esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Related Work
### Graph Neural Network Methods
#### 2.2.2 Heterogeneous Graph Methods  
However, the inherent heterogeneity in real-world data presents new challenges, leading the current research focus to shift toward Heterogeneous Graph Neural Networks.  
Heterogeneous Graph Neural Networks (HetGNNs) [55], metapath2 vec [56], HAN [25], and Metapath Aggregated Graph Neural Networks (MAGNNs) [57] are typical methods from earlier studies. HetGNN strengthens node content representation through a combination of random walks and Bi-LSTM, especially encoding heterogeneous content such as text and images. However, it was not specifically designed to handle spatiotemporal trajectory information in LBSNs. HAN is the first hierarchical attention model that simultaneously considers both node-level and semantic-level importance. However, it only focuses on the two terminal nodes and ignores the information between them. MAGNN overcomes this limitation by aggregating information both within and between metapaths, effectively extracting structural and semantic information from different types of nodes and edges. However, MAGNN relies on manually designed metapaths to guide information propagation and lacks a dedicated mechanism to handle spatiotemporal information and dynamic changes. Thus, it is limited when dealing with user behaviors with spatiotemporal characteristics in LBSNs. The Heterogeneous Temporal Graph Neural Network (HTGNN) [58] focuses on capturing the dynamic changes of social relationships, suitable for modeling temporal information, but does not model the noise characteristics in LBSNs, which may limit its robustness when faced with noisy data. Some subsequent studies have also focused on processing heterogeneous graphs. HeteroGraphRec [59] uses graph convolution to analyze user interest similarities and considers multiple connection paths. The H2 Re [60] model uses a random walk strategy to generate node sequences, combining homogeneous and heterogeneous information to improve recommendation accuracy, but the sparsity issue may affect convergence speed. and the model is highly sensitive to edge weights, which may ignore some important information.
## 3 Results and Discussion
### Static Analysis Results  
The Stress Contour Map is presented in Figure 9, providing a visual representation of the stress distribution.  
Figure 9: (**a**) the stress contour map of the hydraulic cylinder’s fixed component; (**b**) the stress contour map of the workbench and (**c**) the stress contour map of the saw’s fixed component.  
Through an in-depth analysis of the stress contour map of the hydraulic cylinder's fixed component, we have precisely calculated its equivalent stress value to be 143.7 MPa (\(\sigma_{r}=143.7\) MPa). Given the known upper limit of the permissible stress, which is 230 MPa (\([\sigma]=230\) MPa), we have rigorously verified that the equivalent stress of the hydraulic cylinder's fixed components (\(\sigma_{r}\)) is significantly below the threshold of the permissible stress \([\sigma]\). This conclusion robustly demonstrates that the structural strength of the hydraulic cylinder meets the predetermined safety requirements, thereby ensuring its stability and reliability during operation.  
Through a thorough analysis of the stress contour map of the swrkbench, we have precisely calculated its equivalent stress value at 104.7 MPa (\(\sigma_{r}=104.7\) MPa). Given the established upper limit of permissible stress at 230 MPa (\([\sigma]=230\) MPa), we are able to conclusively verify that the equivalent stress is significantly below the threshold of the permissible stress. This finding effectively demonstrates that the structural strength of the workbench not only meets but exceeds the predetermined safety requirements, thus, ensuring its stability and reliability during operation.  
Through a rigorous analysis of the stress contour map of the saw's fixed components, we have precisely determined its equivalent stress value to be 32.24 MPa (\(\sigma_{r}=32.24\)MPa). Given the established upper limit of the material's permissible stress (\([\sigma]=230\) MPa), which is 230 MPa, we have rigorously verified that the equivalent stress borne by the fixed components of the saw is significantly below the threshold of the permissible stress. This result forcefully demonstrates that the structural design of the saw not only fulfills the predetermined safety standards in terms of strength, but also possesses a notable degree of redundancy, thus, ensuring stability and reliability in practical working environments.
