esa-sceva/satcom-chunk-collection huggingface dataset:
## 6 Numerical Examples
### Tiling Examples Where All Solutions Are Sought
#### 6.2.1 Case 1  
We give an example of the monohedral polyomino type, where applying colouring techniques splits the full (uncoloured) polyomino tiling problem into multiple parionino tiling subproblems, with a reduction in complexity.  
**Example 1**.: _Find all ways of tiling the 9-by-9 single-notched square_  
_all orientations permitted. The area of \(R\) is 80, so we need 20 copies of the \(L\)-shaped tetromino. The associated binary ILP file, constructed with the program LPMARE_POLYONIWOES_FIGUREE2, has \(n=442\) unknowns, \(m=80\) constraints, and \(f=363\) free variables. CPLEX found 1,709,594 solutions in 367.9 \(s\)._  
_Using colouring techniques we wish to tile the checkerboard coloured region \(\widehat{R}\) shown in Figure 12(a) using 20 parioninoes from the set_  
\[\{P_{1}^{+},P_{1}^{-}\}=\Bigg{\{}\]  
_all orientations permitted._  
_As the tetromino and \(R\) have zero parity and \(P_{1}^{+}\
eq P_{1}^{-}\) we automatically obtain 21 tiling subproblems to consider with \(a_{1}^{+}\) and \(a_{1}^{-}=20-a_{1}^{+}\) copies of \(P_{1}^{+}\) and \(P_{1}^{-}\) respectively, given by \((a_{1}^{+},a_{1}^{-})\) for \(a_{1}^{+}=0,1,\ldots,20\). Solving the subproblems in CPLEX yielded the data for the nine feasible solutions shown in Table 1, where we report the number of solutions found (# solns.), and the runtime (in seconds)._  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \(a_{1}^{+}\) & 20 & 18 & 16 & 14 & 12 & 10 & 8 & 6 & 4 \\ \hline \(a_{1}^{-}\) & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 \\ \hline \# solns. & 406 & 9762 & 72,308 & 252,844 & 475,908 & 503,612 & 296,004 & 88,498 & 10,212 \\ \hline runtime (s) & 0.09 & 2.16 & 16.30 & 72.49 & 121.67 & 138.52 & 83.01 & 28.88 & 3.15 \\ \hline \end{tabular}
\end{table}
Table 1: Number of tiling solutions (# solns.) and runtimes in seconds for CPLEX to find the feasible solutions of the parionino tiling problem in Example 1.  
_A single (optimal) tiling solution corresponding to the subproblem with \((a_{1}^{+},a_{1}^{-})=(4,16)\) is shown in Figure 13, i.e., using four copies of \(P_{1}^{+}\) and \(16\) copies of \(P_{1}^{-}\). The ILP file in this case was constructed using the program LPMAKE_PARIORINUOES_FIGURE2 (similar programs were used to construct the ILP files for the other cases). The subproblems with either \(a_{1}^{+}=20\) and \(a_{1}^{-}=0\), or \(a_{1}^{+}=0\) and \(a_{1}^{-}=20\), yielded \((m,n,f)=(80,220,144)\) and \((m,n,f)=(80,222,145)\) respectively. All other subproblems yielded \((m,n,f)=(82,442,362)\). The maximum runtime for the infeasible solutions was 0.62 s. The subproblem with the maximum runtime of \(138.52\) s yielded 503,612 solutions, thus the potential speedup when using the colouring technique is about 2.7\(\times\)._
## 2 Materials and Methods
### Field Operation and Data Collection  
Five surveys altogether covering a seven-month period are considered in this study: one at Sillon de Talbert and four at La Palue (Table 1). For the latter, only the first survey (17 September 2020) is described and analyzed in detail, the other three (repeat) surveys being used for assessing measurements' replicability (cf. Section 2.6). Figure 2: Field surveys. Orthophotos showing camera locations (black dots), DRTK-2 drone mobile station (green square), ground photogrammetric targets (triangles; the five fixed targets present at La Palue during the September survey are shown in red), GNSS base station (yellow square) and geodetic marks (yellow star) at (**a**,**b**) La Palue, and (**c**) Sillon de Talbert field sites, respectively. RTK-GNSS survey points used for the vertical evaluation of photogrammetry at La Palue are shown in red. At Sillon de Talbert, the GNSS base station and DRTK-2 drone mobile station were installed one after the other