esa-sceva/satcom-chunk-collection huggingface dataset:
# A Sparsity-Invariant Model via Unifying Depth Prediction and Completion
## 2 Related Work
### Sparsity-Invariant Depth Completion  
Early works designed some sparsity-aware convolutions like sparse convolution [18] and normalized convolution [21; 22]. [PERSON] et al. [70] considered different sparse patterns and proposed an end-to-end network with a graph convolution module, which effectively utilized the relationships between 3D points and their neighborhoods. In experiments, they compared four quasi-random sampling strategies against random sampling, verifying its generalization ability in indoor scene depth completion.  
Some studies [19; 23; 24] utilize pre-trained monocular depth estimation networks to address sparse generalization issues. [PERSON] et al. [24] consider different sensor configurations and decompose the depth completion into two subtasks: relative depth map estimation and scale recovery. The model first estimates a relative depth map from a single color image and then incorporates sparse depth as scale information to obtain the final depth map. [PERSON] et al. [19] directly utilize depth map priors obtained from pre-trained monocular depth estimation models trained on large-scale datasets for individual color images. Subsequently, this prior is used as input for completing sparse, semi-dense, or noisy depth maps obtained from various depth sensors or multi-view reconstruction algorithms. They also simulate various sparse patterns in the training data for network training. [PERSON] et al. [23] propose a plug-and-play module. Given a pre-trained depth prediction model, the module can accept depth maps under arbitrary sparse patterns as input. By iteratively updating intermediate feature maps in the pre-trained depth estimation model, the method ensures consistency between the model output and the given sparse depth, thereby improving the final depth prediction results.  
Differently, [PERSON] et al. [38] did not choose to directly feed sparse depth points to convolutional layers but rather iteratively merge the sparse input points with multiple depth maps predicted by the network to handle highly variable data sparsity. In addition, [PERSON] et al. [19] leverage diverse data augmentation to improve the model's generalization to different data domains and noise. [PERSON] et al. [20] simultaneously use sparse depth maps with various lidar scan-lines as input during training, and they proposed a consistency loss between them to obtain a scan-line resolution-invariant depth completion model. G2-MonoDepth [73] introduced a novel unified loss to handle varying depth sparsity in input raw data and diverse scales of output scenes. Additionally, it employed a data augmentation pipeline to simulate various real-world artifacts in raw depth maps for training.
# Research on Panel Flutter Considering the Effect of Convective Active Cooling
###### Abstract
[12] analyzed the dynamic response of panels in a hypersonic flight environment and pointed out that there are differences in the history of panels to reach chaotic motion at different flight Mach numbers. [PERSON] et al. [13] considered both aerodynamic nonlinearity and structural nonlinearity in panel flutter analysis, in which third-order piston theory was used for nonlinear aerodynamic loading. The effects of each item of piston theory on panel flutter were studied. The results showed that the geometric term in the quadratic term is the main cause of nonlinearity. [PERSON] et al. [14] developed a comprehensive aerothermoelastic model for the analysis of panel structures in hypersonic flow, and investigated the impact of fluid-thermal-structural coupling on aerothermoelastic behavior using [PERSON]'s method and the third-order piston theory. [PERSON] et al. [15] analyzed the aeroelastic flutter of a composite panel with functionally graded material. The result illustrated that adding a few amounts of graphene nanoplatelets can effectually enhance the aeroelastic properties of the plates. The displacement and acceleration feedback control are used to suppress the occurrence of the panel flutter. During hypersonic flight, the outer surface wall structure of the vehicle is subjected to a rather harsh aerodynamic thermal environment, which seriously affects the performance and flight safety of the vehicle [16]. The convection cooling system is one of the most commonly used thermal protection strategies [17; 18; 19; 20]. For instance, [PERSON] [18] presented an effective endothermic fuel platform for regeneratively cooled hypersonic vehicles. The current research on the convection cooling thermal protection system mainly focuses on optimal control [21], thermal protection efficiency improvement [16; 22], structure simplification, and mass reduction [23], but has not yet considered the influence of the coolant force on the stability of the wall plate. Therefore, the dynamics model of panel flutter under the action of coolant is established in this paper based on [PERSON]'s large deformation theory and the Kirchhoff-Love hypothesis. The kinetic equations are discretized by [PERSON]'s method in the space domain and solved by the fourth Runge-Kutta method in the time domain. Based on this, the effects of the head-panel pressure of the coolant, the pressure drop ratio, the coolant injection direction, and the inertial resistance and viscous resistance on panel stability and flight stability were investigated, respectively, and the suppression method of panel flutter was proposed. This paper is organized as follows. Section 2 presents the dynamic analytical model of panel flutter under the effect of coolant and verifies the accuracy of the model. Section 3 analyzes the panel stability under the influence of coolant. Section 4 analyzes the flight stability of the panel and proposes the suppression method of panel flutter. The conclusions are summarized in Section 5.
