esa-sceva/satcom-chunk-collection huggingface dataset:
# Utility Distribution Strategy of the Task Agents in Coalition Skill Games
## 3 Definition of the Problem Model
### Task Selection Strategy of Service Agent  
To facilitate the description of the algorithm, some notations are given first:  
1. \(H_{i}^{R}(\tau)=1\) indicates that \(r_{i}\) is still in the system and waiting to select a task at time \(\tau\). \(H_{i}^{R}(\tau)=0\) indicates that \(r_{i}\) is deleted from the system at time \(\tau\). \(H_{k}^{T}(\tau)=1\) (\(H_{k}^{T}(\tau)=0\)) indicates that \(t_{k}\) is still (is not) in the system.
2. \(P(i,k,\tau)\) denotes the set of skills that can be provided to \(t_{k}\) by \(r_{i}\) at time \(\tau\), that is: \[P(i,k,\tau):=\{s_{j}\in S\,|\,RS_{i,j}=1\wedge ST_{j,k}=1\wedge\
eg\exists r_{ i}\in R/\{r_{i}\}(RTS_{i^{\prime},0}(\tau)=k\wedge RTS_{i^{\prime},j}(\tau)=1)\}\]
3. _complete_(\(i,k,\tau)=1\) (_complete_(\(i,k,\tau)=0\)) indicates that \(t_{k}\) can (cannot) be completed if \(r_{i}\) selects \(t_{k}\) at time \(\tau\).
4. \(N_{i}(\tau)\) denotes the set of task agents which need the skills possessed by \(r_{i}\in R\) at time \(\tau\): \[N_{i}(\tau):=\{t_{k}\in T\,|\,H_{k}^{T}(\tau)=1\wedge P(i,k,\tau)\
eq\Phi\}\]
5. \(C_{i}(\tau):=\{t_{k}\in T\,|\,H_{k}^{T}(\tau)=1\wedge\textit{complete}(i,k, \tau)=1\}\).
6. \(f(i,k,\tau)\) denotes the share of utility \(r_{i}\in R\) can get if it selected \(t_{k}\in T\) at time \(\tau\) without considering whether it can be completed or not: \[f(i,k,\tau):=\sum_{s_{j}\in P(i,k,\tau)}TS_{k,j}(\tau)\]  
It is assumed that \(f(i,0,\tau)=0\), which means that the individual revenue of \(r_{i}\) is 0 if it does not select any task at time \(\tau\).  
1. \(R^{1}(k,j,\tau):=\{r_{i}\in R\,|\,H_{i}^{R}(\tau)=1\wedge RS_{i,j}=1\wedge ST_ {j,k}=1\wedge RTS_{i,0}(\tau)=k\wedge RTS_{i,j}(\tau)=1\}\).
2. \(R^{2}(k,j,\tau):=\{r_{i}\in R\,|\,H_{i}^{R}(\tau)=1\wedge RS_{i,j}=1\wedge ST _{j,k}=1\wedge RTS_{i,0}(\tau)\
eq k\wedge f(i,k,\tau)>f(i,RTS_{i,0}(\tau), \tau)\}\).
3. \(R^{3}(k,j,\tau):=\{r_{i}\in R\,|\,H_{i}^{R}(\tau)=1\wedge RS_{i,j}=1\wedge complete (i,k,\tau)=1\wedge j\in P(i,k,\tau)\}\).
4. \(R^{4}(k,j,\tau):=\{r_{i}\in R\,|\,H_{i}^{R}(\tau)=1\wedge RS_{i,j}=1\}\).
5. \(T^{1}(j,\tau):=\{t_{k}\in T\,|\,H_{k}^{T}(\tau)=1\wedge ST_{j,k}=1\wedge R^{1} (k,j,\tau)\cup R^{2}(k,j,\tau)=\Phi\}\).  
Sub-procedure 1 describes the task selection strategy of service agent \(r_{i}\in R\) at time \(\tau\). The output is \(t(i,\tau+1)\), which denotes \(r_{i}\)'s next-step selection.  
