esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Mathematical Framework
### gPCE Surrogate Model
For \(\mathbf{U}(\mathbf{Z})\in L^{2}_{dF_{Z}}\), the coefficients \(\mathbf{c_{\mathbf{\alpha}}}\) can be computed by defining \(\tilde{\mathbf{U}}_{N}\) as the orthogonal projection of \(\mathbf{U}\) onto the polynomial space \(\mathcal{Z}=\text{span}\{\Phi_{\mathbf{\alpha}}\}\). By prescribing the orthogonality condition \(\mathbf{U}-\tilde{\mathbf{U}}_{N}\perp\text{span}\{\Phi_{\mathbf{\alpha}}\}\):  
\[\int_{\Sigma}\left[\mathbf{U}(\mathbf{Z})-\tilde{\mathbf{U}}_{N}(\mathbf{Z})\right]\Phi_{\mathbf{ \alpha}}dF_{Z}=\mathbf{0} \tag{13}\]the coefficients \(\mathbf{c_{\mathbf{\kappa}}}\) simply read  
\[\mathbf{c_{\mathbf{\kappa}}}=\frac{1}{\gamma_{\mathbf{\kappa}}}\mathbb{E}[\mathbf{U}(\mathbf{Z})\Phi _{\mathbf{\kappa}}(\mathbf{Z})]=\frac{1}{\gamma_{\mathbf{\kappa}}}\int_{\Sigma}\mathbf{U}(\mathbf{z} )\Phi_{\mathbf{\kappa}}(\mathbf{z})dF_{Z}(\mathbf{z})\quad|\mathbf{\kappa}|\leq N, \tag{14}\]  
that is, they can be numerically computed as an integral of the product of \(\Phi_{\mathbf{\kappa}}\) and \(\mathbf{U}\). The expansion terms of Equation (14) guarantees the optimal approximation of \(\mathbf{U}\) in the sense of the norm defined in \(L^{2}_{dF_{Z}}\). The coefficients \(\mathbf{c_{\mathbf{\kappa}}}\) of the approximating gPCE are numerically computed by a non-intrusive approach, where the forward model providing \(\mathbf{U}(\mathbf{Z})\) is used in a black-box fashion. We use a pseudo-spectral projection, with the integral term approximated by a high-dimensional quadrature rule:  
\[\mathbf{c_{\mathbf{\kappa}}}\approx\tilde{\mathbf{c}}_{\mathbf{\kappa}}=\sum_{j=1}^{n_{q}}\bm {U}(\mathbf{z}^{j})\Phi_{\mathbf{\kappa}}(\mathbf{z}^{j})w(\mathbf{z}^{j}) \tag{15}\]  
with \(\mathbf{z}^{j}\) and \(w(\mathbf{z}^{j})\) the \(n_{q}\) integration nodes and weights, respectively. Since \(\Phi_{\mathbf{\kappa}}\) is at most of degree \(N\), the integrand function has at most degree \(2N\). In the univariate case, this requires the use of a \((n_{q,1}=N+1)\)-point Gaussian quadrature rule, while in the multivariate case with \(n\) random variables the number of points grows up to \(n_{q}=(N+1)^{n}\). Using this approximation, the surrogate model needs the evaluation of \(\mathbf{U}\) through the the numerical solver \(\mathcal{S}\) of the forward model at the \(n_{q}\) integration points \(\mathbf{z}^{j}\). In our application, we denote with \(\mathbf{U}\) the vector of state variables, that is, displacements and stresses on the points and times of interest, provided by the solution of problem (1) via a FE numerical solver \(\mathcal{S}\). The random variables \(\mathbf{Z}\) are the material parameters defined by the visco-elasto-plastic VN constitutive law, that is, \(\lambda^{*},\rho_{\mathbf{\kappa}},\rho_{\mu},\) and \(R\), with \(n\) at most equal to 4.
# Research on the Hydrodynamic Performance of a Pentamaran in Calm Water and Regular Waves
## 6 Conclusions  
In this paper, the hydrodynamic performance of a monohull and a pentamaran was numerically simulated in calm water and regular waves. The RANS equation was solved on the basis of the finite volume method. The resistance prediction of the pentamaran in calm water and regular waves was completed, and the changes of each resistance component compared with monohull were explored. This paper draws the following conclusions:  
(1) In calm water, the adverse effect of the side hulls on the resistance is mainly reflected in the low-speed range. In the high-speed range, the influence of the side hulls on the resistance can be ignored. At high speeds, the main hull and side hulls of the pentamaran will produce favorable wave-making interference, thereby improving the wave-making performance of the pentamaran.  
