Left view of thrusters No. 2 and 6. (**c**) Front view of thrusters No. 1 and 2. (**d**) Rear view of thrusters No. 5 and 6.  
Figure 13: Horizontal thruster vector layout views in various orientations. (**a**) Top view of 2 thrusters. (**b**) Left view of the No. 4 thruster.  
the projection analysis of the thrust of the four vertical thrusters is performed. The thrust generated on the \(ox\)-axis, \(oy\)-axis, and \(oz\)-axis is  
\[T_{X1}=T_{1X}+T_{2X}-T_{5X}-T_{6X}=T_{1}\cos\alpha+T_{2}\cos\alpha-T_{5}\cos \delta-T_{6}\cos\delta \tag{1}\]  
\[T_{Y1}=T_{1Y}-T_{2Y}+T_{5Y}-T_{6Y}=T_{1}\cos\beta-T_{2}\cos\beta+T_{5}\cos \varepsilon-T_{6}\cos\varepsilon \tag{2}\]  
\[T_{Z1}=T_{1Z}+T_{2Z}-T_{5Z}-T_{6Z}=T_{1}\cos\gamma+T_{2}\cos\gamma-T_{5}\cos \varsigma-T_{6}\cos\varsigma \tag{3}\]  
The component forces of the No. 1, No. 2, No. 5, and No. 6 propellers on the \(x\)-axis are \(T_{1X}\), \(T_{2X}\), \(T_{5X}\), and \(T_{6X}\); the component forces on the \(y\)-axis are \(T_{1Y}\), \(T_{2Y}\), \(T_{5Y}\), and \(T_{6Y}\); and the component forces on the \(z\)-axis are \(T_{1Z}\), \(T_{2Z}\), \(T_{5Z}\), and \(T_{6Z}\). At this time, the resultant forces of the four thrusters on the three coordinate axes are \(T_{X1}\), \(T_{Y1}\), and \(T_{Z1}\), respectively.  
If there is an angle between the four thrusters and any coordinate axis, then the sum of the rolling moment \(M_{X1}\), the sum of the pitching moment \(M_{Y1}\), and the sum of the yaw moment \(M_{Z1}\) generated by the component force on the \(ox\)-axis, the \(oy\)-axis, and the \(oz\)-axis are  
\[M_{X1}=T_{1Y}z-T_{2Y}z+T_{5Y}z-T_{6Y}z-T_{1Z}y_{1}+T_{2Z}y_{1}+T_{5Z}y_{3}-T_{ 6Z}y_{3} \tag{4}\]  
\[=T_{1}\cos\beta z-T_{2}\cos\beta z+T_{5}\cos\varepsilon z-T_{6}\cos \varepsilon z-T_{1}\cos\gamma y_{1}+T_{2}\cos\gamma y_{1}+T_{5}\cos\varsigma y _{3}+T_{6}\cos\varsigma y_{3}\] \[M_{Y1}=-T_{1X}z-T_{2X}z+T_{5X}z+T_{6X}z-T_{1Z}x_{1}-T_{2Z}x_{1}-T _{5Z}x_{3}-T_{6Z}x_{3}\] \[=-T_{1}\cos\alpha z-T_{2}\cos\alpha z+T_{5}\cos\delta z+T_{6}\cos \delta z-T_{1}\cos\gamma x_{1}-T_{2}\cos\gamma x_{1}-T_{5}\cos\varsigma x_{3}-T _{6}\cos\varsigma x_{3} \tag{5}\]  
Figure 14: Thrust decomposition diagram of the vertical thruster.  
Figure 15: Thrust decomposition of No. 1 and No. 5 thrusters. (**a**) Thrust decomposition of No. 1 thruster. (**b**) Thrust decomposition of No. 5 thruster.  
\[\begin{split}& M_{Z1}=T_{1X}y_{1}-T_{2X}y_{1}-T_{5X}y_{3}+T_{6X}y_{3}+T_{1Y }x_{1}-T_{2Y}x_{1}-T_{5Y}x_{3}+T_{6Y}x_{3}\\ &=T_{1}\cos\alpha y_{1}-T_{2}\cos\alpha y_{1}-T_{5}\cos\delta y_{3 }+T_{6}\cos\delta y_{3}+T_{1}\cos\beta x_{1}-T_{2}\cos\beta x_{1}-T_{5}\cos \varepsilon x_{3}+T_{6}\cos\varepsilon x_{3}\end{split} \tag{6}\]
# Numerical Solution for the Single-Impulse Flyby Co-Orbital Spacecraft Problem
## 4 Numerical Method without Derivation for the Two Equations  
### Solution of Lambert Problem without Derivation  
[PERSON]'s iteration method is typically used to solve the above problems. However, the [PERSON] iteration method is susceptible to the initial value. If the initial value is not suitable, the solution cannot converge. At the same time, when using the [PERSON] iteration method, the above implicit function needs to be derived, which further increases the complexity of solving this problem. Since the transfer time \(\Delta t\) is a monotonically increasing function of the vertical component \(e_{T}\) in the interval of the domain of the definition [34], a quadratic interpolation secant method was proposed in this study. The basic process is shown in Figure 4.  
