esa-sceva/satcom-chunk-collection huggingface dataset:
# Coseismic Stress Change and Viscoelastic Relaxation after the 2008 Great Sichuan Earthquake
## 4 Discussion  
### Earthquake Triggering in the Study Area  
Sichuan and the adjacent western region are the most seismically active areas in China [76; 77; 78], and the geological structure and seismic structure are very complex. Therefore, the background seismicity in this area is high. To analyze the long-term rates of earthquakes, the catalog in the study area from 1 January 2000 to 1 January 2020 was provided by the China Earthquake Networks Center (CENC), which was divided into four subgroups with different cutoff magnitudes. Figures 9 and 10 show that the seismicity in the study area is distributed over time.  
Figure 9 illustrates that before the Wenchuan earthquake in 2008, the seismicity in this area was relatively active, and there were few events with M \(\geq\) 6. Since 2008, a dense seismic cluster has formed in the study area. After the Wenchuan earthquake in 2008, the seismicity in this area increased; more earthquakes with magnitudes of M \(\geq\) 7 occurred than before, and seismicity with magnitudes of M \(\geq\) 6 increased. Earthquakes with magnitudes of M \(\geq\) 4 or M \(\geq\) 5 also increased obviously. Until 2020, the seismicity trend remained high. In Figure 10, the sudden increase in M \(\geq\) 2 earthquake activity was caused by the large number of Wenchuan earthquake aftershocks in 2008, after which the occurrence frequency gradually returned to a normal level. The rapid increase in the scale of M \(\geq\) 4 and M \(\geq\) 5 events in 2008 is more remarkable than that of M \(\geq\) 2 events, indicating the change in faulting instability in this region (e.g., [79]).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Date** & **Earthquake** & **Latitude (\({}^{\circ}\))** & **Longitude (\({}^{\circ}\))** & **S1 (MPa)** & **S2 (MPa)** \\ \hline
12 May 2008 & Wenchuan Ms 8.0 & 31.10 & 103.30 & & \(-\)1.370 \\
14 April 2010 & Yushu Ms 7.1 & 33.20 & 96.60 & \(-\)0.004 & \(-\)1.299 \\
20 April 2013 & Lushan Ms 7.0 & 30.28 & 102.96 & 0.152 & \(-\)1.255 \\
22 November 2014 & Kangding Ms 6.3 & 30.30 & 101.80 & 0.169 & 0.019 \\
25 November 2014 & Kangding Ms 5.8 & 30.20 & 101.75 & \(-\)0.605 & \(-\)0.632 \\
8 August 2017 & Jiuzhaigou Ms 7.0 & 33.20 & 103.82 & 0.0362 & \(-\)0.479 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Stress changes due to cumulative coseismic slip and postseismic relaxation. S1 indicates the stress changes induced by all the previous earthquakes. S2 refers to the stress changes caused by previous earthquakes and this event. When calculating the stress, the receiving fault is the source fault of this main earthquake. Six input motions were selected for this table because the six events are the largest in the past decade in the Sichuan area after the Ms 8.0 Wenchuan earthquake in 2008.
