esa-sceva/satcom-chunk-collection huggingface dataset:
# A Stackelberg Game Approach to Model Reference Adaptive Control for Spacecraft Pursuit-Evasion
## 3 Stackelberg Equilibrium-Based Model Reference Adaptive Control Algorithm
### Existence and Uniqueness of Stackelberg Equilibria  
For a unique Stackelberg equilibrium to exist, the following conditions must be met [25]:  
1. The strategy sets for the leader and follower are non-empty compact convex sets.  
3. For a given follower's strategy, a unique optimal solution for the leader exists. We now verify that these three conditions are met: 1. (Non-empty compact convex set): The strategy spaces are subsets of Euclidean space and are non-empty. The cost functions (3) and (4) are quadratic, and thus continuous, with respect to the control actions. As \(\mathbf{J}_{p}\) and \(\mathbf{J}_{e}\) are strictly convex and tend to infinity as the norms of the control actions approach infinity, this ensures the existence of a minimum and that the set of optimal strategies is compact and convex. 2. (Unique follower solution): For any given leader's strategy \(\mathbf{a}_{e,t}\), the follower's (pursuer's) cost function \(\mathbf{J}_{p}\) in (4) is strictly convex in \(\mathbf{a}_{p,t}\). Strict convexity is guaranteed because its quadratic weighting matrix, \((\mathbf{W}_{1,p}+\mathbf{Y}_{p}^{\mathrm{T}}\mathbf{P}_{p,t+1}\mathbf{Y}_{p})\), is positive definite. This holds because \(\mathbf{W}_{1,p}\) is chosen as positive definite, and \(\mathbf{P}_{p,t+1}\), as a solution to the Riccati equation, is also positive definite, making \(\mathbf{Y}_{p}^{\mathrm{T}}\mathbf{P}_{p,t+1}\mathbf{Y}_{p}\) positive semi-definite. A strictly convex function has a unique minimum. 3. (Unique leader solution): Similarly, when the follower's strategy is given, the leader's (evader's) cost function \(\mathbf{J}_{e}\) in (3) is strictly convex in \(\mathbf{a}_{e,t}\), as \(\mathbf{W}_{2,e}\mathbf{Y}_{e,t+1}\mathbf{Y}_{e}\) is designed to be positive definite. This guarantees a unique optimal solution for the leader.  
Furthermore, the uniqueness of the solution is guaranteed by the invertibility of the coupling matrix \(\mathbf{\psi}_{t}\) in Equation (10), which is ensured by the conditions above.
# A Framework for Fall Detection Based on OpenPose Skeleton and LSTM/GRU Models
## 2 System Architecture and Method
### Data Set  
The UR Fall Detection Dataset is produced by the Interdisciplinary Center for Computational Modeling of Rzeszow University. The content contains 70 (30 falls and 40 activities of daily living) sequences at a rate of 30 frames per second. Both fall events and other daily living activities such as standing, squatting down to pick up objects, and lying down were recorded. The environment has sufficient lighting. Two Microsoft Kinect cameras were used to record the fall event with the corresponding accelerometer data. The fall events were recorded with two cameras, and only one camera and an accelerometer were used for recording daily activities. As shown in Figure 2a, the height of the device is around the waist of a human body, and the image size is 640 \(\times\) 480. We group these image sequences into a group of 100, and after data enhancement, there are 792 groups in total.  
Figure 1: Block diagram of the proposed fall detection framework process.  
For the Fall Detection Dataset presented in [23,24], data were recorded in five different rooms from eight different viewing angles. There were five participants in this study, including two males and three females. The activities the participants were instructed to perform include standing, sitting, lying down, bending and crawling, and they were recorded at a rate of 30 pictures per second. As shown in Figure 2b, the height of the device position is about 45 degrees of elevation of the human body's line of sight. The original image size is 320 \(\times\) 240, the adjusted image size is 640 \(\times\) 480, the image sequence is a group of 100, and after data enhancement, there is a total of 936 groups.  
We mixed these two datasets, on the one hand to ensure a sufficient amount of data, on the other hand to increase sample diversity to avoid overfitting. As shown in Table 1, we extracted the same amount of fall and non-fall events data from each dataset, respectively, to form a Mix Dataset in this study for model training.