# Physics-Informed Neural Networks for Cantilever Dynamics and Fluid-Induced Excitation
## 3 Experiments
### Flutter of a Slender Cantliever in Axial Flow
#### 3.2.4 Results  
The following experiment tested whether the PINN could accurately describe the sub-critical behavior of a cantilevered plate in axial flow [44; 45]. Two different conditions were studied, corresponding to the stable and fluttering modes at a dimensionless velocity of \(\widetilde{U}=\sqrt{\mu/B}UL\) of around 2.6 and 15.8, respectively, at the given dimensionless mass of \(\widetilde{m}=\rho_{f}LI/\mu\) of around 0.14. It is important to note that the critical dimensionless velocity of flutter was expected to be around 15, based on [PERSON] et al. (2007). Below the critical velocity, the free vibration of a cantilever would be attenuated by stabilizing fluid dynamic pressure. On the other hand, beyond the critical velocity, the incoming fluid flow would destabilize the cantilever, leading to fluid-induced flutter with excitation of higher bending modes [46; 47].  
Figure 4 exhibits the predictions of the proposed PINN model for the stable mode (Figure 4a) and the fluttering mode (Figure 4b). The critical behavior of the fluttering cantilevered beam is successfully captured by the proposed PINN model. In Figure 4a, snapshots over one cycle are shown, starting from the release of the initial end load condition, with ten consecutive deflection profiles depicted in chronological order from dark to light red. The amplitude of displacement significantly decayed as the fluid dynamic pressure acted like a damping force. The displacement curve of the cantilever end for prolonged cycles is shown as a black line in Figure 4c, clearly demonstrating that the fluid-dynamic force stabilized the vibration of the cantilever by gradually reducing the amplitude of the oscillation.  
As the incoming fluid velocity increased, the emergence of fluttering behavior was predicted via the PINN model. Whereas the higher-order bending mode appeared in the deflection profiles of the cantilever, as shown in Figure 4b, the domination of the first bending mode was observed in both free vibration (Figure 2b) and the stable mode (Figure 4a). The predicted profile corresponds to a single-neck flutter, widely observed in previous numerical simulations [43; 44] and experiments [45; 46; 47] in flag flutter. The displacement profile of the cantilever end, depicted as a red line in Figure 4c, also confirms the appearance of periodic flutter in the PINN prediction. It is remarkable that the PINN could capture the emergence of the critical behavior of the cantilever in axial flow by resolving coupled differential Equations (5) and (7).
