esa-sceva/satcom-chunk-collection huggingface dataset:
# Shallow Water Waves and Conservation Laws with Dispersion Triplet
## 2 Single Nonlinearity (KdV Equations)
### Modified KdV Equation  
Here, \(F(q)=aq^{2}\) for any real-valued constant \(a\). From (1), this leads to [8]  
\[q_{t}+aq^{2}q_{x}+b_{1}q_{xxx}+b_{2}q_{xxt}+b_{3}q_{xtt}=0, \tag{20}\]  
which means that (5) transforms into  
\[6\sigma g^{2}-ag^{4}-6\Big{(}b_{1}-b_{2}v+b_{3}v^{2}\Big{)}\big{(}g^{\prime} \big{)}^{2}=0. \tag{21}\]  
Thus, Equation (20) is the generalization of Equation (6) for the mKdV equation with the dispersion triplet. This is also the generalized version of the KdV equation that was first proposed during 1977 [8]. Finally, separating variables and integrating yields a solitary wave solution as follows:  
\[q(x,t)=A\text{sech}[B(x-vt)]. \tag{22}\]  
Here, the inverse width is \(B\) and \(A\) is the amplitude of the wave; they are defined as  
\[A=\sqrt{\frac{6\upsilon}{a}}, \tag{23}\]and  
\[B=\sqrt{\frac{v}{b_{1}-b_{2}v+b_{3}v^{2}}}, \tag{24}\]  
which would once again imply the parameter constraint as given by (11). This time, the amplitude of the solitary wave imposes the restriction  
\[av>0. \tag{25}\]  
Figure 2 displays the surface plot of a solitary wave (22) of the mKdV equation with triple dispersion terms. The parameter values chosen are \(a=1\), \(v=1\), \(b_{1}=1\), \(b_{2}=1\), and \(b_{3}=1\).  
Conservation laws  
In this case, the multipliers, conserved densities, and fluxes are given as  
Case 1:  
\[Q=1\text{ and }T^{t}=-\frac{2}{3}b_{3}q_{xt}-\frac{1}{3}b_{2}q_{xx}-q. \tag{26}\]  
Case 2:  
\[Q=q\text{ and }T^{t}=-\frac{2}{3}qb_{3}q_{xt}-\frac{1}{3}b_{2}q_{xx}q+\frac{1}{3 }b_{3}q_{x}q_{t}+\frac{1}{6}{b_{2}q_{x}}^{2}-\frac{1}{2}q^{2}. \tag{27}\]  
Case 3:  
\[Q=\frac{1}{2b_{2}}\Big{(}aq^{3}+3b_{1}q_{xx}+3b_{2}q_{xt}+3b_{3}q_{xt}\Big{)}, \tag{28}\]  
and  
\[\begin{array}{c}T^{t}=2 aq^{3}-b_{1}b_{2}qq_{xxxx}+b_{1}b_{2}q_{x}q_{xxx}+2b _{1}b_{2}q_{xx}{}^{2}-2b_{1}b_{3}qq_{xxxt}\\ +4b_{1}b_{3}q_{t}q_{xxx}-2b_{1}b_{3}q_{t}q_{xtxt}+4b_{1}b_{3}q_{t}q_{xt}-b_{2 }^{2}q_{xxxt}+b_{2}^{2}q_{x}q_{xtxt}\\ +2b_{2}{}^{2}q_{xt}q_{xx}-3b_{2}b_{3}qq_{xtxt}+4b_{2}b_{3}q_{t}q_{xtxt}+2b_{2 }b_{3}q_{tt}q_{xx}-b_{2}b_{3}q_{t}q_{xtxt}\\ +4b_{2}b_{3}q_{xt}{}^{2}-2b_{3}{}^{2}qq_{xtxt}+4b_{3}{}^{2}q_{t}q_{xtxt}+4b_{ 3}{}^{2}q_{tt}q_{xt}\\ -2b_{3}{}^{2}q_{tt}q_{x}+6b_{1}q_{xx}+3b_{2}qq_{xt}+3b_{2}q_{t}q_{x}+6b_{3}q_ {t}{}^{2}.\end{array} \tag{29}\]  
Thus, for mKdV equation, the conserved quantities are  
\[M=\int\limits_{-\infty}^{\infty}T^{t}dx=\int\limits_{-\infty}^{\infty}qdx= \frac{\pi A}{B}, \tag{30}\]  
Figure 2: Profile of a solitary wave for the mKdV equation, without radiation.  