# Hard Fusion Based Spectrum Sensing over Mobile Fading Channels in Cognitive Vehicular Networks
## 2 System Model and Problem Formulation
### Sensing Model  
Spectrum sensing is a binary hypothesis detection issue, with the null (\(\mathcal{H}_{0}\)) and alternative (\(\mathcal{H}_{0}\)) hypotheses associated to the absence and presence of PU in a given frequency band, respectively. We consider a cognitive vehicular network consisting of \(N\) collaborative SVUs. Assume \(L\) sampling  
Figure 1: An illustrative example of cooperative sensing operation for cognitive vehicular networks. There is a PU, a cognitive BS and multiple cooperative SVUs over wireless sensing/reporting channels.  
observations can be used within a sensing interval. Under both hypotheses, the received observations by the \(i\)-th SVU can then be expressed as, respectively  
\[x_{i}(k)=\left\{\begin{array}{ll}n_{i}(k)&\mathcal{H}_{0}\\ h_{i}(k)s(k)+n_{i}(k)&\mathcal{H}_{1}\end{array}\right., \tag{2}\]  
where \(s(k)\) is the signal from the PU, \(x_{i}(k)\) is the received signal by the \(i\)-th SVU, \(h_{i}(k)\) is the channel gain between the PU and the \(i\)-th SVU with E\([|h_{i}(k)|^{2}]=1\), and \(n_{i}(k)\) is the complex additive white Gaussian noise (AWGN) with mean zero and variance \(\sigma_{n}^{2}\), i.e., \(n_{i}(k)\sim\mathcal{CN}(0,\sigma_{n}^{2})\). And, \(s(k)\), \(h_{i}(k)\) and \(n_{i}(k)\) are assumed to be independent of each other, which is reasonable for a practical situation.  
To reduce the complexity and reporting channel overhead, each SVU employs a mapping rule to its observations, to produce a quantized information denoted by \(q(x_{i})\). In this paper, we suppose each SVU makes a binary decision \(u_{i}=q(x_{i})\in\{+1,-1\}\) with probabilities of false-alarm and mis-detection \(P_{fi}\) and \(P_{mi}\). These decisions are then reported to the FC via a fading reporting channel or link, bit error may happen, which further affects the sensing performance at the FC. We will model the reporting channel as a Rayleigh fading channel [22]. The received observation at the FC from the \(i\)-th SVU can be described as  
\[z_{i}=g_{i}u_{i}+w_{i}, \tag{3}\]  
where \(g_{i}\) is the fading gain of reporting channel and \(w_{i}\) is a zero-mean Gaussian random variable with variance \(\delta_{i}^{2}\), i.e., \(w_{i}\sim\mathcal{N}(0,\delta_{i}^{2})\). Once the noisy observation \(\{z_{i};i=1,2,\cdots,N\}\) is received and decoded, the FC makes a global decision on which hypothesis is more likely to be true.  
In the ordinary sense, an optimal fusion rule for hard combination behaves in the form of a counting rule [23]. This argument proves to be true even when those decisions are received via unreliable communication channels, provided that the channels are also independent and identical distribution (IID). Later in this paper, we focus on energy detection for spectrum sensing and look at the detection performance of the counting rule in Rayleigh fading channels.
## 6 Conclusions  
This study proposes a joint planning method of WT/PV ES connected to offshore oil-gas platforms. Based on the power-flow stability indicator, the cluster-partition principle of voltage and loss-sensitivity analysis, and the initial investment, an algorithm based on a PSO algorithm and power-flow calculation was used to solve the two proposed methods. The findings are summarized as follows:  
* The optimal planning method of WT/PV ES proposed in this paper can effectively improve the power-flow stability of offshore oil-gas platform distribution networks, improve the penetration of renewable energy, reduce the burden of the distribution network and gas turbines, and improve the economic indicators.
* The cluster-partition principle and the ES connection method proposed in this paper can effectively improve the impact of the uncertainty of WT/PV output power on the distribution network and reduce the distribution network loss and voltage fluctuation.  
Through experiments, it was proven that the method proposed in this paper increased the new-energy penetration rate by 55.43-99.4%, reduced the voltage fluctuation by 18.6-35.5%, and reduced the total power loss by 48.2-56.8% by rationally siting and sizing the WT/PV under circumstances in which the output of the gas turbine was reduced by 30-70%. At the same time, after rational siting and sizing for ES, voltage fluctuation was again reduced by 12.9-18.6%, and total power loss was reduced by 13.6-21.3%.  
Overall, the WT/PV ES siting and sizing method proposed in this paper can effectively utilize the abundant offshore wind/solar resources, proving the feasibility of offshore large-scale access to decentralized WT/PV power generation projects, which is conducive to the \"carbon-neutral\" operation of offshore oil-gas platforms in the future.  
Conceptualization, C.H. and C.L.; investigation, C.L.; writing--original draft preparation, J.D.; supervision, C.H. and S.L.; writing--review and editing, J.D. and X.L.; validation, H.L. All authors have read and agreed to the published version of the manuscript.  
The National Key R&D Program of China (2021 YFE0103800); the Basic Research Business Fee Project of the Municipal Education Commission (KM201710009002).  
Figure 19: Multi-objective Pareto optimality.