## 2 Related Literature Review
### Deep Learning Models
#### 2.2.2 LSTM  
Recurrent neural networks (RNNs) employing the long short-term memory (LSTM) architecture are used to manage long-term information values. These networks were designed to mitigate the inherent vanishing gradient problem of RNNs. In LSTM architecture, gates are employed to control the flow of inputs and outputs. LSTM cells generally comprise three distinct types of gates. The input gate, as the principal gate, governs the transmission of new information values to memory. The second gate, referred to as the forget gate, regulates the duration for resetting memory cells and the retention interval for input values inmemory. The output gate, the terminal component, governs the timing of data value release from memory. The gates control the dissemination of information [29; 45; 46]. Currently, deep learning approaches are producing promising outcomes in several NLP tasks, with LSTM recognized as the most successful RNN variation for these applications, including word sense disambiguation.  
LSTM cells are designed to capture long-range dependencies via memory cells that store and modify information over time, hence alleviating the vanishing gradient issue prevalent in traditional recurrent neural networks (RNNs). The LSTM cell is governed by the input, forget, and output gates, represented mathematically [46] as follows:  
\[i_{t}=\sigma(W_{i}\cdot[h_{t-1},\ x_{t}]+b_{i})\ (\text{input gate}) \tag{3}\]  
\[f_{t}=\sigma\Big{(}W_{f}\cdot[h_{t-1},\ x_{t}]+b_{f}\Big{)}\ (\text{ forget gate}) \tag{4}\]  
\[o_{t}=\sigma(W_{o}\cdot[h_{t-1},\ x_{t}]+b_{o})\ (\text{output gate}) \tag{5}\]  
\[\dot{C}_{t}=tanh(W_{C}\cdot[h_{t-1},\ x_{t}]+b_{C})\ (\text{cell state candidate}) \tag{6}\]  
\[C_{t}=f_{t}*\ C_{t-1}+i_{t}*\ C_{t}\ (\text{new cell state}) \tag{7}\]  
\[h_{t}=o_{t}*\tanh(C_{t})\ (\text{new hidden state}) \tag{8}\]  
where  
* \(x_{t}\) is the input at time \(t\);
* \(h_{t-1}\) is the hidden state from the previous time step;
* \(i_{t},\ f_{t},\ o_{t}\) are the input, forget, and output gates, respectively;
* \(C_{t}\) is the cell state at time \(t\);
* \(W_{i},\ W_{f},\ W_{o},\ W_{C}\) are weight matrices, and \(b_{i},\ b_{f},\ b_{o},\ b_{C}\) are biases;
* \(\sigma\) is the sigmoid activation function, and tanh is the hyperbolic tangent activation function.  
Long-term dependencies are maintained with LSTM [46], which makes them perfect for WSD tasks where word order and sequence information are crucial. The cell state, shown by the horizontal line along the top of Figure 1, is the main concept of LSTM, and the gates that add or delete information from the cell state are the input, forget, and output gates (Equations (3)-(8)). When it comes to processing temporal information, the LSTM model is widely used, which, with very little variation, is used throughout most works.  
Figure 1: The GRU framework [47].
## 2 Experimental Section
### Property Characterization  
The electrochemical and physical properties of the tailor-made membrane, including water content (\(W_{c}\)), thickness, bursting pressure (\(P\)), ion exchange capacity (\(IEC\)), membrane area electric resistance (\(r\)) and apparent transport number (\(t^{+}\)), were compared to the commercial homogeneous and heterogeneous membranes as controls. For the water content analysis, the Na-form dry membranes were completely soaked in deionized water overnight, the surface water was removed with filter paper and immediately weighed. After being dried under vacuum at 80 \({}^{\circ}\)C for at least 12 h, the water content was calculated as the mass percentage of soaked water per gram of dry sample, \(W_{c}=(W_{\text{wet}}-W_{\text{dry}})/W_{\text{dry}}\times 100\%\), in which \(W_{\text{dry}}\) and \(W_{\text{wet}}\) respectively denoted the weights of the dry and the wet samples. The thickness was directly recorded with a screw thread micrometer, and the average value of five data respectively at the four corners and the middle of a 30 \(\times\) 50 mm rectangular sample was reported. To evaluate the bursting pressure, a circular membrane sample (50 mm in diameter) was fixed tightly at the bottom of a stainless steel column and then filled with glycerol. With the increase of the given air pressure from the column top, the membrane would break suddenly, where the bursting pressure was recorded. The average pressure from three tests was reported [17]. The membranes' ion exchange capacities were also determined by the back titration method [16].  