\[P=\int\limits_{-\infty}^{\infty}T^{t}dx=\frac{1}{6}\int\limits_{-\infty}^{\infty} \{3q^{2}-(b_{2}-6 vb_{3})q_{x}^{2}\}dx=\frac{A^{2}}{9B}\{9-B^{2}(b_{2}-6 vb_{3})\}, \tag{31}\]  
\[H=\int\limits_{-\infty}^{\infty}T^{t}dx=\int\limits_{-\infty}^{\infty}\Big{\{}2 aq^{3}-6\Big{(}b_{1}-v^{2}b_{3}\Big{)}q_{x}^{2}\Big{\}}dx=\frac{A^{2}}{3B} \Big{\{}3\pi aA-4B^{2}\Big{(}b_{1}-v^{2}b_{3}\Big{)}\Big{\}}. \tag{32}\]
## 3 Methodology
### Input Variables  
This study selected four types of variables as input indicators for the model: vegetation growth, surface moisture, radiative energy, and others. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithms** & **Main Parameters** \\ \hline Random Forest & n\_estimators = 20, max\_depth = 50 \\ Backpropagation neural network & hidden\_layer\_sizes = (50, 50), activation = ’relu’, max\_iter = 200, learning\_rate = 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Definitions of input variables extracted from Landsat observations. Vegetation growth is characterized by spectral indices constructed with reference to the relevant literature. Here, 11 commonly used spectral indices are selected, as shown in Table 4. Through correlation analysis, it can be seen that these indices have varying degrees of correlation with ET and NEE, demonstrating their potential for accurately estimating ET and NEE. All the VIs were derived from the six optical bands--blue, green, red, near-infrared, and two shortwave infrared bands captured by both Landsat 7 and Landsat 8. A Pearson correlation (Equation (4)) analysis was conducted between ET and NEE, utilizing vegetation indices (VIs) derived from satellite observations to prove the potential of the Vis:  
\[r=\frac{\sum_{i=1}^{n}\left(X_{i}-\overline{X_{i}}\right)\left(Y_{i}-\overline{ Y_{i}}\right)}{\sqrt{\sum_{i=1}^{n}\left(X_{i}-\overline{X_{i}}\right)^{2}} \sqrt{\sum_{i=1}^{n}\left(Y_{i}-\overline{Y_{i}}\right)^{2}}} \tag{4}\]  
where X and Y are the variables, as illustrated in Figure 3. Divergent outcomes emerged for ET and NEE. Among them, SAVI exhibited the strongest correlation with ET, achieving a correlation coefficient (r) of 0.66. CVI, NDVI, AFRI, GCI, ENDVI, and LSWI followed, all demonstrating comparable r values exceeding 0.5. Conversely, EVI, NPCI, and MDWI showed a weak correlation with r values below 0.1. When considering NEE, the correlations with VIs were generally weaker compared to those with ET. The majority of the correlations between various VIs and NEE were less than 0.2, with MNDVI, EVI, NPCI, and MDWI falling below 0.1. Surface moisture conditions can influence vegetation transpiration and photosynthesis to some extent, as well as soil evaporation. Here, surface temperature (Ts), Temperature Vegetation Drought Index (TVDI), and Surface-Air Temperature Difference (SATD) are selected to represent surface moisture conditions. Ts were obtained from Landsat 7/8 thermal band [27]. TVDI was calculated based on Ts-NDVI space (Equation (5)) [61].
