esa-sceva/satcom-chunk-collection huggingface dataset:
# Stochastic Safety Radius on UPGMA
## 3 Probability on the Three Point Condition  
From Equation (1), we have the _three point condition_ which is defined below: for all distinct leaves \(i,j,k\in X\) we have  
\[d_{ij} \leq d_{ik} \tag{3}\] \[d_{ij} \leq d_{jk}\]  
and, by Theorem 5, if \(d\) is an ultrametric and is a tree metric of an equidistant tree \(T\), then Equation (3) satisfies for all distinct leaves \(i,j,k\in X\).  
Suppose a subtree of \(T\) is a tree shown in Figure 3. Then we have the following:  
\[d_{ij} = e_{i}+e_{j}, \tag{4}\] \[d_{ik} = e_{i}+e_{k}+w,\] \[d_{jk} = e_{j}+e_{k}+w.\]  
In addition, from Equation (4), we have  
\[\delta_{ij} = e_{i}+e_{j}+\epsilon_{ij}, \tag{5}\] \[\delta_{ik} = e_{i}+e_{k}+w+\epsilon_{ik},\] \[\delta_{jk} = e_{j}+e_{k}+w+\epsilon_{jk}.\]  
Therefore, by Equation (5) and Equation (4), we have the following: for all distinct leaves \(i,j,k\in X\) we have  
\[e_{i}+e_{j}+e_{ij} \leq e_{i}+e_{k}+w+\epsilon_{ik} \tag{6}\] \[e_{i}+e_{j}+\epsilon_{ij} \leq e_{j}+e_{k}+w+\epsilon_{jk}.\]  
Figure 3: Equidistant tree with three leaves on labels \(X=\{i,j,k\}\). \(w,e_{i},e_{j},e_{k}>0\) are branch lengths.  
Then we have  
\[e_{j}+w+e_{ij} \leq e_{k}+2w+e_{ik} \tag{7}\] \[e_{i}+w+e_{ij} \leq e_{k}+2w+e_{jk}.\]  
Since \(e_{i}+w=w_{k}\) and \(e_{j}+w=w_{k}\), we have  
\[\epsilon_{ij} \leq 2w+e_{ik} \tag{8}\] \[\epsilon_{ij} \leq 2w+e_{jk}.\]  
Therefore, we have  
\[\epsilon_{ij}-\epsilon_{ik} \leq 2w \tag{9}\] \[\epsilon_{ij}-\epsilon_{jk} \leq 2w.\]  
Since \(\epsilon_{ij},\epsilon_{ik},\epsilon_{jk}\) are independently and identically distributed (i.i.d.) from the normal distribution \(N(0,\sigma)\), \(e_{ij}-\epsilon_{ik}\) and \(e_{ij}-e_{jk}\) are i.i.d. from the normal distribution \(N(0,2\sigma)\). Therefore, we have  
\[P(\min\{\epsilon_{ij}-\epsilon_{ik}\}\leq 2w) \text{for all }i,j,k\in X\] \[= 1-P(\min\{\epsilon_{ij}-\epsilon_{ik}\}>2w) \text{for all }i,j,k\in X\] \[= 1-P(\frac{\min\{e_{ij}-\epsilon_{ik}\}}{2}>w) \text{for all }i,j,k\in X\] \[= 1-P(\frac{\epsilon}{2}>w)^{(3)}_{(3)} \text{where }e^{\prime}\sim N(0,2\sigma)\] \[= 1-P(\epsilon>w)^{(3)}_{(3)} \text{where }\epsilon\sim N(0,\sigma)\] \[= 1-P(\frac{\epsilon}{w}>1)^{(n)}_{(3)} \text{where }\epsilon\sim N(0,\sigma)\] \[= 1-P(\epsilon>1)^{(3)}_{(3)} \text{where }\epsilon\sim N\Big{(}0,\frac{\sigma}{w}\Big{)}.\]  
Let \(w=w_{\min}\) where \(w_{\min}\) is the smallest branch length for an internal edge in an equidistant tree \(T\) on leaves \(X\). Then we have  
\[P(M(\delta)=T)\geq 1-P(\epsilon>1)^{(n)}_{(3)},\]  
where \(\epsilon\sim N(0,\frac{\sigma}{w_{\min}})\). Let \(\sigma=\frac{c^{2}}{\log(n)}\) for \(c>0\) and \(\eta=P(\epsilon>1)^{(\frac{n}{3})}\). Let \(c=s\cdot w_{\min}\). Then we have  
\[\left(\frac{\sigma}{w_{\min}}\right)=\left(\frac{s^{2}\cdot w_{\min}}{\log(n) }\right)<\left(\frac{s^{2}}{\log(n)}\right)\]  
by Remark 8.
