esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Mathematical Model for Drawing a Hierarchical Hypergraph with Orthogonal Hyperedges and Ports
Hence, one has to ensure a minimum distance between the horizontal positions of the port vertices connected to these segments. The following conditions ensure the absence of non-feasible overlaps of hyperedge segments:\[\left|X_{u}-X_{v}\right|\geq M\times HO_{c_{1},\rho_{2}}+\theta(e_{1},e_{2})\] \[\forall\ e_{1}=(S_{1},T_{1}),\ e_{2}=(S_{2},T_{2})\in E_{H^{\prime} }:e_{1}\prec e_{2} \tag{16}\] \[\forall\ u\in S_{1}\,,\quad\forall\ v\in T_{2}\,.\] \[\left|X_{u}-X_{v}\right|\geq M\times(1-HO_{c_{1},e_{2}})+\theta( e_{1},e_{2})\] \[\forall\ e_{1}=(S_{1},T_{1}),e_{2}=(S_{2},T_{2})\in E_{H^{\prime} }:e_{1}\prec e_{2},\] (17) \[\forall\ u\in T_{1}\,,\quad\forall\ v\in S_{2}\,.\]  
The transitivity condition is to be satisfied for the positions of the horizontal segments of any triplet of hyperedges:  
\[ \begin{split} 0\leq HO_{c_{1},e_{2}}-HO_{c_{1},e_{3}}+HO_{c_{2},e_{3}} \leq 1\\ \forall\ e_{1},\ e_{2},\ e_{3}\in E_{H^{\prime}}:e_{1}\prec e_{2 }\prec e_{3}\,.\end{split}  \tag{18}\]  
Finally, we determine the domains for all of the variables in the problem:  
\[X_{u}\geq 0\quad\forall\ u\in V^{\prime}\quad\text{and}\quad LMX_{e},\ RMX_{e}\in \mathbb{R}\quad\forall\ e\in E_{H^{\prime}}\,. \tag{19}\]  
\[HO_{c_{1},e_{2}},\ UC_{c_{1},e_{2}},\ LC_{c_{1},e_{2}}\in\{0,\,1\}\quad\forall \ e_{1},\ e_{2}\in E_{H^{\prime}}:e_{1}\prec e_{2}\,. \tag{20}\]  
\[AC_{e,u}\in\{0,\,1\}\quad\forall\ e=S,T\in E_{H^{\prime}},\ \forall\ u\in V^{ \prime}:\exists\ v\in S\cup T,\ \lambda^{\prime}(u)=\lambda^{\prime}(v)\,. \tag{21}\]  
The standard linearization procedure for nonlinear expressions (6)-(9), (11), (16), and (17) allows one to obtain a multi-objective mixed-integer program (5)-(21). Figure 9 illustrates an example of the optimal layout of a hypergraph that was obtained on the basis of the model discussed above. Two additional post-processing steps are required for an optimal hypergraph layout: first, all dummy vertices must be rendered as points, and second, all subsets of the port vertices corresponding to a generated vertex must be merged back into one vertex.
## 4 Proposed Solution  
As mentioned earlier, while applying network slicing to heterogeneous networks with multiple domains, hierarchical SDN controller architecture is largely preferred. In such cases, different SDN controllers, each spanning a different domain, are needed to synchronize with the root controller to preserve the consistency and reliability within the network as well as to further utilize the benefits of edge enabled network slicing mechanism. In this respect, despite various proposals on how to realize edge enabled network slicing, most of them overlooked the question of how exactly controllers should synchronize with each other and assumed that the logically centralized network view somehow existed.  
Motivated by this idea and the benefits of ML, we propose a synchronization method for hierarchically distributed SDN controllers using RL aiming to improve the decisions of controllers on slice life-cycles, resource management, routing paths, and offloading mechanisms, towards more effective edge-enabled network slicing. In this respect, there are two main reasons why we believe that RL is a good candidate for the controller synchronization problem. The first reason is that, in wireless networks where several applications with human involvement exist, it is almost impossible to find labelled data for training the ML algorithms, whereas unlabelled data are often abundant and easily available [62]. Secondly, optimizing the synchronization process for heterogeneous networks is indeed a long-term decision that is affected by multiple conditions. Such problems are considered decision-making tasks where RL offers fast near-optimal solutions; this is also validated by other research in the literature [63, 64].  