**Sub-Procedure 1** Task selection strategy of service agent \(r_{i}\in R\)  
```
1:IF\(N_{i}(\tau)\cap C_{i}(\tau)\
eq\Phi\)THEN
2:\(t(i,\tau+1)\leftarrow\underset{t_{k}\in N_{i}(\tau)\cap C_{i}(\tau)}{\text{ argmax}}\,f(i,k,\tau)\);
3:ELSEIF\(N_{i}(\tau)\
eq\Phi\wedge C_{i}(\tau)=\Phi\)THEN
4:\(t(i,\tau+1)\leftarrow\underset{t_{k}\in N_{i}(\tau)}{\text{argmax}}f(i,k,\tau)\);
5:ELSE
6:\(t(i,\tau+1)\leftarrow\)0;
7:END IF
```
## 6 Conclusions  
In this study, a VMD-GWO-GRU model for predicting water quality parameters was developed based on the historical correlation and fluctuation characteristics of these parameters. The main conclusions drawn are the following:  
1. Box plots and linear interpolation were utilized to remove and supplement anomalous data, the raw water quality parametric data were decomposed using the VMD decomposition algorithm, and the main changed characteristics of the water quality parameter series were extracted.
2. Aiming at the problem that the traditional GRU model needs to manually adjust its model parameters, good results were achieved by using the grey wolf optimizer for adaptive optimization of the model parameters, modeling and predicting the dissolved oxygen data after VMD decomposition, respectively, and inputting the optimal hyperparameters into the model.
3. The VMD-GWO-GRU water quality parametric prediction model developed in this paper achieved better results in both the RMSE and MAPE evaluation indexes, indicating that the model has lower error and a higher prediction accuracy in water quality parametric prediction compared to the unoptimized model. Moreover, the lag of the water quality parametric prediction model was significantly improved.  
The model VMD-GWO-GRU proposed in this study can offer superior predictive performance for anticipating water quality parameters. It is capable of forecasting the trajectory of these parameters, offering dependable guidance for water treatment companies to enhance their capacity and efficiency.  
**Author Contributions**: Conceptualization, B.L. and F.S.; data curation, F.S. and J.X.; funding acquisition, B.L.; methodology, F.S.; resources, B.L.; software, F.S. and J.Z.; validation, B.L. and Y.L.; writing--original draft, F.S.; writing--review and editing, F.S. and Y.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported by the Science and Technology Project of the Jilin Province Education Department under Grant No. JJKH20210746 KJ, and the Jilin Province Science and technology development plan project in 2020 under Grant No. 20200403131 SF.  
**Institutional Review Board Statement**: Not applicable.  
**Informed Consent Statement**: Not applicable.  
**Data Availability Statement**: The data presented in this study are available upon request from the corresponding author. The data are not publicly available due to [Experimental data from actual subject projects, not convenient for public disclosure].  
**Conflicts of Interest**: The authors declare no conflicts of interest.
## 3 System Model
### Macro- and Micro-Mobility Models  
In our study, we account for both macro- and micro-mobilities of UE. We represent macro-mobility by independent unbiased diffusion over the \(x\)- and \(y\)-axis confined in \((0,L)\), where \(L\) is the compartment width and length. Recall that for one-dimensional confined diffusion, the time-dependence of the probability density function \(p(x,t|x_{0},t_{0})\) to find the Brownian particle at position \(x\) at time \(t\), given that it was at position \(x_{0}\) at time \(t_{0}\), is governed by [PERSON]'s second law of diffusion and described by the Fokker-Planck equation [43].  
\[\frac{\partial p(x,t|x_{0},t_{0})}{\partial t}=D\frac{\partial^{2}p(x,t|x_{0},t_{0})}{\partial x^{2}}, \tag{4}\]  
with the initial condition \(p(x,t|x_{0},t_{0})=\delta(x-x_{0})\); \(D\) is the diffusion constant describing the rate of diffusion.  
The only two parameters required to represent micro-mobility patterns are \(D_{x}\) and \(D_{y}\)-diffusion constants over the \(x\)- and \(y\)-axes. These can be estimated from the statistical data.  
The micro-mobility refers to rapid rotations of UE in the hands of a user [40; 44], leading to frequent antenna misalignment [22]. To capture this phenomenon, we utilize the model proposed in [22] and parameterize it using the statistical data reported in [6] for X-VR applications. Specifically, the model assumes that rotations along the transverse and normal axes are modeled using the independent Brownian motions governed by (4), with diffusion constants \(D_{T}\) and \(D_{N}\). To reflect the micro-mobility effect on the UE side, we consider additional vertical and horizontal misalignment angles due to rotations of the UE in the user's hands, \(gamma_{H}(t)\) and \(gamma_{V}(t)\). These rotation processes impose the most impact on the connection properties [22]. In our model, by following [22], we assume the small displacements of the UE are negligible.
## 5 Discussion and Conclusions
### Limitations of the Work  
One of the limitations is associated with interpretability. GRU-LightGBM offers a good result in prediction, but the interpretability of some features, e.g., network layer parameters, is weak. The reason is that the network layer features extracted from the GRU model are numerical relations for model computation, and, usually, they are physically meaningless.  