# Pyramid Spatial-Temporal Graph Transformer for Skeleton-Based Action Recognition
## 4 Experiments
### Datasets  
**NTU-RGBD 60**.The NTU-RGBD 60 dataset [40] is a widely used skeleton-based action recognition dataset consisting of 56,880 samples divided into 60 categories. These samples were performed by 40 different persons and captured by 3 cameras to ensure the diversity of the actions. Each sample comprised 25 joints of humans, which were the 3D coordinates specifically. The evaluation of this dataset included both the cross-view (CV) benchmark and the cross-subject (CS) benchmark. They verified the diversity of the actions by the model under different viewpoints and by different characters. For the CV benchmark, the training data came from camera 2 and 3, and the testing data came from camera 1. For the CS benchmark, the training data were from 20 subjects, and the testing data were from the other 20 subjects.  
**NTU-RGBD 120**. The NTU-RGBD 120 dataset [41] is a large 3D skeleton dataset for human action recognition which is an extension of the NTU-RGBD 60 dataset. This version has 113,945 skeleton clips categorized into 120 classes. These actions are performed by 106 persons captured by 3 cameras as well. The validation benchmarks also have two methods: cross-subject (X-sub) and cross-set-up (X-set). The training data came from 53 subjects, and the testing data came from the other 53 subjects for the X-sub benchmark. For the X-set benchmark, the training data were from samples with even collector set-up IDs, and the testing data were from samples with odd IDs.  
**Northwestern-UCLA**. The Northwestern-UCLA dataset [42] is a popular skeleton dataset captured by Kinect cameras. The actions are divided into 10 classes for 1494 skeleton sequences. Concretely, the actions were performed by 10 different subjects. The evaluation set-ups were similar to the cross-view benchmark of the NTU-RGBD 60 dataset. The training data were captured by cameras 1 and 2, and the testing data were from camera 3.
## 4 Implementation Method for Improving Accuracy
### Correction of Sampled Value  
The actual sampled voltage value shows a certain deviation from the expected value. The red sampled point in Figure 6 shows that the exponential function curve cannot be formed. The result calculated by the sampled value must be a large error. Therefore, to obtain satisfactory results, the sampled values must be corrected with a loop iterative correction method. \(\phi_{11\_1}(i)\),\(\phi_{11\_2}(i)\),\(\phi_{11\_3}(i)\),\(\phi_{12\_1}(i)\),\(\phi_{12\_1}(i)\),\(\phi_{12\_3}(i)\),\(\phi_{21\_1}(i)\),\(\phi_{21\_3}(i)\),\(\phi_{21\_1}(i)\),\(\phi_{21\_3}(i)\),\(\phi_{22\_1}(i)\), and \(\widetilde{v}_{22\_3}(i)\) are set as the \(i\)th correction voltage values. After the 12 voltages of \(v_{11}\), \(v_{12}\), \(v_{21}\), and \(v_{22}\) are sampled completely, the counter is set as \(i=0\). The 12 voltage values are substituted into the following equation, and the sampled value is used as the initial correction value.  
