esa-sceva/satcom-chunk-collection huggingface dataset:
# Alternating Direction Method of Multipliers for Generalized Low-Rank Tensor Recovery
## 3 Related Works  
Tensor completion and MRPCA are two important and appealing applications of LRTR. In this section, we review the related works on the aforementioned two applications.  
As the higher order generalization of matrix completion, tensor completion aims to recover all missing entries with the aid of the low-rank (or approximately low-rank) structure of a data tensor. Although low-rank tensor decompositions are practical in dealing with missing values [15; 16; 17; 18], we have to estimate properly the rank of an incomplete tensor in advance. In the past few years, the matrix nuclear norm minimization model has been extended to the tensor case [13]. Given an incomplete data tensor \(\mathbf{\mathcal{D}}\in\mathbb{R}^{\mathbf{I}_{1}\times\mathbf{I}_{2}\times\cdots \times I_{N}}\) and a corresponding sampling index set \(\mathbf{\Omega}\subset[\mathbf{I}_{1}]\times[\mathbf{I}_{2}]\times\cdots\times[ \mathbf{I}_{N}]\), we define a linear operator \(\mathbf{P}_{\mathbf{\Omega}}():\mathbb{R}^{\mathbf{I}_{1}\times\mathbf{I}_{2} \times\cdots\times\mathbf{I}_{N}}\rightarrow\mathbb{R}^{\mathbf{I}_{1}\times \mathbf{I}_{2}\times\cdots\times I_{N}}\) as follows: if \(\left(\mathbf{i}_{1},\mathbf{i}_{2},\cdots,\mathbf{i}_{N}\right)\in\mathbf{\Omega}\), \(\left(\mathbf{P}_{\mathbf{\Omega}}(\mathbf{\mathcal{D}})\right)_{i\mathbf{i}_{2}\cdots i _{N}}=\mathbf{d}_{i\mathbf{i}_{2}\cdots i_{N}}\), otherwise, \(\left(\mathbf{P}_{\mathbf{\Omega}}(\mathbf{\mathcal{D}})\right)_{i\mathbf{i}_{2}\cdots i _{N}}=\ \mathbf{0}\), where \(\left[\mathbf{or its corresponding unconstrained formulation:  
\[\min_{\mathbf{\mathcal{X}}}\lambda\,||\,\mathbf{\mathcal{X}}\,||_{*}+\frac{ \mathbf{1}}{2}\,||\,\mathrm{P}_{\mathbf{\Omega}}(\mathbf{\mathcal{X}})-\mathrm{P}_{\mathbf{ \Omega}}(\mathbf{\mathcal{D}})\,||\,\mathrm{F}_{\mathbf{\mathsf{F}}}, \tag{6}\]  
where the regularized parameter \(\mathbf{\lambda}(\geq 0)\) is used to balance the low-rankness and the approximate error, and \(\eta\) is a known estimate of the noise level.  
In RPCA, a data matrix is decomposed into the sum of a low-rank component and a sparse component, and it is possible to recover simultaneously the two components by principal component pursuit under some suitable assumptions [2]. [PERSON] _et al._[14] extended RPCA to the case of tensors and presented the framework of MRPCA, which regards the data tensor \(\mathbf{\mathcal{D}}\) as the sum of a low-rank tensor \(\mathbf{\mathcal{A}}\) and a sparse noise term \(\mathbf{\mathcal{E}}\). Mathematically, the low-rank and the sparse components can be simultaneously recovered by solving the following tensor nuclear norm minimization problem:  
\[\min_{\mathbf{\mathcal{A}}\mathbf{\mathcal{E}}}\,||\,\mathbf{\mathcal{A}}\,||_{*}+\mathbf{ \lambda}\,||\,\mathbf{\mathcal{E}}\,||_{\mathbf{\mathsf{1}}},\text{ s.t. }\mathbf{\mathcal{D}}=\mathbf{\mathcal{A}}+\mathbf{\mathcal{E}}. \tag{7}\]  
In [22], MRPCA is also called as robust low-rank tensor recovery.