Although there are a few existing works related to our research question, our solution differs from them in the following ways [65, 66]: (i) As opposed to existing works where only some of the controllers are being synchronized at each time, our solution aims to synchronize all controllers at once. By doing that, we are expecting to have lower run time complexities as well as lower energy consumption in the long run compared to the partial synchronization method. (ii) Previous works assumed that the synchronization times are given. Contrarily, in our study, the more realistic case of detecting the synchronization times as well as the frequency is going to be explored.  
An example system architecture is presented in Figure 3. In particular, the data that we are going to use in our RL solution are the number of users and devices, mobility of users, link quality, CPU load, and memory usage of each edge server. During implementation, we are also aiming to address several issues such as dependencies among different slices and resources and the security of individual controllers, as well as edge cases such as the procedures that we are going to apply in case of a main controller failure.
## 3 Materials and Methods
### Ablation Study of the Proposed Model (OLSTM)  
We performed four experiments as part of an ablation investigation, by altering different parts of the suggested improved LSTM model. It is feasible to produce a more reliable design with increased classification accuracy by altering different components. Changes were made to the LSTM layers, dense layers, dropout layers, activation function, kernel initializer, and optimizer during the ablation investigation.
## 3 Results and Discussion
Typically high values of this index were calculated for the P18 piezometer. It is surprising, however, that the value of the EF index in the P19A piezometer was higher than in P18 in 2010. Another surprising result is the higher HF value in the P17 piezometer than in P17A. Chlorides had a large share of the increased value of the index for the P17 piezometer in 2021. Chlorides contributed approximately 50% to the final index value. Another component that increases the values of this index for most parameters is the ammonium ion. The enrichment factor has mainly been used for soil contamination [64; 65; 66]. For groundwater, it was used in one study [67]. The values of this indicator ranged from \(-61.2\) to \(43.42\), suggesting a low risk. The index values for a single component in this article exceeded 4000. It is not possible to compare the obtained values of this indicator with that of other groundwater in the area of landfills in Poland, because it was only used to assess the quality of sediments. The health risk assessment is one of the most important elements in the risk assessment in the vicinity of landfills. The Hazard Index (HI) is an effective tool for calculating the non-carcinogenic health risk in different intake forms [60]. The results calculated for non-carcinogenic health risks for people in the study area indicate the highest risk in the event of consumption of water from the area of the P18 piezometer and piezometers collecting water from the lower part of the aquifer (P17A and P19A), as well as from the area of the P10 piezometer (Figure 7). It is worth noting that this index was calculated without taking into account sulphates or chlorides. In this situation, the high values of the index were mainly determined by the concentrations of ammonium, iron, and cadmium. For example, these three parameters constitute up to 99.9% of the index value in the P10 piezometer. The ammonium ion caused 99.97% of the high value of the indicator for the P18 piezometer. This proves that there is little risk from metals in this area. HQ indices and the total value of indices (HI) have been used many times in various research centers [68; 69; 70; 38; 71]. The HQ indices varied widely, from about 0.001 to about 30 [72]. The authors identified a high risk of contamination with lead and copper. The total valuesof the indicator reached about 90. These values were definitely lower than those obtained in the area of the described landfill in Tychy. Much more often, health risk assessment is performed based on the quality of water or the emission of pollutants generated from waste. In Poland, a human health risk assessment was carried out in the vicinity of landfills, but it was a study based on the measurement of atmospheric pollution by gases generated as a result of a waste fire [73]. In addition, an assessment of human health was also carried out on the basis of data on the quality of groundwater, but in selected cities [74]. Health was also assessed on the basis of microbiological risk, e.g., in the work of [PERSON] et al. [75].