\[\left\{\begin{array}{l}\hat{v}_{11\_1}(0)=v_{11\_1}\\ \hat{v}_{11\_2}(0)=v_{11\_2}\\ \hat{v}_{11\_3}(0)=v_{11\_3}\\ \end{array}\right.,\left\{\begin{array}{l}\hat{v}_{12\_1}(0)=v_{12\_1}\\ \hat{v}_{12\_2}(0)=v_{12\_2}\\ \hat{v}_{12\_3}(0)=v_{12\_3}\\ \end{array}\right.,\left\{\begin{array}{l}\hat{v}_{22\_1}(0)=v_{21\_1}\\ \hat{v}_{21\_2}(0)=v_{21\_2}\\ \hat{v}_{21\_3}(0)=v_{21\_3}\\ \end{array}\right.,\left\{\begin{array}{l}\hat{v}_{22\_1}(0)=v_{22\_1}\\ \hat{v}_{22\_2}(0)=v_{22\_2}\\ \hat{v}_{22\_3}(0)=v_{22\_3}\\ \end{array}\right., \tag{16}\]  
Figure 5: Waveform of the bridge voltage.
## 3 Results and Discussion
### Dosimetric Characterization
#### 3.2.8 Minimum Detectable Dose  
The minimum detectable dose or lowest detection limit is important in clinical, personal and environmental radiation dosimetry. The lowest detection limit is strongly influenced by the dosimeter composition, shape and size, as well as the TLD reader characteristics. The synthesized material was observed to detect doses as low as 6.16 mGy, which is comparable to previously reported studies, i.e., 0.01 mGy and 0.05 mGy [5; 11]. The difference between the minimum detectable doses could be attributed to the defect population, which strongly depends on the nature of the synthesized material, i.e., crystalline or amorphous.
# Spacing Allocation Method for Vehicular Platoon: A Cooperative Game Theory Approach
###### Abstract  
Recently, spacing policies of the vehicular platoon have been widely developed to enhance safety, traffic efficiency, and fuel consumption. However, the integrated spacing policies aim to maximum overall benefit, and the distributed spacing policies intense to get optimal monomer benefit. Ignoring the fairness of the benefit allocation of each vehicle will reduce the motivation to constitute the platoon. To fill this critical gap, this study proposes a spacing allocation method by treating spacing decisions as cooperative games. A flock's model which is used to be the payoff function is introduced based on bionic motion principles. We present a characteristic function of the platoon for the cooperative game model considering the specific structure of the platoon. The \(\tau\) value, Shapley value, and average lexicographic value are introduced and applied to allocate the spacing fairly. Proposed methods are compared with constant distance policy in some typical situations. The simulation results demonstrate that the spacing policy based on cooperative game theory improved the stable time for consistency control and the convergence of longitudinal following error.  
spacing allocation; platoon control; cooperative game theory; motion control +
Footnote †: journal: Applied Sciences
## 4 The Prediction Model When Signal Approaches the Ground Station (Section B)
### Developing the Predictive Model  
For the prediction method, a deep-learning (DL) algorithm was used, with the following steps:  
(1) Accept the training and experiment dataset.  
As mentioned, Table 2 is an example of the training and experiment dataset required as input for the predicting system. The label class in this case can be binary (e.g., +1 (if attenuation = 0), \(-1\) (if attenuation \(\
eq\) 0)).  
(2) Execute the prediction deep-learning algorithm.  
The following notation demonstrates the prediction procedure:  
\[X_{m\times n,d,t}\to Y_{m^{*}\times 1,d,t+\Delta t}\left(train\ file\right) \tag{6}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & **Time (min)** & \multirow{2}{*}{**Azimuth** **(deg)**} & **Elevation** & **Range** & **EIRP** & **Xmtr Gain (dB)** & **Xmtr EIRP** & **Atmos** & **Urban Terres** \\  & **2020 H-12** & & & & & & & & \\ \hline
1 & 18:20 & 79 & 5 & 2092 & -528.5 & -558.5 & 538.5 & 0.3663 & 2.33 \\ \hline
2 & 18:21 & 82 & 5.048 & 2088 & -528.3 & -588.3 &  
\[X_{\tilde{m}\times n,d^{+},d}\to Y_{\tilde{m}^{+}\times 1,d^{+},t+\Delta t}\ ( experiment\ file) \tag{7}\]  
\(X\) represents samples of satellite data, with matrices size \(m\times n\) produced at a specific date \(d\) and specific time \(t\) with class labels \(m^{*}\) produced for the same date \(d\) but with different time \(t+\Delta t\). The trained classifier classified the experiment samples (made from latterly date \(d^{*}\) and specific time \(t\)). Because the algorithm classifier labels for future times, it predicts satellite attenuation.  