# The Analysis and Verification of Unbiased Estimator for Multilateral Positioning
## 5 Experiments and Results
### Experimental Verification and Discussion  
Experiments were also carried out to perform the verification based on SX1280 chip (LoRa 2.4G). A basketball court with an area of about 30 m \(\times\) 40 m was selected as the actual test site, as shown in Figure 5. The anchors are at the four corners of the outdoor basketball court. Three anchors are placed at \(S_{1}(0,0)\), \(S_{2}(28.2,0)\) and \(S_{3}(28.2,34.8)\) respectively, and the target node is placed at \(T(24.2,15.2)\).  
Figure 4: CDF (Cumulative Distribution Function) graph of two algorithms.  
Figure 3: Two algorithm positioning scatter plots.  
It is known from the above that the SX1280 ranging error model approximately obeys the formula \(\hat{d}_{i}=d_{i}(1+e)\), so the obtained data is processed: it is known that the actual distances from the target node to the three anchors are \(d_{1}\) 28.5 m, \(d_{2}\) 15.7 m, and \(d_{3}\) 20 m respectively. Therefore, the ranging data \(\hat{d}_{i}\) is processed to obtain \(\frac{\hat{d}_{i}-\hat{d}_{i}}{d_{i}}\), which is the \(e\) in the error model, and frequency statistics are performed to obtain a histogram, as shown in Figure 6.  
As can be seen from Figure 6, the error data \(e\) is a random sequence with a mean of approximately 0 and a standard deviation of 0.16078 m. Once the standard deviation of the ranging error distribution is known, the unbiased estimator can be used for positioning optimization.  
For the actual experimental data obtained, the position of the target node is estimated by the multilateral positioning method and the unbiased multilateral positioning method respectively. The root mean square error is used to evaluate the positioning accuracy of the two, and the results are shown in Table 1. The results show that unbiased multilateral positioning method can improve the accuracy of the positioning system.  
\begin{table}
\begin{tabular}{c c} \hline
**RMSE of Multilateral Positioning Method** & **RMSE of Unbiased Multilateral Positioning Method** \\ \hline
6.10904 & 5.95985 \\ \hline \end{tabular}
\end{table}
Table 1: Location error data under two algorithms.  
Figure 5: The basketball court environment.  
Figure 6: Histogram distribution of ranging error data \(\frac{d_{i}-\hat{d}_{i}}{d_{i}}\).
## 3 Results and Discussion
### Feature Importance  
Table 1 provides the description of some selected features from the list of topmost important features. Using the Random Forest model, the importance of different material properties on the superconductor critical temperature prediction was examined. In Figure 4c, the top 25 features are displayed in the bar plot, which makes it evident which features, in accordance with the model, have the greatest influence on Tc. Features like average deviation in the Goldschmidt volume per atom and average deviation of the space group numbers are at the top of the list, indicating that atomic volume changes and crystal structure symmetry are important factors in determining Tc. Notable is the feature average variation in electronegativity, which suggests that superconducting behavior can be strongly predicted by the average difference in element electronegativities within a  
Figure 4: Machine learning model performance and feature importance in predicting superconducting critical temperatures. **(a)** The scatter plot for the training dataset, with the predicted Tc plotted against the actual Tc, achieving a coefficient of determination (R\({}^{2}\)) of 0.98. **(b)** A similar scatter plot for the test dataset, achieving an R\({}^{2}\) of 0.92, indicates high accuracy of the model on unseen data. Each green square represents a data point, and the proximity of these points to the diagonal line indicates the precision of the predictions. **(c)** Feature importance bar graph, derived from the machine learning model, which ranks the relative importance of each feature in predicting Tc. Features such as average Goldschmidt volume per atom and space group show the highest importance. compound. Some prominent features highlight the significance of atomic sizes and periodic table trends, respectively:'mode CovalentRadius' and 'range MendeleevNumber'. Figure 5 presents a set of scatter plots (panels a-f) that demonstrate the performance of our trained model across different groups of superconducting materials categorized by their composition types, such as Oxide, Stannide, Telluride, Nitride, Fluoride, and Sulfide. Incorporating data from a diverse range of superconducting materials beyond nitrides--including oxides, halides, and sulfides--allows the model to learn more generalized patterns. While the dataset could have been increased even further by adding other types of well-studied superconducting structures, such as cuprates, kagomes, and Fe-based structures, this initial study has sought to include only similar classes of materials to maintain the underlying physics of NbN-based systems. This approach enhances the model's prediction ability by making it more adaptable and less dependent on specific composition types or stoichiometries. Although this strategy introduces some uncertainty due to differences between material classes, it also strengthens the model's capability to predict Tc for less-represented systems like nitrides, where data are currently limited.