## Appendix B  
In this section, we will show forward kinematics and inverse kinematics of the six DoFs revolute robot manipulators. The results are consistent with the model ABB IRB 4600. Forward kinematics refers to the use of kinematic equations of a robot to compute the position of the end-effector from specified values for the joint angles and parameters. The equations are summarized in the below:  
\[ \begin{split} n_{x}&=c_{1}s_{23}(s_{4}s_{6}-c_{4}c_{5 }c_{6})-s_{1}(s_{4}c_{5}c_{6}+c_{4}s_{6})-c_{1}c_{23}s_{5}c_{6}\\ n_{y}&=s_{1}s_{23}(s_{4}s_{6}-c_{4}c_{5}c_{6})+c_{1}(s_{4 }c_{5}c_{6}+c_{4}s_{6})-s_{1}c_{23}s_{5}c_{6}\\ n_{z}&=c_{23}(s_{4}s_{6}-c_{4}c_{5}c_{6})+s_{23}s_{5}c_{6 }\\ \end{split}  \tag{1}\]  
\[ \begin{split} s_{x}&=c_{1}s_{23}(s_{4}c_{6}+c_{4}c_{5 }c_{6})+s_{1}(s_{4}c_{5}s_{6}-c_{4}c_{6})+c_{1}c_{23}s_{5}s_{6}\\ s_{y}&=s_{1}s_{23}(s_{4}c_{6}+c_{4}c_{5}c_{6})-c_{1}(s_{4 }c_{5}s_{6}-c_{4}c_{6})+s_{1}c_{23}s_{5}s_{6}\\ s_{z}&=c_{23}(s_{4}c_{6}+c_{4}c_{5}c_{6})-s_{23}s_{5} s_{6}\\ a_{x}&=-c_{1}s_{23}c_{4}s_{5}-s_{1}s_{4}s_{5}+c_{1 }c_{23}c_{5}\\ a_{y}&=-s_{1}s_{23}c_{4}s_{5}+c_{1}s_{4}s_{5}+s_{1 }c_{23}c_{5}\\ a_{z}&=c_{23}c_{4}s_{5}-s_{23}c_{5}\\ d_{x}&=L_{t}(-c_{1}s_{23}c_{4}s_{5}-s_{1}s_{4}s_{5}+c_{1 }c_{23}c_{5})+c_{1}(L_{3}s_{23}+L_{2}s_{2}+a_{1})\\ d_{y}&=L_{t}(-s_{1}s_{23}c_{4}s_{5}+c_{1}s_{4}s_{5}+s _{1}c_{23}c_{5})+s_{1}(L_{3}s_{23}+L_{2}s_{2}+a_{1})\\ d_{z}&=L_{t}(c_{23}c_{4}s_{5}-s_{23}c_{5})+L_{3}c_{ 23}+L_{2}c_{2}+L_{1}\\ \end{split}  \tag{2}\]  
\[ \begin{split}\text{Note : }c_{i}\equiv\cos(q_{i}),\;s_{i}\equiv \sin(q_{i})\\ c_{i,j}\equiv\cos\left(q_{i}+q_{j}\right),\;s_{i,j}\equiv\sin(q_{i}+q_{ j})\\ i,j\in\{1,2,3,4,5,6\}\end{split}  \tag{3}\]  
where \(\left[n_{x},n_{y},n_{z}\right]^{T}\), \(\left[s_{x},s_{y},s_{z}\right]^{T}\) and \(\left[a_{x},a_{y},a_{z}\right]^{T}\) are the end-effector's directional vector of Yaw, Pitch and Roll in the base frame \(O_{0}X_{0}Y_{0}Z_{0}\) (Figure 1). And \(\left[d_{x},d_{y},d_{z}\right]^{T}\) are the vector of the absolute position of the center of the end-effector in the base frame \(O_{0}X_{0}Y_{0}Z_{0}\). For a specific model ABB IRB 4600-45/2.05 (Handling capacity: 45 kg/Reach 2.05 m) the dimensions and mass are summarized in Table 1.  
Inverse kinematics refers to the mathematical process of calculating the variable joint angles needed to place the end-effector in a given position and orientation relative to the inertial base frame.
## 6 Three-Parameter Splitting Iterative Scheme  
A generalization of Equation (35) was proposed in [31; 36] as follows:  
\[[(1+\sigma)\mathbf{D}-w\mathbf{L}]\mathbf{x}_{k+1}=r\mathbf{b}+[(1+\sigma-r) \mathbf{D}+r\mathbf{U}+(r-w)\mathbf{L}]\mathbf{x}_{k}, \tag{48}\]  
which is named a parametric-AOR (POR), accompanied by an extra parameter \(\sigma\). The QAOR method in Equation (35) is a special case of Equation (48) with \(\sigma=r\).  
