esa-sceva/satcom-chunk-collection huggingface dataset:
# Enhanced Knowledge Graph Embedding by Jointly Learning Soft Rules and Facts
## 4 Our Method
### Discussions  
#### 4.4.1 Complexity  
In the embedding learning stage of SoLE, we followed ComplEx to represent entities and relations as complex valued vectors. Thus, the space complexity was \(O(n_{e}d+n_{r}d)\), where \(d\) is the dimensionality of the embedding space, \(n_{e}=|E|\) is the number of entities, and \(n_{r}=|R|\) is the number of relations. As we can see from Algorithm 1, during the learning procedure, each iteration required a time complexity of \(O(n_{l}d+n_{g}(M+1)d)\), where \(n_{l}=|L^{b}|\) is the number of labeled triples in a mini-batch, \(n_{g}=|G^{b}|\) is the number of groundings in a mini-batch, and \(M\) is the maximum rule length. SoLE had a space and time complexity that scaled linearly with \(d\), which was the same as ComplEx. However, the time complexity of SoLE was much larger than ComplEx, which only required \(O(n_{l}d)\) per iteration, since SoLE needed to compute the truth values of rules besides the scores of triples. In addition, the space and time complexity of the grounding generation stage were trivial compared to the embedding learning stage, due to the high efficiency of reasoning and the restrictions on the rule mining module in practice, e.g., the PCA confidence threshold not lower than 0.5 and the length of rules not longer than two. Therefore, we could ignore it when analyzing the time and space complexity of SoLE.  
```
1:KG triples \(\mathcal{T}=\{(e_{i},r_{k},e_{j})\}\);  Logical rules \(\mathcal{F}=\{(f_{p},c_{p})\}\) and their corresponding groundings \(\mathcal{G}=\cup_{p=1}^{p}\mathcal{G}_{p}\).
2:Entity and relation embeddings \(\Theta\).
3:Initialize entity and relation embeddings \(\Theta^{(0)}\) randomly
4:for\(n\gets 1\) to \(N\)do\(\triangleright\)\(N\) is the number of iterations
5: Sample a mini-batch \(\mathcal{T}^{b}\),\(\mathcal{G}^{b}\) from \(\mathcal{T}\),\(\mathcal{G}\)
6: Generate a set of negative triples \(\mathcal{T}^{b}_{neg}\) from \(\mathcal{T}^{b}\)
7:\(\mathcal{L}^{b}\leftarrow\emptyset\)\(\triangleright\)\(\mathcal{L}^{b}\) is the set of labeled triples
8:for each \(x_{l}\in\mathcal{T}^{b}_{neg}\cup\mathcal{T}^{b}\)do
9:\(y_{l}=\pm 1\)
10:\(\mathcal{L}^{b}\leftarrow\mathcal{L}^{b}\cup\{(x_{l},y_{l})\}\)
11:endfor
12: Generate a batch of logical rules \(\mathcal{F}^{b}\) from \(\mathcal{G}^{b}\) and \(\mathcal{F}\)
13:\(\Theta^{(n)}\leftarrow\Theta^{(n-1)}-\eta\Big{(}\frac{1}{|\mathcal{L}^{b}|} \sum_{(x_{l},y_{l})\in\mathcal{L}^{b}}\
abla_{\Theta}L(-f(x_{l})\cdot y_{l})+ \frac{1}{|\mathcal{F}^{b}|}\sum_{(f_{p},c_{p})\in\mathcal{F}^{b}}\
abla_{ \Theta}\|\sum_{\mathcal{G}\eta}\log\pi(g_{pq})-\log c_{p}\|^{2}\Big{)}\)\(\triangleright\) cf. Equation (14)
14:endfor
15:return\(\Theta^{(N)}\)
```  
**Algorithm 1** Joint training algorithm of SoLE.
# Adaptive DecayRank: Real-Time Anomaly Detection in Dynamic Graphs with Bayesian PageRank Updates
## 6 Discussion
### Comparison with State-of-the-Art Methods
#### 6.1.4 Robustness Against Noise  
Figure 4 demonstrates that Adaptive-DecayRank maintains **high precision across various anomaly thresholds**, effectively suppressing false positives, an essential feature for cyber-security and fraud detection applications. For **Top-500 anomalies** (as shown in Table 5), it retains a precision above **0.520** on DARPA, **0.544** on CTU-13, and **0.528** on RTM-30, whereas AnomRank drops to **0.30** or lower under similar conditions, highlighting its superior reliability in distinguishing true anomalies from random fluctuations.  