# Bidirectional Sliding Window for Boundary Recognition of Pavement Construction Area Using GPS-RTK
## 1 Introduction
### GPS-RTK Positioning Technology  
GPS provides single-point ten-meter-level positioning accuracy, and in order to obtain higher positioning accuracy, we usually use Differential GPS (DGPS) technology. This includes pseudorange differential positioning technology with decimeter-level positioning accuracy and RTK positioning technology with centimeter-level accuracy. The principle of these two different DGPS technologies is the same, that is, the base station determines errors in spatial correlation, the transmitting station broadcasts the error information and the mobile station receives both the GPS signal and the error information, based on which it quickly performs error correction. GPS-RTK was adopted for the work described in this paper, by which the carrier phase collected by the base station can be sent to the mobile station for precise single-point positioning.
# A Review of High-Sensitivity Tracking Techniques for Satellite Navigation Signals
## 1 Introduction
Second, this paper provides an in-depth analysis of mainstream tracking technologies and sensitivity enhancement strategies, focusing on techniques such as coherent integration time extension, oscillator noise modeling and mitigation, and advanced filtering algorithms. Finally, this paper outlines emerging research directions, including integrating deep learning techniques into filter structures to enhance adaptability and robustness in dynamic environments; developing multi-channel collaborative estimation schemes for oscillator noise, incorporating external signal data such as 4G/5G communication signals to improve system performance; and designing low-complexity approximations for open-loop tracking to better align with hardware resource constraints while maintaining sensitivity and dynamic performance.Collectively, these contributions offer theoretical guidance for the design and optimization of high-sensitivity GNSS receivers and provide a clear roadmap for future research in this field.
## 3 The Radiative Transfer Equation
### RTE Numerical Solutions
#### 3.4.2. Invariant-Imbedding Method
\(R_{s}\) vs. linkspan with a Double-Gamma Function (DGF) fitted \(R_{s}\) for coastal and harbor water scenarios utilising the HG-SPF. It is worth noticing that the \(\alpha\) for the DGF-fitted \(R_{s}\) for harbor waters is higher than for coastal waters. This indicates that the harbor waters have higher cumulative scattering than the coastal waters, as observed in the DOM approach in Figure 10.  
When implementing the invariant-imbedding method approach, there are several potential issues to watch out for to ensure accuracy and efficiency:  
* Consistency with Physical Assumptions: Verify that the implementation accurately reflects the problem's physical assumptions, such as isotropic scattering, energy conservation, and boundary conditions. * Discretisation: Ensure the proper discretisation of the spatial domain, angular domain, and wavelength (if applicable). The choice of discretisation parameters can impact the solution's accuracy and computational efficiency. * Invariant-Embedding Formulation: Implement the RTE's invariant-embedding formulation accurately, including decomposing the radiation field into embedded and unembedded components and ensuring appropriate coupling between these components. * Solver Accuracy: Choose appropriate numerical methods and solvers for solving the coupled system of equations arising from the invariant-embedding method and ensure that the solver is accurate and stable for the given scenario characteristics. * Boundary Conditions: This is a make-or-break issue. Implement boundary conditions consistent with the seawater linkspan. Boundary conditions may include incoming radiation from external sources, reflective or absorbing boundaries, or symmetry conditions. * Convergence Criteria: Define convergence criteria for iterative solvers used in the invariant-embedding method. Monitor convergence during the solution process and adjust convergence criteria to ensure accurate results. * Computational Efficiency: Optimise the implementation for computational efficiency, particularly for problems with large spatial domains or complex geometries. Techniques such as parallelization, adaptive mesh refinement, or model reduction should be considered to improve efficiency. This step typically should be the last step. * Validation: Validate the implementation against analytical solutions, benchmark scenarios, or experimental data where available by comparing results obtained using the  
Figure 11: Invariant-imbedding solutions. invariant-embedding method with results from other numerical methods to ensure accuracy and reliability. * Error Handling: Implement robust error handling and debugging capabilities to diagnose and address any issues that arise during the solution process. By addressing these potential implementation issues and carefully validating the results, we can ensure the accuracy and reliability of the invariant-imbedding method for solving the RTE.