(2) The side hulls have a great influence on the pressure resistance but have no obvious influence on the friction resistance. The rear hulls can rectify the tail flow field.  
(3) In regular waves, although the added resistance of the pentamaran is increasing most of the time, its amplitude is smaller than that of the monohull under the same wave condition. The shorter the wave period, the more obvious this conclusion.  
(4) The amplitude of heave motion and pitch angle of the pentamaran in waves are less than that of monohull, which shows that the pentamaran is more stable in wave navigation, and its seakeeping performance is better than that of a monohull ship in the same scale.  
(5) It is worth noting that the pentamaran is always in a state of sinking during wave navigation. The phenomenon of rising waves on the deck frequently occurs, and the area of rising waves is large. Therefore, in the design of the pentamaran, the main dimensions, speed, water environment, and the wave phenomenon on the deck should be comprehensively considered.  
Conceptualization, D.Z. and B.Z.; methodology, D.Z. and H.J.; software, J.S.; validation, D.Z. and B.Z.; formal analysis, D.Z. and B.Z; investigation, J.S. and B.Z; resources, D.Z.; data curation, J.S.; writing--original draft preparation, D.Z.; writing--review and editing, D.Z.; visualization, J.S. and B.Z.; supervision, D.Z. and J.S.; funding acquisition, D.Z. and H.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Program for Scientific Research Start-up Funds of Guangdong Ocean University, grant number 060302072101; Zhanjiang Marine Youth Talent Project- Comparative Study and Optimization of Horizontal Lifting of Subsea Pipeline, grant number 2021E5011; and the National Natural Science Foundation of China, grant number 62272109.  
Not applicable.  
The authors declare no conflict of interest.
###### Abstract  
Mediterranean grasslands provide different ecosystems and social and economic services to the Mediterranean basin. Specifically, in Spain, pastures occupy more than 55% of the Spanish surface. Farmers and policymakers need to estimate the Gross Primary Production (GPP) to make sustainable management of these ecosystems and to study the role of grasslands acting as sinks or sources of Carbon in the context of climate change. High-frequency satellites, such as Sentinel-2, have opened the door to study GPP with a higher spatial and lower revisit time (10 m and 5 days). Therefore, the overall objective of this research is to estimate an ecosystem light use efficiency (eLUE) GPP model for a Mediterranean grassland in central Spain using Sentinel-2 NDVI Normalized Difference Vegetation Index (NDVI), complemented with meteorological information at the field scale for a relatively long period (from January 2018 to July 2020). The GPP models studied in this research were the MODIS GPP product, as well as the four eLUE models built with MODIS or Sentinel-2 NDVI and complemented by the inclusion of minimum temperature (T\({}_{\text{min}}\)) and soil water content (SWC). The models were validated through the GPP obtained from an eddy-covariance flux tower located in the study site (GPP_T). Results showed that the MODIS GPP product underestimated the GPP_T of the grassland ecosystem. Besides this, the approach of the eLUE concept was valid for estimating GPP in this Mediterranean grassland ecosystem. In addition, the models showed an improvement using Sentinel-2 NDVI compared to MODIS GPP product and compared to the models that used MODIS NDVI due to its higher spatial and temporal resolution. The inclusion of T\({}_{\text{min}}\) and SWC was also a determinant in improving GPP models during winter and summer periods. This work also illustrates how the main wind directions of the study area must be considered to appropriately estimate the footprint of the eddy covariance flux tower. In conclusion, this study is the first step to efficiently estimating the GPP of Mediterranean grasslands using the Sentinel-2 NDVI with complementary meteorological field information to make the management of these ecosystems sustainable.  