## 4 Recent Advancements in Applications
### Gamification and Virtual Reality  
Many advanced applications of employing data captured by MMSs are now possible, thanks to powerful 3D engines such as Unity and Unreal engines. These frameworks can efficiently generate highly realistic renders of urban environments [134] for use in applications such as gaming, simulation, and various engineering applications. MMSs are among the most valuable sources of data for creating detailed models within these engines. The incorporation of physics-based simulations in these platforms enables the creation of virtual environments that can be utilized for innovative applications, such as generating synthetic training data for robotic and autonomous systems [135]. This capability is particularly useful for developing and testing algorithms in controlled, yet highly realistic, virtual environments.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Category** & **Selected Literature** & **Key Applications** \\ \hline Natural resource monitoring & An individual tree segmentation [114], forest digital twin [136] & -Individual tree detection -Trunk recognition from point-cloud \\  & Forest parameter estimation at single-tree level [137], 3D mapping [138], biomass and CO\({}_{2}\) estimation [139], Individual tree detection [140] & -Biomass estimation -Forest digital twin -CO\({}_{2}\) estimation \\ Environment monitoring & Rocky landslide monitoring [141] & -Camera-based MMS -Hazardous site mapping -Image-based point clouds -UAV MMS platforms -Harvest estimation; -yield mapping and monitoring -Crop classification [143] & -Camera-based MMS -Hazardous site mapping -Image-based point clouds -UAV MMS platforms -Harvest estimation; -yield mapping and monitoring -Crop classification [143] & -UAV MMS platforms -Harvest estimation; -yield mapping and monitoring -Crop classification -Irritation planning monitoring -Water stress monitoring; -pest detection \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of important literature on mobile mapping systems and key applications.  
Beyond the primary domains discussed, MMS technologies have found a wide range of miscellaneous applications across various fields. For instance, MMS has been successfully employed for underwater monitoring [155], enabling the collection of high-resolution spatial data in aquatic environments. This application is particularly valuable for marine research, underwater infrastructure inspection, and environmental monitoring. Additionally, MMS has been utilized in areas such as autonomous driving [97; 159], indoor collision avoidance [162], archaeology, disaster response, and even entertainment, where precise 3D mapping is required for virtual reality experiences or film production. The versatility of MMS continues to expand as new use cases emerge, demonstrating its potential to address diverse challenges across multiple industries.
## 3 Machinery
### Rewrite Systems  
Next, we introduce term rewrite systems and the special form in which we will use them here.  
* A _rewrite rule_ is an oriented pair of terms, denoted \(\ell\to r\), such that \(sort(\ell)=sort(r)\) and \(var(r)\subseteq var(\ell)\). Because of the last requirement, generally \(r\rightarrow\ell\) is not a legal rewrite rule, and rewrite rules cannot be reversed without generating unbound variables. Furthermore, we disallow \(\ell\in V\), as such a rule would allow to rewrite _any_ term, while \(r\in V\) is perfectly legal.
* A _term rewrite system_\(R\) is a finite set of such rewrite rules. The rewrite relation induced by \(R\), written \(\rightarrow_{R}\), is the smallest relation closed under context and substitution containing each rule of \(R\). In other words, a term \(t\) rewrites to a term \(u\), written \(t\rightarrow_{R}u\), if there exist a position \(p\) in \(t\), a rule \(\ell\to r\) in \(R\) and a substitution \(\sigma\) such that \(t|_{p}=\ell\sigma\) and \(u=t[r\sigma]_{p}\). \(\rightarrow_{R}^{*}\) is the reflexive transitive closure of \(\rightarrow_{R}\).
* In the sequel, we will consider term rewrite systems with disjoint signatures. We say that \(R\) is a term rewrite system _with disjoint signatures_ if it is possible to partition \(F\) into two subsets \(\zeta\) and \(\Sigma\) such that for each rule \(\ell\to r\) of \(R\), the left-hand side \(\ell\) belongs to \(T(\zeta,V)\), and the right-hand side \(r\) belongs to \(T(\Sigma,V)\). In this manuscript, \(\zeta\) is called the _core signature_, and \(\Sigma\) the _satellite signature_. Ground terms of \(T(\zeta)\) are called _core terms_. \(\zeta\) and \(\Sigma\) can both contain an associative binary operator, denoted \(\sim_{\zeta}\) and \(\sim_{\Sigma}\) respectively (see below).  