According to the classical test method [17; 18; 19], a two-compartment electrolytic cell system was employed to determine the cation apparent transport number (\(t^{+}\)) and the area resistance (\(r\)). In this system, the geometric parameter of the cell (\(\kappa\)) was 1.0 cm\({}^{-1}\), and the effective surface area of membrane sample (\(A\)) was 1.0 cm\({}^{2}\). Therefore, the \(r\) was simplified to be the difference between 1/\(\sigma_{1}\) and 1/\(\sigma_{0}\), where \(\sigma_{0}\) and \(\sigma_{1}\) referred to the conductivities of the blank and the sample-loaded systems, respectively. As far as the cation apparent transport number was concerned, the system was loaded with a membrane sample to hold-off 0.1 N KCl and 0.01 N KCl solutions. After the electric potential between two sides was read by a digital multimeter, the membrane potential and the \(t^{+}\) value could be estimated by the Nernst equation.
## 3 5G RCS Message Filtering Models and Methods
### The CNN Model for RCS Message Filtering
#### 3.3.3 MaxPooling to Avoid over Fitting  
After the convolution operation process, each RCS message matrix \(M\) is transferred into a relevant feature matrix, represented by \(K\), which has only non-negative values. These relevant features, also known as hidden features, may not share the same importance and may contain redundant information. To avoid over-fitting and to reduce this high-level vector representation, a max pooling layer is present after the convolutional layer; a method called pooling is also applied to extract the most important one. Among the pooling functions, such as max-pooling, min-pooling and average pooling, max-pooling is found to yield the best results. The max-pooling function returns the maximum value of a given window's size, represented by \(k_{maxpooling}\). The window slides over the feature matrix to produce an output matrix, which consists of the maximum values of each window, and the weak activation information generated by the ReLU function is removed.
# Crop Yield Prediction Based on Agrometeorological Indexes and Remote Sensing Data
## 6 Conclusions  
In this paper, we combined technical yields, agrometeorological indexes, and remote sensing vegetation parameters together to build maize yield estimation models for Liaoning and Jilin Provinces. We validated the accuracy of yield estimations models built in this study, compared the differences of the two variable selection methods and discussed the importance of different variables on yield estimation. The main conclusions are as follows:  
First, the validation results show that the models built in this study have good application potential and are suitable for both normal and disaster years. R\({}^{2}\), CCC, and MARE of yield estimation model built in Jilin Province were 0.8201, 0.9761, and 0.0942, and they were 0.7353, 0.8783 and 0.1128 in Liaoning Province, respectively. The average error of yield estimation for the three disaster years was 0.12 in Jilin Province and 0.13 in Liaoning Province.  
Second, the accuracy of the two-stage importance evaluation method was better than, or equivalent to, that of the other method, but it used the fewest variables. It is better to group the variables according to their physical meaning, and to select important variables from each group, than to input all variables at one time and select important variables to build the model.  
Third, the contribution of the agrometeorological indexes to the improvement of the overall modeling accuracy in the two provinces was greater than that of the remote sensing parameters. The ATT variables were more important than the EDD variables. SPI2 in July has a great impact on maize yield in both Jilin and Liaoning Provinces. GPPa (NDVIa) in August is more important than the GPPa (NDVIa) variables in the other months.  
Our study can not only be used as yield estimation tool for the related users, but also guide the relevant researchers to establish similar yield estimation models in other regions. In future, we can build such models using the cloud computing platform, which will greatly reduce the time cost and computer storage cost.  
Conceptualization, X.Z.; Data curation, X.Z., R.G., T.L. and K.X.; Formal analysis, R.G.; Funding acquisition, X.Z.; Investigation, R.G.; Methodology, X.Z.; Software, R.G.; Validation, R.G.; Visualization, X.Z. and R.G.; Writing--original draft, X.Z.; Writing--review and editing, X.Z., R.G., T.L. and K.X. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Key R&D Program of China (Grant No. 2019 YFA0606900) and the National Natural Science Foundation of China (Grant No. 42077436).  
Data Availability Statement: Data is available upon request.  
**Acknowledgments:** We thank the journal's editors and reviewers for their kind comments and valuable suggestions to improve the quality of this paper.  