ecosystem light use efficiency; MODIS; Sentinel-2; eddy covariance; meteorological variables; footprint estimation; sustainable management
## 4 Methodology
### Model Performance  
For comparison purposes, the effect of the PANN model without PCA processing is also shown. It is worth noting that before applying the PANN model, data preprocessing is also required to improve the prediction accuracy. The respective prediction effects of the two models (PCA-PANN model and PANN model) are shown in Figure 8. The horizontal coordinate in Figure 8 represents the data number. Figure 8 shows that the FoS error generated by the PCA-PANN model is close to zero on most datasets, with an \(R^{2}\) value of 0.988. This error is negligible when predicting FoS, which indicates that the PCA-PANN model has high prediction accuracy. To better support these results, Table 4 lists the prediction results of the two models. \(RMSE\) quantifies the spread of measured values around the mean of predicted values. \(MAE\) calculates the average absolute error between predicted and actual values. \(R^{2}\) is a statistical metric that assesses the strength of the relationship between two variables using N pairs of measured and predicted values. Higher \(R^{2}\) value and lower error values (\(RMSE\) and \(MAE\)) show better predictability of measured values from the prediction model. It is obvious that the prediction results of the PCA-PANN model proposed in this paper are the closest to the measured values, and the prediction errors are the smallest (\(RMSE\) = 0.13, \(R^{2}\) = 0.971, and \(MAE\) = 0.125). The PANN model combined with the PCA method enables the proposed PCA-PANN model to efficiently explore the most appropriate computational parameters using the principal component information, thus improving the accuracy of FoS prediction.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factor** & **Eigenvalue** & **Percent of Variance (\%)** & **Cumulative Percent of Variance (\%)** \\ \hline
1 & 2.593 & 43.20947 & 43.20947 \\
2 & 1.09 & 18.16364 & 61.373 \\
3 & 0.825 & 13.74771 & 75.121 \\
4 & 0.595 & 9.91501 & 85.036 \\
5 & 0.546 & 9.09848 & 94.134 \\
6 & 0.352 & 5.86569 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Principal component eigenvalue and contribution rate.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{F_{1}}\) & \(\mathbf{F_{2}}\) & \(\mathbf{F_{3}}\) & \(\mathbf{F_{4}}\) \\ \hline \(\gamma^{*}\) & 0.796 & \(-\)0.014 & 0.333 & \(-\)0.215 \\ \(c^{*}\) & 0.63 & \(-\)0.413 & 0.38 & 0.328 \\ \(\varphi^{*}\) & 0.67 & 0 Overall, the proposed model is effective in addressing nonlinear FoS caused by multiple variables, and this trained ML model can provide a reference for experienced team members. Admittedly, in terms of current ML research results, ML models cannot completely replace traditional methods to estimate FoS. However, if possible, using ML methods to accurately estimate the FoS of slopes with known design parameters based on datasets from previous studies will greatly reduce the test time and cost.
## 2 Related Work
### Cluster Validity Indices  
The cluster validity indices are qualitative methods, like the statistical mathematical functions, for evaluating the clustering quality of a clustering algorithm. A cluster validity index has the capacity to accurately determine the cluster number in a dataset, as well as find the proper structure of each cluster in the dataset [56]. The principal concerns of most validity indices in clustering are to determine clustering compactness, separation, and cohesion. The cluster validity indices are presented as the fitness function during the optimization process of the clustering algorithms. The DB index and CS index are used as the cluster validity indices to evaluate the quality of the clustering results.  
The DB index determines the quality of a clustering result by using the average inter-cluster similarity between any two clusters and the intra-cluster similarity between data objects within a cluster. The average intra-cluster similarity value is evaluated against the average inter-cluster similarity value using Equations (16) and (17). In the DB index, the fitness function is minimized during the data clustering. This implies that a smaller index value indicates better compactness or separation, and vice versa:  
\[f_{dbi}=\frac{1}{K}\sum_{K}^{1}d\big{(}cc_{i},cc_{j}\big{)} \tag{16}\]  
\[d\big{(}cc_{i},cc_{j}\big{)}=max\left\{\frac{wc_{dist(i)}-wc_{dist(j)}}{ic_{ dist(ij)}}\ |1\leq i,j\leq K,\ i\
eq j\right\} \tag{17}\]  
where \(wc_{dist(i)}\) and \(wc_{dist(j)}\) represent the within-cluster distance for clusters \(i\) and \(j\), \(ic_{dist(ij)}\) represents the inter-cluster distance between the two clusters \(i\) and \(j\). The \(d\big{(}cc_{i},cc_{j}\big{)}\) is the inter-cluster distance between the two cluster centroids \(cc_{i}\) and \(cc_{j}\) of the respective clusters \(i\) and \(j\).  