Figure 4: Flowchart of the quadratic interpolation chord cut algorithm.  
The quadratic interpolation function stated in the flowchart is  
\[e_{T}=\frac{a}{\Delta t^{2}}+\frac{b}{\Delta t}+c \tag{25}\]  
where the parameters are calculated using  
\[\begin{bmatrix}a\\ b\\ c\end{bmatrix}=\begin{bmatrix}\frac{1}{\Delta t_{first}^{2}}&\frac{1}{\Delta t_{ first}}&1\\ \frac{1}{\Delta t_{first}^{2}}&\frac{1}{\Delta t_{full}^{2}}&1\\ \frac{1}{\Delta t_{last}^{2}}&\frac{1}{\Delta t_{last}^{2}}&1\\ \end{bmatrix}^{-1}\begin{bmatrix}e_{T,first}\\ e_{T,mid}\\ e_{T,last}\end{bmatrix} \tag{26}\]  
The final iterative formula is as follows:  
\[\begin{cases}e_{T,k+1}=e_{T,k}-\frac{f(\mathbb{R}_{0,\omega_{0},\omega_{0}},\mathbb{R}_{1,\omega_{1},\lambda_{1}},e_{T,k})(e_{T,k}-e_{T,k-1})}{f(\mathbb{ R}_{0,\omega_{0},\omega_{0},\mathbb{R}_{1,\omega_{1},\lambda_{1}},e_{T,k})}-f( \mathbb{R}_{0,\omega_{0},\mathbb{R}_{1,\omega_{1},\lambda_{1}},e_{T,k-1})}}\\ f\big{(}\mathbb{R}_{0,\omega_{0},\omega_{0},\mathbb{R}_{1,\omega_{1},\lambda_ {1}},e_{T}}\big{)}=\frac{M_{1,\omega_{1},\lambda_{1},\lambda_{1}}-M_{0,\omega _{0}},\omega_{0}}{n_{2}}-\Delta t\end{cases} \tag{27}\]  
Several points need to be clarified here. It is necessary to find the initial points instead of selecting the first and last points as the initial points because the primary motivation is that the interpolation between the time \(\Delta t\) corresponding to the first and last points is too large, typically surpassing \(10^{-6}\), preventing the iterations from proceeding correctly. Simultaneously, the initial value-finding algorithm can significantly reduce the number of iterations. The second point that must be addressed is why quadratic functions are employed. Using quadratic functions reduces the amount of computing required, while quadratic functions fit the curve better than linear interpolation, with the mean degree-of-freedom-adjusted coefficient of the determination being 0.998 for 100,000 random tests.
# A Single Wearable Sensor for Gait Analysis in Parkinson's Disease: A Preliminary Study
## 2 Design of the Proposed System
### Extraction of Heel Strike and Toe Off  
For Heel Strike (HS) and Toe Off (TO) extraction, previous studies have shown the correspondence between the local minima and maxima of the Continuous Wavelet Transform (CWT) with the HS and TO events in healthy adults and PD patients [28; 33]. According to such studies, the proposed algorithm is based on the CWT approach [21] for the HS and TO extraction. The anterior posterior acceleration was integrated and differentiated by CWT, using an estimated wavelet scale and Daubechies first-order (\(db_{1}\)) wavelet. The estimated scale parameter (\(a_{1}\)) was computed as follows:  
\[a_{1}=\frac{CEN_{1}}{\frac{DF}{Ts}}, \tag{3}\]  
where \(CEN_{1}\) is the center frequency of the \(db_{1}\) wavelet, \(DF\) is the most dominant frequency of the spectrum of the AP acceleration, \(Ts\) is the sampling period. The local minima of the differentiated signal are the detected HS events. Subsequently, the first-order differentiated signal is differentiated again by using CWT with estimated wavelet scale and Daubechies second-order (\(db_{2}\)) wavelet. The estimated scale parameter (\(a_{2}\)) was computed as follows:  
\[a_{2}=\frac{CEN_{2}}{\frac{DF}{Ts}}, \tag{4}\]  
where the \(CEN_{2}\) is the center frequency of the \(db_{2}\) wavelet. The local maxima of the latter signal are the detected TO events. Figure 4 shows an example of step detection from a walking segment where HS and TO events are identified.  
Figure 4: Temporal representation of first–order (CWT1, in red) and second–order (CWT2, in blue). Continuous Wavelet Transform from AP acceleration. The first local minima indicate the HS events (red circles), the second local maxima indicate the TO events (blue circles).