# Accuracy of Extraoral Digital Impressions with Multi-Unit Implants
## 4 Discussion
In IOS, the larger the area to scan, the more images must be overlapped, accumulating distortions of the generated area. Laboratory scanners do not reveal this pattern since large parts of the impression are simultaneously captured, minimizing the effect of error [20]. Furthermore, it is difficult to acquire accurate scans due to narrow and deep shapes that may be hidden in the impressions [8]. However, in impressions from completely edentulous patients, there are no deep surfaces, which increases the scan accuracy potential [27]. Also, screwing the ScanAnalog into the coping might be easier in edentulous arches. In addition to accuracy, there are some limitations for a complete digital workflow in full-arch implant rehabilitation which are mostly related to digital facebows and the virtual articulation of the casts [20]. One of the limitations of this study is the use of an antireflective spray, which may increase discrepancies in ScanBodies and ScanAnalogs scanning. Another limitation of our study is the use of a reference model designed with parallel multiunits of the same brand, given that the results could be different if some or all of them had very subgingival angulations or positions. However, it should be noted that in full-arch impressions, the appropriate selection of the abutment often allows for the correction of the most unfavorable situations [24]. In addition, further in vivo research is required. The use of rotational ScanBodies in this investigation does not allow one to extrapolate the results in terms of accuracy for single rehabilitations. This was limited by the fact that the brand of the implants used did not present a non-rotational digital library for the multiunits used since their indication is for non-unitary clinical situations. Further investigations with non-rotation ScanBodies may increase clinical indications for the techniques used in our study. Also, the potential wear on scanBodies and scanAnalogs due to repeated tightening may affect the accuracy [20]. In our study, we changed these components every five uses; however, this parameter was not assessed in this investigation. Taking into account that for long-span scanning, the IOS cannot achieve the necessary accuracy for implant rehabilitation, more studies on the digitization of conventional impressions should be carried out, especially for trans-arch implants. In the future, clinical decision making between IOS and scanning impressions should be based on several aspects, such as number of implants or the distances between implants. These promising results allow for the execution of new investigations into the impact of discrepancies found in the passivity of structures in implant-supported prostheses. More studies are needed with respect to the complete CAD-CAM process.
# Fake Base Station Detection and Link Routing Defense +
## 5 Our Scheme
### Our Link Routing Scheme for Active Defense  
We design the link routing part of our scheme as an active defense to recover the user equipment from the fake base station after it builds awareness from the detection discussed previously in Section 5.1.
## 3 Results
### Comparison of Computational Complexity Between Optimization Algorithm and Traditional Algorithm  
The optimization algorithm utilizes a particle swarm algorithm to calculate the optimal solution for the length and number of queues in the output ports of the onboard switch, iterating over all possible combinations of queue lengths and numbers. As can be seen in Figure 12, compared to the traditional traversal algorithm, the traversal algorithm needs to calculate all 1200 times to determine the optimal result, while the PSO-QSO mechanism only needs to iterate 105 times to obtain the optimal result. With a time-monitoring program, it takes 6.20 ms for the traversal algorithm to calculate all 1200 combinations, and 0.55 ms for the PSO algorithm to calculate 105 times. The time required for the PSO-QSO mechanism to obtain the optimal solution is only 8.9% of the time required by the traversal algorithm. Therefore, the optimization algorithm has a lower computational complexity and computational overhead.  
As shown in Figure 12, there is no improvement in the fitness function for up to 30-40 iterations. These are the initial iterations of the PSO algorithm. In the initial iterations, the particles are exploring the search space widely. The random initialization of particle positions and velocities ensures that the search space is explored from multiple starting points. During this phase, the particles are moving in different directions, and this can lead to periods where the global best position _gbest_ does not change significantly. It is common for the fitness function to show little to no improvement for 30-40 iterations.  