**Conflicts of Interest:** The authors declare no conflict of interest.
## 1 Introduction
Originally, [PERSON]'s theory was introduced to describe scattering by isotropic spheres [38; 39], but later, it was extended to describe scattering by bi-isotropic [40], rotationally symmetric and anisotropic [41], orthorhombic and dielectric-magnetic [42], magneto- and electro-gyrotropic [43; 44; 45], and spherically-symmetric bianisotropic [46] spheres. Despite this activity, the theory of scattering by a generic bianisotropic sphere has not yet been constituted [47]. The plane waves which can propagate in bianisotropic media belong to Fresnel wave surfaces, which can be characterized using the method of the index of refraction's operator [31; 32; 33]. The Fresnel wave surfaces in bianisotropic media follow quartic dispersion equations, and, therefore, can be classified using the taxonomy of [PERSON] et al. [31; 32; 33], which includes the five hyperbolic classes: non-, mono-, bi-, tri-, and tetra-hyperbolic materials [31; 32; 33; 34; 35; 36; 37; 38; 39; 48; 50; 49; 51; 52; 53; 54; 55; 56; 57; 58; 59]. The prefix in the name of each topological class indicates the number of double cones that the iso-frequency's k-surface has in its high-k limit. Note that hyperbolic metamaterials, which are already known for their applications in optical imaging, hyper-lensing, and emission rate and directivity control, utilize the diverging optical density of high-k states [51; 52; 53; 54; 55; 56; 57; 58; 59]. In Figure 1a, we show an example of an iso-frequency Fresnel wave surface for a tetra-hyperbolic bianisotropic medium with the effective material parameter matrix \(\hat{M}\) color-coded in Figure 1b. Figure 1: (a) Iso-frequency Fresnel wave surface for a tetra-hyperbolic bianisotropic medium with the effective material parameters matrix \(\hat{M}\) color-coded in (b); (c) eigenvalues of the index of refraction’s operator [31; 32; 33] in a complex plane for the same material. The Fresnel wave surfaces only include the plane waves with real wave vectors \(\mathbf{k}\). Nevertheless, the inhomogeneous plane waves with an imaginary \(\mathbf{k}\) are also important. In Figure 1c, we plot the eigenvalues of the index of refraction's operator [31; 32; 33] in a complex plane for the material color-coded in Figure 1b for plane waves propagating in directions spanning the entire solid angle with steps in the angles \(\Delta\theta=\pi/40\) and \(\Delta\phi=2\pi/40\). Note that in Figure 1c, only the eigenvalues on the horizontal axis \(\text{Re}\{k/k_{0}\}\) correspond to the real wave vectors belonging to the Fresnel wave surfaces depicted in Figure 1a. In unbounded homogeneous bianisotropic media, plane waves represent the set of solutions of Maxwell's equations which is typically used, but to consider the scattering of electromagnetic waves by bianisotropic spheres, it is more convenient to express the electromagnetic fields inside such spheres in terms of vector spherical harmonics. In this study, we proposed a theory of scattering by bianisotropic spheres with arbitrary effective media parameters \(\hat{M}\). To accomplish this, we introduced bianisotropic orbitals composed of vector spherical harmonics.
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & \
\begin{tabular}{c} **Wettability Angles** \\ **(\(\alpha\)-bromonaphthalene)**[\({}^{\circ}\)] \\ \end{tabular} & \(\sigma\) [\({}^{\circ}\)] &
\begin{tabular}{c} **Wettability Angles** \\ **(Glycerin)**[\({}^{\circ}\)] \\ \end{tabular} & \(\sigma\) [\({}^{\circ}\)] \\ \hline A & 22.7 & 3.28 & 70.1 & 6.64 \\ B & 27.51 & 3.46 & 79.55 & 3.17 \\ C & 27.91 & 3.32 & 74.54 & 5.42 \\ D & 23.84 & 3.03 & 70.77 & 3.36 \\ E & 24.08 & 1.47 & 67.92 & 2.55 \\ F & 27.09 & 1.83 & 76.68 & 4.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Contact angles for \(\alpha\)-bromonaphthalene and glycerin. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & \ \begin{tabular}{c} **Wettability Angles** \\ **(\(\alpha\)-bromonaphthalene)**[\({}^{\circ}\)] \\ \end{tabular}  & \(\sigma\) [\({}^{\circ}\)] & \begin{tabular}{c} **Wettability Angles** \\ **(Glycerin)**[\({}^{\circ}\)] \\ \end{tabular}  & \(\sigma\) [\({}^{\circ}\)] \\ \hline A & 22.7 & 3.28 & 70.1 & 6.64 \\ B & 27.51 & 3.46 & 79.55 & 3.17 \\ C & 27.91 & 3.32 & 74.54 & 5.42 \\ D & 23.84 & 3.03 & 70.77 & 3.36 \\ E & 24.08 & 1.47 & 67.92 & 2.55 \\ F & 27.09 & 1.83 & 76.6 surface of the oxide layer, the higher the surface free energy. The value of surface free energy also varies with the current density of the oxide layer deposition. However, it cannot be clearly stated whether it increases inversely in proportion to the current density, due to the fact that some differences in the results are within the error limits.
