esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Theory and Formulations
### Modelling Beam Element
Substituting Equation (43) into Equation (41), the differential equation governing the motion can be written in the following form as in Equation (44), with the applied clamped boundary conditions for \(q_{1}\) and \(q_{p}\) being zero. Subscript \"\(s\)\" in Equation (44) stands for the matrices with the boundary condition applied. \[\Big{(}[K_{s}]+i[H_{s}]-\omega^{2}[M_{s}]\Big{)}\{q_{o}\}=\{F_{\max}\} \tag{44}\]  
At nodes \(1\) and \(p\), since the system is clamped (Figure 4), reaction forces \(R_{1}\) and \(R_{p}\) occur. In the global stiffness matrix, only \(K(1,2)\) and \(K(p,p-1)\) elements remain non-zero after boundary conditions are applied. Multiplying these elements by the corresponding displacements (\(q(2,1)\) and \(q(p,p-1)\)) gives the total reaction forces (Equation (45)). The maximum total magnitude of reaction forces (also defined as force transmitted to ground) at the clamped ends and its ratio by maximum force \(F_{max}\) can be defined as force transmissibility \(T_{R}\) (Equation (46)). \[ \begin{array}{l}R_{1}=\big{(}(K(1,2)+iH(1,2))-\omega^{2}M(1,2)\big{)}q_{2} \\ R_{p}=\big{(}(K(p,p-1)+iH(p,p-1))-\omega^{2}M(p,p-1)\big{)}q_{(p-1)}\end{array}  \tag{45}\]  
\[T_{R}=\bigg{[}\frac{R_{1}+R_{p}}{F_{max}}\bigg{]} \tag{46}\]
# Exploring Safety-Stability Tradeoffs in Cooperative CAV Platoon Controls with Bidirectional Impacts
## 4 Analytical Verification on Specific Car-Following Models
### Linear Car-following Model
For the velocity difference bidirectional Helly's model, by applying the partial differential equations to Equation (12), we obtain Equation (32). \[\frac{\partial TTC_{n+1}^{\Delta v}(t+\Delta t)}{\partial f_{\Delta\varphi_{n+ 1}}}\bigg{|}_{(\overline{v},\,\overline{s})}=\frac{(\varphi_{n+1}(t+\Delta t) +s_{e})\mu_{n+1}(t)\Delta t}{\left(\mu_{n+1}(t+\Delta t)-\gamma_{v}\mu_{n+1}(t )\Delta t\right)^{2}} \tag{32}\]  
Since \(\frac{\partial TTC_{n+1}^{\Delta v}(t+\Delta t)}{\partial f_{\Delta\varphi_{n+ 1}}}>0\), it can be observed that when \(f_{\Delta\varphi_{n+1}}>0\) (IP), \(TTC_{n+1}^{\Delta v}(t+\Delta t)\) increases, implying lower collision risk. On the contrary, when \(f_{\Delta\varphi_{n+1}}<0\) (OP), \(TTC_{n+1}^{\Delta v}(t+\Delta t)\) decreases, leading to higher collision risk. The above rear-end collision risk analyses on [PERSON]'s model demonstrate the findings presented in Tables 2 and 3. We now proceed to derive the stability condition of the bidirectional Helly's model. Applying the partial differential equations to Equations (22) and (26), we can obtain the stability transition curves for both the spacing and velocity difference bidirectional models from the neutral stability criterion. Figure 4 presents the stability transition curves for both models. Figure 4a shows the stability transition curve of the spacing bidirectional [PERSON]'s model, while Figure 4b shows the stability transition curve of the velocity difference bidirectional Helly's model. The traffic flow is considered stable when the equilibrium space gap lies above the stability line. The black dashed line represents the phase transition curve of [PERSON]'s model when \(\gamma_{x}=0\) and \(\gamma_{v}=0\). Figure 4: Stability transition curves for (**a**) spacing, (**b**) velocity difference bidirectional [PERSON]’s model. Figure 4a for the spacing bidirectional [PERSON]'s model indicates that the stability region expands when \(\gamma_{x}<0\) (IP). On the contrary, when \(\gamma_{x}>0\) (OP), the stability region shrinks. Figure 4b for the velocity difference bidirectional [PERSON]'s model reveals that when \(\gamma_{v}>0\) (IP), the stability region shrinks, and the stability region expands when \(\gamma_{v}<0\) (OP). The above string stability analyses on [PERSON]'s model demonstrate the findings presented in Tables 2 and 3.
