esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Error Sensitivity Analysis of the TE Caused by Components of the Cycloidal Gear Transmission
### Principle of Error Sensitivity Analysis Based on Tayler Expansion
If the sensitivity index of an error factor is negative, it indicates that the error factor can decrease the TE of the RV speed reducer. The most important innovation of this study is to decrease the TE of the RV speed reducer by modifying error factors with negative sensitivities. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Error Factor** & **Error Coefficient** & **Sensitivity Index** \\ \hline Pinwheel center circle radius error \(\delta_{a}\) & \(\sqrt{1-K_{1}^{\prime}2}\) & 1 \\ Pinwheel housing radius error \(\delta_{b}\) & \(-1\) & \(-1.6308\) \\ Pinwheel groove matching clearance \(\delta_{c}\) & \(0.5\) & \(0.8154\) \\ Cycloidal gear ring radial runout \(\delta_{d}\) & \(0.25\) & \(0.4077\) \\ Pinwheel housing circumferential position error \(\delta_{e}\) & \(K_{1}^{\prime}\) & \(1.2882\) \\ Isometric tooth profile modification error \(\delta_{f}\) & \(1\) & \(1.6308\) \\ Shifting tooth profile modification error \(\delta_{g}\) & \(-\sqrt{1-K_{1}^{\prime}2}\) & \(-1\) \\ Cumulative error of circumference \(\delta_{h}\) & \(-K_{1}^{\prime}/2\) & \(-0.6441\) \\ Eccentricity error \(\delta_{i}\) & \(k_{n}\) & \(-0.00024\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Error coefficients and sensitivity indices of error factors. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Pinwheel center circle radius \(r_{p}\)/mm & 76 \\ Pinwheel radius \(r_{rp}\)/mm & 3 \\ Cycloid tooth number \(z_{c}\) & 39 \\ Number of pinwheel teeth \(z_{p}\) & 40 \\ Number of center teeth \(z_{1}\) & 22 \\ Number of planetary gear teeth \(z_{2}\) & 60 \\ Eccentricity \(a\)/mm & 1.5 \\ Isometric tooth profile modification \(\Delta r_{rp}\)/mm & \(-0.022\) \\ Shifting tooth profile modification \(\Delta r_{p}\)/mm & \(-0.0437\) \\ Short-formed coefficient \(K_{1}^{\prime}\) & 0.78993 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of the initial rotary vector (RV) speed reducer prototype.
# Advances in the Biosynthesis and Molecular Evolution of Steroidal Saponins in Plants
## 2 Biosynthesis of Steroidal Saponins  
Steroidal saponins are spirostand or fuorstand derivatives biosynthesized through a series of processes on the squalene molecular backbone, including oxidation, hydroxylation, and glycosylation [1; 3; 17]. Thus, the biosynthesis of steroidal saponins can be divided into three stages: the biosynthesis of 2,3-oxidosqualene via the mevalonate (MVA) pathway and 2-C-methyl-d-erythnitol-4-phosphate (MEP) pathway, cholesterol/\(\beta\)-sitosterol generated by a series of catalytic reactions of 2,3-oxidosqualene, and steroidal saponins formed by the hydroxylation, oxidation, and glycosylation of cholesterol or \(\beta\)-sitosterol at side chains, such as the C-16, C-22, and C-26 positions [1; 3; 17; 18; 19] (Figure 2).
## 2 Materials and Methods
### Falling Head Permeability Test Method and Test Scheme  
Initially, soil samples acquired from on-site excavations were combined, employing either Malan loess or loess-like silt as the foundational material. For preliminary enhancement, a proportion of Lishi loess or argillaceous sandstone was introduced. Subsequently, the permeability coefficient of the preliminarily improved loess material was assessed. Soil samples, each with distinct dry densities, were meticulously prepared for permeability tests through controlled adjustments in the compaction process. Finally, an analysis was conducted to determine the influence of admixtures, specifically cement or lime, on the improved loess. For specimens containing admixtures, the test was conducted after a one-day curing period post sample preparation, without considering the influence of curing time on the permeability coefficient. The sample preparation process and the test apparatus are illustrated in Figure 3.  
