esa-sceva/satcom-chunk-collection huggingface dataset:
## Materials and Methods
### Spectral Feature Selection Algorithms
#### 2.3.1 Neighborhood Rough Set
The main steps for selecting spectral feature bands based on the NRS model are as follows:  
(1) The collected spectral data should be preprocessed, and a decision information table is further constructed as follows:  
\[\text{M}= \begin{bmatrix}s_{11}&s_{12}&\cdots&s_{1m}&d_{1}\\ s_{21}&s_{22}&\cdots&s_{2m}&d_{2}\\ \vdots&\vdots&\ddots&\vdots&\vdots\\ s_{n1}&s_{n2}&\cdots&s_{nm}&d_{n}\end{bmatrix}  \tag{3}\]  
where the matrix \(\mathbf{S}\) represents the spectral information of the sample and can be considered as a conditional attribute, and \(\mathbf{s}_{nm}\) refers to the spectral value of the nth sample at wavelength m. Matrix d represents the category of the sample and can be considered as a decision attribute. (2) The different \(\beta\) and \(\delta\) are set for modeling, and the NRS model is trained starting from an empty set using heuristic search algorithms until the model's discriminative ability no longer increases after adding any conditions. Furthermore, the feature variables with strong representativeness are gradually selected and placed in the subsets. Finally, a series of feature subsets are generated for subsequent analysis. (3) Different algorithms are used as classifiers for comparison. A series of feature subsets are selected as input vectors of classifiers for training and recognition. The final reduction result is to select a subset that maximizes recognition accuracy and contains the least number of bands.
# Impacts of Thermal Maturity on the Carbon Isotopes of
## 3 Results and Discussion
### Geological Significances  
According to early studies, the \(\delta^{13}\)C values of monomeric hopane hydrocarbons can indicate depositional environments and biological sources. The experimental data of this study showed that thermal maturity significantly affects the carbon isotope values of hopane hydrocarbons, and different hopane hydrocarbons respond inconsistently to thermal maturity. The impact of thermal maturity should not be ignored when comparing oil sources and inferring the source of organic matter. [PERSON] et al. [19] reported the \(\delta^{13}\)C values of hopane hydrocarbons from lacustrine deposits of the Lucaogou Formation in the Junggar Basin, with the \(\delta^{13}\)C values as low as \(-63\)%, indicating active aerobic CH\({}_{4}\) oxidation in the overlying water column. This reveals the dynamic methane cycling recorded by the Lucaogou Formation, with increasing CH\({}_{4}\) emissions contributing to the termination of the late Paleozoic Ice Age and subsequent climate warming. [PERSON] et al. [47] measured the \(\delta^{13}\)C values of hopane compounds for the mudstones and oil shales in Member Qing-1 of the Songliao Basin. The distribution scope of the \(\delta^{13}\)C values of hopane compounds is \(-40.18\)%\(\sim\)\(-58.9\)%, which is characterized by medium-layer water bacteria and addicted methane bacteria. By combining these findings with the carbon isotope features of other biomarker compounds, it was concluded that the majority of hydrocarbon sources in FuYang oil reservoirs originated from Member Qing-1 source rocks of the Songliao Basin. However, the conclusion provides a solid theoretical foundation and supplementary for studying the specific structural changes in hopane hydrocarbons at different evolutionary stages. Further research, including additional sample analyses and more comprehensive isotopic studies, is required to fully elucidate the relative contributions of thermal maturity and other factors and to establish a more definitive understanding of their effects on the carbon isotopes of monomeric hopane hydrocarbons.
# Mobile Network Operators' Assessment Based on Drive-Test Campaign in Urban Area for iPerf Scenario
## 3 Correlation Analysis of QoS Metrics  
### PCC Results for TCP  
Our analysis is based on the Pearson Correlation Coefficient (PCC) [7] between a pair of two variables represented by analyzed parameters. The description of PCC and interpretation of its values [54] is shown in Appendix B. Based on Equation (A1), we determined the correlation degree for every pair of two measured metrics defined in Section 2.4. The PCC results for TCP are presented in Figure 4. This figure depicts one heatmap averaged for all MNOs (a); and four heatmaps for each MNO, i.e., (b) Orange, (c) Play, (d) Plus, and (e) T-Mobile, respectively. Each heatmap shows PCCs for UL and DL illustrated in upper-right and lower-left edges, respectively.  