## 4 Results and Discussion
### Determination of the Maximum Value of the Electric Field Norm  
A model was built to determine the maximum value of the electric field norm at the point probe without any specimen. The mesh of the model is shown in Figure 5a. The simulation resulted in \(E_{max}\) equal to 6440 V/m. Figure 5b shows the slice plot for a cross-section in the \(y-z\) plane passing through the model's center point. Figures 5c-e show the slice plot in the \(x-y\) plane for three \(z\) coordinates corresponding to distances (\(d\)) of 0.1 mm, 1 mm, and 2 mm from the plane determined by rings (4) and (5) in Figure 3 (which corresponds to the bottom surface of the specimen (8)).
## 4 Analysis and Discussion
### Datasets and Learning Paradigms
The first thing that stands out for the localization tasks depicted in the right graph is the accumulation of (binary- or single-class) localization datasets with a balance score of one. This is primarily attributable to the fact that it is seldom specified whether and how many images without inspection targets are contained in the datasets, specifically for segmentation. The general correlation between class balance and performance is visible as well, but the gradient of an imaginary regression line would be slightly lower compared to classification. This can be explained by the higher resilience of localization models to dataset imbalance based on the property that there are generally fewer areas of interest or foreground in an image than background, and in this task, they have to be explicitly marked. In our literature review, we found that 14 datasets were utilized more than once. Table 6 lists them in descending order by the number of publications in which they have been used. Most of them are concerned with enforcing a binary differentiation between damaged and intact or background, respectively, via the computer vision tasks classification or segmentation (SDNET 2018, CFD, RSSDD, Deep Crack, Crack Tree, Ozgenel crack dataset, Crack 500, Crack LS 315, Aigle RN). This places them at the bottom end regarding class-induced complexity. In many cases, framing the learning like this may be the only way of making it manageable at 500 or fewer samples with a certain performance goal in  
Figure 8: Performance of models in classification (**left**) and localization tasks (**right**) plotted against the balance score. mind. The cost of data acquisition and annotation certainly plays a role, as well. Lastly, the applications all come from a maintenance context, where the basic recognition of damages in the field can be a satisfactory first step, and a more detailed inspection will be performed by the personnel repairing the damage. Statements about the imbalance of the segmentation datasets are possible in different levels of detail. [PERSON] et al. [121] report the pixel area percentages of cracks and background for DeepCrack, CrackTree 260, Crack LS 315, and Crack 500, which are very pronounced, with the highest balance being 0.35 for Crack 500. The balance reaches as low as 0.32 for Crack LS 315 and CrackTree, which poses a significant challenge compared to anything deemed feasible in classification problems. CFD, RSDD, and Aigle RN do not allow a statement to be made, as there is no information about images without damage, the number of class instances, or the area ratios between classes. The two classification datasets SDNET 2018 and Ozgenel crack dataset are far more balanced, with scores of 0.51 and 1.0, as well as offering significantly more data samples. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Dataset Name** & \# **Samples** & **Resolution** & **Learning Task** & **Class Distribution** & **B-Score** & **\# Publications** & **References** \\ \hline \multirow{6}{*}{ \begin{tabular}{c} NEU Surface \\ Defect Database \\ \end{tabular}
## 4 Discussion
### WGCNA Analyses on Volatiles and Gene Modules  
The present work performed WGCNA on the filtered DEGs and detected volatiles, in order to seek relationships between volatile production and gene expression. From a total of 1785 DEGs, 1299 DEGs screened with average FPKM 0.1 are clustered into eight modules (Figure S3 and Table S8). The correlation results are shown in Figure S4 and the prominent correlations were depicted in Figure 4.  