The penetration ring, measuring 61.8 mm in diameter and 40 mm in height, was utilized. Post preparation, the reshaped ring was saturated through a controlled pumping process prior to undergoing the penetration test. Lime, in the form of chemically pure Ca(OH)\({}_{2}\), and ordinary silicate cement (P. O42.5) were employed as admixtures.  
The permeameter which contained the prepared specimen was connected to the water head apparatus. Distilled water was introduced into the variable head tube using a supply bottle, raising the water level to a predetermined height. Once the water level stabilized, the water supply was cut off and the inlet clamp was opened to allow water to permeate through the soil sample. When water started to overflow from the outlet, the initial water head height and the initial time in the variable head tube were recorded. Subsequently, the water head and time were recorded at 1800 s intervals, and the water temperature at the outlet was measured. This process was repeated twice consecutively. The test was repeated five times using different initial water heads. The test concluded when the permeability coefficient error value fell within the acceptable range. Comprehensive details regarding the test scheme and corresponding results are tabulated in Table 2.
## 4 Discussion
### Synergy of 5G, IoT, and AI in Education  
The pervasive integration of 5G networks with IoT architectures, as noted by [5; 9], has been a driving force in modernizing classrooms beyond simple digital content delivery. Already, institutions testing large-scale sensor deployment demonstrate an ability to collect real-time student engagement data, environmental signals, and live content usage, enabling AI-driven resource optimization and genuinely interactive learning. Real-time feedback loops in 5G-enabled classrooms generate more nuanced student profiles, which teachers can then use to adjust pedagogical strategies on the spot.  
This tight coupling of data, connectivity, and machine learning holds immense potential, from facilitating language practice in VR environments to personalizing instruction for learners with disabilities through AI-driven educational networks. These networks, though, require sophisticated data structuring and ranking methodologies to optimize performance and reduce computational overhead. For example, bi-functional machine learning approaches, which combine clustering and ranking in heterogeneous information networks (HINs), could be integrated into 5G educational ecosystems, streamlining real-time energy distribution, network efficiency, and AI-driven content delivery [67].  
Nevertheless, bridging the digital divide remains a significant hurdle, as [68] emphasizes. Urban schools often lead in deploying cutting-edge IoT hardware and 5G infrastructures, whereas remote or underfunded institutions struggle with inadequate bandwidth and outdated devices. Although projects can employ local caching or partial 5G nodes to accommodate variable connectivity, such arrangements can hinge on ongoing external support and technical expertise. Without systematic policy interventions or long-termfunding models, these disparities risk becoming further entrenched, undermining the inclusive ethos of AI-enabled education.
## 6 ArTIC-MS Use Case Specification  
This section describes ArTIC-MS from an operational perspective. In this respect, the UML use case diagram shown in Figure 9 outlines the responsibilities of the following ArTIC-MS users.  
* **Simulation expert (SE):** Responsible for the elicitation and specification of MSaaS application requirements.
* **Simulation service provider (SSP):** Responsible for the development and the provisioning of M&S services;
* **Simulation developer (SD):** Responsible for the development of MSaaS applications. Specifically, the SD deals with the identification of appropriate M&S services and their composition to build a MSaaS application compliant with the simulation requirements provided by the SE;
* **TOSCA expert (TE):** Owns appropriate knowledge of the TOSCA standard. She/he is also in charge of supporting other users for the specification of the required YAML-based templates;
* **Simulation user (SU):** Final user of the simulation application;
* **ArTIC-MS administrator (ADM):** The user who possesses the required skills for managing the ArTIC-MS platform. Its main task is to provide other users with the required environment for building, executing, and monitoring simulation experiments.  
The following sections detail the use cases that focus on the development and deployment of a MSaaS simulation built as an orchestration of available M&S services. It is worth noting that this paper only considers the case in which the federated MSaaS infrastructure includes heterogeneous cloud implementations, as discussed in Section 5.3. A scenario dealing with all TOSCA-based cloud implementations has already been discussed in previous work [12]. Finally, the use cases dealing with ArTIC-MS management and simulation experiment execution/evaluation are not further discussed in this work.  
Figure 9: ArTIC-MS use case diagram.