**Theorem 10**.: _A new iterative form of the POR method is_  
\[\mathbf{x}_{k+1}=\mathbf{x}_{k}+\mathbf{u}_{k},\ [(1+\sigma)\mathbf{D}-w \mathbf{L}]\mathbf{u}_{k}=r\mathbf{r}_{k}. \tag{49}\]  
Proof.: Equation (48) is rewritten as  
\[[(1+\sigma)\mathbf{D}-w\mathbf{L}]\mathbf{x}_{k+1}=[(1+\sigma) \mathbf{D}-w\mathbf{L}]\mathbf{x}_{k}\] \[+r\mathbf{b}+[(1+\sigma-r)\mathbf{D}+r\mathbf{U}+(r-w)\mathbf{L}] \mathbf{x}_{k}-[(1+\sigma)\mathbf{D}-w\mathbf{L}]\mathbf{x}_{k},\]  
which can be rearranged to  
\[[(1+\sigma)\mathbf{D}-w\mathbf{L}]\mathbf{x}_{k+1}=[(1+\sigma)\mathbf{D}-w \mathbf{L}]\mathbf{x}_{k+1}+r\mathbf{b}-r[\mathbf{D}-\mathbf{U}-\mathbf{L}] \mathbf{x}_{k}.\]  
Equations (8) and (11) lead to  
\[[(1+\sigma)\mathbf{D}-w\mathbf{L}]\mathbf{x}_{k+1}=[(1+\sigma)\mathbf{D}-w \mathbf{L}]\mathbf{x}_{k}+r\mathbf{r}_{k}.\]  
The proof for Equation (49) is complete, upon moving \([(1+\sigma)\mathbf{D}-w\mathbf{L}]\mathbf{x}_{k}\) to the left-hand side, and setting \(\mathbf{x}_{k+1}-\mathbf{x}_{k}=\mathbf{u}_{k}\).  
[PERSON] et al. [31] further generalized Equation (48) to  
\[[(1+\sigma)\mathbf{D}-w\mathbf{L}]\mathbf{x}_{k+1}=r\mathbf{b}+[(1+\sigma-r) \mathbf{D}+r\mathbf{U}+(r-w)\mathbf{L}]\mathbf{x}_{k}-r\mathbf{w}\mathbf{r}_ {k}, \tag{50}\]  
which is named a parametric reaccelerated overrelaxation (PROR) method. Like that in Theorem 9, we can prove the following result.  
**Theorem 11**.: _The PROR method is obtained from the POR method by applying the extrapolation technique (19) and (20) by a parameter \(\beta=1-w\); it generates the following iterative form:_  
\[\mathbf{x}_{k+1}=\mathbf{x}_{k}+(1-w)\mathbf{u}_{k},\ [(1+\sigma)\mathbf{D}-w \mathbf{L}]\mathbf{u}_{k}=r\mathbf{r}_{k}. \tag{51}\]  
Proof.: As that done in Theorem 10, Equation (50) can be expressed as  
By applying the extrapolation technique (19) and (20) on Equation (49) by a parameter \(\beta=1-w\), Equation (51) can be derived again.  
When \(\mathbf{w}_{k}\) in Equation (52) is replaced by \(\mathbf{u}_{k}\), the PROR method can also be written as  
\[\mathbf{x}_{k+1}=\mathbf{x}_{k}+\mathbf{u}_{k},\ [(1+\sigma)\mathbf{D}-w \mathbf{L}]\mathbf{u}_{k}=r(1-w)\mathbf{r}_{k}.\]  
**Remark 4**.: _QAOR is a special case of POR with \(\sigma=w\). The PROR method is the \(\beta=1-w\)-extrapolation of POR._
# A Cross-Medium Uplink Communication Model Merging Acoustic and Millimeter Waves
## 2 Model of Cross-Medium Communication Channel
### Model Adjustments and Analysis  
#### 2.2.1 Multipath Fading Correction  
Multipath fading occurs when acoustic waves encounter various propagation paths in water, such as direct, reflected, and scattered paths, leading to signal interference at the receiving end. In our experimental condition, the short transmission distance and relatively small time delay expansion result in narrowband fading, where only a random process reflecting a random amplitude and phase is added during the merging of multipath signals.  
Due to the close transmission distance, multipath fading caused by the reflection of acoustic waves cannot be ignored, leading to an interference effect on the sound pressure at the water-air interface.  