## 5 Review of Related Articles
### FC-Based Design
They mention the necessities of developing the application as far as real-time user communication, awareness of the location and the requirement for geo-distributed end nodes, and FC attends to these problems. The authors have contributed more knowledge into the appropriateness of FC for IoT applications with a couple of use cases, including smart wind farms and intelligent traffic light systems in the accompanying paper [149]. Furthermore, [PERSON] et al. [120] proposed a multi-level cloud structure where the traffic flows over the cloud units efficiently to reach the slave section from the master section in TI system, to reduce unnecessary waiting times. Along similar lines, a multitier infrastructure [142] is introduced in which edge cloud servers are differentiated into various level as per their separations to the edge. If the task on the edge cloud server of a given level surpasses its computational limit, the additional outstanding task is sent to a higher-level service. One of the FC areas is that many fog nodes are distributed and deployed over vast geographical territory. Nonetheless, this can bring about a noteworthy increment in energy consumption. Moreover, [PERSON] et al. [143] influenced the distributed approach of fog nodes to enhance awareness of the location in Vehicular Ad hoc Networks (VANETs). They tested their framework to the application case of lane-changing assistance. Additionally, they used the fog layer's services to execute and find an optimal parking spot, where the aggregated data were gathered from different fog devices, demonstrating the concept of the distributed idea of fog devices. In Reference [150], an adaptive energy scheme was developed for fog nodes to work at various transmit powers with variable data rates. [PERSON] et al. [151] correlated energy consumption of applications using centralised (CDCs) with applications employing nano data-centres under the FC infrastructure. [PERSON] et al. [116] proposed a new fog-based sensor cloud architecture for IoT. They facilitated the fundamental ways for physical sensor virtualisation, dynamic provisioning of virtual sensor group and service instance for key issues. Furthermore, [PERSON] et al. [123] explored the joint communication and computation resource allocation to minimise the weighted-sum delay (RTT) of all devices in a cloud-edge collaboration system. In summary, the advantages of FC compared to traditional cloud computing are featured in [152; 153]. In Reference [154], the programming framework is designed to deliver resources to numerous IoT end-user devices by considering mobile FC. Therefore, at the primary level within FC, the examination has been accomplished for resource allocation with the FC framework. Finally, FC has its capabilities and competencies as follows. It has location awareness and can be located at the edges of a network. It incurs low latency, which supports large-scale complex sensor networks and storage capabilities in a wide-area distributed network. Network faults can be analysed online and be integrated with the back-end cloud system.
# Efficient Approaches to the Mixture Distance Problem
## 3 An \(O(nh_{1}h_{2})\)-Time Algorithm
### Algorithm MixtureDistance  
Algorithm MixtureDistance, as shown on Algorithm 1, proceeds the nodes of \(T_{1}\) by breadth-first search. For each internal node \(v\) in \(T_{1}\), we find out the leaves of \(T_{1}\) such that \(v\) is exactly the LCA of each pair of leaves, and then compute the LCA \(u\) of the leaves in \(T_{2}\) which are mapped into the found leaves of \(T_{1}\). Finally, the difference of the mutation times between \(u\) and \(v\) is calculated. For convenience, we define \((a,b)*(c,d)=ad+bc\) for any two ordered pairs \((a,b)\) and \((c,d)\) in this algorithm, where \(a,b,c\) and \(d\) are any four integers.  
The algorithm adopts a 2-coloring method [22] on the leaves in \(T_{1}\) and \(T_{2}\) for easy implementation. For each iteration associated with an internal node \(v\) of \(T_{1}\) in line 4, the leaves of the left and right subtrees rooted by \(v\) are colored by red and green, respectively. The mapped leaves in \(T_{2}\) have the same coloring as one in \(T_{1}\). The mixture distance between each internal node \(u\) in \(T_{2}\) and \(v\) is calculated according the coloring scheme in \(T_{2}\) (in lines 16-17), and the coloring information of \(u\) would be derived for the computation of its parent node (in line 18).  
The coloring information of \(u\), denoted by \(color(u)\), indicates the coloring information of the subtree in \(T_{2}\) rooted by \(u\). \(color(u)\) includes two numbers of \(u\)'s descendant leaves colored by red (\(color(u)[0]\)) and green (\(color(u)[1]\)), respectively. \(color(u)\) is derived by the coloring information of its two children. That is, \(color(u)[0]=color(u_{L})[0]+color(u_{R})[0]\) and \(color(u)[1]=color(u_{L})[1]+color(u_{R})[1]\), where \(u_{L}\) and \(u_{R}\) separately denote the left and right children of \(u\) in \(T_{2}\).  