Satellite data may vary according to days and time (h/min/sec). This section denotes by \(X_{m\times n,d,t}\) a dataset of size \(m\) with \(n\) features, collected on day \(d\) and at time (h/min/sec) \(t\) and, by \(Y_{m\times 1,d,t}\), the class labels associated \(X_{m\times n,d,t}\). Therefore, the prediction problem is given a dataset \(X_{m\times n,d,t}\) known for every time \(t\) to estimate \(Y_{\tilde{m}\times 1,d+\Delta d,t+\Delta t}\), where \(\Delta d\) and \(\Delta t\), respectively, define a variation of day and time (h/min/sec).  
The proposed estimation procedure then can be decomposed into four steps:  
Collect two samples of data, \(X_{m\times n,d,t}\), and \(X_{m\times n,d,t+\Delta t}\), \(\Delta t>0\);  
Compute the class labels \(Y_{m\times 1,d,t+\Delta t}\);  
Compute a new training set \(Z_{m\times n+1,d}\), using \(X_{m\times n,d,t}\), and \(Y_{m\times 1,d,t+\Delta t}\) by concatenation, that is \(Z_{m\times n+1,d}=[X_{m\times p,d,t};Y_{m\times 1,d,t+\Delta t}]\);  
Collect the test set \(X_{\tilde{m}\times n,d+\Delta d,t}\) (\(\Delta d>0\)) and compute \(Y_{\tilde{m}\times 1,d+\Delta d,t+\Delta t}\) using the machine-learning algorithm on \(Z_{m\times n+1,d}\) and \(X_{\tilde{m}\times n,d+\Delta d,t}\).
# Extraction of Periodic Terms in Satellite Clock Bias Based on Fourier Basis Pursuit Bandpass Filter
## 4 Experimental Analysis
### Time-Frequency Analysis of the BDS Satellite Clocks
effectively identified in the STFTs using rectangular, Hanning, or Blackman windows due to sidelobe interference and main-lobe broadening.
## 4 Discussion
### Characteristics of Fresh and Packed Nettle Leaves
#### 4.4.5 Phenolic Compounds
In addition, leafy vegetables, including nettle leaves, continue their respiration process after harvest, consuming O\({}_{2}\) and producing CO\({}_{2}\) and water in the packaging, while higher respiration rates can lead to the degradation of phenolic compounds as the plant tissue uses these compounds for its metabolic needs during storage [90]. One of the limiting factors during the storage period for the phenolic compounds can also be the transpiration rate, which leads to a loss of water in the plant material, causing the degradation of the cells and resulting in the loss of the phenolic compounds [92; 93]. Phenolics are a diverse group of bioactive compounds, susceptible to different environmental conditions, so storage and packaging conditions can affect the distribution of individual phenolic compounds differently. Several studies have investigated the phenolic profile of stinging nettle leaves, but since there is no research on nettle packaging, there is also no data on the influence of different packaging materials and the composition of gases during storage on the content of individual phenols in nettle leaves. The phenolic profile of nettle leaves determined in this study by analyzing fresh, unpackaged leaves corresponds with previous research [25; 26; 27; 94; 95; 96]. Caffeeoylmalic acid has already been established as the most dominant phenolic compound, followed by chlorogenic acid [95; 96], and the same findings were obtained in the present research both in fresh leaves and packed leaves during the storage period. The highest content of caffeoylmalic and chlorogenic acid was determined in nettle leaves packed in LDPE after 6 days and the lowest in PA/PE after 14 days of storage, the same as measured for total polyphenolic compounds. LDPE and BOPP used in this study had similar gas permeability, with relatively similar O\({}_{2}\) and CO\({}_{2}\) content during the storage period. During storage, the atmospheric conditions within those packages remained moderate with a gas composition that is desirable for the packaging of leafy vegetables [11], which consequently positively affected the final content of phenolic compounds. Specifically, the gas composition created in LDPE packages had a good impact on the preservation of caffeoylmalic and chlorogenic acid in nettle leaves during storage, while the gas ratios in PA/PE packages were too extreme due to excessive O\({}_{2}\) and CO\({}_{2}\) levels. The results of the research show that the type of packaging material and the length of storage also have a strong effect on other individual phenolic compounds, which were found in significantly lower amounts, with the potential to significantly slow down their deterioration.