Existing research [1,2] has shown that several anomaly detection models struggle with _false positive rate (FPR)_, meaning the proportion of normal instances that are incorrectly classified as anomalies, particularly in highly dynamic datasets, where normal variations may be misclassified as anomalies. Adaptive-DecayRank mitigates this issue through its adaptive decay mechanism, which prioritizes recent, sustained anomalies while filtering out transient noise.  
A practical example of this robustness is observed in the **CTU-13** dataset, where botnet interactions often mimic normal traffic patterns, making static ranking approaches like AnomRank highly prone to false positives. In contrast, Adaptive-DecayRank effectively differentiates meaningful botnet behaviors from normal fluctuations, achieving a **6.71%** higher precision than DecayRank and a **66.49%** improvement over AnomRank (as shown in Tables 4 and 5).
# Seasonal Variations of Carbon Dioxide, Water Vapor and Energy Fluxes in Tropical Indian Mangroves
## 3 Flux Calculations and Corrections
### Flux Partitioning  
The CO\({}_{2}\) flux data after u* threshold correction were partitioned into gross primary productivity (GPP) and ecosystem respiration. The reliable nighttime data (_i.e._, after removal of low turbulent flux data) is regressed with air temperature using the Lloyd-Taylor regression model [39]. The air temperature is used as a proxy for ecosystem respiration to estimate daily respiration rates over a 14-day period. GPP is subsequently calculated as the difference between NEE and respiration. During nights, GPP cannot be negative or non-zero; such values are treated as errors and are forced to zero. Duringsuch cases, the ecosystem respiration was estimated to be the same as NEE due to the uncertainty in the regression model. For the secondary corrections, gap-filling and flux partitioning procedures, we used the REddyproc package [40] in an open source R environment along with MATLAB scripts to form the continuous datasets. REddyproc implements the same standardized methods as those described by [PERSON] _et al._[36] and is currently employed by CarboEurope.
## 3 Experiments and Results
### Performance Evaluation Metrics of the Network Model
#### 3.2.3 F1-Score  
The F1-score is the harmonic mean of precision and recall, providing a comprehensive measure of the balance between the model's ability to detect positive samples and its control over false positives. It is defined as follows:  
\[\text{F1-score}=\frac{2\cdot\text{Precision}\cdot\text{Recall}}{\text{ Precision}+\text{Recall}} \tag{8}\]
## 6 Discussion  
The introduction of multiple mobile sinks for WSNs can balance energy consumption, prolong network lifetime, and reduce sensor nodes' overhead near mobile sink nodes. Besides, they are well suited for sparse or disconnected sensor networks. They can also provide well guaranteed network connectivity. However, the cost of mobile sinks is relatively higher than that of normal sensor nodes. Thus, selection of an appropriate number of mobile sink nodes needs to be further studied under various applications to optimize the tradeoff between cost and network performance.  
If sink nodes move along a predefined path in the sensor network, the predefined movement path and park positions need to be carefully designed. We assume that there is no big obstacle in the movement path, so that mobile sinks can move along the trajectory smoothly and sojourn at those park positions to collect monitored data from static sensor nodes in a multi-hop transmission manner.  
This is a joint optimization problem of both sink moving strategy and routing algorithm, which is a NP-hard problem. As sink nodes are moving, the network topology is changing accordingly and route information will also get updated. The key problem is how to define relevant models like energy and traffic model to calculate network metrics like energy consumption and lifetime under different sink node(s) moving strategies or applications.  
In our experiments, the number of mobile sink nodes is obtained by analyzing the performance with different mobile sink numbers. We analyze the performance of the network using one to three mobile sink nodes, respectively, and finally choose to deploy two mobile sink nodes for data collection. In addition, the sojourn location of each mobile sink node which is elected from parking positions is relatively hard to determine. In order to make the sensor network have better flexibility, parking positions are elected based on the X_axis or the Y_axis coordinate and transmission range of the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Network Environment** & **Node ID** & **Round** \\ \hline Interval of zero parking position & 5 & 2994 \\ Interval of one parking position & 5 & 4450 \\ Interval of two parking positions & 62 & 7087 \\ Interval of three parking positions & 28 & 5012 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Round when the first node dies.  
boundary neighbor node in the moving direction, and sojourn locations will be chosen from these parking positions.