The number of particles determines the extent of the coverage of the search space. Increasing the number of particles allows the algorithm to explore the solution space more comprehensively, thereby enhancing the global search capability and increasing the probability of finding the global optimal solution, which is particularly important for complex optimization problems. However, more particles mean more information needs to be exchanged and processed, which reduces the local search efficiency of the algorithm as it approaches the optimal solution, leading to a slower convergence rate. The number of iterations and time required to find the optimal solution will also increase. In considering that the application scenario of the PSO algorithm in this paper is a two-dimensional scenario, the number of particles \(NP\) was set to 20 in this study.  
Figure 12: Comparison of computational complexity between PSO algorithm and traversal algorithm.
# Comparison of the Sentinel-3A and B SLSTR Tandem Phase Data Using Metrological Principles
## 2 Materials and Methods
### Overview of Methodology  
Despite the small time-delay between S3A and B during the tandem phase, pixel-level inter-comparison of co-registered SLSTR-A and B L1 scenes shows that large match-up errors can dominate the observed sensor-to-sensor differences. Such errors are caused by a combination of effects such as geolocation differences, pixel footprint differences, and changes between scenes caused, for example, by cloud movement. These differences affect the L1 data in particular since these scenes are more highly variable than the approximately cloud-free, relatively smoothly varying SST data. An example of this at L1 is shown in Figure 1, where the small radiometric differences found in homogeneous areas are dominated by large differences of up to several kelvin in inhomogeneous areas. The fringing in the difference image is the effect of the nearest-neighbour regridding from the instrument viewing geometry to the image geometry during the L1 ground processing.  
For this reason, for the L1 data, comparing a larger region of binned pixels can be preferable, since match-up errors will tend to cancel out. An efficient way to aggregate L1 pixels into larger regions that facilitates a global comparison (enabled by sensors flying in tandem) is to grid the radiometry data onto a regular latitude-longitude grid (often called a Level 3 grid). Match-up errors are further minimised by then filtering for homogeneous grid cells, allowing a more direct comparison of the remaining radiometric biases (described in Section 2.2.2).  
L1 products were therefore gridded into 0.5\({}^{\circ}\times\) 0.5\({}^{\circ}\) grid cells, chosen to balance data volume and match-up error reduction with obtaining a sufficient number of comparison samples to allow statistically robust conclusions across the sensor dynamic range. For the SST data, where we do not expect the same level of spatial variability when compared to the L1 data, the same gridding algorithm was used but on a finer grid of 1 km size (the nominal sub-satellite resolution). Furthermore, only pixels with a \(30\pm 1\) s time difference between sensors were kept, so, for the SST data, this in general means a single observation only.
## 5 Smart-BEEM For IoT Systems in 5G Scenarios
### Smart-BEEM Algorithm Analysis  
Our former work BEEM is focusing on CH election to construct the structure for the inter-clustering communication. It elects CHs not only based on the residual energy level, but also the node density. Through this algorithm, not only the power consumption will be reduced, but also the coverage of the network can be maintained longer. However, BEEM has not specified the CH selection scheme. A Node will just choose to join the nearest CH.  