The limited availability of comprehensive data poses another limitation. The integrity of the dataset holds significant importance in adopting GRU-LightGBM. In this research, a crucial factor contributing to the effective performance of GRU-LightGBM in predicting the sales of Product A is the completeness of its sales data, characterized by fewer discontinuous points. It is important to note that the success of GRU-LightGBM does not imply exclusivity to the Product A dataset; rather, it highlights the model's reliance on high-quality data. The model demonstrates its efficacy when the data exhibit completeness and minimal disruptions, emphasizing the importance of maintaining such data quality standards for optimal performance across various datasets. In future work, authors and potential researchers could replicate and validate the proposed methods with more extensive and varied datasets.
## 3 Methodology
### Frequency Domain Feature Extraction Module  
#### 3.3.1 Data Processing and Analysis Based on FFT  
In the real world, data often exhibit complex patterns that combine both periodicity and trends. Traffic flow data, which is collected by sensors over a specific time period, displays distinct characteristics depending on factors like weekdays versus weekends, and working hours versus non-working hours. This makes it a typical example of a periodic discrete signal. The amplitude of seasonal fluctuations or the trend-cycle components exhibit relatively small variations as the level of the time series changes. Therefore, traffic flow data can be analyzed using an additive model. Specifically, the time series can be expressed as the sum of various components, as follows:  
\[y_{t}=S_{t}+T_{t}+R_{t} \tag{8}\]  
where: \(y_{t}\) denotes time series data, \(S_{t}\) denotes the period term, \(T_{t}\) denotes the trend term, and \(R_{t}\) denotes the residual term.  
Fourier Transform (FT) is a mathematical tool used to convert a signal from the time domain to the frequency domain, decomposing it into sinusoidal components of different frequencies. The core idea is that any periodic or non-periodic signal can be represented as a series of sinusoidal waves with varying frequencies, amplitudes, and phases. However, since computers typically process discrete signals, the Discrete Fourier Transform (DFT) is used to approximate FT.  
FFT is one of the most important algorithms in signal processing and data analysis, providing an efficient computation of the DFT. While dealing with discrete time series data, applying FFT enables frequency-domain analysis, allowing for the identification of periodic components and noise within the time series.  
If the data is represented as \(X=\left\{x^{1},x^{2},x^{3},\ldots x^{t}\ldots,x^{M}\right\},X\in R^{M\times T}\), where \(T\) represents the length of the time series, \(M  
in \(X=\left\{x^{1},x^{2},x^{3},\ldots x^{t}\ldots,x^{M}\right\}\) is subjected to FFT, and the result \(f^{j}=\left\{f^{j}_{1},f^{j}_{2},f^{j}_{3},\ldots,f^{j}_{T}\right\}\) is obtained.
# Research on Path Planning Based on the Integrated Artificial Potential Field-Ant Colony Algorithm
## 3 Basic Algorithms
### APF Method
#### 3.2.3 Resultant Force and Motion  
The resultant force \(F(q)\) acting on the robot is the vector sum of the attractive force \(F_{att}(q)\) and the repulsive force \(F_{rep}(q)\), that is:  
\[F(q)=F_{att}(q)+F_{rep}(q) \tag{10}\]  
The robot adjusts its movement direction and speed based on the direction and magnitude of the resultant force it experiences. In an ideal situation, the robot will move towards the TP under the pull of gravity while avoiding obstacles due to the repulsive force.
## 6 Results and Discussions
### Impact of LLM Choice on EoH-MR Performance  
To evaluate the impact of the LLM backend on the performance of the proposed framework, EoH-MR was tested using three different LLMs: gpt-4o, gemini-2.5-flash, and claude-sonnet-4 on the AGV scheduling task (Table 5), and gemini-2.5-flash on the TSP and ODE tasks (Table 6). The results indicate that while the overall convergence pattern is stable, the choice of LLM indeed affects solution quality, diversity, and computational cost. In the AGV task, claude-sonnet-4 achieved the best final score (\(-114\),\(012.0\)), despite requiring only 53 LLM calls and the fewest total tokens. gemini-2.5-flash produced slightly worse scores but demonstrated the highest diversity (168 unique scores), suggesting strong exploratory behavior. gpt-4o yielded moderate performance with reasonable stability and runtime, indicating a balanced trade-off between generation cost and quality. In the TSP and ODE tasks, gemini-2.5-flash enabled robust convergence, with best scores of \(-6.2209\) (TSP) and \(-0.0654\) (ODE), accompanied by high success rates and acceptable diversity. While the total computation time for TSP was notably higher (over 14 h), early-stage solutions already matched or exceeded baseline performance, and the model maintained reliable search stability. These findings suggest that stronger or more instruction-tuned LLMs can lead to better early solutions with fewer generations, but model-specific differences in prompt adherence, token usage, and variance can influence overall efficiency. The choice of backend should therefore be made based on task complexity, diversity requirements, and available computational budget.