## 3 Data Description and Model Evaluation Index
### Model Evaluation Index  
To assess and compare the detection performance of the improved model, this paper introduces four commonly used performance evaluation metrics: Precision, Recall, Average Precision for a single class (AP), mean Average Precision across all classes (mAP), and F1-score. These metrics are used to evaluate the performance of the pavement distress detection model trained on the source domain when transferred to the testing domain. Their calculation formulas are as follows:  
\[Precision=\frac{T_{P}}{T_{P}+F_{P}} \tag{9}\]  
\[Recall=\frac{T_{P}}{T_{P}+F_{N}} \tag{10}\]  
\[AP=\int_{0}^{Recall}Precision(Recall) \tag{11}\]  
\[mAP=\frac{\sum\limits_{i=1}^{k}AP_{i}}{k} \tag{12}\]  
\[F1=2\times\frac{Precision\times Recall}{Precision+Recall} \tag{13}\]  
where \(T_{P}\) represents the number of correctly identified pavement distresses; \(F_{P}\) represents the number of other targets incorrectly identified as pavement distresses; \(F_{N}\) represents the number of pavement distresses missed in detection; and \(k\) represents the number of categories of pavement distresses.  
The pavement distress detection model provides a confidence score for each target during distress identification, indicating the degree to which the target is considered a positive sample. Determining predicted positive samples involves comparing the confidence scores with a set confidence threshold. Therefore, the values of \(T_{P}\), \(F_{P}\), and \(F_{N}\) are related to the confidence threshold setting. _Precision_ represents the model's ability to correctly identify distresses, while _Recall_ measures the model's capability to successfully detect pavement distresses. Both are related to the confidence threshold and exhibit a trade-off relationship: increasing the confidence threshold typically leads to higher _Precision_ but lower _Recall_. Typically, the confidence threshold is set at 0.5. AP, mAP, and F1-score are determined based on _Precision_ and _Recall_, providing a comprehensive evaluation of model accuracy.
## 2 Monte Carlo Point Probability Model and the Modeling of Light Sources
### Photon Modeling of Gaussian Laser Beam  
Next, we considered the situation of a laser beam. The distribution of the intensity of a laser beam with its angle can be considered a Gaussian distribution [32; 33]. In order to facilitate subsequent comparison with the classic communication model [28], we regarded the light source as a point light source. The brightness of the light source was uniform at all azimuth angles and the light intensity followed a normal distribution with the off-axis angle \(\xi_{\Theta}\), and \(\xi_{\Theta}\sim N(0,\sigma)\).  
According to the \(3\sigma\)-principle in the probability distribution, the probability that \(\xi_{\Theta}>3\sigma\) can be considered a small probability event. Let \(3\sigma\) equal 1. We know that when \(X\sim N\left(\mu,\sigma^{2}\right)\), the probability density function (PDF) of X can be written as in Equation (4).  
\[f(x,\mu,\sigma)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(x-\mu)^{2}}{2\sigma^{2}}}. \tag{4}\]  
Furthermore, when \(a\) and \(b\) are real numbers,  
\[aX+b\sim N\left(a\mu+b,\left(a\sigma\right)^{2}\right) \tag{5}\]  
Therefore, if \(Y\sim N(0,1)\), we have \(X=Y/3\sim N\left(0,\left(1/3\right)^{2}\right)\). Remove the case where X = Y/3 is less than 0. The off-axis angle of the initial launch of each photon can be obtained from Equation (6).  
\[\cos\left(\theta_{\xi_{\Theta}}\right)=1-\xi_{\Theta}(1-\cos\phi_{T}). \tag{6}\]  
Figure 2: (**a**) Plot of the LED’s normalized light intensity \(I(\theta)/I_{0}\) contrast as a function of off-axis angle \(\theta\). (**b**) \(H\left(\theta_{\xi}\right)\) vs. \(\theta_{\xi}\) curve drawn by Mathematica.  
In conclusion, Figure 3 shows the relationship between the light intensity of different sources (with different \(\phi_{T}\)) and the off-axis angle \(\theta\).
# Effects of Atmospheric Turbulence on OAM-POL-FDM Hybrid Multiplexing Communication System
###### Abstract  
This paper proposes a 32-channel-hybrid-multiplexing system on atmospheric turbulence. With the utilization of the hybrid multiplexing of orbital angular momentum (OAM), polarization, and frequency, the communication speed of the system can be significantly improved, and this system can be well combined with the existing frequency division multiplexing (FDM) optical communication network. Within this communication system, we discuss the effects of different turbulence intensities on the phase, OAM crosstalk, spectrum, and bit error rate (BER) in turbulent channels. Under strong turbulence, 46.8% of the energy leaks to the neighbor OAM and become noise when multiple topological charge states are transmitted. The research reflects the impact of various parameters of the OAM hybrid multiplexing system under turbulence, which is closer to a practical application scenario and is significant for implementing OAM communication in the turbulence channel.  