In line 16, \(number(u)\) is achieved by the special product of the color vectors of \(u\)'s two children, \(number(u)=color(u_{L})[0]\times color(u_{R})[1]+color(u_{L})[1]\times color(u_{R})[0]\), which means the number of times that \(u\) is an \(LCA\) of a red leaf and a green leaf. We multiply the difference of their mutation times by \(number(u)\) in line 17, for computing the mixture distance between each internal node \(u\) in \(T_{2}\) and \(v\). At the end of Algorithm MixtureDistance, \(\mathcal{D}\) indicates the mixture distance of \(T_{1}\) and \(T_{2}\).  
Since the numbers of internal nodes in \(T_{1}\) and \(T_{2}\) (\(=\mathcal{I}_{1}\) and \(\mathcal{I}_{2}\)) are both equal to \(n-1\), two for-loops will take \(O(n)\) time, and the innermost for-loop always takes 2 (a constant) time units. Therefore, Algorithm MixtureDistance requires \(O(n^{2})\) computational time.
## 1 Introduction
[23] introduced the Cox proportional risk regression model to analyze the relationship between traumatic failure time and degradation value and gave the general model and parameter estimation method of competing failure when traumatic failure and degradation failure coexist; [PERSON] [24] constructed a competing failure model under the assumption that traumatic and degradation failures were dependent and that traumatic failure obeyed the Weibull distribution and degradation failure obeyed the Wiener process. The results showed that if only degradation failure is considered, the evaluation results would be optimistic, and the correlation between traumatic failure and degradation failure had a great impact on the accuracy of reliability evaluation. However, the above studies constructed competing failure models when traumatic failure information existed but did not involve the zero traumatic failure data situation. To summarize, it better reflects engineering reality to model the reliability and evaluate a product's life from competing points of view. However, many studies constructed competing failure models when traumatic failure information existed [25; 26; 27; 28]. They did not involve a zero traumatic failure data situation, which is the most common actual engineering situation during the period of using a product with high reliability. In order to solve the above problems, supposing that the failure rate ratio of the tested products does not change with time under different stress levels, this paper built a subdistribution competing risk model. Basic reliability with zero traumatic failure data is modeled by the unilateral confidence limit method under a two-parameter Weibull distribution. Performance degradation data are taken as covariates. The regression coefficients of the covariates are calculated and tested by SPSS software (version 22) [29]. The correctness and rationality of the method proposed in this paper are verified by a comparison with the modified maximum likelihood parameter estimation method [30], which does not consider competing failure and is only based on degradation information. The rest of this paper is organized as follows. Section 2 introduces the modeling process of the subdistribution competing risk model with zero traumatic failure data. Section 3 evaluates the life of a motorized spindle using the subdistribution competing risk model proposed in this paper and compares the result with the other method. Section 4 analyzes the evaluation results. Some concluding remarks are presented in Section 5.
# Error Correction of Water Vapor Radiometers for VLBI Observations in Deep-Space Networks
## 3 Error Source Analysis and Calibration  
The WVR brightness temperature measurement error and the WVR inversion error contribute the most to the standard deviation of the wet path delay difference measured by the water vapor radiometer. Any error in the WVR instrument translates into a brightness temperature error and then into a wet path delay error. The calibration of the WVR for this project consists of the following four steps:  
(1) Absolute system calibration is performed once a month, which includes the tip curve procedure discussed below;  
(2) Receiver gain error calibration is performed. Noise standard temperatures are applied to calibrate receiver gain fluctuations in conventional radiometer observations;  
(3) The temperature noise error of the antenna system is calibrated;  
(4) Oblique path calibration is performed.  
In the following, we analyze the different errors and their calibration results by experimental data.