using the same geodetic mark. Data collection starts with centimetric-accuracy RTK-GNSS (Topcon Hyper V) measurements of geodetic marks (cast metal disks installed on stable ground) and photogrammetric targets (red plastic plates 30 cm in diameter fixed to the ground using tent poles) for data georeferencing and validation (cf. Figure 2). Between 20 and 30 photogrammetric targets, including fixed targets, were deployed to be used either as GCPs or ChkPts (cf. Tables 1 and 2). Measurements are carried out in rapid-static mode (10 s average) using GNSS rovers mounted on a 2-m pole equipped with a bubble level. To provide RTK corrections, a GNSS base station was materialized at both sites using a geodetic mark. Fixed coordinates were obtained using long-static averaging with a tripod (\(\sim\)240 min), over several periods of time, and postprocessed in comparison with nearby IGN (Institut Geographique National) GNSS stations. Repeated measurements of other geodetic marks provide insights on georeferencing quality. For example, using between three and seven survey marks, the standard error (SE) was estimated to be 0.004 m horizontally and 0.002 m vertically on average at La Palue across four consecutive surveys. Geographic coordinates are referenced to the French legal systems for this region, i.e., RGF93-Lambert 93 for planimetry and NGF-IGN69 for altimetry. Elevation zero (m NGF) corresponds to approximately 0.5 m below mean sea level (MSL).
## 3 Mathematical Modelling, Theoretical Aspects
### Formulation of the Stability Analysis  
Based on Equation (41), internal forces \(\{F_{e}\}\), can be obtained with respect to the nodal and non-nodal displacements \(\{a_{e}\}\) and the axial force \(Q\). By expressing the nodal and non-nodal displacement vector from Equation (41), Expression (42) is obtained [23].  
\[\{a_{e}\}=[K]^{-1}\{F_{e}\}=\frac{1}{|[K]|}[K]^{*}\{F_{e}\} \tag{42}\]  
In Expression (42), \([K]^{*}\) represents the adjunct matrix of the elastic stiffness matrix, whose diagonal entries are the determinant of the elastic stiffness matrix \([K]\). Based on Expression (42), the failure of a beam-type element occurs when there is an infinitesimal increase in the axial force \(Q\) the displacements tend to infinity. Therefore, in the case of  
Figure 5: Representation of the beam-type element with elastic support connections, where \(L\)—is the length of the beam-type element; \(x\)—marks the distance to a current cross-section; \(X\)—is the local reference system axes along the axes of the beam-type element; \(y\)—is the local reference system axes perpendicular to the beam-type element axes; \(I\)—the moment of inertia of the cross-section in a general form; \(I(x)\)—the moment of inertia of cross-section at section \(x\); \(Q\)—is the axial force; \(r_{I}\)—denotes the stiffness for a hindered transversal displacement for joint \(i\); \(r_{2}\)—denotes the stiffness for a hindered rotation for joint \(i\); \(r_{3}\)—denotes the stiffness for a hindered transversal displacement for joint \(j\); \(r_{4}\)—denotes the stiffness for a hindered rotation for joint \(j\).  
beam-type elements, the loss of stability occurs when Equation (43) is satisfied, called an eigenvalue problem [23].  
\[|[K]|=\big{|}[K_{e}]-Q\big{[}K_{ge}\big{]}\big{|}=0 \tag{43}\]  
Equation (43), denotes the characteristic equation of the eigenvalue problem, which leads to a homogeneous system of equations, presented in Equation (44) [23].  
\[\big{(}[K_{e}]+\big{[}K_{ge}\big{]}\big{)}\{v\}=\{0\} \tag{44}\]  
The solution of the eigenvalue problem and of Equation (44), represents vector \(\{\lambda\}\) with the proper eigenvalues \(\lambda_{i=\overline{1:n}}\) and the corresponding eigenvectors in a matrix \(\{v_{i}\}\). The minimum value of \(\{\lambda\}\) represents \(\lambda_{1}\) which denotes the critical buckling load, and the corresponding eigenvector \(\{v_{1}\}\) the deflection shape.