In Figure 4, undecane is similarly varied with the yellow module. Genes in this module were enriched into several KEGG pathways, including protein processing and glycosphingolipid biosynthesis (Figure S5A). Styrene, correlated with the grey module (0.91), was degraded from ethylbenzene via the catalyzation of naphthalene 1,2-dioxygenase. Since this step has not been identified in grapes, the relative genes in the grey module might enrich the knowledge of the styrene-generated pathway in grapes. Genes in the brown module were expressed similarly to 2-octanone and (E,Z)-2,6-nonadienal. As depicted in Figure S5B, phytohormones might be involved in their production. KEGG classification exhibited an enrichment in hormone signal transduction, which raises the possibility of these components as external chemical regulators.  
Notably, the turquoise module, correlated with several sesquiterpenoids, including \(\alpha\)-cadinene, \(\alpha\)-muurolene and \(\alpha\)-calsacorene, with correlated values ranging from 0.93 to 0.98, comprised the genes that enrich photosynthesis (Figure S5C), hence providing evidence for the light regulation of sesquiterpenoids. Notably, those sesquiterpenoids were consistently more abundant in US than in TS. Previously, a study concerning light intensity with regard to _Salvia dolomitica_ showed a decline in \(\delta\)-cadinene in samples exposed to high light intensity [36]; thus, it can be inferred that sesquiterpenoid accumulation in grape berries might be influenced by light intensity. On the other hand, transcription factors _ERF110_, _ERF5_, _HSF30_ and _HSFA_ were included in the turquoise module. Therefore, the above TFs are assumed to respond toward light conditions and might regulate terpenoid accumulation in grape berries.  
Figure 4: The high correlation among gene modules and several volatiles from WGCNA results. Colors stand for different gene modules. Compounds are labeled by numbers consistent with Tables S2 and S3.
## 5 Numerical Experiments
### QUBO Formulation of the QSAP-C  
In this section, we present the QUBO formulation of the proposed model inspired by [11; 60] and show the potential for acceleration through quantum computing. QUBO problems are unconstrained, quadratic, and of binary form generally defined as follows:  
\[E(x)=x^{T}Qx+q \tag{12}\]  
where \(Q\) represents a \(m\times m\) matrix, q is a constant term, a solution \(x=(x_{1},\ldots,x_{m})\), \(x_{i}\in\{0,1\}\) is an m-dimensional binary vector, and \(E(x)\) is the energy (or fitness) of \(x\).  
The QSAP-C can be formulated as QUBO using Equation (14) where the cost function \(c(x)\) and the constraint function \(g(x)\) are presented in Equations (15) and (A1), respectively. The penalty weight is denoted by \(\alpha\) and set according to the method described in [61; 62].  
\[E(x)=c(x)+\alpha g(x) \tag{13}\]  
\[\begin{array}{c}c(x)=\sum\limits_{k\in K}\sum\limits_{l\in L}\sum\limits_{j \in l}f_{kj}d_{kl}x_{kl}+\sum\limits_{l\in L^{\prime}}\sum\limits_{l\in L^{ \prime}}\sum\limits_{k\in K}\sum\limits_{j\in l}f_{kj}d_{ll^{\prime}l^{\prime }}x_{kl}y_{lj}+\sum\limits_{l^{\prime}\in L^{\prime}}\sum\limits_{j\in l}\sum \limits_{k\in K}f_{kj}d_{l^{\prime}j}y_{l^{\prime}j}\\ g(x)=\sum\limits_{k\in K}\left(1-\sum\limits_{l\in L}x_{kl}\right)^{2}+\sum \limits_{j\in l}\left(1-\sum\limits_{l^{\prime}\in L}y_{l^{\prime}j}\right)^{ 2}+\sum\limits_{(l,l^{\prime})\in(L,l^{\prime})}(Cap_{(l,l^{\prime})}-\\ \sum\limits_{k\in K}\sum\limits_{j\in l}x_{kl}f_{kj}-\sum\limits_{k\in K}\sum \limits_{j\in l}y_{l^{\prime}j}f_{kj}+\sum\limits_{k\in K}\sum\limits_{j\in l }x_{kl}y_{lj}f_{kj}-\sum\limits_{i=0}^{n}2^{i}x_{ll^{\prime}}^{n})^{2}\end{array} \tag{15}\]  
According to the preceding procedure, Transformation # 1 proposed by [11] that transforms the general problem into an equivalent QUBO model, which requires all constraints to be equations rather than inequalities, we convert constraints (4) to equations by including slack variables \(s_{4}\) via a binary expansion. To accomplish this, we first estimate upper bounds on the constraints, that is \(0\leq s_{4}\leq\sum_{k\in K}\sum_{j\in l}f_{kj}\), which can be regarded as a basis for determining how many binary variables will be required to represent the slack variables in the binary expansions. Assume that we need \(n\) binary variables and \(n=\max\limits_{n}\left\{2^{n}<\sum_{k\in K}\sum_{j\in l}f_{kj}\right\}\), then \(s_{4}\) can be expressed as \(s_{4}=\sum_{i=0}^{n}2^{i}x_{ll^{\prime}}^{i}\).