Figure 4: PCCs for TCP, UL/DL: (**a**) averaged all MNOs, (**b**) Orange, (**c**) Play, (**d**) Plus, and (**e**) T-Mobile.  
Figure 4 shows that \(PCC=-1\) for LDR and RDR. It means that the relationship between these parameters is linear, as shown in the results from Equation (3). So, next, we only analyze RDR.  
For TCP and UL, we may see that Th-Rx is very strongly correlated with the Tx-Sx, Th-Rate, and RDR for all MNOs. In the case of TCP and DL, Th-Rx is very strongly correlated only with Tx-Sx for all MNOs. The correlation between Tx-Rx and Th-Rate is weak or moderate, and the correlation between Th-Rx and RDR is moderate or strong. Generally, for UL and DL, we can classify the relationship between QoS metrics (i.e., Th-Rx, Th-Rate, and RDR) and signal parameters (i.e., RSRP, SINR, RSRP-5G, SINR-5G, RSRQ-5G) as moderate. In the DL case, only the Th-Rate weakly correlates with the signal metrics, whereas the PCCs for signal parameters indicate a moderate or strong correlation between them. By determining PCCs for the entire data set, i.e., for all MNOs (see Figure 4a), we can notice that the correlation degree is usually smaller than for individual MNOs. This is due to the fact that the data set of analyzed parameters for MNOs varies, as is illustrated later in the paper. The RSRQ-5G example shows the best. In this case, the averaged PCCs for all MNOs indicate a very weak correlation, while the corresponding PCCs for individual MNOs are much larger.
## 4 Discussion
### Key Space and Exhaustive Search Attack Analysis  
The proposed encryption scheme has high strength for resisting the exhaustive search attack. In this scheme, the secret key (58 by 58 matrix, each element with value of complex number) space of the encryption system is greater than 2100, therefore will take significant computational power for exhaustive search able to attack the proposed scheme. More specifically, the secret key is a complex matrix generated by EMD. In our research, the size of matrix is 58 \(\times\) 58, which also can be expanded depending on the need. Furthermore, the value of the matrix is a complex number, which further increases the complexity for resisting the exhaustive search attack.
## 4 Optimizations for Structural Parameters
### Optimization Results  
BP network prediction accuracy is analyzed in Figure 13. The model regression state is shown in Figure 13a. One hundred process parameter combinations were randomly selected in the test set to compare with the actual value. The result showed that the prediction model regression was excellent, and the \(R^{2}\) value was calculated as 0.9998. As shown in Figure 13b, the error analysis was performed on the training set, validation set, and test set, and the error obeyed a normal distribution with minimal values, which satisfied the prediction requirements.  
The ISSA optimization results corresponded to structural parameters of \(l_{1}*\) = 213.59 mm, \(l_{2}*\) = 42 mm, and \(a^{*}\) = 31.8 mm, which were enlarged to increase the ventilation efficiency compared with the original structural parameters. The transmission coefficient was obtained by solving the analytical model with optimized structural parameters, as shown in Figure 14a. Due to the constraints of Equation (15), in the optimized model, the resonant frequency was 378.9 Hz, which was highly consistent with the constraint of 378.5 Hz. The increase in ventilation area raised the transmission coefficient by a minor amount, which was an adverse effect, but in practice, the effect is negligible. The WU was redesigned according to the optimized structural parameters. After the numerical model, the SPL distribution is shown in Figure 14c. It maintained a satisfactory noise-reduction performance while increasing the ventilation efficiency compared with the original WU shown in Figure 14b. The optimization results show that the optimiza  
Figure 13: BP network prediction accuracy. (**a**) Regression state and (**b**) error distribution.  
precisely optimize the structural parameters. It means that in practical applications, after clarifying the noise frequency, the WU structure can be targeted to be formed for noise suppression and to maximize ventilation and heat exchange.
# NTT and Inverse NTT Quantum Circuits in CRYSTALS-Kyber for Post-Quantum Security Evaluation
## 2 Background
### CRYSTALS-Kyber  
Quantum computers pose significant threats to classical cryptographic schemes, necessitating a transition to quantum-resistant algorithms. The post-quantum cryptography (PQC) competition was launched to respond to this. Its primary goals involve discovering, evaluating, and standardizing cryptographic methods resistant to quantum threats. CRYSTAL-Kyber is one of the candidate algorithms submitted to PQC. CRYSTAL-Kyber [23] is an IND-CCA2-secure key encapsulation mechanism (KEM) with the hardness of Module-LWE [24] on a lattice. This cryptographic, which is designed to be robust in the post-quantum era, was one of the finalists of the post-quantum cryptography project conducted by NIST. The security foundation is based on the hardness of resolving learning-with-error (LWE) problems for module lattices.