## 3 Nelder-Mead Algorithm for the Optimal Completion of Incomplete PCMs
### Nelder-Mead Algorithm
while\(\max_{2\leq j\leq k+1}||\mathbf{x}_{j}-\mathbf{x}_{1}||_{\infty}>\texttt{ TolX }\) & \(\max_{2\leq j\leq k+1}|f_{j}-f_{1}|>\texttt{TolFun}\)do \(\overline{\mathbf{x}}\leftarrow\frac{1}{k}\sum_{j=1}^{k}\mathbf{x}_{j}\)\(\triangleright\) Calculate centroid. \(\mathbf{x}_{r}\leftarrow(1+\rho)\overline{\mathbf{x}}-\rho\mathbf{x}_{k+1}\)\(\triangleright\)Reflection\(f_{r}\gets f(\mathbf{x}_{r})\) if\(f_{r}<f_{1}\)then \(\mathbf{x}_{e}\leftarrow(1+\rho\chi)\overline{\mathbf{x}}-\rho\chi\mathbf{x}_{k+1}\)\(\triangleright\)Expansion\(f_{e}\gets f(\mathbf{x}_{e})\) if\(f_{e}<f_{r}\)then \(\mathbf{x}_{k+1}\leftarrow\mathbf{x}_{e}\)\(\triangleright\) Accept \(\mathbf{x}_{e}\) and replace the worst vertex \(\mathbf{x}_{k+1}\) with \(\mathbf{x}_{e}\) else \(\mathbf{x}_{k+1}\leftarrow\mathbf{x}_{r}\)\(\triangleright\) Accept \(\mathbf{x}_{r}\) and replace the worst vertex \(\mathbf{x}_{k+1}\) with \(\mathbf{x}_{r}\) endif elseif\(f_{1}\leq f_{r}<f_{k}\)then \(\mathbf{x}_{k+1}\leftarrow\mathbf{x}_{r}\)\(\triangleright\) Accept \(\mathbf{x}_{r}\) and replace \(\mathbf{x}_{k+1}\) with \(\mathbf{x}_{r}\) elseif\(f_{k}\leq f_{r}<f_{k+1}\)then \(\mathbf{x}_{oc}\leftarrow(1+\rho\gamma)\overline{\mathbf{x}}-\rho\gamma\mathbf{x }_{k+1}\)\(\triangleright\)Outside contraction\(f_{oc}\gets f(\mathbf{x}_{oc})\) if\(f_{oc}\leq f_{r}\)then \(\mathbf{x}_{k+1}\leftarrow\mathbf{x}_{oc}\)\(\triangleright\) Accept \(\mathbf{x}_{oc}\) and replace \(\mathbf{x}_{k+1}\) with \(\mathbf{x}_{oc}\) else  Compute \(k\) new vertices \(\mathbf{x}_{j}=\mathbf{x}_{1}+\sigma(\mathbf{x}_{j}-\mathbf{x}_{1})\), \(j=2,\ldots,k+1\)\(\triangleright\)Shrink\(f_{j}\gets f(\mathbf{x}_{j})\), \(j=2,\ldots,k+1\) endif else \(\mathbf{x}_{ic}\leftarrow(1-\rho)\overline{\mathbf{x}}+\rho\mathbf{x}_{k+1}\)\(\triangleright\)Inside contraction\(f_{ic}\gets f(\mathbf{x}_{ic})\)if\(f_{ic}<f_{k+1}\)then \(\mathbf{x}_{k+1}\leftarrow\mathbf{x}_{ic}\)\(\triangleright\) Accept \(\mathbf{x}_{ic}\) and replace \(\mathbf{x}_{k+1}\) with \(\mathbf{x}_{ic}\) else  Compute \(k\) new vertices \(\mathbf{x}_{j}=\mathbf{x}_{1}+\sigma(\mathbf{x}_{j}-\mathbf{x}_{1})\), \(j=2,\ldots,k+1\)\(\triangleright\)Shrink\(f_{j}\gets f(\mathbf{x}_{j})\)\(\forall j=2,\ldots,k+1\) endif endif  Update vertices \(\{\mathbf{x}_{j}\}_{j=1,\ldots,k+1}\). Apply the coordinate transformation (6) for each new (accepted) vertex \(\mathbf{x}_{j}\), \(j=1,2,\ldots,k+1\). \(S\leftarrow\{\mathbf{x}_{j}\}_{j=1,\ldots,k+1}\). Compute \(f_{j}=f(\mathbf{x}_{j})\), \(j=1,2,\ldots,k+1\). Sort the \(k+1\) vertices of the simplex \(S\) with an increasing objective function values endwhile
```  
**Algorithm 1** One iteration of the standard Nelder-Mead algorithm. Here, we apply the proposed algorithm for solving the _constrained eigenvalue minimization_ (4) for the given _incomplete_PCM **A**. Moreover, we use [PERSON]'s inconsistency ratio (CR) for our inconsistency measure hereinafter.