# Group Authentication Scheme for Neighbourhood Area Networks (NANs) in Smart Grids
## 3 The Smart Grid Network Model
### Case 1--Star-Star Topology  
In this scenario, we consider a star for NAN topology in the group, with \(GW_{g}\) at the centre. The GW nodes directly communicate with the NOC. This scenario is simple since each SM has a direct link (one-hop) to its GW. This means that no network discovery needs to be made, since GW can detect its network. The process of SM authentication is also simple, because each SM can be directly authenticated by the \(GW_{g}\).  
First, the pre-deployment phase is discussed. This phase assigns the master key \(MK_{NOC}\) to the NOC and is depicted in Figure 4.  
Secondly, the smart meter authentication is highlighted. Specifically, a \(SM_{ng}\) that wants to join a group needs to be authenticated by \(GW_{g}\). As shown in Figure 5, initially, the new \(SM_{ng}\) will send a request message to \(GW_{g}\). This message includes B, which is the encrypted message (serial number of new \(SM_{ng}\)) using symmetric key \(K_{sm,noc}\). Identity number of new smart meter, \(SM_{ng}\), and a timestamp, TS (this is used to mitigate the replay attacks).  
Figure 4: Pre-deployment for NAN in a star topology.  
The gateway \(GW_{g}\) will re-encrypt the message using \(K_{GW_{g}}\) and forward the message to the NOC. The NOC received B and decrypted it using \(K_{sm,noc}\) and in order to validate the serial number of the new \(SM_{ng}\). The NOC responds to \(GW_{g}\) with a confirmation after validating the serial number of the new \(SM_{ng}\). The NOC will encrypt (\(K_{Gw,sm},\ TS\)) using \(K_{sm,noc}\) and send it to the new \(SM_{ng}\) via \(GW_{g}\). After \(SM_{ng}\) receives the message it decrypts it using \(K_{sm,noc}\) and obtains the shared key with \(GW_{g}\). \(K_{GW,sm}\ SM_{ng}\) then replies with an acknowledgement message encrypted with the key.
## 5 Discussion
### Prospects for Further Research
#### 5.3.2 Evaluation Unit  
The selection of the evaluation unit is a prerequisite for the LRA model. The most commonly used evaluation units include grid cells, unique condition units, and hydrological slope units [11]. Among them, the hydrological slope unit can better reflect the relationship between landslide occurrence and geomorphological factors [3; 17; 63]. The extraction of hydrological slope units is usually based on digital elevation model (DEM) data and GIS software [22]. This method is often time-consuming and labor-intensive when dealing with large-scale regional data, resulting in numerous distorted hydrological slope units. Some studies have found that the automatic extraction of slope units can effectively achieve rapid modeling and improve the predictive performance of the LHR model [65]. However, the existing automatic extraction methods for slope units often produce unreasonable outputs when dealing with complex geomorphological conditions. Therefore, a refined method for the extraction of hydrological slope units needs to be further studied.
## 2 Neural Network Architecture
### Building Blocks of the Network  
As already mentioned, the proposed PSCNN network is a photonic adaption of [36]. It consists of five layers designated as the Contrast Detection Layer (CDL), the First Convolutional Layer (CL\({}_{1}\)), the Second Convolutional Layer (CL\({}_{2}\)), the Third Convolutional Layer (CL\({}_{3}\)) and the Output-Classification Layer as shown in Figure 2. Each of these layers consists of neurons, which in our approach are assumed to be two-section gain-absorber VCSELs. Furthermore, between two consecutive layers a synchronization layer is used. This modification is imperative for the proper function of the PSCNN due to the time-multiplexing; it ensures the simultaneous injection of spikes at every layer. To shed light on every aspect of our network an extensive description of each layer's structure and function follows.  
Figure 1: (**a**) VCSEL operation in excitable regime for different levels of input power. For \(P_{IN}\) = 0.1 mW no spike is generated (under threshold stimuli) while for higher \(P_{IN}\) values a spike is fired. Higher \(P_{IN}\) decreases the latency and enables the timing encoding of the input’s power level. The bias current is \(I_{b}\) = 2.32 mA while the duration of the applied stimuli is \(T_{ON}\) = 0.5 ns. (**b**) VCSEL operation in spiking regime for different biases. Higher \(I_{b}\) decreases the \(T_{sp}\) (interspike interval). (**c**) Photonic VCSEL neurons and Radio Frequency (RF) synapse configuration, PD stands for photodiode.