Keywords:orbital angular momentum (OAM); free space optical (FSO); atmosphere turbulence; multiplexing communication +
Footnote †: journal: Applied Sciences
# Liquid-Crystal-on-Silicon for Augmented Reality Displays
## 3 Fringing Field Effect and Novel Solution
### Pretilt Angle Pattern Determining Method  
The basic concept of our design is to find an optimized pretilt angle pattern for minimizing FFE. The initial step is to identify the phase retardation profile as a function of location in the pixel region. Since FFE is most pronounced when the largest voltage difference occurs between adjacent pixel electrodes, two worst scenarios are used in our evaluation and optimization. These are (1) maximum operation voltage applied to the central pixel electrode while minimum operation voltage applied to the adjacent pixel electrodes; and (2) minimum operation voltage for the central pixel while the maximum voltage for the neighboring ones.  
After basic evaluation, there are two determining methods to optimize the pretilt angle pattern. The first is to control the phase retardation error over the whole pixel region within a predetermined percentage level. As a general determining approach, the lack of a convergent solution makes the optimization complicated, and the iterative algorism results in heavy computation loads. Therefore, here we introduce the second determining method. As shown in Figure 6b, based on the initially identified phase retardation profile, we divide the pixel region into two zones with an FFE border width \(w\). From Figure 7, we can see that the pretilt angle of the inner zone and outer zone is optimized  
Figure 6: The fringing field effect (FFE) of a VA cell: (**a**) cell gap effect; (**b**) pixel pitch effect. \(p\), \(d\), and \(w\) stand for pixel pitch, cell gap, and FFE border width, respectively (unit: \(\upmu\)m).  
to be \(\alpha_{i}\) and \(\alpha_{o}\), respectively. The target of the optimization is to reduce the overall phase retardation error. With this simpler determining approach, pretilt angle patterns with an FFE-opposing feature can be designed.
## 2 Numerical Simulation of LCO
### Wind-Bridge Interaction  
The sectional bridge deck motion can be simplified as a two degrees-of-freedom vibration system with the corresponding governing equations expressed as:  
\[m\left(\ddot{h}+2\xi_{h}\omega_{h}\dot{h}+\omega_{h}^{2}h\right)=L \tag{3}\]  
\[I_{m}\left(\ddot{\alpha}+2\xi_{a}\omega_{a}\dot{\alpha}+\omega_{a}^{2}\dot{ \alpha}\right)=M \tag{4}\]  
where the \(h\) and \(\alpha\) respectively represent the vertical and torsional displacements; the overdot denotes the derivative with respect to time; \(m\) and \(I_{m}\) are the mass and inertial moment per unit length of the deck section; \(\omega\) and \(\xi\) are the natural circular frequency and damping ratio; and \(L\) and \(M\) are the aeroelastic lift force and torsional moment on the bridge deck section, respectively. To satisfy the geometrical compatibility and the equilibrium conditions on the interface between the wind and bridge, the weak coupling method was employed for the sake of computational efficiency. Once the flow field was initialized (with a steady state), the basic procedure of solving the wind-bridge interactions could be summarized as below:  
Step 1. The pressure on the bridge deck surface is calculated and used to obtain the lift force and torsional moment.  
Step 2. The bridge deck motion is accordingly solved using the Newmark-\(\beta\) algorithm.  
Step 3. The obtained displacements are used to determine the deck section position for the next time step, and the mesh around the section is accordingly updated.  
Step 4. Based on the new deck position and grid (mesh) velocity, the flow field is then calculated and the corresponding aeroelastic forces is acquired.  
Step 5. The Steps 1-4 are repeated until the prescribed motion duration and maximum displacement conditions are satisfied.
# Improving the Sensory Quality of Black Tea by Blending Varieties During Processing
## 3 Results and Discussion
### Analysis of the Main Taste Compounds
#### 3.2.1 Analysis of Catechins and Relevant Compounds
This suggests that the addition of fresh leaves from oolong varieties can promote the accumulation and formation of theaflavins during black tea processing. Moreover, the content of theaflavins in AFJX and AFJG also showed a slight increase, although without statistical significance (Supplementary Materials Figure S3A). This further indicates that JGY and JX only provide a cumulative effect on the content of theaflavins in AFJX and AFJG. However, differences were observed between the content in fresh leaf blending samples and that in finished tea blending samples (Supplementary Materials Figure S4A). CAF, a natural purine alkaloid [27], is highly correlated with the bitterness intensity of tea soup [28; 29]. GA contributes multiple taste characteristics, including astringency, sourness, and sweet aftertaste in tea soup [30]. The content of CAF and GA significantly decreased in FJX and FJG (\(p<0.05\)) compared with Fud, confirming that blending with fresh leaves of oolong varieties can enhance the taste profiles during black tea processing, particularly by decreasing bitterness and astringency. Figure 2: Comparative analysis of catechins, caffeine, gallic acid, theaflavins, and amino acids between fresh leaf blended black tea and Fud black tea: (**A**) Comparison of the contents of catechins, caffeine, gallic acid, and theaflavins in Fud, FJG, and FJX; (**B**) Comparison of the contents of amino acid components in Fud, FJG, and FJX. Note: Different letters indicate a statistically significant (\(p<0.05\)) difference between groups.