## 3 Evacuation Warning and Region Division  
Wildfires may involve the evacuation of large groups of people from large locations, often across long distances. The increasing frequency of these catastrophes shows that suitable evacuation strategies for wildfire-prone areas are required.  
The ability to communicate evacuation orders clearly and effectively is one of the most important requirements for an evacuation. The initial response to disaster warnings is generally one of skepticism, which must be overcome in this communication [27; 28]. The urge with which individuals evacuate, the places from which they go, and the destinations they choose can all be greatly influenced by the wording and content of evacuation instructions (the message), the person providing the message (the source), and the distribution channel [29]. It is interesting how vocabulary varies greatly throughout one location while exhibiting little consistency between regions. The use of acronyms on the Internet and in social media could further undermine consistency [30]. Recent research on evacuation procedures revealed the variety of language used by public officials when issuing evacuation orders and the intended meaning they are attempting to communicate. The terms \"Mandatory\" and \"Voluntary\" evacuation were the most popular among survey participants. However, it is noteworthy that the legal definition of \"mandatory\" is unclear because disaster management and law enforcement organizations know that it would be impossible to execute an order requiring citizens to evacuate. However, when advising potential evacuees to flee, the word \"mandatory\" carries certain significance [31].  
The study area can be divided into geographic zones to help let the public know who must evacuate. Depending on the sort of catastrophic event, the number and size of zones may change [32]. Adequate zoning is also very important for evacuation modeling, especially at macro/meso scale models [33].
## 2 Analytical Model for Guided Waves in a Hollow Cylinder
\begin{array}{l}\lambda\frac{\partial^{2}u_{r}}{\partial r^{2}}+\frac{1}{ r^{2}}\alpha\frac{\partial^{2}u_{r}}{\partial\theta^{2}}+G\frac{\partial^{2}u_{ r}}{\partial\theta^{2}}+\frac{1}{r}(\lambda+3G)\frac{\partial^{2}u_{\theta}}{ \partial r\theta\theta}+(\lambda+3G)\frac{\partial^{2}u_{z}}{\partial r \theta\frac{1}{2}}\\ \hskip 14.226378 pt+\frac{1}{r}\lambda\frac{\partial u_{r}}{\partial r}-\frac{1 }{r^{2}}(\lambda+G)\frac{\partial u_{\theta}}{\partial\theta}-\frac{1}{r^{2}} \lambda u_{r}=\rho\frac{\partial^{2}u_{r}}{\partial t^{2}}\\ \hskip 14.226378 ptG\frac{\partial^{2}u_{\theta}}{\partial r^{2}}+\frac{1}{r^{2 }}\lambda\frac{\partial^{2}u_{\theta}}{\partial\theta^{2}}+G\frac{\partial^{2 }u_{\theta}}{\partial\theta^{2}}+\frac{1}{r}(\lambda+3G)\frac{\partial^{2}u_{ z}}{\partial r\theta\theta}+\frac{1}{r}(\lambda+3G)\frac{\partial^{2}u_{z}}{\partial \theta\theta^{2}}\\ \hskip 14.226378 pt+\frac{1}{r}G\frac{\partial u_{\theta}}{\partial r}+\frac{1}{ r^{2}}(\lambda+G)\frac{\partial u_{r}}{\partial\theta}-\frac{1}{r^{2}}Gu_{ \theta}=\rho\frac{\partial^{2}u_{z}}{\partial t^{2}}\\ \hskip 14.226378 