## 1 Introduction
In addition, an innovative strategy has been put forward to augment the system's energy dissipation capabilities without changing the ABH beam's truncation thickness. The structure of the remainder of this paper is as follows: Section 2 provides a detailed account of the establishment and analytical solution of the governing equation for a symmetric ABH beam. Subsequently, Section 3 examines the impact of damping layer parameters on the energy dissipation efficiency of the ABH beam, determining the expression form of the thickness function with higher energy dissipation efficiency by comparing the energy consumption effects of various damping layer thickness functions. Based on this expression form, Section 4 outlines the deployment and training procedures of the BP neural network model, presents the expression form of the optimal damping layer thickness function, and verifies it through numerical results. In Section 5, the BP algorithm is applied to optimize the analysis of the thickness function of the damping layer for an altered symmetric ABH beam, suggesting an innovative method to boost the system's energy dissipation efficiency without modifying the truncation thickness of the ABH beam. In the last section, the pivotal conclusions drawn from this research are synthesized.
## 2 Ultrasonic Diffraction Theory Background
### Flight Diffraction Model  
The ultrasonic diffraction system contains two angle probes in a transmitter-receiver configuration, as shown in Figure 1a. They are separated PCS distance by a rigid bar on the scanning device. The PCS is determined by the following equation:  
\[\text{PCS}=\frac{4}{3}T\text{tan}\,\theta \tag{1}\]  
\(T\) is the thickness of the specimen to be detected and \(\theta\) is the main beam angle of the probe. When an ultrasonic pulse is generated by the transmitter, two typical waves will generally be received by the receiver. One is the surface wave that propagates along the surface of the weld, and the other is backwall wave that is reflected on the backwall. When a crack is present in the specimen under test, two diffracted waves from the top and bottom tip of the defect appear between the surface wave and backwall wave, as shown in Figure 1b. The presence of defect can be established by the detection of diffracted waves. Measuring the arrival time of the waves, the depth and height of the defect can be calculated by corresponding geometric relation.  
The arrival time of diffracted waves is calculated by Equation (2):  
\[t(x)=\frac{D^{2}}{c(D^{2}+d^{2})^{\frac{3}{2}}}x^{2}+\frac{2\sqrt{D^{2}+d^{2}} }{c} \tag{2}\]  
where \(D\) is the depth at which the diffracted wave is generated, \(d\) is half of PCS, \(c\) is the ultrasound velocity, and \(x\) is the distance of the defect away from the middle of the probes (see Figure 1a). In actual detection, \(x\) can be ignored. So, Equation (2) is reduced to this form.  
\[t=\frac{2\sqrt{D^{2}+d^{2}}}{c} \tag{3}\]  
Further, the depth of the diffracted wave is derived from Equation (3).  
\[D=\sqrt{\frac{t^{2}c^{2}}{4}-d^{2}} \tag{4}\]  
Therefore, the height of the defect is given by Equation (5).  
\[H=\sqrt{\frac{t_{2}^{2}c^{2}}{4}-d^{2}}-\sqrt{\frac{t_{1}^{2}c^{2}}{4}-d^{2}} \tag{5}\]  
\(t_{1}\) and \(t_{2}\) are, respectively, the arrival time of diffracted waves from the top and bottom tip of the defect, which can be measured using an A-scan signal. From Equations (4) and (5), it is apparent that whether the arrival time can be accurately measured directly determines the measurement accuracy of defect height and depth.
## 3 Methods
### Optirrg Simulations  
#### 3.2.1 Simulated SSM Evolution  
Optirrg simulates the soil water balance and crop yield on a daily basis by combining a soil module and a crop module, assuming that water is the sole limiting factor. The soil module comprises a three-reservoir system [57; 84] that spans from the surface layer to the maximum rooting depth. The first reservoir, with a shallow depth of 10 cm, controls the water balance at the soil surface. In this reservoir, the evaporation demand is reduced for increasing values of the leaf area index (LAI), while the transpiration demand progressively takes over by means of a partitioning coefficient. The second reservoir, referred to as R\({}_{2}\), accounts for the root section and its capacity expands as roots grow. Before the potential root area is fully occupied by the second reservoir, the third reservoir represents the remaining portion of the soil root zone. Initially, water is extracted from the shallow reservoir (R\({}_{1}\), 10 cm deep) through evaporation, and subsequently, the plant draws water exclusively from the second reservoir. Therefore, Optirrg allows for the simulation of SSM at 10 cm depth for different irrigation scenarios. Those simulations serve to compare the effect of different irrigation applications on the SSM to the observed SSM from Sentinel-1, and thus, retrieve the irrigation that leads to the same SSM behavior between SAR acquisitions.  