## 2 Motivation and Background Analysis
### Edge Computing
#### 2.1.2 Why Edge Computing is Required?  
The future network architecture will be service-oriented, and the contents of the user should be kept closer to the user, so that they can access their required content within a very short time. A lot of IoT devices were already deployed and the data generated from the deployed IoT devices will be 2.3 trillion gigabytes at each day. The generated data is not all useful, or some data need to be preprocessed or cached before sending to the cloud server. Therefore, a local processing mechanism is required to handle a huge amount of generated IoT data per day. The EC can provide all the requirements as we discussed before. Besides, we describe the following key reasons for using the EC to satisfy the end-users and for the efficient traffic and bandwidth management.  
Autonomous driving, AR, VR, and other real-time applications need very low latency communication to fulfill their goals. The current network architecture and even the current centralized cloud architecture cannot fulfill the goals of the real-time delay-sensitive applications. In many cases, EC can fulfill the expectations of real-time and delay-sensitive applications and; therefore, the quality of services (QoS) for the end-users will be increased.  
Traffic Management  
The current network traffic is increasing towards some specific paths for a certain specific service provider due to the centralized cloud network architecture. Higher traffic flows create network congestion and packet loss due to insufficient bandwidth for a network. By considering the trillions of gigabytes of IoT data per day, the centralized cloud network will be unable to handle the huge amounts of contents. Therefore, the traffic should be handled nearby from the billions of source devices to optimize the bandwidth utilization and to reduce the traffic in the core networks. As a result, the EC paradigm is an appropriate candidate to play a meaningful role in traffic reduction on the core network.  
Scalability  
The deployed IoT and end-user devices are increasing every day, and it is predicted that the number of IoT and the end-user devices will be millions and billions, which may create a scalability challenge soon. These millions and billions of devices will generate a huge amount of local traffic that will create congestion in the data centers or cloud centers. Therefore, the local edge servers can handle the huge amount of data in a decentralized manner. If the data flow is increased enormously towards a certain local edge server and the local edge server is unable to handle the data flow, then it can distribute the data flow towards the proximity local edge servers. Therefore, scalability challenge can be handled by distributed local edge servers.
## 2 Materials and Methods
### Selection of Statistical Models  
To evaluate the goodness-of-fit of the distribution models, statistical tests such as the Kolmogorov-Smirnov (K-S), Anderson-Darling, or chi-squared (\(\chi^{2}\)) tests can be considered. To select the model that best suits the purpose of this study, simulations of the Kolmogorov-Smirnov and Anderson-Darling tests were performed to demonstrate the adequacy of the Weibull, lognormal, and exponential distributions to our data. A dataset simulating the time-to-failure (TTF) for the components analyzed in this paper was generated. The statistical software R ([[https://www.r-project.org/](https://www.r-project.org/)]([https://www.r-project.org/](https://www.r-project.org/)), accessed on 23 March 2025) was utilized to perform the goodness-of-fit tests, and Kolmogorov-Smirnov and Anderson-Darling tests were applied for each distribution (Weibull, lognormal, exponential, gamma, normal) and each simulated dataset. The results obtained are presented in tabular form, including test statistics, \(p\)-values, and their interpretation. A \(p\)-value greater than 0.05 indicates that there is insufficient evidence to reject the null hypothesis (i.e., the data follows the tested distribution). The Kolmogorov-Smirnov and Anderson-Darling test statistics measure the distance between the empirical distribution of the data and the theoretical distribution. Smaller values indicate a better fit. The results obtained from this simulation are presented in Table 4.  
Based on the simulated results, we can observe that the Weibull, lognormal, and gamma distributions exhibit the best fits to the simulated data, showing high \(p\)-values. The normal distribution shows the poorest fit, which is expected gi  
\begin{table}
\begin{tabular}{c c c c} \hline
**Distribution** & **Test** & **Test Statistic** & \(p\)**-Value** \\ \hline [PERSON] & [PERSON]–[PERSON] & 0.05 & 0.80 \\  & [PERSON]–[PERSON] & 0.30 & 0.90 \\ \hline  & [PERSON]–[PERSON] & 0.08 & 0.60 \\  & [PERSON]–[PERSON] & 0.50 & 0.70 \\ \hline  & [PERSON]–[PERSON] & 0.12 & 0.40 \\  & [PERSON]–[PERSON] & 0.70 & 0.60 \\ \hline  & [PERSON]–[PERSON] & 0.07 & 0.70 \\  & [PERSON]–[PERSON] & 0.40 & 0.80 \\ \hline  & [PERSON]–[PERSON] & 0.15 & 0.30 \\  & [PERSON]–[PERSON] & 0.90 & 0.50 \\ \hline \end{tabular}
\end{table}
Table 4: Simulated results of the [PERSON]–[PERSON] and [PERSON]–Darling goodness-of-fit tests for Weibull, lognormal, exponential, gamma, and normal distributions.  