ptG\frac{\partial^{2}u_{z}}{\partial r^{2}}+\frac{1}{r^{2}}G \frac{\partial^{2}u_{z}}{\partial\theta^{2}}+\lambda\frac{\partial^{2}u_{z}}{ \partial z^{2}}+(\lambda+3G)\frac{\partial^{2}u_{\theta}}{\partial r\theta z}+ \frac{1}{r}(\lambda+3G)\frac{\partial^{2}u_{\theta}}{\partial\theta\theta z}\\ \hskip 14.226378 pt+\frac{1}{r}(\lambda+3G)\frac{\partial u_{r}}{\partial z}+ \frac{1}{r}G\frac{\partial u_{z}}{\partial r}=\rho\frac{\partial^{2}u_{z}}{ \partial t^{2}}\\ \hskip 14.226378 pt\end{array}  \tag{5}\]  
Equation (5) is the wave equation expressed by the displacement vector component and the vascular mechanical constant. Finally, the boundary condition of the hollow cylinder model satisfies as stress-free on the inner and outer surfaces, which can be written as:  
\[ \begin{array}{l}\sigma_{r}|_{r=a,b}=0,\ \sigma_{r\theta}|_{r=a,b}=0,\ \sigma_{r}|_{r=a,b}=0\\ \end{array}  \tag{6}\]  
Simplify Equation (6) with Equations (2), (3) and (A8), the boundary condition can be expressed as:  
\[ \begin{array}{l}(\lambda+2G)\frac{\partial u_{r}}{\partial r}+\frac{\lambda }{r}(u_{r}+jun_{\theta})+jk\lambda u_{z}|_{r=a,b}=0\\ \hskip 14.226378 ptG\frac{\partial u_{\theta}}{\partial r}+\frac{G}{r}(jun_{r}- u_{\theta})|_{r=a,b}=0\\ \hskip 14.226378 ptG\frac{\partial u_{z}}{\partial r}+jkGu_{r}|_{r=a,b}=0\\ \hskip 14.226378 pt\end{array}  \tag{7}\]  
By using the similar method in [23; 26], Legendre polynomials are introduced to simplify Equation (5) and eliminate the derivative terms (the detailed simplification process is in Appendix A), then it can be derived that: \begin{table}
\begin{tabular}{c} **Young’s** \\ **Modulus (kPa)** \\ \end{tabular} \\ \hline
500 & 0.48 & 2 & 0.2 & 1100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of representative blood vessels [13; 14; 25]. The group velocity can also be expressed as follows:  
\[c_{g}=\frac{d\omega}{dk}=c_{p}+k\frac{dc_{p}}{dk} \tag{13}\]
## 4 Fluid Dynamic Model of Abrasive Flow  
### Turbulence Model  
As presented in Section 1, abrasive flow is a typical two-phase engineering fluid media, and with the characteristics of high velocity, weak viscosity and turbulent state [56]. Based on the above characteristics of abrasive flow, the particle group is supposed as a pseudo-fluid interpenetrated with fluid.  
Standard \(k\)-\(\epsilon\) model is a commonly used classical turbulence model, but it will be distorted for the strongly swirling flow, curved wall flow and curving streamline flow. In the constrained flow passage, it could result in negative normal stresses. Different from the standard \(k\)-\(\epsilon\) turbulence model, the expression for the turbulent viscidity in realizable \(k\)-\(\epsilon\) model introduces rotation and curvature, so it will be able to adapt to avoid the negative normal stress [57; 58; 59]. Accordingly, a fluid dynamic model for abrasive flow processing is set up based on the realizable \(k\)-\(\epsilon\) turbulence model. Based on the model, the profiles of pressure and velocity of abrasive flow on the workpiece surface are obtained, and the optimized processing conditions and constrained modules could be confirmed.  