The SSM\({}_{\text{r}_{(1)}}\) values obtained from Optirrg for rainfed conditions are affected by rainfall only, while the SSM values derived from Sentinel-1 at the plot scale (SSM\({}_{\text{P}}\)) are affected by rainfall and irrigation. In fact, the aim of this study was to detect potential irrigation that occurred between a SAR acquisition date (t\({}_{\text{(I)}}\)) and the previous date t\({}_{\text{(I)}}\)). Therefore, the rate of change of SSM\({}_{\text{r}}\) (\(\Psi\)SSM\({}_{\text{r}}\)) between t\({}_{\text{(I)}}\) and t\({}_{\text{(I)}}\) was computed in order to quantify the effect of rainfall alone on the SSM:  
\[\Psi\text{SSM}_{\text{r}_{(1)}}=\frac{\text{SSM}_{\text{r}_{(1)}}-\text{SSM}_ {\text{r}_{(1)}}}{\text{SSM}_{\text{r}_{(1)}}} \tag{4}\]  
The approach assumed that when there was an increase in SSM\({}_{\text{P}}\) between t\({}_{\text{(I)}}\) and t\({}_{\text{(I)}}\), resulting in a positive rate of change (\(\Psi\)SSM\({}_{\text{P}_{(1)}}\), Equation (2)), it was mainly due to the rise in SSM\({}_{\text{P}}\) caused by rainfall and/or irrigation. On the other hand, an increase in SSM\({}_{\text{r}}\) values could indicate a rainfall event between the SAR acquisitions, leading to a positive \(\Psi\)SSM\({}_{\text{r}_{(1)}}\). Therefore, a \(\Psi\)SSM\({}_{\text{P}_{(1)}}\) value higher than the \(\Psi\)SSM\({}_{\text{r}_{(1)}}\) value between t\({}_{\text{(I)}}\) and t\({}_{\text{(I)}}\), provided indirect evidence of irrigation occurrence.
## 2 Middle Rock Pillar Classification Index Analysis
### Factors Influencing the Stability of the Middle Rock Pillar
#### 2.1.1 Characteristics of Middle Rock Pillar  
The essential characteristics of the middle rock pillar include its physical and mechanical characteristics, structural state, water-bearing state, initial stress state, and degree of weathering.  
The physical and mechanical properties of the middle rock pillar reflect the weight, compressive strength, shear strength, compression modulus, water content, cohesion, and internal friction angle of the rock mass. Rock masses with high gravity and strength have good quality and stability.  
The structural state of the middle rock pillar refers to the primary structure and secondary variation characteristics of the rock mass. The structural state is refined into the development degree, undulation and extension properties, filling and cementation conditions, and number and density of structural planes, which can reflect the integrity and compactness of the rock mass itself.  
The water content in the middle rock pillar will affect the softening, strength reduction, and even instability of the rock mass. For the middle rock pillar, when there is a weak structural plane or interlayer, water reduces the friction resistance of the structural plane and induces the rock mass to slide along the weak plane. Meanwhile, the dissolution of water in the soluble rock and clay rock obviously affects the quality of the rock mass.  
The stress release and redistribution caused by the excavation of the tunnels on both sides of the small clear-distance tunnel directly affect the secondary stress state of the middle rock pillar. When the initial stress is not high and the middle rock pillar is strong enough to withstand the secondary stress after tunnel excavation, the initial stress has no significant impact on the stability of the rock mass. When the initial stress is sufficiently high to prevent the rock mass from withstanding the secondary stress, the excavation of the tunnels on both sides will be affected and the middle rock pillar will be unstable and destroyed.  
The weathering degree of the middle rock pillar affects the physical and mechanical properties of the rock mass, changing the solid rock into soft rock, expanding the opening of the original structural plane, and evolving new cracks while affecting the hardness and integrity of the rock mass.