# Distributed Average Consensus Algorithms in d-Regular Bipartite Graphs: Comparative Study
### Our Contribution  
As seen in the literature preview, there is a lack of papers concerned with an analysis of distributed consensus algorithms in \(d\)-regular bipartite graphs even though this critical graph topology can cause the divergence of an algorithm [51]. As mentioned earlier in this paper, we focus our attention on a comparative study of frequently applied distributed consensus algorithms in randomly generated \(d\)-regular bipartite graphs with various connectivities. Namely, we chose the following algorithms for examination:  
Maximum-Degree weights (MD);  
Local-Degree weights (LD);  
Metropolis-Hastings algorithm (MH);  
Best-Constant weights (BC);  
Convex Optimized weights (OW);  
Constant weights (CW);  
Generalized Metropolis-Hastings algorithm (GMH).  
More specifically, we examined these algorithms by applying a common metric for performance evaluation with the assumptions that their execution is bounded by a stopping criterion with various precisions, and the arithmetic mean from the initial inner states of all the agents in MASs was estimated. As identified in our recent paper [52], MD and LD do not converge in \(d\)-regular bipartite graphs as the third convergence condition is broken in this topology. However, as shown in [53], the inner states of both algorithms oscillate between two values instead of approaching infinitely high values (as shown in [52], the divergence usually results in the second case). Despite the mentioned divergence, it is, thus, meaningful to also include these two algorithms in our analyses since the consensus can theoretically be achieved due to the mentioned oscillation and the application of a stopping criterion. The primary intention of this paper was to identify the best-performing distributed consensus algorithm and verify whether all the algorithms with bounded execution can achieve the consensus in \(d\)-regular bipartite graphs. Moreover, the experimentally obtained results are compared to related papers where these algorithms are examined in non-regular non-bipartite graphs.
## 7 Conclusions  
Based on the idea of control-protection synergy, this paper investigates the CHC injection protection scheme for the distribution network with IBDGs. The contribution of this paper can be summarized as follows:  
1. The CHC injection-control strategy of IBDG based on the d-axis and q-axis is proposed. Injection starting criteria are established based on the mutation of phase current and voltage.
2. The fault characteristics of CHCs after injection are analyzed. For asymmetrical short-circuit faults, a differential protection criterion based on the distortion rate of NSCCHCs is proposed; for symmetrical short-circuit faults, the proposed differential protection criterion utilizes the distortion rate of A-phase CHCs.  
Theoretical analysis and simulation experiments show that the proposed CHC injection system can accurately and reliably operate under normal operation or fault conditions;  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fault Resistance** & **Fault Type** & **Distortion Rate Difference Values** & **Trip or Not** \\ \hline \multirow{4}{*}{0.1 \(\Omega\)} & A–G & 0.18 & Yes \\  & AB–G & 0.06 & Yes \\  & A–B & 0.055 & Yes \\  & ABC & 0.04 & Yes \\ \hline \multirow{4}{*}{20 \(\Omega\)} & A–G & 0.52 & Yes \\  & AB–G & 0.34 & Yes \\  & A–B & 0.15 & Yes \\  & ABC & 0.035 & Yes \\ \hline \multirow{4}{*}{50 \(\Omega\)} & A–G & 1.14 & Yes \\  & AB–G & 0.87 & Yes \\ \cline{1-1}  & A–B & 0.33 & Yes \\ \cline{1-1}  & ABC & 0.036 & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation results of faults with high fault resistance occur at \(f_{2}\).  
Figure 17: Distortion rates of the A-phase CHCs under the three-phase fault with 20 \(\Omega\) fault resistance.  
the proposed IHCDP can sensitively and reliably trip under symmetrical or asymmetrical faults and has a solid ability to withstand high transition resistance.  