The CS index estimates the quality of a clustering result by finding the ratio of the sum of the intra-cluster scatter to the inter-cluster separation using Equation (18):  
\[f_{csi}=\frac{\sum_{i=1}^{K}\Bigl{[}\frac{1}{|\mathbb{C}_{i}|}\sum_{\text{$wc_{ scant(i)\in C_{i}}$}}max_{\text{$bc_{exp(j)\in C_{i}}$}}\Bigl{\{}d\Bigl{(}wc_{ scant(i)},bc_{sep(j)}\Bigr{)}\Bigr{\}}\Bigr{]}}{\frac{1}{K}\sum_{i=1}^{K}\left[min_{j\in K,\,j\
eq i}\;\{V\bigl{(}cc_{i},\,\,c_{j}\bigr{)}\}\right]} \tag{18}\]  
where \(wc_{scat(i)}\) and \(bc_{sep(j)}\) represents within-cluster scatter and between-cluster separation with the distance measure given as \(d\left(wc_{scat(i)},bc_{sep(j)}\right)\). The CS index is rated as being more computationally intensive but more efficient, compared with the DB index, and gives a more quality solution than the DB index. In the CS index, the fitness function is also minimized, therefore a lower validity index implies better separation or compactness, while a higher index value implies weak separation or compactness.
## 4 Simulation Results  
### Conditions  
The Monte Carlo simulations are used to evaluate the performance of the proposed algorithm. Unless specifically stated, the simulation parameters are shown in Table 1. The selected key performance indicators are the system throughput and QoS satisfaction degree. The system throughput is expressed as follows:  
\[C=\sum_{i=1}^{N_{u}}C_{i} \tag{25}\]  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Room size & \(15\times 15\times 3\) m\({}^{3}\) \\ Transmit optical power of AP, \(P_{t}\) & 9 W \\ Vertical distance between the AP and terminal, \(L\) & 2.15 m \\ Half-intensity radiation angle, \(\phi_{1/2}\) & 60\({}^{\circ}\) \\ FOV of a receiver, \(\varphi_{FOV}\) & 60\({}^{\circ}\) \\ The refractive index, \(n\) & 1.5 \\ Detector responsivity, \(r\) & 0.53 A/W \\ The physical area of a receiver, \(A\) & \(10^{-4}\) m\({}^{2}\) \\ Power spectral density of noise, \(n_{0}\) & \(10^{-21}\) A\({}^{2}/\)Hz \\ Bandwidth of each optical AP, \(B\) & 40 MHz \\ The gain of the optical filter, \(T_{S}(\varphi)\) & 1 \\ Average required data rate, \(\overline{R}\) & 40 Mbps \\ Average blocking probability, \(\overline{p}\) & 0.1 \\ The access point density, \(\rho_{A}\) & 0.11 APs/m\({}^{2}\) \\ The terminal density, \(\rho_{u}\) & 0.44 terminals/m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.  
The QoS satisfaction degree of the \(i\)-th terminal is given by [14]:  
\[\chi_{i}=\left\{\begin{array}{ll}C_{i}/R_{i},&C_{i}<R_{i}\\ 1,&C_{i}\geq R_{i}\end{array}\right. \tag{26}\]  
A higher QoS satisfaction degree indicates a better QoS guarantee. The terminal whose QoS satisfaction degree equals to 1 is defined as a satisfied terminal.  
We choose the inter-point method in references [31; 32], the RDR-PA method in references [16; 17; 18] and the conventional uniform allocation method in references [21; 22] as comparison methods.
## 2 Materials and Methods
### The Experimental System  
The experimental system consists of three parts: an RTS subsystem, a UWB subsystem, and a PC. The connection relationship between them is shown in Figure 2. The control software, which runs on the PC, communicates with the RTS and UWB through WiFi and USB interfaces, respectively. The UWB tag and the 360\({}^{\circ}\) prism are bound together as the moving target and are mounted on the top of a surveying pole (see Figure 3). The vertical offset between the UWB antenna and the center of the prism is precisely determined by the RTS observation, and the horizontal offset is omitted since it is minimal. The \(z\) coordinate of the prism (retrieved through RTS) will be converted to the UWB antenna by adding the vertical offset.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Indicator** & **Value** \\ \hline Angular accuracy & 0.5\({}^{\prime\prime}\) \\ Distance accuracy and time & 1 mm + 1.5 ppm (standard mode, 1.5 s) \\ Minimum working distance & 3 mm + 1.5 ppm (continuous mode, 0.05 s) \\ \multicolumn{2}{c}{} & 1.5 m \\ \multicolumn{2}{c}{} & GPR1 prism: 10 km; GRZ4/GRZ12 prism: 3 km; \\ Maximum range & GRZ10 prism: 1.5 km; \\ \multicolumn{2}{c}{} & non-prism: 2.4 km \\ Maximum allowed speed for & Tangential: 9 m/s (20 m), 45 m/s (100 m) \\ \multicolumn{2}{c}{} & Radial: 5 m/s \\ \hline \hline \end{tabular}
\end{table}
Table 2: Main technical indicators of the RTS Leica MS60.  