## 2 The Analyzed Numerical Methods
* The shifted-hopscotch-CNe (SH-CNe) algorithm [29] applies the same space-time structure as the SH method, but uses only the CNe formulas (4) appropriately. For example, the calculation at the first stage is the following: \[u_{i}^{n+1}=u_{i}^{n}\cdot e^{-2r}+\frac{u_{i-1}^{n}+u_{i+1}^{n}}{2}\Big{(}1-e ^{-2r}\Big{)},\]0 (13)
* The asymmetric-hopscotch (ASH) method [46] is similar to the SH one, but with only three stages. As is shown in Figure 1c, there are two half and one full time step size stages with the \(\theta\) formula, which together span one full time step for all nodes. Based on numerical experiments, the algorithms have optimal performance if \(\theta=0\) is used at the first, \(\theta=\
icefrac{{1}}{{2}}\) at the second, and \(\theta=1\) at the third stage (A1 algorithm in [46]). * The asymmetric-hopscotch-CNe (ASH-CNe) algorithm applies the same structure as the SH method, but uses the CNe Formulas (13) and (4) appropriately. * The next method is the leapfrog-hopscotch (LH) method [28]; see Figure 1d. As we will see, this is a very powerful method if one uses \(\theta=0\) at the first stage and \(\theta=\
icefrac{{1}}{{2}}\) in all other stages (L2 algorithm in [30]). * The leapfrog-hopscotch-CNe (LH-CNe) method [30] is obtained if one replaces the \(\theta\) formulas in the previous LH algorithm with the CNe formula in each stage of the LH structure (Figure 1d), appropriately. The algorithms and some of their properties are summarized in Table 1; for example, the order of temporal convergence, marked by 'O'. All of the twenty algorithms are unconditionally stable for the linear diffusion equation, i.e., the previously mentioned CFLlimit is not valid for them. Some of them have the additional, stronger feature that the new \(u_{i}^{n+1}\) values are the convex combination of the initial \(u_{j}^{0}\) values, which is indicated in the last column of the table. It implies that the maximum and minimum principles ([PERSON] et al., 2016) (p. 87) are always fulfilled and unphysical oscillations are never produced, even for very large time step sizes. On the other hand, this favorable property restricts the speed of the convergence of these methods, so they are often the least accurate for small and medium time step sizes, as we will observe later. It means they significantly underestimate the speed of the diffusion process, especially for large and medium time step sizes. All methods containing the CNe or LNe formula, as well as the LH, RH, SH, ASH and the PI methods, have been recently constructed by our research group, which is indicated after the name of the method in the Table. In our original papers, some analytical proofs, verifications using analytical solutions and numerical tests to compare performances are presented. However, in most cases, the truncation error has not been calculated (marked by a '-' sign in the \"known LTE\" column).
# Estimation of Terrestrial Water Storage Changes at Small Basin Scales Based on Multi-Source Data
## 4 Results
### Evaluation of Small-Basin-Scale TWSC  
#### 4.6.1 Comparison with Other TWSC Data  
To verify the accuracy of the method in this study, we first compared the TWSC calculated in this study with two TWSC datasets in the whole GRB, considering the coarse resolution of GRACE. The first dataset was the CSRM product. The temporal gaps in CSRM were filled with datasets published by [PERSON] et al. [60]. With the second data, we used the method proposed by [PERSON] et al. [61] to reconstruct the daily TWSA, and further calculated the TWSC of the natural month in the GRB.  
Due to the low resolution of GRACE satellites, we evaluated the overall TWSC in the GRB (as shown in Figure 10). The RMSE for the TWSC calculated in this study compared with the CSRM from 2003 to 2018 is 37.1 mm/month. The RMSE between the TWSC calculated in this study and the reconstructed TWSC datasets further reduce to 21.9 mm/month, and the RMSE between CSRM and the reconstructed TWSC is 29.8 mm/month.