## 4 Results and Comparison
### RUL Estimation for Test Instance Bearings
#### 4.1.2. RUL Estimation for Test Instance Bearing1-5  
Based on the specified segment of the range [0, 825] (time cycles) within the 2 nd PC feature sequence of the learning instance Bearing1-2, the nine synthetic feature sequences are generated with the scaling factor \(\alpha\) of 2.80, 2.90, 3.00, 3.10, 3.20, 3.30, 3.40, 3.50, and 3.60, as shown in Figure 12. The duration \(\Delta\) is equal to 45 (time cycles) in this case. Table 3 presents the results of similarity evaluation of synthetic sequences and the selected segment  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **PC1** & **PC2** & **PC3** & **PC4** & **PC5** \\ \hline Bearing1-1 & 91.27\% & 5.13\% & 1.48\% & 0.14\% & 0.03\% \\ Bearing1-2 & 49.78\% & 37.45\% & 9.24\% & 1.71\% & 0.98\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Accounts for variability of principal components of learning instances.  
Figure 9: The mean and the first five PCs of the spectrogram of learning instance Bearing1-2. Note: the horizontal axis’ ticks represent 10 Hz per tick mark.  
in the range of [0, 2303] (time cycles) of Bearing1-5. Based on the seven synthetic sequences of \(\alpha\) = 2.90, 3.00, 3.10, 3.20, 3.30, 3.40, and 3.50, the final RUL estimate of Bearing1-5 can be computed as \(RUL_{e}=160\) (time cycles) using the proposed ensemble method. As the actual RUL of Bearing1-5 is known as \(RUL_{u}=161\) (time cycles), the relative error of estimation is calculated as \(E_{r}=0.92\%\).  
Figure 10: Spectrograms and PC feature sequence test instances. (**a**) Bearing1-4; (**b**) Bearing1-5; (**c**) Bearing1-6; (**d**) Bearing1-7. (Note: The same range of time cycle in x-axis [0-3000] is used for all subfigures to illustrate the large variations of bearing lifespans in the PRONOSTIA datasets.).
# Coordinate Descent for Variance-Component Models
## 2 Basic Coordinate Descent
### Implementation  
The non-trivial component of Algorithm 1 is to compute the line search,  
\[\underset{x\geq 0}{\text{arg min}}\ G(\mathbf{\Omega}_{-k}+x\mathbf{V}_{k}),\]  
where \(\mathbf{\Omega}_{-k}:=\mathbf{\Omega}-\gamma_{k}\mathbf{V}_{k}\). When \(\mathbf{\Omega}_{-k}\) is invertible, this step can be simplified to a one-dimensional algebraic expression that can be numerically solved without repeated evaluations of the terms \(\mathbf{y}^{\top}(\mathbf{\Omega}_{-k}+x\mathbf{V}_{k})\mathbf{y}\) and \(\ln\det(\mathbf{\Omega}_{-k}+x\mathbf{V}_{k})\). The simplification is achieved using the Generalized Eigenvalue Decomposition (GEV) [13] to decompose \((\mathbf{V}_{k},\mathbf{\Omega}_{-k})\rightarrow(\mathbf{D}_{k},\mathbf{U}_{k})\) such that,  
\[\mathbf{V}_{k}\mathbf{U}_{k}=\mathbf{\Omega}_{-k}\mathbf{U}_{k}\mathbf{D}_{k}\quad \text{and}\quad\mathbf{U}_{k}^{\top}\mathbf{\Omega}_{-k}\mathbf{U}_{k}=\mathbf{I }_{n},\]  
where \(\mathbf{D}_{k}\in\mathbb{R}^{n\times n}\) is a diagonal matrix with non-negative entries and \(\mathbf{U}_{k}\in\mathbb{R}^{n\times n}\) is invertible. Using the above expressions we obtain the factorized expression, \(\mathbf{\Omega}_{-k}+x\mathbf{V}_{k}=\mathbf{U}_{k}^{-\top}(\mathbf{I}+x\mathbf{ D})\mathbf{U}_{k}^{-1}\). Therefore, we can express the inverse and log-determinant terms in \(G(\mathbf{\Omega}_{-k}+x\mathbf{V}_{k})\) as,  
\[(\mathbf{\Omega}_{-k}+x\mathbf{V}_{k})^{-1} =\mathbf{U}_{k}(\mathbf{I}_{n}+x\mathbf{D}_{k})^{-1}\mathbf{U}_{k }^{\top}, \tag{5}\] \[\ln\det(\mathbf{\Omega}_{-k}+x\mathbf{V}_{k}) =\ln\det(\mathbf{I}_{n}+x\mathbf{D}_{k})-2\ln\det\mathbf{U}_{k}. \tag{6}\]  
From (4), we have that,  
\[G(\mathbf{\Omega}_{-k}+x\mathbf{V}_{k})=\mathbf{y}^{\top}\mathbf{U}_{k}(\mathbf{I}_{n }+x\mathbf{D}_{k})^{-1}\mathbf{U}_{k}^{\top}\mathbf{y}+\ln\det(\mathbf{I}_{n}+x \mathbf{D}_{k})+\text{const}.\]  