In the realizable \(k\)-\(\epsilon\) turbulence model, the transport formulae for turbulent kinetic energy \(k\) and dissipation rating \(\epsilon\) are described as:  
\[\frac{\partial(\rho k)}{\partial t}+\frac{\partial(\rho ku_{i})}{\partial x_{i }}=\frac{\partial}{\partial x_{j}}\left[\left(\mu_{1}+\frac{\mu_{t}}{\sigma_{ k}}\right)\frac{\partial\epsilon}{\partial x_{j}}\right]+G_{k}-\rho\epsilon \tag{10}\]  
\[\frac{\partial(\rho\epsilon)}{\partial t}+\frac{\partial(\rho\epsilon u_{i})} {\partial x_{i}}=\frac{\partial}{\partial x_{j}}\left[\left(\mu_{1}+\frac{\mu _{t}}{\sigma_{\epsilon}}\right)\frac{\partial\epsilon}{\partial x_{j}}\right] +\rho C_{1}E\epsilon-\rho C_{2}\frac{\epsilon^{2}}{k+\sqrt{\
u\epsilon}} \tag{11}\]  
where \(\rho\) is fluid density; \(x_{i}\) and \(x_{j}\) are coordinate components; \(\sigma_{k}\) and \(\sigma_{\epsilon}\) are turbulent Prandtl numbers of turbulent kinetic energy \(k\) and dissipation rate \(\epsilon\); \(G_{k}\) is turbulent kinetic energy resulted from average velocity gradient; \(\mu_{1}\) is molecular viscosity coefficient; and \(\mu_{t}\) is turbulence viscosity coefficient. \(\sigma_{k}=1.0\), \(\sigma_{\epsilon}=1.2\), and \(C_{2}=1.9\)[60; 61; 62].
## 3 Methodology
### Model Training  
#### 3.3.1 Convolutional Neural Network (CNN)  
Initially, we employed a convolutional neural network (CNN) model [27], considering its widespread use and success in image classification. CNNs consist of (1) convolutional layers that apply filters to extract meaningful features from the input images, (2) pooling layers that reduce the spatial dimensions, preserving important features while reducing computational complexity, and (3) fully connected layers perform classification based on the extracted features. We trained a CNN model from scratch to establish a baseline performance for trunk posture classification. The model consists of three convolutional layers with increasing filter sizes (32, 64, and 128), each followed by a max-pooling layer. The output is then flattened and passed through two fully connected layers. We used ReLU activation functions in the convolutional layers and a SoftMax activation function in the output layer to classify the trunk posture categories. The model was trained using the Adam optimizer with a learning rate of 0.001 for 20 epochs.  
Moreover, to mitigate overfitting and improve the model's generalization capability, we explored the application of data augmentation techniques. Data augmentation [32] involves applying various transformations, such as rotation, scaling, and flipping, to artificially expand the diversity of the training data.
## 3 Experiments and Results
### Ablation Study of ACE Module  
In Section 3.4, we explained the characteristics of the different types of asymmetric convolution for crack extraction and proposed a solution to the feature saturation caused by parallelization of the asymmetric convolutions. To verify the effectiveness of our proposed asymmetric convolutional feature enhancement module, we designed ablation experiments using the same dataset as in Section 3.1, and the results are shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **MIOU** & **MPA** & **Recall** & **F1 Score** & **Inference Time (ms)** \\ \hline With ACE & 0.7705 & 0.9868 & 0.8047 & 0.8485 & 4.74 \\ Without ACE & 0.7424 & 0.9850 & 0.7604 & 0.8276 & 4.17 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Ablation study of the ACE module.  
Figure 12: Precision-recall curve for different ratios on the test set.  
Compared with the model without the asymmetric feature enhancement module, the MIOU for the model with the feature enhancement module was improved by 0.0281, the MPA by 0.18%, the recall by 0.0443, and the F1 score by 0.0209. The inference speed was increased by 0.6 ms. This proves that although the asymmetric convolutional feature enhancement module increases the inference time to a certain extent, its asymmetric convolutional special perceptual field, which is exactly adapted to the narrow features of cracks, plays an important role in the shallow feature extraction network and can extract the information on the crack more comprehensively.