Conceptualization, C.Y. and Z.G.; data curation, C.Y. and Z.L.; formal analysis, C.Y., Z.G. and Z.T.; funding acquisition, Z.G.; methodology, C.Y., Z.G. and Z.L.; project administration, Z.G.; software, C.Y.; validation, C.Y. and Z.G.; visualization, C.Y. and Z.T.; writing original draft, C.Y.; writing review and editing, C.Y., Z.G. and Z.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the Science and Technology Project of State Grid Corporation of China (52060019001H).  
Not applicable.  
The data presented in this study are available in the article.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript or in the decision to publish the results.
## 5 Numerical Examples  
On the basis of the numerical procedure presented in the previous section, two numerical examples were conducted to verify applicability, effectiveness, and accuracy of the approximation method. The first example was inspired by an example in Reference [15] by [PERSON]. The second example was a practical optimization problem of a large-scale satellite.  
In the following examples, emphasis is placed on the change in the theoretical magnification of the constrained local frequency, \(P_{1}\), relative to the practical magnification calculated with the optimization result, \(P_{2}\). Thus, in each example, variation from the relative error \(E=|P_{1}-P_{2}|/P_{1}\) was a measure of the accuracy of the approximate method.
## 4 Biosynthesis of Phenolic Acids in _S. miltiorrhiza_
multiorrhiza_, and part is from the pathway showed with green arrows. PAL: phenylalanine ammonialyase, C4H: cinnamic acid 4-hydroxylase, 4 CL: 4-coumaroyl: CoA ligase, TAT: tyrosine aminotransferase, HPPR: 4-hydroxyphenylpyruvate reductase, RAS: rosmarinic acid synthase. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Gene (Genbank No.)** & **Highest Expression Sites** & **Elietor** & **Reference** \\ \hline _SmPAL1_ (EF462460) & root, leaf & ABA, wounding and dehydration, PEG, MJ, SA, Ca\({}^{3}\), GA, ethylene & [66, 67, 68, 71, 69, 72, 73, 74, 75] \\ _SmPAL2_ (GO249111) & stem, flower & PEG and MJ & [66, 68, 71] \\ _SmPAL3_ (KF220569) & rootleaf & PEG and MJ & [66, 71] \\ _SmC4 III_ (EF3737) 7D335979) & root, stem & MJ, ABA, UV-B, Ag\({}^{4}\) & [35, 71, 76, 77] \\ _SmC4 II_ (AF220564) & stem, root & [71] \\ _Sm4 CL1_ (AY237163) & leaf & MJ, VE & [69, 70] \\ _Sm4 CL2_ (AY237164) & root & MJ, VE, Ag\({}^{4}\) & [35, 69, 70, 71] \\ _Sm4 CL3_ (KF220565) & root & MJ & [71] \\ _Sm4 CL-like_ (KF220557) & root & MJ & [71] \\ _Sm4 CL-like_ (KF220558) & & MJ & [71] \\ _Sm4 CL-like_ (KF220559) & & & [71] \\ _Sm4 CL-like_ (KF220560) & root & [71] \\ _Sm4 CL-like_ (KF220561) & & MJ & [71] \\ _Sm4 CL-like_ (KF220562) & & MJ & [71] \\ _Sm4 CL-like_ (KF220563) & & MJ, ABA, SA, UV-B, GA, ethylene, Ag\({}^{4}\), YE & [35, 65, 72, 74, 78] \\ _Sm4T1_ (DW343606 FF192320) & stem & MJ, ABA, SA, UV-B, GA, ethylene, Ag\({}^{4}\), YE & [35, 65, 72, 74, 75] \\ _Sm4T2_ (K220575) & flower & MJ & [71] \\ _Sm4T3_ (KF220555) & Stem, root & [71] \\ _SmIPPI_ (DQ099741 DQ266514 EF458148) & stemflower & MJ, SA, GA3, ABA, UV-B, Ag\({}^{4}\) & [35, 71, 79] \\ _SmIPPI_ (KF220565) & Stem,leaf & [71] \\ _SmIPPIPI_ (KF220566) & stem & [80] \\ _Sm4 RLS-Like_ (GU647199) & stem & _Pseudomonas tachymans_, MJ, light, and SA & [81] \\ _SmRAS1_ (FJ906696) & root & MJ, Ag\({}^{4}\) & [15, 35] \\ _Sm4T1_ (KF220570) & root & [71] \\ _Sm4T5_ (KF220571) & stem & MJ & [71] \\ _Sm4T3_ (KF220572) & stem & MJ & [71] \\ _Sm4T4_ (KF220573) & stem & MJ & [71] \\ _Sm4T5_ (KF220574) & stem & MJ & [71] \\ _CYP9814_ (HQ316179) & root & MJ, Ag\({}^{4}\) & [15, 35] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The genes involved in phenolic acids biosynthesis in _S. miltiorrhiza_.