## 3 Results
### Particle Size of the Microcapsules  
The size of the microcapsules varied between 7.98 and 13.36 \(\upmu\)m in all experiments, except for encapsulated ethanolic seed extracts, which had a larger size of 60.96 \(\upmu\)m (Table 3). However, the size variation of microcapsule powders is a particular characteristic of spray-dried microcapsules [55]. According to [PERSON] et al. [56], the particle diameter of microcapsule products obtained via the spray drying technique ranged from 1 to 15 \(\upmu\)m. Our data were generally similar to those expressed in the literature, where the droplet size of the capsules ranged from 2 to 10 \(\upmu\)m in diameter [31]. These characteristics of microcapsules have been reported in previous works, such as a study by [PERSON] et al. [57], who highlighted a particle size greater than 50 \(\upmu\)m for the microencapsulation of peel extract. The molecular structure of the carrier agents explains the differences in microcapsules size [58]. Probably due to its higher emulsion viscosity, okra seed showed a larger size. [PERSON] et al. [49] suggested that the presence of pectin has a significant effect on particle size. Also, according to [PERSON] et al. [59], capsules obtained via complex coacervation can have particle sizes ranging from 1 to 500 \(\upmu\)m. On the other hand, a relationship was estimated between particle size distribution and span values, where a span with lower values indicates a more homogeneous particle size distribution [60]. In the same context, it has been reported in the literature that higher span values indicate a wider range of particle size distribution [61]. Subsequently, the smallest span values were detected for the spray-dried aqueous leaves and seeds, with span values below 2. Smaller diameters were also found for these samples.  
Figure 2: Anti-oxidant activity values of non-encapsulated and encapsulated phenolic powder. Data are shown as means \(\pm\) standard deviation (\(n=3\)). The different lower-case letters indicate significantly different values (\(p<0.05\)).  
Furthermore, the microcapsules obtained in our study were smaller than 100 \(\upmu\)m, which allowed them to function as effective delivery systems and may simplify their utilization in food products [62]. In particular, the release rate of bioactive molecules increased as the size of the microcapsules was reduced [63]. Our findings are in line with the results of previous studies, which reported that the size of microcapsules used for food applications should be less than 100 \(\upmu\)m to avoid affecting the oral sensation (i.e., grititness) from the product [64]. In other ways, the small size of the capsules makes it possible to control the continuous release of the encapsulated molecules [65]. Moreover, more the microcapsules means decreased particle size and encapsulated core distribution becoming more narrow, which maintains product consistency.
# Joint Channel Estimation Algorithm Based on DFT and DWT
## 5 Joint Channel Estimation Algorithm Based on DFT and DWT
### MSE Estimation of DWT and ST-DFT Channel Estimation Algorithms  
By substituting Equation (35) into Equations (26) and (32), the MSE estimates for the DWT algorithm and the ST-DFT algorithm separately:  
\[\widetilde{\text{MSE}}_{\text{DWT}}[k]=\frac{L_{\text{total}}-L_{0}}{L_{\text {total}}}\sigma_{s\text{-}wf}^{2}. \tag{36}\]  
\[\widehat{\text{MSE}}_{\text{ST-DFT}}[k]\approx\left\{\begin{array}{rl}\sum \limits_{n=0,n\in\Theta}^{N-1}\left|\hat{h}_{\text{V}}[n]\right|^{2}+\frac{N_{ \text{P}}}{N}\hat{\sigma}_{s\text{-}wf}^{2}-2\frac{KN_{\text{P}}}{N^{2}}\hat {\sigma}_{s\text{-}wf}^{2}&T=P_{\text{max}},\\ \sum\limits_{n=0,n\in\Theta}^{N-1}\left|\hat{h}_{\text{V}}[n]\right|^{2}+ \frac{N_{\text{P}}}{N}\hat{\sigma}_{s\text{-}wf}^{2}-2\left(\frac{K}{N}+\frac {1}{2}\left(1-\frac{K}{N}\right)\ln\left(1-\frac{K}{N}\right)\right)\frac{N_{ \text{P}}}{N}\hat{\sigma}_{s\text{-}wf}^{2}&\text{otherwise},\end{array}\right. \tag{37}\]when there are no prior conditions, for a given CIR, based on the MSE estimated value of each algorithm given by Equations (36) and (37), the ST-DFT estimation algorithm and the DWT-based estimation algorithm can be selected optimally.