## 6 Conclusions  
This study proposes the STL-DCSInformer-ETS hybrid model for medium- and long-term sales forecasting of FMCG. By combining STL decomposition, the enhanced DCSInformer model, and the ETS model, the proposed approach effectively captures complex temporal dependencies, seasonal fluctuations, and long-term trends. Feature engineering, using the RF-RFE method, played a crucial role in identifying and optimizing key predictive features across time, geography, economy, product, and weather dimensions, thus providing a solid foundation for accurate forecasting. The STL method decomposes the data into trend, seasonal, and residual components, simplifying the data structure. The enhanced DCSInformer model incorporates dilated causal convolutions and multi-scale feature extraction to better capture both long-term trends and short-term fluctuations. Meanwhile, the ETS model specializes in modeling seasonal variations, further refining the forecasting accuracy. This integration enables the model to effectively adapt to features across multiple time scales, ensuring a comprehensive understanding of sales patterns. The experimental results show that the STL-DCSInformer-ETS model outperforms traditional methods, including LSTM, Transformer, and Informer models, across key metrics such as MSE, MAE, RMSE, MAPE. The STL-DCSInformer-ETS hybrid model stands out in FMCG sales forecasting by addressing the unique challenges of high volatility, short-term promotional effects, and seasonal trends. This demonstrates the model's superiority in handling the volatility of FMCG sales, making it a valuable tool for supply-chain optimization, inventory management, strategic decision-making, and providing policymakers with actionable insights for policy formulation in economic planning and market regulation Future research could enhance the model by incorporating real-time consumer sentiment data or broader macroeconomic indicators, which could provide more dynamic insights. Additionally, exploring the application of the model in other industries, such as electronics, retail, and pharmaceuticals, could validate its versatility and generalizability. Additionally,future research can integrate real-time data. Integrating real-time data requires efficient algorithms and data-processing techniques, and adapt the model to different market scenarios to ensure its robustness and accuracy in diverse environments.  
Conceptualization, L.H. and J.Z.; methodology, Y.M. and J.Z.; software, J.Z. and Y.M.; validation, J.Z. and Y.M.; writing--original draft preparation, Y.M.; writing--review and editing, L.H. and J.Z.; funding acquisition and resources, L.H. and J.Z.; supervision, L.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by \"Leading Goose\" R&D Program of Zhejiang (Grant No. 2022C01238).  
Not applicable.  
The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.
## 3 Experimental Evaluation  
### Data source and Configuration Analysis  
To verify the performance of BDS PPP, observation data of 17 global stations from 1 December 2020 to 20 December 2020 were used. BDS B1 CB2a, B1 HB3I, and GPS signals can be received by the test stations. Taking a day at one station as a sample, there are in total 340 data samples. The observation data interval is 30 s. Since BDS-3 was built to serve the world, to ensure the objectivity of the evaluation, the selection of the stations around the world should be as uniform as possible. The detailed distribution of the stations is shown in Figure 1.  
The precise ephemeris and orbit provided by the IGS analysis centers include final, rapid, ultra-rapid, and real-time (RTS) products. The accuracy of the products provided by each analysis center is slightly different [45]. The precise orbit and clock products used in this research are the GBM products provided by GFZ (Geo Forschungs Zentrum, Potsdam, Germany). The coordinate reference of the stations is the SNX file provided by IGS. It should be noted that the PCO and PCV corrections of some antennas of the receiver only provide corrections for GPS and GLONASS [27]. Therefore, the PCO and PCV corrections of GPS are used to correct for BDS.  
The GNSS multi-function precision positioning software Net_Diff is used for PPP in this research ([[https://github.com/YizeZhang/Net_Diff](https://github.com/YizeZhang/Net_Diff)]([https://github.com/YizeZhang/Net_Diff](https://github.com/YizeZhang/Net_Diff))) (accessed on 20 August 2021). The specific settings for PPP are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameters** & **Models** \\ \hline \multirow{5}{*}{**Observation**} & \multirow{2}{*}{
\begin{tabular}{c} GPS: L1 \& L2, BDS: B11 \& B3I, \\ BDS: B1c \& B2a \\ \end{tabular} } \\  & & & \\ \cline{1-1}  & & &