## 3 Determination of VSC
If the CIE standard sky classification is known, the luminance in each sky patch, \(\mathrm{L_{P}}\), can be obtained using Equation (11):  
\[\mathrm{L_{P}}=\left(1+\mathrm{c}\cdot\left[\mathrm{e}^{\mathrm{d}\chi}- \mathrm{e}^{\frac{\mathrm{d}\pi}{2}}\right]+\mathrm{e}\mathrm{\cdot}\mathrm{ \cos^{2}\chi}\right)\left(1+\mathrm{a}\mathrm{\cdot}\mathrm{e}^{\frac{ \mathrm{b}}{\mathrm{\cos\,\alpha_{P}}}}\right). \tag{11}\]  
Coefficients \(\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d},\mathrm{and}\ \mathrm{e}\), are defined by CIE [23] as functions of the sky type, as shown in Table 4. \(Z_{\mathrm{P}}\) is the sky element zenith angle and \(\chi\) is the dispersion angle, calculated from Equation (12):  
\[\chi=\mathrm{\arccos}(\mathrm{\cos\,Z_{\mathrm{s}}\mathrm{\cos\,Z_{P}}+\mathrm{ \sin\,Z_{\mathrm{s}}\mathrm{\sin\,Z_{P}}\mathrm{\cos\,}}}\mathrm{\left| \mathrm{\phi_{P}}-\mathrm{\phi_{s}}\right|}), \tag{12}\]  
where \(\mathrm{\phi_{P}}\) is the azimuth angle of the sky element, \(\mathrm{p}\), and \(Z_{\mathrm{s}}\) and \(\mathrm{\phi_{s}}\) are the zenith and azimuth angles of the sun. The \(\chi\) represents the shortest angular length between the sky element, \(\mathrm{p}\), and the sun, as is shown in Figure 3. Once the luminance in each sky element is known, Equations (7)-(10) can be applied to calculate \(\mathrm{L_{dh}}\), \(\mathrm{L_{dv}}\) and, therefore, VSC. Figure 4 shows the VSC calculation for each CIE standard sky type as a function of the dispersion angle, \(\chi\). As can be seen, sky types 1, 3, and 5 present constant VSC values, regardless of \(\chi\). Therefore, the orientation of the vertical surface has no effect on the level of illumination. The predicted VSC values for these sky types (1, 3, and 5) were 38.5%, 45% and 50%, respectively. The VSC showed a great dependency on the scattering angle of the other CIE standard sky types, with a minimum value of around 30% and a scattering angle close to 120  
Figure 3: The angles of the sun and the sky element \(\mathrm{p}\).
## 4 Experimental Results and Discussions  
### Experimental Environments  
In the LSTM and SLSTM models, the sales volume datasets were split into three subsets, with the first 60% of the data considered as the training set, the next 20% as the validation set, and the most recent 20% as the test set. The validation set was used to estimate the hyperparameters of the individual models. We found a reasonable hyperparameter setting using the validation set for the LSTM model and used the same values for the SLSTM model. Our setting was that the number of hidden nodes is 128, the learning rate is le-04, the optimizer is Adam, the loss function is mean squared error (MSE), the number of epochs is 500, and the batch size is 1. In the auto_arima and Prophet models, the dataset was split into two subsets, with the first 80% used as the training set and the remaining 20% as the test set.  