In practice, core signatures may share function symbols with satellite signatures (possibly not with the same arity). Often, they share the alphabet. By convention, when a shared symbol occurs in a rewrite rule, it belongs to the signature \(\zeta\) on the left-hand side, and to \(\Sigma\) on the right-hand side. Elsewhere, symbols of \(\zeta\) will be subscripted for clarity.
* Syntactic conditions: Rewrite rules may have associated syntactic conditions for their applicability, as in \[f(a,b,X)\to X{\sim}a\textbf{ if }a=b\text{ for }a,b\in\mathcal{A}\] In our framework, these conditions will only refer to characters from a finite alphabet. This is merely a shorthand against having to write too many similar rules, and does not contribute computational power. It must not be confused with general conditional term rewriting as in \(f(x,y)+y\to 2*x\textbf{ if }x=y\), where the rule is applicable if \(x\) and \(y\) can be rewritten to a joint reduct by the given rewrite system.
## 3 Performance Analysis Methods
### Expressions for Path Loss and Average Path Loss
#### 3.1.1 The Average Path Loss for LOS Links  
The rays from the LOS link are the main source of received power. From (9), it can be seen that the average path loss of the LOS link is closely related to \(D_{LOS,j}^{V_{i}-PD}\), and \(D_{LOS,j}^{V_{i}-PD}=\sqrt{{L_{h_{j}}}^{2}+{I_{V_{1}-PD}}^{2}}\). \(L_{h_{j}}\) takes on different ranges of values when Tx1 is located at different positions relative to the center axis of PD. Therefore, the average path loss for LOS links needs to be discussed separately. Refer to Appendix A for the detailed derivation process. Therefore, the closed-form expression for the average path loss of the LOS link is obtained as follows:  
\[\begin{array}{rl}h_{LOS}^{PL\_av}&=\frac{{{D_{R}}^{2}{\epsilon}^{2}{ \epsilon}^{-\frac{{c_{C}D_{R}}}{\epsilon}}}}{{{2\zeta^{2}{I_{V_{1}-PD}}{ \left({L_{w}-w}\right)}{\left({Gamma_{\left[1+\frac{1}{\epsilon}\right]}} \right)}}}}\left\{{2\sqrt{\pi}{Gamma}}\left[\frac{1}{2}+\frac{1}{\epsilon} \right]\right.\\ &\left.-{Gamma}\left[1+\frac{1}{\epsilon}\right]\left\{{Beta\left[\frac{{4{I_{V _{1}-PD}}^{2}}}{{4{I_{V_{1}-PD}}^{2}+{L_{w}}^{2}}},\frac{1}{2}+\frac{1}{ \epsilon},\frac{1}{2}\right]+Beta\left[\frac{{4{I_{V_{1}-PD}}^{2}}}{{4{I_{V_{1 }-PD}}^{2}+{(L_{w}-2w)}^{2}}},\frac{1}{2}+\frac{1}{\epsilon},\frac{1}{2}\right] }\right\}\right\}.\end{array} \tag{12}\]
## 2 Related Work
### The Proposed Approach  
The MFHS (Mist-based fuzzy healthcare system) operates across four layers: the Edge layer, the Mist layer, the Fog layer, and the Cloud layer, each playing a crucial role in processing data for healthcare systems. In the following section, we provide a detailed description of these layers and outline their functionalities within our approach. Additionally, Figure 1 provides a concise overview of the system design, illustrating all the components utilized in our proposed approach.  
1. Edge layer: It collects medical data such as body temperature using sensor devices. The Edge layer sends the sensed data to the Mist layer, which categorizes data based on the patient's condition. The Edge layer only sends the sensed data that a Mist layer requires for categorization, which means some medical sensor devices can be removed without affecting the system.