Let \(\mathbf{\alpha}_{k}=\mathbf{U}_{k}^{\top}\mathbf{y}\) and \(\mathbf{d}_{k}=\text{diag}(\mathbf{D}_{k})\). Then, the function to be minimized at the \(k\)-th component is of the form,  
\[g_{k}(x):=G(\mathbf{\Omega}_{-k}+x\mathbf{V}_{k})=\sum_{j=1}^{n}\frac{\alpha_{k,j }^{2}}{d_{k,j}x+1}+\ln(1+d_{k,j}x)+\text{const}. \tag{7}\]  
where \(d_{j}\geq 0\) for all \(j\). Unless \(n=1\), in general, there is no closed-form expression for the minimum. We thus resort to a numerical method, such as [PERSON]'s method or the Golden-section search method. With the above simplification the majority of the cost is attributed to the GEV, which has a time complexity of \(O(14n^{3})\). Alternatively, one could employ iterative methods without prior simplification of \(g_{k}(x)\) via the GEV. In that case, however, evaluation of \(g_{k}(x)\) and its derivatives at each step requires one full Cholesky factorization, costing \(O(n^{3})\). Either way, for problems where \(n\) is large, basic CD is too costly per one update.
## Methods  
### Land Surface Phenology Modeling  
#### 3.1.1 EVI2 time series from ARD and HLS surface reflectance  
The two-band Enhanced Vegetation Index (EVI2) was calculated from ARD and HLS surface reflectance products (red--R and near infrared--NIR bands) using Equation (1) [23]. EVI2 was chosen over the more commonly used Normalized Difference Vegetation Index (NDVI) to avoid the well-known loss of sensitivity that NDVI experiences with denser canopies. EVI2 performs similarly to its predecessor, the 3-band EVI, especially with continuing advancements in atmosphere corrections. Poor-quality observations--snow, high confidence cloud, or cloud shadow pixels--were all masked out using quality control layers delivered with the ARD and HLS products. EVI2 values outside the valid range (from 0 to 1) were also excluded. The remaining \"good\" EVI2 values at each pixel werethen stacked in chronological order from the first day of the year (DOY = 1) to the final day of the year (DOY = 365 or 366 in leap years).  
\[\text{EVI2}=2.5\,\frac{(\text{NIR}-\text{R})}{(\text{NIR}+2.4\text{R}+1)} \tag{1}\]
## 3 Statistics of Collision Rates  
Normally, accident statistics are derived from historical accident databases to acquire the probability of disasters. A typical example was conducted by the World Association for Waterborne transport, Navigation, Ports, and Waterways (PIANC) to derive the probability of bridge collision by ships [15]. The accident rates were obtained by dividing the number of accidents by the total number of ship passages. An international database becomes a valuable source for statistics. Collisions for each year between 1960 and 1995 and collision rates were collected. These statistics show that human error is the main cause of collisions.  
The causes of the collisions are also derived from statistical analysis, and it was found that the causes of collisions can be divided into three main groups: human error (approximately 64%), technical failure (21%), and extreme circumstances (15%) [16]. Human error is the main cause of ship position aberrancy. However, collisions often stem from a combination of human error, technical failure, and extreme circumstances.  
The advantage of the field of statistics is that it is easy to understand and simple to apply. However, the disadvantage is that consistent databases are not always available, as small accidents are not always recorded, and the reports may not mention every useful detail of the accidents. Even if the historical data is available, this simple and direct model may not reflect what could happen in the future with different conditions. This is because the rules and the design of the bridges and ships navigating underneath are different.  