The forecasting performances were evaluated in terms of three error measures: mean absolute error (MAE), root mean squared error (RMSE), and normalization mean absolute error (NMAE). These measures are defined as follows in Equation (4), where \(y_{i}\) and \(p_{i}\) are the true value and predicted value, respectively, and \(n\) is the number of samples in the test set.  
\[\begin{array}{l}\text{MAE}:\ \frac{1}{n}\sum_{i=1}^{n}\bigl{|}y_{i}-t_{i} \bigr{|}\\ \text{RMSE}:\ \sqrt{\frac{1}{n}\sum_{i=1}^{n}\bigl{(}y_{i}-t_{i}\bigr{)}^{2}} \\ \text{NMAE}:\ \frac{1}{n}\sum_{i=1}^{n}\frac{\bigl{|}y_{i}-t_{i}\bigr{|}}{t_{i}} \end{array} \tag{4}\]  
The measures can assume values greater than or equal to 0, where lower values are considered to be better. MAE expresses the absolute error, so it is easy to understand. RMSE assigns high penalties to large errors since the prediction errors are squared. NMAE is advantageous because it has the same scale across different products. For example, for the product with (1100,1000) for y and p, the NMAE is \(|1100-1000|/1000=0.1\). For another product with (110,100), the NMAE is \(|110-100|/100=0.1\). In terms of NMAE, these two products, with different scales, have the same error, 10%; by contrast, the MAE differs substantially from \(|1100-1000|=100\) to \(|110-100|=10\).  
Figure 8: Seasonal long short-term memory (SLSTM) input data creation. (**a**) Data sampling with seasonality extension (\(w=3\), \(h=2\)\(S_{i}=\)\(S_{i}^{w}\) ). (**b**) Representation of feature vector X and label Y.  
The experiment was performed on a computer equipped with an Intel(R)Xeon(R) Gold 6126 CPU (2.60 GHz) and an NVIDIA GeForce RTX 2080 Ti GPU.
# Hierarchical Resource Management for Mega-LEO Satellite Constellation
## 7 Performance Assessments  
### Assessment Metrics  
Based on system design and resource scheduling, we evaluate the effectiveness of service area planning and resource scheduling. This evaluation aims to provide insights and recommendations to users, such as system administrators and stakeholders, for optimizing the system's design. The evaluation focuses on the following four key aspects.
## 1 Introduction
Some researchers [17; 18] have used the stopping criteria of these tests as the FT in their studies on the IMS dataset. However, others [19; 20] have employed a constant value of the vibration features as the FT in IMS tests. Therefore, the end of life (EoL) may differ from the end of the test in these studies. Reviewing the literature, it can be seen that the details of defining a proper FT were less extensively considered in the RUL prediction of REBs. As the second class of approaches mentioned in the previous paragraphs deal with the uncertainty of the FT, a proposal of a probability distribution for the FT is accordingly desired. In this paper, a procedure to define the FT for REBs is proposed. The extracted feature from the principal component analysis (PCA) is employed to describe the defect growth in the elements of REBs. The copula method is used to relate the fluctuation of the vibration features to the defect growth and selection of a proper FT. The procedure proposed in this paper is applied to experimental run-to-failure data, including accelerated life tests in the lab and the actual field data of an industrial machine. For the accelerated life test dataset, three different scenarios for types of failure that could occur in the tests are planned and studied. The results show that different FTs can be used for the various probable failure modes in REBs. Furthermore, applying the proposed method to the actual field data shows that it provides a proper FT suggestion in the industrial case.
## 3 ICA and ICT
### Related Work
#### 3.2.4 Trust Region ICA  
Inspired by the work of [PERSON] et al., [PERSON] et al. [111; 112; 113] proposed the relative trust region method. This method computes the ICA by solving jointly two cost functions, one absolute and one relative. For a given iteration \(k\), this cost function can be formulated as:  
\[\underset{||\textbf{p}||\leq\Delta^{(k)}}{argmin}\,m^{(k)} =f^{(k)}+\left[\
abla\textbf{f}^{(k)}\right]^{T}\textbf{p}+\frac{1}{2} \textbf{p}^{T}\textbf{B}^{(k)}\textbf{p} \tag{14}\] \[\underset{||\textbf{p}||\leq\Delta^{(k)}}{argmin}\,m^{(k)}_{r} =f^{(k)}_{r}+\left[\
abla\textbf{f}^{(k)}_{r}\right]^{T}\textbf{p}+\frac{1}{2} \textbf{p}^{T}\textbf{f}^{(k)}_{r}\textbf{p} \tag{15}\]  
where \(\Delta^{(}k)\) is the trust region, \(||.||\) is the Euclidean norm **B** is a symmetric matrix, **p** is the search direction vector, \(f^{(k)}\) is the objective function for the current iteration for the absolute sub-problem, \(f^{(k)}_{r}\) is the objective function for the current iteration for the relative sub-problem. The objective function for each case as well as their derivative \(\
abla\textbf{f}^{(k)}\) and \(\
abla\textbf{f}^{(k)}_{r}\).  