# Research on Non-Contact and Non-Fixed Cable Force Measurement Based on Smartphone
## 3 Experiment and Validation  
A light-weight method for cable force determination using smartphone digital images has been proposed starting from the video data collection of cable vibration, imagery data processing for displacement detection and tracking to cable force estimation. In order to validate its feasibility and accuracy, two real-life cable-stayed bridge projects were used.
## 4 Results  
### Thin Section and SEM Analyses  
Core fragments F1 and F4 can both be classified as siltstones to fine-grained sandstones, and are heavily cemented. Hardly any porosity can be recognized on photomicrographs with plane polarized light (Figure 6A,C). Angular to sub-rounded grains of \(\sim\)50 \(\upmu\)m diameter can be seen; from visual inspection, these consist of \(\sim\)60% quartz, \(\sim\)10% potassium feldspar, \(\sim\)10% micas, and \(\sim\)20% clay minerals. Linear contact points between the quartz grains and bending within the micas suggest that this sediment has been moderately compacted. The abundant calcite cement, visible with cross polarized light (Figure 6B,D), suggests deposition as a calcite-rich mud, the primary calcite having re-crystallized, following burial, into the calcite cement. SEM analysis indicates the presence of kaolinite, muscovite, and illite clays (Figure 7).  
Thin sections indicate that fragment F3 is a medium grained feldspathic quartz arenite sandstone with fine (\(\sim\)125 \(\upmu\)m), angular to sub-rounded, well sorted grains (Figure 8A,B). Little to no cementing or clay mineralization is recognized, which explains the unconsolidated nature of this sample. Contacts between grains are dominantly linear and concave, suggesting moderate compaction. SEM images show that the few clay grains present are predominantly kaolinite, small amounts of chlorite, illite, and montmorillonite being also present (Figure 9A-D). A small amount of authigenic quartz was also observed (Figure 9B), which may be a side-product of the transformation of montmorillonite to smectite. This transformation produces silica in solution (e.g., [40]), which could be deposited as authigenic quartz and reduce porosity and permeability in the aquifer. The unconsolidated grains in this sample are most likely easily mobilized and could therefore clog pore space and reduce permeability.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Boundary Name** & **Type** & **Velocity Field** & **Pressure Field** \\ \hline Inlet & patch & fixed velocity & zero gradient \\ Outlet & patch & zero gradient & fixed pressure \\ Side & wall & slip & zero gradient \\ Walls & wall & no-slip & zero gradient \\ \hline \hline \end{tabular}
\end{table}
Table 4: Boundary conditions in numerical flow experiments.  
Figure 6: Photomicrographs of samples F1 and F4. (**A**) Sample F1 under plane polarized light. (**B**) Sample F1 under cross-polarized light. (**C**) Sample F4 under plane polarized light. (**D**) Sample F4 under cross-polarized light.  
Figure 7: SEM images of sample F4. (**A**) Wide, low-resolution view of part of this sample, showing diverse secondary mineralization. (**B**) Higher resolution image of a smaller part of the sample, showing secondary kaolinite.