## 5 Performance Evaluation
### Estimation Model Results Analysis
#### 5.2.3 Performance According to the Number of Neurons in the Embedding Layer  
Different network architectures may lead to the widely varying performance of the network. One of the essential tasks of the estimation model is to interpret weather and distance information in the environment. As mentioned in Section 4.2, different embedding layers are used to handle weather and distance information. We take \(n_{W}\) as the number of  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Method** & **MAE** \\ \hline Linear Smoothing & 0.114 \\ Exponential Smoothing & 0.062 \\ SVR & 0.032 \\ Proposed method & 0.014 \\ \hline \hline \end{tabular}
\end{table}
Table 4: MAE of Different Methods.  
Figure 5: CDF of MAE for different methods in estimation model to predict SNR in different locations.  
neurons in the weather embedding layer and \(n_{D}\) as the number of neurons in the distance embedding layer.  
The experimental results are shown in Table 5, and it can be seen that the best performance is achieved when \(n_{W}\) and \(n_{D}\) are 3 and 5, respectively. This value corresponds exactly to the number of dimensions of the data in the input states.
## 4 Discussion
### Interpretation and Clinical Relevance  
The results of this review align with previous research highlighting the role of auditory cueing in bypassing dysfunctional basal ganglia circuits and facilitating motor performance [47; 48]. Visual cues, while effective for spatial guidance, appeared less impactful for temporal gait improvements. The sustained benefits observed in structured, supervised interventions compared to home-based programs emphasize the importance of intervention intensity and clinician oversight.  
The findings from this review suggest that cueing interventions, particularly auditory stimuli, may have the potential to improve gait parameters and dynamic balance in individuals with Parkinson's disease (PD). However, given the small sample sizes, methodological variability, and inconsistent follow-up in the included studies, these results should be interpreted with caution.  
Auditory cues appear to offer more benefits for temporal gait parameters, such as walking speed and step length, compared to visual cues, which seem more effective for spatial guidance. Structured, supervised interventions, rather than home-based programs, might provide greater and more sustained improvements, but further research is necessary to confirm these findings. Clinicians could consider incorporating cueing strategies as part of a broader rehabilitation plan for PD, particularly for improving dynamic stability and gait performance.  
Nevertheless, it remains unclear whether cueing interventions alone can address static balance deficits or lead to measurable improvements in quality of life. As such, these strategies should be viewed as adjunctive tools rather than standalone solutions. Combining cueing with other interventions, such as targeted balance training, cognitive-motor exercises, or assistive technologies, may offer a more comprehensive approach to managing motor impairments in PD.  
The variability in the outcomes observed across studies may be explained by differences in cueing protocols, patient characteristics, and disease severity. For instance, studies with more frequent or supervised cueing interventions tended to show greater improvements in gait and balance outcomes ([PERSON] et al., 2019 [34]; [PERSON] et al., 2020 [35]). Conversely, less intensive home-based interventions yielded more modest results. Additionally, variations in patient motor abilities, such as baseline gait impairments and Hoehn and Yahr stages, likely influenced responsiveness to cueing strategies. These findings underscore the importance of tailoring cueing interventions to individual patient profiles to optimize effectiveness.  
Future research, particularly high-quality trials with standardized protocols and larger sample sizes, is needed before definitive recommendations for clinical practice can be made.