## 4 Discussion
These results are presented visually in Figure 13, showcasing the corresponding bandgap--structures for the optimal unit cell in each unit cell design configuration. Additionally, Table 1 provides detailed information on the optimal unit cell design parameters and the bandgap coverage. The table also organizes the optimal unit cells based on their bandgap coverage from highest to lowest. Upon evaluation of Table 1, it is revealed that the optimal unit cells associated with the new--class unit cell configuration have demonstrated a slightly enhanced bandgap coverage performance compared to the optimal unit cell derived from the morphology of the Basic--Periodic unit cell design configuration. This is evident through their ability to achieve a wider bandgap coverage within the audible frequency range. The efficacy of the optimal newly developed unit cells will be further demonstrated in the actuation scenario subsection. The optimal Semi--Periodic unit cell surpasses other optimal unit cells in achieving the widest bandgap coverage within the audible frequency range, despite what may appear upon initial visual impressions. Figure 13: Optimal unit cell design combinations in each unit cell design category. The optimal unit cell design and the corresponding bandgap—structure are represented side by side. (**A**) Optimal Basic—Periodic unit cell. (**B**) Optimal Semi—Periodic unit cell. (**C**) Optimal Tapered—Diverging unit cell. (**D**) Optimal Tapered—Converging unit cell. The exploration of the new designs presented in the current work and the further optimizations for both these new designs, as well as the ones previously investigated in [28], have led to significant improvements for both the bandgap coverage (95% compared to 60% in [27; 34; 35; 37]), as well as wider frequency range coverage of 20 kHz compared to 16 kHz. This highlights the significance and the necessity of employing an extensive design analysis--based framework that offers the end--user with the optimal design options while ensuring reasonable computational time, which is what this work's framework provides. Furthermore, it is crucial to emphasize that the substantial data generated by the framework could be furtherly utilized as training input for machine learning models, enabling the development of a machine learning--based design framework for metamaterials' properties [17; 43; 44; 45].
# NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training
## 2 Background
### Physics-Informed Neural Networks  
In our work, we consider computing data-driven solutions to partial differential equations (PDEs) of the general form  
\[u_{t}+\mathcal{N}[u:\lambda]=0,\quad x\in\Omega,t\in[0,T] \tag{1}\]  
Here, \(u\) represents the solution of the PDE, \(\Omega\subset\mathbb{R}^{d}\) represents the spatial domain, and \(\mathcal{N}[:]\) denotes a differential operator.  
The goal of PINN is to learn a parametric surrogate \(u_{\theta}\) with trainable parameters \(\theta\) that approximates the solution \(u\). To achieve this goal, a neural network is constructed, and the total loss function of PINN is minimized. The total loss function consists of several components: residual loss, initial loss, boundary loss, and data loss, i.e,  
\[\mathcal{L}_{total}=w_{f}\mathcal{L}_{res}+w_{g}\mathcal{L}_{ics}+w_{j} \mathcal{L}_{bc}+w_{h}\mathcal{L}_{data}. \tag{2}\]  
We use the coefficients \(w\) to balance the loss terms. Each loss term is calculated by applying the L2 approximation [25]. In particular, \(\mathcal{L}_{res}\) denotes the residual loss, which is the difference between the exact value of the PDE and the predicted value from the PINN deep neural network (DNN):\[\mathcal{L}_{res}=\frac{1}{N_{r}}\sum_{i=1}^{N_{r}}||u_{\theta}(x_{i}^{r})-u(x_{i}^ {r})||^{2} \tag{3}\]  
In the above, we only considered the problem in the spatial domain for the sake of simplicity. Extending it to the temporal domain is straightforward. Moreover, \(u_{\theta}(x_{i}^{r})\) represents the output value of the PINN DNN on a set of \(N_{r}\) points sampled within the spatial domain \(\Omega\). This can be computed using automatic differentiation methods [26]. On the other hand, \(u(x_{i}^{r})\) denotes the true solution of the PDE.  
The initial or boundary loss represents the difference between the true solution and the predicted value from the PINN DNN at the initial or boundary condition. For instance, the boundary loss (for a given boundary condition \(h\)) at a set of \(N_{b}\) boundary points \(x_{i}^{b}\) is defined as follows:  
\[\mathcal{L}_{bc}=\frac{1}{N_{b}}\sum_{i=1}^{N_{b}}||u_{\theta}(x_{i}^{b})-h(x_ {i}^{b})||^{2} \tag{4}\]  
Furthermore, if we tackle inverse problems and have a set of \(N_{d}\) experimental data points \(y_{i}^{d}\), we can calculate the data loss using the PDE equation as follows:  
\[\mathcal{L}_{data}=\frac{1}{N_{d}}\sum_{i=1}^{N_{d}}||u_{\theta}(x_{i}^{d})-y_ {i}^{d}||^{2} \tag{5}\]  
As shown in Equation (2), the loss value of a physics-informed neural network (PINN) is calculated as a simple linear combination with soft constraints. In this paper, we consider each part of the loss as an objective as shown in Figure 1.