2. Mist layer: The Mist layer receives the sensed data from the Edge layer. It categorizes data based on the patient's health condition and the computing capacity of Mist using two fuzzy logic systems, namely MFHS1 and MFHS2. MFHS1 focuses on data categorization, where the Mist broker employs fuzzy rules to classify the data based on the patient's health condition and its priority. On the other hand, MFHS2 is responsible for estimating the computing capacity of the Mist nodes, enabling the system to determine whether the data should be processed in the Fog, Cloud, or within the Mist layer itself.
3. Fog layer: The Fog layer via the Fog broker is responsible for exceptional cases, such as when the Mist layer is unable to process data due to storage or capacity limitations. The Fog broker takes charge of distributing these data among the Fog nodes based on the clustering of these nodes.
4. Cloud layer: The Cloud layer receives high-priority cases directly from the Mist layer for processing. Additionally, it acts as a recipient of data when the computing capacity of both the Mist and Fog nodes is insufficient to handle the workload.
# InSAR-CTPIM-Based 3D Deformation Prediction in Coal Mining Areas of the Baisha Reservoir, China
## 4 Real Experiments  
### Experimental Area and Experimental Data  
Jiansheng Coal Mine is located southwest of Bisha Reservoir in Dengfeng City, Henan Province, and its geographical location is shown in Figure 6b; the red box in Figure 6a is the Sentinel-1A up-orbiting satellite image coverage, and the blue rectangular box in Figure 6c is the study area of this paper, which covers an area of 16.4 km\({}^{2}\). The distribution of mineral resources around the study area is extremely dense, mainly dominated by coal mines; due to the close proximity to the reservoir, the underground water content around the mining area is relatively rich, coupled with long-term mining activities, resulting in exposed rock strata and sparse vegetation in the area, and the long-term cumulative deformation has made the area highly susceptible to accidents, such as surface cave-ins and mine water penetration.  
In this paper, the SAR data are processed using the SBAS-InSAR technique, and 12 views of Sentinel-1A up-orbit SAR images covering the study area from 13 November 2015 to 19 November 2016 are processed with pre-differential interferometric processing as observation data, and the cumulative deformations from 13 November 2015 to 1 December 2016, 18 January 2017, 23 February 2017, and 7 March 2017 are taken as the validation data to verify the reliability of the proposed method. The basic information of the SAR image is shown in Table 3. The spatio-temporal baseline distribution is shown in Figure 7; in  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Analog Value** & **Real Value** & **Inaccuracies** & **Relative Error** \\ \hline \(q\) & 0.711 & 0.722 & 0.011 & 1.5\% \\ \(d\) & 0.326 & 0.335 & 0.009 & 0.9\% \\ \(\tan\beta\) & 1.251 & 1.239 & 0.012 & 2.7\% \\ \(\theta_{0}\) & 83.29 & 81.14 & 2.15 & 2.5\% \\ \(S_{1}(m)\) & 7.71 & 8.04 & 0.33 & 4.2\% \\ \(S_{2}(m)\) & 11.22 & 11.85 & 0.63 & 5.6\% \\ \(n\) & 0.167 & 0.175 & 0.008 & 4.8\% \\ \(c\) & 8.261 & 8.443 & 0.182 & 2.2\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Model parameter by InSAR-3D-CTPM.  
Figure 5: Comparison between the true value of deformation and the value predicted by the InSAR-3D-CTPM model.  
addition, the geological parameters of the survey area are \(G_{1}\) = [0.66 m, 620 m, 580 m, 4.5\({}^{\circ}\), 84\({}^{\circ}\), 300 m, 750 m, and 2 m/d].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Serial** & **Acquisition** & **Orbital** & **Polarization** & **Absolute** \\
**Number** & **Time** & **Direction** & **Mode** & **Orbit** \\ \hline  
\hline \hline \end{tabular}
\end{table}
Table 3: SAR image parameters.  
Figure 6: Map of the study area and SAR image coverage.