The human factor is so complex that it is not adequately taken into consideration in the existing models for risk analysis. There are studies that try to interpret human factors statistically, as an element in risk analyses. The human element is studied in collision events [17], maneuvering behavior [18], human performance with different environmental conditions [19], and ship operation [20; 21].
# A Traceable and Verifiable Tobacco Products Logistics System with GPS and RFID Technologies
## 3 The Proposed Scheme
### Logistics Phase
When LG arrives at the RCP location, LG starts communication and sends the batch of tobacco products to RCP. First, LG selects a random number \(k_{9}\) and generates a message with a list of TID:  
\[h_{SHP_{1}}=H(M_{7}) \tag{61}\]8  
LG calculates the hash value and executes the function \"Sign\" in Algorithm 2 to generate the signature:  
\[h_{SHP_{1}}=H(M_{7}) \tag{61}\]9  
\[(r_{SHP_{1}},s_{SHP_{1}})=Sign(h_{SHP_{1}},k_{7},d_{SHP}) \tag{62}\]0  
A message is encrypted by the RCP's public key:  
\[(r_{SHP_{1}},s_{SHP_{1}})=Sign(h_{SHP_{1}},k_{7},d_{SHP}) \tag{62}\]1  
Then, LG executes chaincode \"Shipping\", as shown in Algorithm 4. Next, LG sends the message \((ID_{LG},ID_{RCP},C_{LG_{2}},(r_{LG_{2}},s_{LG_{2}}))\) to RCP. 1. RCP receives the message at \(T_{18}\), then decrypts the cipher message by its private key:  
\[(r_{SHP_{1}},s_{SHP_{1}})=Sign(h_{SHP_{1}},k_{7},d_{SHP}) \tag{62}\]2Then, RCP checks for the validation of the timestamp:  
\[(r_{SHP_{1}},s_{SHP_{1}})=Sign(h_{SHP_{1}},k_{7},d_{SHP}) \tag{62}\]3  
Next, RCP calculates the hash value and executes the function \"Verify\" in Algorithm 2 to validate the signature:  
\[(r_{SHP_{1}},s_{SHP_{1}})=Sign(h_{SHP_{1}},k_{7},d_{SHP}) \tag{62}\]4  
\[(r_{SHP_{1}},s_{SHP_{1}})=Sign(h_{SHP_{1}},k_{7},d_{SHP}) \tag{62}\]5  
If the signature is valid, RCP uses MR to trigger a chaincode \"Receiving\" to scan and check that \(List<TID>\) is equal to the actual tobacco products, as shown in Algorithm 4. If the batch of tobacco products has no problem, then RCP sends a response message to LG. RCP selects a random number \(k_{10}\) and generates a message:  
\[(r_{SHP_{1}},s_{SHP_{1}})=Sign(h_{SHP_{1}},k_{7},d_{SHP}) \tag{62}\]6  
Next, RCP calculates the hash value and executes the function \"Sign\" to generate the signatures:  
\[(r_{SHP_{1}},s_{SHP_{1}})=Sign(h_{SHP_{1}},k_{7},d_{SHP}) \tag{62}\]7  
\[(r_{SHP_{1}},s_{SHP_{1}})=Sign(h_{SHP_{1}},k_{7},d_{SHP}) \tag{62}\]8  
A response message is encrypted with the LG's public key:  
\[(r_{SHP_{1}},s_{SHP_{1}})=Sign(h_{SHP_{1}},k_{7},d_{SHP}) \tag{62}\]9  
Then, the RCP sends the message \((ID_{RCP},ID_{LG},C_{RCP_{1}},({r_{RCP_{1}}},{s_{RCP_{1}}}))\) to LG. 1. LG receives the message, then uses its private key to decrypt the cipher message:  
\[C_{SHP_{1}}=E_{Puk_{LG}}(M_{7}) \tag{63}\]0  
Then, LG checks for the validation of the timestamp:  
\[C_{SHP_{1}}=E_{Puk_{LG}}(M_{7}) \tag{63}\]1  
If the timestamp is valid, LG calculates the hash value and executes the function \"Verify\" to validate the received signatures:  
\[C_{SHP_{1}}=E_{Puk_{LG}}(M_{7}) \tag{63}\]2  
\[C_{SHP_{1}}=E_{Puk_{LG}}(M_{7}) \tag{63}\]3  
If the signature is valid, then a round of shipping from the SHP to RCP is done.