## 3 Fuzzy MPC Algorithm with Advanced Generation of Prediction
### Generation of the Dynamic Matrix  
The dynamic matrix, needed to obtain forced response in the prediction can be calculated using an easy-to-obtain fuzzy Takagi-Sugeno model which has local models in the form of step responses [34]. Design process of such a model is very simple, because it is sufficient to collect a few sets of step responses (near a few operating points). These step responses can be obtained directly on the control plant or using a nonlinear model of the process. Next, the premises of the model should be formulatedusing expert knowledge, and then tuned, for example, by means of a fuzzy neural network [7]. Thus, the model has the following form:  
Rule _f_: (20) \[\text{if}\,y_{k}^{y_{y}}\text{ is }B_{1}^{f,j_{y}}\text{ and }\dots \text{ and }y_{k-n+1}^{j_{y}}\text{ is }B_{n}^{f,j_{y}}\text{ and }\] \[u_{k}^{j_{u}}\text{ is }C_{1}^{f,j_{u}}\text{ and }\dots \text{ and }u_{k-m+1}^{j_{u}}\text{ is }C_{m}^{f,j_{u}}\] \[\text{ then }\tilde{y}_{k}^{j,f}=\sum_{m=1}^{n_{u}}\sum_{n=1}^{p_{d}-1} a_{n}^{j,m,f}\cdot\Delta u_{k-n}^{m}+a_{p_{d}}^{j,m,f}\cdot u_{k-p_{d}}^{m}\,\]  
where \(y_{k}^{j_{y}}\) is the value of \(j_{y}\)th output variable at the \(k\)th sampling instant, \(u_{k}^{j_{u}}\) is the value of \(j_{u}\)th manipulated variable at the \(k\)th sampling instant, \(B_{1}^{f,j_{y}},\dots,B_{n}^{f,j_{y}}\), \(C_{1}^{f,j_{u}},\dots,C_{m}^{f,j_{u}}\) are fuzzy sets, \(a_{n}^{j,m,f}\) are the coefficients of step responses in the \(f\)th local model, \(j_{y}=1,\dots,n_{y}\), \(j_{u}=1,\dots,n_{u}\), \(f=1,\dots,l\), \(l\) is number of fuzzy rules. The output values of the model (20) can be calculated using the following formula:  
\[\tilde{y}_{k}^{j}=\sum_{m=1}^{n_{u}}\sum_{n=1}^{p_{d}-1}\tilde{a}_{n}^{j,m} \cdot\Delta u_{k-n}^{m}+\tilde{a}_{p_{d}}^{j,m}\cdot u_{k-p_{d}}^{m}\, \tag{21}\]  
where \(\tilde{a}_{n}^{j,m}=\sum_{f=1}^{l}\tilde{w}_{f}\cdot a_{n}^{j,m,f}\) and \(\tilde{w}_{f}\) are the normalized firing strengths of the fuzzy rules calculated using fuzzy reasoning, see for example, References [43; 44]. Note that one can consider the model (21) as the step response describing behavior of the control plant near the current operating point. This model is then used at each sampling instant of the proposed algorithms to obtain a new, updated dynamic matrix:  
\[\mathbf{A}_{k}=\left[\begin{array}{cccc}\mathbf{A}_{k}^{11}&\mathbf{A}_{k}^{12}&\dots &\mathbf{A}_{k}^{1n_{u}}\\ \mathbf{A}_{k}^{21}&\mathbf{A}_{k}^{22}&\dots&\mathbf{A}_{k}^{2n_{u}}\\ \vdots&\vdots&\ddots&\vdots\\ \mathbf{A}_{k}^{n_{y}1}&\mathbf{A}_{k}^{n_{y}2}&\dots&\mathbf{A}_{k}^{n_{y}n_{u}}\\ \end{array}\right], \tag{22}\]  
\[\mathbf{A}_{k}^{jm}=\left[\begin{array}{cccc}\tilde{a}_{p}^{j,m}&0&\dots&0&0\\ \tilde{a}_{2}^{j,m}&\tilde{a}_{1}^{j,m}&\dots&0&0\\ \vdots&\vdots&\ddots&\vdots&\vdots\\ \tilde{a}_{p}^{j,m}&\tilde{a}_{p-1}^{j,m}&\dots&\tilde{a}_{p-s+2}^{j,m}&\tilde {a}_{p-s+1}^{j,m}\\ \end{array}\right]. \tag{23}\]