In the experimental conditions, multipath fading was observed along two main paths, as depicted in Figure 2. One (Path 1) involved the vertical reflection of acoustic waves from the water surface to the speaker, followed by another vertical reflection from the speaker back to the water surface, resulting in multipath fading. The other (Path 2) was caused by the reflection of acoustic waves from the wall of the water tank covered with silencing cotton, resulting in multipath fading at the water-air interface.  
Correcting for narrowband fading caused by multiple paths was not considered in the physical process; thus, a correction coefficient \(\zeta\) was added to the sound pressure at water surface. The correction equation is as follows:  
\[\delta_{1}=\zeta\delta_{0} \tag{7}\]
## 3 Intelligent Contact Tracing Based on Transmission Characteristics
### Trajectory-Based Outdoor GPS Contact Tracing
#### 3.3.1 Step 1: Calculate Contact  
To bolster the accuracy of outdoor contact detection, we first refine the GPS data with the EKF. Subsequently, we compute the cosine similarity of trajectory vectors.  
When GPS data, \(G_{t}\), at a specific time \(t\), are represented as a pair of latitude (\(lat_{t}\)) and longitude (\(lon_{t}\)), the GPS data after applying the EKF are expressed as \(G_{t}^{f}\). \(G_{t,u}\) means the confirmed person's GPS data, and \(G_{t,v}\) refers to the GPS data of a potential contact, \(v\), at time \(t\). To calculate the distance using the filtered location information of a confirmed person and potential contacts, we utilize the Haversine formula [25], which is used to calculate the distance between points on a sphere. The distance (\(D_{t}(u,v)\)) is calculated using \(G_{t,u}^{f}\) and \(G_{t,v}^{f}\).  
If \(D_{t}(u,v)\) is greater than the maximum infection distance (\(R_{max}\)), it is considered non-contact at that time \(t\). If \(D_{t}(u,v)\) is within \(R_{max}\), we calculate the similarity of the movement between the confirmed person and potential contact, rather than simply determining contact based on distance information. The similarity of the movement path (\(S_{t}(u,v)\)) is obtained through the trajectory vector (\(\vec{T_{t}}\)) expressed as Equation (2), containing the movement tendency information of a person.  
\[\vec{T_{t}}=\overline{G_{t}^{f}\zeta_{t+1}^{f}}^{\gamma} \tag{2}\]  
We set the moving tendency vector of the confirmed person to \(\vec{T_{t,u}}\) and the vector of potential contacts to \(\vec{T_{t,v}^{f}}\). \(S_{t}(u,v)\) can be obtained with Equation (3).  
\[S_{t}(u,v)=\frac{\vec{T_{t,u}^{*}}\cdot\vec{T_{t,v}^{*}}}{||\vec{T_{t,u}^{*}}|| ||\vec{T_{t,v}^{*}}||} \tag{3}\]  
If \(S_{t}(u,v)\) exceeds the threshold value (\(S_{max}\)), it is called casual contact. The determination of the casual contact status (\(C_{t}(u,v)\)) between \(u\) and \(v\) at a specific time \(t\) is obtained by Equation (4).  
\[C_{t}(u,v)=\begin{cases}1,&\text{if }D_{t}(u,v)<R_{max}\text{ and }S_{t}(u,v)>S_{max}.\\ 0,&\text{otherwise}.\end{cases} \tag{4}\]
## 3 Architecture
### Fine-Grained Task Migration Model  
There are two main task migration models that are often adopted in MEC. One is coarse-grained task migration and the other is fine-grained task migration. Coarse-grained task migration considers the entire application as a migration object, thus we no longer divide it into multiple subtasks, and the entire task migrates to the edge cloud. On the contrary, fine-grained task migration means that the application can be divided into multiple subtasks, and these subtasks have dependencies on each other, not simple dependencies, but complex dependencies which can be expressed as a directed acyclic graph (DAG). However, both of them have obvious shortcomings. The former does not make full use of the low latency advantage of the edge cloud, while the latter simplifies the complex dependencies between subtasks. Therefore, in order to resolve the shortcomings of the above two task migration models, we propose a new fine-grained task partitioning model. The topology model is shown in Figure 1.  
As shown in Figure 1, the input data source of subtask 5 comes from subtask 3 and subtask 4. When subtask 3 and subtask 4 are both completed, then subtask 5 starts execution. Here, we introduce a real example, a facial expression recognition application, which can benefit from MEC [16; 17].  