simulated data. This comparative analysis provides further evidence to support the choice of the Weibull and lognormal distributions. These statistical results support our choice of models and allow us to provide a more rigorous analysis of equipment reliability and maintainability.
## 3 Results and Discussion
### Water Content and Acid Value of Oil  
As shown in Figure 4, the water content of the oil samples continuously increases during thermal aging. At the early aging stage, the water value of the oil containing the TPEE fiber was lower than that of the oil containing the PTFE fiber. After seven days of aging, the water value of the oil containing the TPEE fiber increases rapidly, exceeding that of the other oil. At 24 days of aging, the water of the two kinds of oil containing fibers showed an exponential growth trend with the oil sample containing the TPEE fiber growing faster.  
According to the fitting relationships between water contents and aging time shown in Table 1, good exponential relationships were observed. The R-squared values of the two exponential relations are all over 0.92.  
\begin{table}
\begin{tabular}{c c c} \hline
**Oil Category** & **Fitting Equation \(W\) = A + B \(\times\) exp(C \(\times\) t)** & \(\mathbf{R}^{2}\) \\ \hline oil containing TPEE fiber & \(W=-309.612+324.164\times\) exp(0.0037 \(\times\) t) & 0.98 \\ oil containing PTFE fiber & \(W=-140.324+157.927\times\) exp(0.0054 \(\times\) t) & 0.95 \\ \hline \end{tabular}
\end{table}
Table 1: Fitting relations between the water contents and aging time.  
Figure 3: Breakdown voltage of oil.  
The acid value results are shown in Figure 5. In the early stages of aging, the acid values of all types of oil samples are approximately equal. As aging progresses, the acid value of each oil sample increases regularly; however, the acid value of oil containing TPEE fiber increases rapidly after 15 days and exceeds that of oil containing the PTFE fiber at 18 days. At the end of aging, the acid value curves of the TPEE-containing oil samples tend to show an exponential growth trend. However, the acid value curves of the PTFE-containing oil samples tend to show much slower growth. According to the fitting relationship between acid values and aging time shown in Table 2, it was observed that the acid value curves of the TPEE-containing oil samples tend to show an exponential growth trend, however, the acid value curves of the PTFE-containing oil samples are slower.
## 3 Results
### Sensing Limit  
The method was originally developed to meet the difficulties of changing environmental conditions caused by considerable concentration changes of either the analyte itself or the gas matrix around. For the application in biogas detection, it is also needed to measure trace components as ammonia with the same device. This section therefore investigates its application for the measurement of small concentrations and for this purpose ammonia was measured in the range between 1060 cm\({}^{-1}\) and 1150 cm\({}^{-1}\) employing the same laser source. Figure 4 shows in green the simulated absorption coefficient derived from HITRAN [11] for 1.5% ammonia in synthetic air. The signal of the second lock-in amplifier is shown in red, i.e., the pure photoacoustic signal is given and the measurement of the power transmitted through the cell is depicted in black for comparison.  
Figure 4: Comparison of transmitted power (black), photoacoustic signal (red), and simulated absorption (green) for 1.5% ammonia in synthetic air.  
The gas mixture was further diluted and the signal of the peak at 1103.6 cm\({}^{-1}\) was further analyzed. Each point in Figure 5 is the mean value of 101 single measurements and the error bars represent the standard deviation for each concentration. The mean value of the standard deviation is 1.62 \(\mu\)V. A linear dependence of the signal on the concentration is found for concentrations up to 1.1%. The limit of detection was derived to be 246 ppm using a 3\(\sigma\) margin. This is sufficient for the application since ammonia is present in the biogas in concentrations up to 1%. [PERSON] et al. describe a system optimized for the detection of ammonia with a custom tuning fork and they achieve a sensing limit of 22 ppm [12]. [PERSON] et al. reached 418 ppb using a custom tuning fork and an amplified source [13] and [PERSON] et al. even reached 17 ppb, also with an amplified excitation source [14].