# Multi-Sensor GA-BP Algorithm Based Gearbox Fault Diagnosis
## 2 Fundamental Theories
### Time-Frequency Domain Feature Extraction  
In terms of time-domain and frequency-domain features, common features: root mean square, root square amplitude, absolute mean, skewness, kurtosis, variance, maximum value, minimum value; barycentric frequency, mean square frequency, the frequency variance were mainly select.  
In the time-frequency-domain feature analysis, the wavelet packet decomposition method can decompose the signal in a full frequency band and at multiple levels. It can make up for the shortcomings that wavelets cannot decompose low-frequency signals, and decompose high-frequency signals at a higher level, thus improving the decomposition rate of the entire signal frequency band. Therefore, the wavelet packet decomposition method is also widely used in the field of fault diagnosis. Wavelet packet signal decomposition diagram, as shown in Figure 2[20]. Furthermore, the decomposed wavelet packet energy ratio was used as the time-frequency domain characteristic index. It is worth noting that the present study adopted three layers of wavelet packet decomposition. The function is db2.  
The wavelet packet is calculated as follows,  
\[\begin{array}{l}d_{i,j,2m}=\sum\limits_{k}h(k-2i)d_{k,j+1,m}\\ d_{i,j,2m+1}=\sum\limits_{k}g(k-2i)d_{k,j+1,m}\end{array} \tag{1}\]  
Figure 1: Multi-sensor decision-level fusion.  
Figure 2: Wavelet Packet Signal Decomposition Diagram.  
The wavelet packet reconstruction is calculated as follows,  
\[d_{i,j+1,m}=\sum_{k}h(i-2k)d_{k,j,2m}+\sum_{k}g(i-2k)d_{i,j,2m+1} \tag{2}\]  
where, \(d_{i,j,m}\) is the \(i\) wavelet packet coefficient of the \(m\) node of \(j\) the layer; \(h(k)\) and \(g(k)\) are the low-pass and high-pass filter coefficients in the filter.  
The energy \(E_{i,j}\) on the different frequency bands is calculated as,  
\[E_{i,j}=\sum_{k=1}^{N}\left|d_{i,j(k)}\right|^{2},j=0,1,2,\cdots 2^{i}-1 \tag{3}\]  
The wavelet packet energy ratio \(P_{i,j}\) is calculated as follows,  
\[P_{i,j}=\frac{E_{i,j}}{\sum\limits_{j=0}^{2^{i}-1}E_{i,j}} \tag{4}\]
## 2 Precise MGEX Orbit and Clock Products
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Item** & & **CODE** & **ESA** & **GFZ** & **CNES/CLS** & **JAXA** & **SHAO** & **TUM** & **WHU** \\ \hline \multirow{3}{*}{Differencing} & Orbit & DD 1 & UD & UD & UD & UD & UD & UD & UD \\  & Clock & UD 2 & UD & UD & UD & UD & UD & UD & UD \\  & Galileo & E1/E5a & E1/E5a & E1/E5a & E1/E5a & / & E1/E5a & E1/E5a & E1/E5a & E1/E5a \\ \multirow{3}{*}{Frequencies} & BDS & B1/B2 & B1/B3 & B1/B2 & / & / & B1/B3 & / & B1/B3 \\  & QZSS & L1/L2 & L1/L2 & L1/L2 & / & L1/L2 & / & L1/L5 & L1/L2 \\ \multirow{3}{*}{Elevation cutoff} & Orbit & 3\({}^{\circ}\) & 10\({}^{\circ}\) & 7\({}^{\circ}\) & 8\({}^{\circ}\) & 10\({}^{\circ}\) & 7\({}^{\circ}\) & 5\({}^{\circ}\) & 7\({}^{\circ}\) \\  & Clock & 5\({}^{\circ}\) & 10\({}^{\circ}\) & 7\({}^{\circ}\) & 8\({}^{\circ}\) & 10\({}^{\circ}\) & 7\({}^{\circ}\) & / & 7\({}^{\circ}\) \\ Arc length & / & 3 d & 1 d & 3 d & 30 h & 7 d & 3 d & 3 d & 1 d \\ \hline \hline \end{tabular}  
* 1 DD stands for double differenced. 2 UD stands for un-differenced.  
\end{table} 
Table 2: Comparison of the processing strategies of MGEX ACs (as of November 2019). Figure 1: Availability of MGEX products provided by different ACs for BDS, Galileo and QZSS as of November 2019.