Based on BEEM, Smart-BEEM proposes a CH selection by adapting to MIMO features for intra-cluster communication. Based on the communication features and requirements, each sensor will have its own preference on the network access interfaces. Firstly, a node should fulfil its responsibilities and obligations in the network. If it is supposed to transmit _Video_ and then it should select an interface that has high bandwidth. On the other hand, if it is designed to transmit _Data_, it can have a larger range of selections for network interfaces. Meanwhile, the nodes also should reduce energy consumption and hence extend coverage sensitive longevity further comparing with BEEM. Hence low power consumption communication interfaces should always be prioritised when QoE is guaranteed. However, three factors should be considered before the nodes makes the final decision: (1) Application requirements on the network. (2) Transmission range of the access interface. (3) Distance between the nodes and CHs. The node itself can have its own preference on the network interfaces even only concerning its own characteristics. In this case, we refer this scenario as self-concerned approach. However, in order to select a suitable CH, the context of the CHs also should be considered. For example, considering its own interest, a node prefers to use Zigbee to transmit data. However, in its Zigbee communication range, no CHs are available. Therefore, this node has to select the secondary choice for interfaces, which has longer communication range. In another case, this node finds a CH in its Zigbee communication range. However, considering distance, the energy cost for using Zigbee is even higher than that of using NB-LTE (This might be an extreme case). At the end, NB-LTE overall  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
\begin{tabular}{c} **Communication** \\ **Interface** \\ \end{tabular} & **CH\({}_{1}\)** & **CH\({}_{2}\)** & **...** & **CH\({}_{m}\)** \\ \hline NAI\({}_{1}\) & QoE\({}_{1,1}\) & QoE\({}_{1,2}\) &... & QoE\({}_{1,m}\) \\ NAI\({}_{2}\) & QoE\({}_{2,1}\) & QoE\({}_{2,2}\) &... & QoE\({}_{2,m}\) \\... &... &... &... &... \\ NAI\({}_{n}\) & QoE\({}_{n,1}\) & QoE\({}_{n,2}\) &... & QoE\({}_{m,m}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Communication Table for Node \(x\).  
may be a better choice than Zigbee. This algorithm aims to make decisions based on the requirements from the nodes themselves and the context of the network.
## 4 Mathematical Formulation
### Constraints  
#### 4.1.1 Train Arrival and Departure Times  
The arrival time of the boundary train at the origin station is a given constant \(a_{1i},\forall i=I-2n+1,\ldots,I\). Other trains have the same headway as their adjacent stopping trains at their origin station \(s^{o}_{l_{si}}\), as shown in Figure 8. For trains starting at station 1, the headways and arrival times are calculated using (3) and (4), as shown in Figure 8. Other short-turning trains are calculated using (5) and (6), where \(J_{sl}\) and \(J_{sl}\) are the adjacent stopping trains with different train types. The arrival and departure times of the trains at other stations, i.e., not the origin station, are calculated using (7) and (8).  
\[h_{si}=\frac{a_{s,I+n+1}-a_{s,I+n}}{1+\sum_{j\leq I}\tau_{s,I_{j}}},\forall i \leq I,s=1 \tag{3}\]  
\[a_{s,I_{si}}=a_{s,I_{si}-1}+\tau_{s,I_{si}}h_{si},\forall i\leq I,s=1 \tag{4}\]  
\[h_{si}=\frac{a_{s,I_{sl}}-a_{s,I_{si}}}{1+\sum_{i<j<i}\tau_{s,I_{si}}x_{s,I_{j}} },\forall i\leq I,s=s^{o}_{l_{si}}\
eq 1 \tag{5}\]  
\[a_{s,I_{si}}=a_{s,I_{si}}+\sum_{i<j\leq i}\tau_{s,I_{si}}x_{s,I_{j}}h_{si}, \forall i\leq I,s=s^{o}_{I_{si}}\
eq 1 \tag{6}\]  
\[d_{s,I_{si}}=a_{s,I_{si}}+t^{(s)}_{s,I_{si}},\forall s\in\mathcal{S},i\leq I+2n \tag{7}\]  
\[t^{(s)}_{s,I_{si}}=x_{s,I_{si}}\Big{(}t^{(s)}_{s,I_{si}}+t^{(s)}_{s,I_{si}} \Big{)},\forall s\in\mathcal{S},i\leq I+2n \tag{8}\]  
\[a_{s+1,I_{si}}=d_{s,I_{si}}+t^{(r)}_{s,I_{si}},\forall s\in\mathcal{S}\backslash \Big{\{}s^{o}_{I_{si}}\Big{\}},i\leq I+2n \tag{9}\]  
\[t^{(r)}_{s,I_{si}}=t^{(r*)}_{s,I_{si}}+x_{s,I_{si}}t^{(0)}+x_{s+1,I_{si}}t^{(1 )},\forall s\in\mathcal{S},i\leq I+2n \tag{10}\]