Figure 1: Topology model of fine-grained task partitioning.  
The facial expression recognition application task consists of eight subtasks, including (1) input video, (2) face detection, (3) facial feature detection, (4) face registration, (5) facial feature extraction, (6) action unit recognition, (7) expression recognition, and (8) output class. When we make an offloading decision for this application task, the following concern should be addressed: the above subtasks can be organized as a workflow with data dependencies. Each subtask in this facial expression recognition application task can be either executed locally on mobile devices or remotely (offloaded) to the edge cloud. Because of their dependencies, if a subtask is offloaded, its following subtask cannot start until the result is returned, even if local resources are available. This is different from traditional independent offloading services where multiple services can be simultaneously offloaded or executed remotely or locally at any time.
## 3 Methodology
### Retrackers
#### 3.2.3 Two-Step Physical-Based Retracker
Therefore, for this physical-based retracker, each single-look power waveform was modeled as follows:\[P_{(k,l)}(P_{u},k_{0},SWH/MSS) \tag{5}\] \[\qquad\qquad=P_{u}\cdot B_{(k,l)}(MSS)\cdot\sqrt{(g_{l}(SWH))}[f_{0} (g_{l}(SWH)\cdot(k-k_{0}))\] \[\qquad\qquad\qquad+T_{(k,l)}(MSS)\cdot g_{l}(SWH)\cdot\frac{\sigma _{2}^{2}}{L_{2}^{2}}\cdot f_{1}(g_{l}(SWH)\cdot(k-k_{0}))]\]  
where \(k\) refers to the range index vector within the received waveform window, \(l\) is the Doppler index or beam pointed to the specific surface, \(P_{u}\) is the amplitude, \(k_{0}\) is the epoch (related to the surface height), \(SWH\) is the significant wave height (referred also as \(H_{s}\)), and \(MSS\) is the mean square slope related to the surface roughness. In the first iteration of the two-step retracker, \(P_{u},\ k_{0},SWH\) are the fitting parameters, while in the second iteration the parameters being adjusted are \(P_{u},k_{0},\)\(MSS\). The terms \(B_{k,l}\) and \(T_{k,l}\) encompass the information related to the antenna pattern, antenna mis-pointing, and surface radiation patterns. They are obtained, respectively, as the constant and first order terms of a Taylor approximation of the antenna and surface radiation pattern's product. The closed expression for these two terms can be found in [65]. A Gaussian-like antenna and surface radiation (as indicated in Equation (5)) patterns were assumed. In Equation (5), \(g_{l}\) refers to the Doppler-dependent (\(l\)) dilation term, and takes into account the instrument configuration and the significant wave height:  
\[g_{l}=\frac{1}{\sqrt{\sigma_{ac}^{2}+\left(2\cdot\sigma_{al}\cdot\frac{L_{2}^ {2}}{L_{g}^{2}}\cdot l\right)^{2}+\sigma_{2}^{2}/L_{2}^{2}}} \tag{6}\]  
where \(\sigma_{ac}\) and \(\sigma_{al}\) refer to the widths of the Gaussian functions that approximate the point target response in the across-track (or range) and along-track (azimuth) dimensions, respectively, and \(\sigma_{2}\) corresponds to the standard deviation of the sea surface height probability density function (PDF) and is related to the SWH as \(\sigma_{z}=\frac{H_{s}}{4}\). The definition of the additional terms in Equation (6) can be found in Table 4, where the main parameters of the SAR ocean model are summarized. Finally, \(f_{0}\) and \(f_{1}\) represent the range-dependent functions modulated by the Doppler-dependent dilation term and can be obtained from the general expression (for \(n=0\) and \(1\)):  
\[f_{n}(\psi)=\int\limits_{0}^{\infty}\left(v^{2}-\Psi\right)^{n}\cdot e^{- \frac{(v^{2}-\Psi)^{2}}{2}}\cdot dv \tag{7}\]  
Figure 3: Operation of the two-step physical-based retracker over peaky-like waveform. r (1 st) is the correlation coefficient for the SWH fit with the original waveform, while r (2 nd) is the correlation coefficient for the MSS fit.