## 3 Experiments and Analysis
### Datasets and Pre-Processing  
#### 3.2.1 Initial Dataset  
The dataset referred to in this paper contains 15 different diseases that may be encountered during the growth of grapes, namely: (1) healthy grapes, (2) healthy leaves, (3) powdery mildew, (4) Black rot, (5) Esca, (6) brown spot, (7) black spot, (8) downy mildew, (9) Sour rot, (10) deficiency, (11) anthracnose, (12) botytis cinerea, (13) felt diseases, (14) leaf roll virus, (15) and phylloxera. These images come from the State Key Laboratory of Plant Pest Biology, which is the authoritative modern agricultural technology industrial system for grapevine pest prevention and control in China, possessing comprehensive and targeted research on grapevine pests and diseases in China and complete data on grapevine diseases and control strategies. Figure 9 shows representative images of some grape diseases in the dataset.  
As shown in Figure 9, grape anthracose manifests itself as small brown circular spots on the fruit surface; grape sour rot manifests itself as weak brown spots or streaks on the grape surface; grape downy mildew manifests itself as polygonal yellow-brown spots consisting of grape leaves; and grape leaf roll manifests itself as a recoiling of the growing leaves from the leaf margin downward.  
Figure 8: Prediction head introduces double residual edges.  
Figure 9: Dataset images. (**a**) Anthracnose; (**b**) Sour rot; (**c**) powdery mildew; (**d**) leaf roll.  
Figure 10 shows the initial data volume of the dataset, with 15 categories and 2566 images. From this figure, it is found that the various types of image data in the original dataset are unbalanced, which may lead to problems such as overfitting and poor generalization of the trained model. Therefore, pre-processing of the original grape disease images is needed.
## 4 Experiments and Results
### Simulation Experiments  
Simulation experiments were mainly divided into four stages: demand forecasting, modeling and solving, testing, and evaluation. In the demand forecast, the parking demand of the Jinding Tiandi parking lot was predicted during peak and non-peak hours. The numbers of departure vehicles in the parking lot were obtained. Then, the timing and inductive control models were established for the parking lot exits. The timing and inductive control schemes of different exits in the intelligent lever lift systems were solved, respectively. The optimal mediation rate of the intelligent lever lift system on the parking lot exits and the maximum waiting time of the plot were obtained.  
In the testing stage, the Jinding Tiandi traffic simulation environment was built using SUMO simulation with TraCI (traffic control interface) for real-time control. SUMO is an open-source microscopic road simulation tool that can simulate vehicle movements, interactions between vehicles, etc. SUMO can use the traffic control interface TraCI to achieve cooperation between simulation tools, and realize real-time interaction and data acquisition using command lines and graphical user interfaces [21; 22]. According to the actual roads in the Jinding Tiandi parking lot, the road topology model was configured in SUMO, as were the queue and speed detection devices on the parking lot exits required for timing and inductive control. Vehicle movement models with different ODs were configured in the simulation platform according to the demand forecast results. According to the control strategy and solution results, the corresponding lever lift frequency and algorithm trigger conditions were loaded in the simulation system. We ran the simulation 1000 times to obtain the test results of the regional road network under different schemes and in different periods.  
In the evaluation stage, to verify the effectiveness of the proposed intelligent control strategy for vehicle departure, the average speed, the average queue length of intersections of main trunk roads (Shenjiang Road), secondary trunk roads (Keqiao Road, Jufeng Road), and internal branch roads of the plots (Hanqiao Road, Zhiqiao Road, Shentao Road, Shenqi Road, Shenlun Road), and the average queue length at the exits of parking lots were used to compare the performance of the non-controlled strategy, the timing control strategy, and the inductive control strategy.
## 3 Methodology
### Phase 2: Optimal Architecture Synthesis
#### 3.2.4 Multi-Scale Architecture Variants  
Three architecture variants were designed to accommodate varying computational constraints and performance requirements. The details of these optimal variants of the FND model are presented in Table 1. The small variant is suitable for resource-constrained environments. The base variant offers a balance between performance and computational efficiency. The large variant is intended for scenarios that require maximum performance. This multi-scale approach enables deployment across various computational environments while maintaining architectural consistency.