## 4 Results and Discussion  
Performance Assessment: Using the NS-2 simulation tool, the suggested routing protocol's execution will be evaluated in relation to the network's lifetime and energy consumption.  
Energy Consumption: The suggested routing protocol would normalise all energy usage, which would be defined as the number of erroneous data that are placed in a network's overhead nodes for communication.  
\[Energy=Power\times Time\]  
Regarding the examination of energy efficiency implementation in Internet of Things devices, up to 100 nodes, the suggested system's energy efficiency will surpass that of the current system, giving the suggested algorithm the upper hand. In contrast, the suggested approach computes preventive measurements and assesses the network lifetime as a whole equally [19; 20].  
CH nodes with an average transmission data network are shown in Figure 4, which makes it evident that the data integrity was low. When there are a lot of CH nodes in a sensor network, the sensor will always be in bad condition because the sensor's lifetime will be shorter, data transmission will be slower, and energy dissipation will quickly cause a shortage in the network. Figures 5-7 determine the efficiency in allocating the sensor nodes and analysing the energy consumption and how to utilise the node, and determine the throughput and average delay for better performance [21; 22; 23; 24; 25].  
Figure 4: Different transmission data values.  
Figure 5: Average delay.  
Figure 6: Energy dissipation with different values.
## 5 Appendix: Optical Performances
### Calculated Transmittance  
The same type of calculation was performed for transmittance \(T\) on double-sided polished silicon substrates in the range of mid-IR, see Figure 11. In part A, a few examples of \(T\) against \(\lambda\) are given for three different coating thicknesses (30, 280, and 500 nm, red curves) and are compared to the transmittance of the bare substrate in blue. Obviously, the silicon substrate is opaque (\(T=0\)) below some \(\lambda\) which actually depends on its thickness, here \(\lambda\approx 1\) \(\upmu\)m for a 325 \(\upmu\)m thick substrate.  
Figure 11: **(A)**: Transmittance \(T\) calculated for a nanoporous CeO2 coatings of variable thickness \(h\) (red curves) deposited on a silicon substrate (blue curve). **(B)**: Transmittance excess \(\Delta T=T_{\text{Si+coat}}-T_{\text{Si}}\) as a function of wavelength and coating thickness \(h\).  
Figure 10: Reflectance \(R\) calculated for a nanoporous CeO2 coatings of variable thickness \(h\) deposited on a silicon substrate. **(A)**: Small thickness \(h\) in the visible and near-IR range; **(B)**: Large thickness in the mid-IR range.  
Above this opacity cut-off, the substrate is basically homogeneously semi-opaque (e.g., \(T\approx 0.57\) at 4 \(\upmu\)m) while adding a thin coating can dramatically enhance the transmittance. Part B of Figure 11 shows a mapping of the increase of transmittance that the coating provides, namely \(\Delta T=T_{\text{Si+coat}}-T_{\text{Si}}\), against \(h\) and \(\lambda\). In the mid-IR range, up to 15% of transmittance enhancement can be observed; obviously, this enhancement depends significantly on \(\lambda\) but can nevertheless be of some interest for monochromatic processes such as imaging.
# Radar Voxel Fusion for 3D Object Detection
## 3 Methodology
### Input Data  
The input data to the network consists of the lidar data with its three spatial coordinates \(x,y,z\), and intensity value \(i\). Similar to [6], colorization from projected camera images is added to the lidar data with \(r\), \(g\), \(b\) features. Additionally, the radar data contributes its spatial coordinates, intensity value \(RCS\)--and the radial velocity with its Cartesian components \(v_{x}\) and \(v_{y}\). Local offsets for the points in the voxels \(dx\), \(dy\), \(dz\) complete the input space. The raw data are fused and processed jointly by the network itself. Due to the early fusion of the input data, any lidar network can easily be adapted to our fusion approach by adjusting the input dimensions.