\[f(\textbf{W},\textbf{X}) =-\log|\det\textbf{W}|+\frac{1}{T}\sum_{i\in N,I\in T}\psi( \textbf{W}_{\textbf{i}}\;\textbf{x}_{\textbf{i}}(t)) \tag{16}\] \[f(\textbf{W},\textbf{X}) =f(\textbf{W})=f(\textbf{w})\] \[f^{(k)} =f(\textbf{w}^{(k)})\] \[\
abla\textbf{f}^{(k)} =\frac{\partial f}{\partial\textbf{w}^{(k)}}\] (17) \[f_{r}(\textbf{w}) =\frac{1}{T}\sum_{i\in N,I\in T}\psi(\textbf{W}_{\textbf{i}}\; \textbf{x}_{\textbf{i}}(t))\] (18) \[\
abla\textbf{f}^{(k)} =flatten\left(-\textbf{I}+\frac{1}{T}\sum_{t\in[1,T]}\textbf{y}(t )(\psi^{\prime}(\textbf{y}(t)))^{T}\right) \tag{19}\]  
where \(T\) is the number of samples, **I** is an identity matrix, \(\psi\) is a activation function, \(\psi^{\prime}\) is the derivation of the of the activation function, \(flatten\) is a matrix flattening operator. As activation function [PERSON] et al. [111] have investigated the same as [PERSON] et al., (Equation (9)) and \(\phi(\textbf{x})=-\frac{1}{4}\textbf{x}^{4}\). During our experiments the activation function we used is \(\psi(\textbf{x})=tanh(\frac{\psi}{2})\).
## 3 Results  
Four ML models namely PSOANFIS, GANFIS, FAANFIS and ANN were constructed and trained for prediction of IRI. For PSOANFIS, GANFIS, and FAANFIS, an initial ANFIS structure was generated based on a number of membership functions. In the learning PSOANFIS, inertia weight, population size, personal learning coefficient and global learning coefficient were initially set as \"0.4\", \"100\", \"1\" and \"2\", respectively, which achieved the best RMSE. In the learning GANFIS, crossover percentage, population size, mutation percentage, gamma and mutation rate were initially set as \"0.4\", \"100\", \"0.7\", \"0.7\" and \"0.15\", respectively. In the learning FAANFIS, initial parameters, namely the light absorption coefficient, attraction coefficient base value, and the mutation coefficient was selected as \"1\", \"2\" and \"0.2\", respectively. These hybrid models used RMSE criteria to validate the models for  
Figure 4: Methodological flow chart of this study.  
0.200 of the FAANFIS, GANFIS and ANN model, respectively. Thus, the PSOANFIS model had the best goodness of fit with training dataset in comparison with other models. Similarly, RMSE values of GANFIS, PSOANFIS, FAANFIS and ANN for testing dataset were 0.155, 0.145, 0.170 and 0.186, respectively, which also indicated that PSOANFIS had good performance in both the training dataset and the testing dataset compared to other models.  
Thus, in this study, PSOANFIS has a good prediction capability in both training dataset and testing dataset compared to other models.  
Validation of statistical difference of the models using the Wilcoxon sign-ranked test was done as shown in Tables 4 and 5. It can be observed in training dataset that \(p\)-value of the pair samples of the models is smaller than 0.05 except the pair sample of GANFIS vs. FAANFIS and the \(z\)-value of the pair samples of the models out of the range from \(-\)1.96 and +1.96 except the pair sample of GANFIS vs. FAANFIS (Table 4). In testing dataset, both \(p\)-value and \(z\)-values of all the pair samples of the models are less than 0.05 and out of the range from \(-\)1.96 and +1.96, respectively (Table 5). Therefore, it can be stated that in testing phase, the difference of all models is statistically significant whereas in training dataset the difference of the models is statistically significant except GANFIS vs. FAANFIS.