The control software can send orders to control the RTS and UWB, and receive their response messages. Once the RTS successfully locks the prism, and the UWB system starts to solve the tag's position, the control software will save their observations (containing time stamps) on the PC as two separate files. After completion of the data acquisition, the two files will be matched to compute the UWB's positioning errors.
## 3 The Optimal Selection Model of the Backhaul Links  
In this section, an optimal selection method of the backhaul links between UAVs and satellites is proposed to meet the various requirements of multiservice IoRT systems.
## 5 Discussion
### XR Remote Collaboration  
Remote collaboration has been one of the fundamental applications of MR devices since Microsoft released the HoloLens2 as an expert remote guidance case. Researchers also have also offered different remote collaboration solutions. For example, a projector-based mixed reality remote collaboration system [41]; a multi-person mixed reality application [42], which supports remote participants to operate engineering equipment and learn operational processes in a shared virtual environment; and Snow Dome which support MR and VR user remote collaboration [35].  
Instead of extending an existing application to four different platforms--Steam VR, Microsoft mixed reality, smartphone, tablet, and desktop [43]--the solution proposed in this paper is to share the same scene between MR, VR, and mobile terminals. Users can access servers based on requirements and actual conditions, sharing the same virtual scenario, and interacting with virtual objects.  
Among the solutions designed in this study is the third-party perspective of MR-Mobile, which is lightweight, low-cost, and based on ARCore. Compared with Microsoft's Spectator View, it is easier to build, and only needs a mobile device, mobile phone or tablet computer. Images captured by mobile devices can also be shared with the public through third-party streaming software, allowing more people to see the interaction between the real world and the virtual world in the holographic scene.  
In MR-MR collaboration, users can see the relative positions of other people through virtual avatars but cannot realize this function in MR-VR collaboration, since the current VR device relies on access to a PC. In the future, it will be expanded to a VR all-in-one machine in order to realize this function.
## 3 Numerical Calculation
### Optimized Parameters after Evaluation
The relationship between the divergence angle \(\gamma_{50\%}\) which is 50% of the totally accumulative intensity of the light after collimation and the dimensional factor \(\eta\) for the six commercial UV-LEDs is shown in Figure 6. The explanation of the dimensional factor is LED-to-lens size ratios. In other words, the case of a smaller dimensional factor is close to ideal point source approximations. Therefore, the divergence angle after collimation is smaller. As an indication of the ratio of the light-emitting area to the lens aperture, the dimensional factor can predict the divergence angle after collimation because \(\eta\) and \(\gamma_{50\%}\) are positively correlated. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Item** & **Directivity** & \(r_{0}\) & \(\xi\) & **DF \(\eta\)** & **DA \(\gamma_{50\%}\)** & **DA \(\gamma_{90\%}\)** & **OE** \\  & \(\theta_{FWHM}\) (\(deg\)) & **(mm)** & & & \((deg)\) & \((deg)\) & **(\%)** \\ \hline
**I** & 120 & 20 & 0.6 & 0.0500 & 1.56 & 4.16 & 50.2 \\
**II** & 100 & 22 & 2.5 & 0.1643 & 2.20 & 3.44 & 56.6 \\ \hline
**III** & 138 & 12 & 0.1 & 0.1667 & 2.84 & 12.84 & 63.0 \\
**IV** & 110 & 28 & 0.3 & 0.0714 & 1.62 & 4.56 & 44.8 \\ \hline
**V** & 60 & 26 & 0.7 & 0.1076 & 1.66 & 2.54 & 72.0 \\
**VI** & 46 & 27 & 0.9 & 0.0740 & 1.58 & 2.30 & 33.8 \\ \hline \end{tabular}
\end{table} 
Table 2: Optimized parameters of collimating lenses for the six UV-LEDs and evaluated results. Figure 5: (from left to right) The collimating lens profiles, illuminance distribution on the detector plane, and statistics of accumulated power as a function of divergence angle for each of the six (**I**–**VI**) UV-LED light sources.