## 4 Reliability, Availability and Fault Tree Analysis
### Component Importance
#### 4.4.2 Criticality Importance  
The criticality importance \(I^{CR}(i|t)\) is a measure particularly suitable for prioritizing maintenance actions [42]. This measure is defined as the probability that component \(i\) is critical at time \(t\) and is failed at time \(t\), knowing that the system is failed at time \(t\), being defined as follows  
\[I^{CR}(i|t)=\frac{I^{B}(i|t)(1-R_{i}(t))}{1-R(t)} \tag{10}\]  
In other words, the criticality importance is the probability that a component \(i\) has caused a system failure, knowing that system is failed at time \(t\).
## 6 Evaluation
### Total Number of Bundles Generated in the Network  
Figure 10 compares the different methods in terms of the total number of bundles generated in the network. The number of bundles generated in _Spray and Wait_ (number of copies: 5), which generates the largest number of bundles, is normalized to 100%. The number of bundles generated by the proposed method is about 40% of that of any existing method. Based on this result and the result shown in Figure 9, we can conclude that the proposed method is the most efficient method of delivering data to shelter terminals. The reason why _Spray and Wait_ (number of copies: 5) generates more bundles than _Epidemic Routing_ is that _Spray and Wait_ enables victim terminals to continue to send hello messages over a longer time than _Epidemic Routing_, which causes batteries of victim terminals to run out quickly.  
In the proposed method, victim terminals start communication only when it receives an \(\mathrm{S_{M}}\) from a carrier terminal. Therefore, the number of bundles generated is proportional to the number of carrier terminals. This is why the proposed method generates fewer bundles than the other methods.  
Figure 9: Delivery rate (rate at which bundles are delivered to shelters).
# A Survey on the Impact of Intelligent Surfaces in the Terahertz Communication Channel Models
## 5 Discussions and Research Directions
### Hardware and Cost Considerations  
To meet the hardware requirements for THz communication, it is imperative to have specialized devices capable of operating within the corresponding frequency band. These devices must demonstrate the ability to transmit and receive signals at high speeds, with a modulation bandwidth of at least 10 GHz [143]. In addition, they must possess an optimum combination of transmit power, antenna gain, and receiver sensitivity, meeting the link budget requirements according to the propagation conditions and the target communication distance [143]. Energy efficiency, low power consumption, and reconfigurability are critical in developing smart, dynamic, and sustainable THz communication and sensor systems, especially in future 6G networks and beyond [144]. These features raise the cost compared to lower-band hardware because of the need for specialized technology to operate in the THz frequency band [143]. Additionally, experimental THz platforms are expensive to build, limiting the ability to evaluate the performance of large THz networks [143]. Although simulation platforms represent a cheaper alternative, they are often based on abstractions or mathematical models of device components and wireless channels. Hardware-in-the-loop emulation platforms may offer an intermediate alternative to more accurately capture the actual behavior of THz devices and channels. However, building and maintaining those platforms can also carry significant costs.  
Hardware operating at THz band can also leverage IS to enable the transference of data on a chip-scale architecture with low latency and small power absorption for wireless networks on chips (WiNoCs) [145]. WiNoCs are used as communication backbones for integration in multi-core system-on-chip (SoC), which are appointed to provide an integrated solution to challenging design problems in the telecommunications, multimedia, and consumer electronic domains [146; 147]. Other investigated solutions to overcome the power and latency constraints of WiNoC are express virtual channels [148], photonic interconnections [149; 150], and radio frequency communication [147; 151]. In general, wireless and wired connections have been studied to satisfy the performance requirements. As for WiNoC inter-chip communication occurring in the THz range, the signals can suffer severe attenuation. As previously stated, IS are employed to shape channel impulse response at mmWave and THz frequencies [133; 152]. With the detailed design of the on-chip IS, considering the impact of the thickness of the silicon layer over the signal attenuation and inter-symbol interference, the results have shown that IS can provide data transmission rates in on-off keying modulation with equalized wireless on-chip channels and double the permissible modulation speed for a given desired bit error rate value at a given noise level.