###### Abstract  
This paper investigates the observer-based fuzzy controller design method for nonlinear discrete-time singular systems that are represented by Takagi-Sugeno (T-S) fuzzy models. At first, the nonlinearity can be well-approximated with several local linear input-output relationships. The parallel distributed compensation (PDC) technology and the proportional derivative (PD) feedback scheme are then employed to construct the observer-based fuzzy controller. To solve the problem of unmeasured states, the impulsive phenomenon of singular systems, and the PD scheme's reasonableness, a novel observer-based fuzzy controller is developed. By using the Lyapunov theory and projection lemma, the stability criteria are built in terms of linear matrix inequalities (LMI). Moreover, the gains of fuzzy controller and fuzzy observer can be calculated synchronously by using convex optimization algorithms. Finally, a biological economic system is provided to verify the effectiveness of the proposed fuzzy control method.  
nonlinear singular systems; T-S fuzzy model; observer design; proportional derivative control +
Footnote †: journal: Applied Sciences
# Semantic Segmentation of Aerial Imagery Using U-Net with Self-Attention and Separable Convolutions
## 5 Conclusions  
In conclusion, the proposed methodology, employing an SA-SC U-Net architecture for semantic segmentation, has proven to be highly effective in handling large-scale image datasets. The workflow, from dataset preprocessing to model training and prediction, showcased a systematic approach to extracting meaningful information from complex visual data. By dividing large images into manageable patches and incorporating self-attention mechanisms along with separable convolutions, the SA-SC U-Net demonstrated  
Figure 8: IoU vs. validation IoU.  
Figure 9: Loss vs. validation loss.  
superior performance compared to other established architectures like FCN, U-Net, and Dense + U-Net. The custom loss function, a combination of Dice Loss and Focal Loss, contributed to the model's robustness and accuracy, ensuring precise segmentation across multiple classes. The model's parameters, including image dimensions, class weights, and training settings, were carefully tuned to achieve optimal results.  
The comparative evaluation against existing models revealed the SA-SC U-Net's superiority in terms of Intersection over Union (IoU) across various classes. Its consistently high IoU scores, especially for critical classes like Building and Water, underscored its capability to discern fine details and complex spatial relationships. The training history, illustrated by the plots of model loss and IoU over epochs, provided insights into the learning process. The model exhibited steady convergence and superior generalization on the validation set, demonstrating its capacity to learn intricate patterns and generalize well to unseen data. In summary, the proposed SA-SC U-Net stands as a powerful tool for semantic segmentation tasks, offering state-of-the-art performance and showcasing its potential for real-world applications in fields such as urban planning, environmental monitoring, and beyond. The success of this project highlights the significance of tailored architectures and thorough parameter tuning in achieving superior results in computer vision tasks.
# Valkyrie--Design and Development of Gaits for Quadruped Robot Using Particle Swarm Optimization
## 4 Gait Development Using PSO
### Mathematical Formulation of Fitness Function  
The Fitness Function is planned to be formulated in such a way that an optimized inverse kinematic solution will be obtained considering the following constraints.  
1. _Center of mass (CoM) and center of gravity (CoG)_--For the robot to stay stable during static and dynamic conditions, the CoM and CoG of the robot must stay within the support polygon.
2. _Maximum angle of links of the robot_--It must be ensured that the legs do not cross the maximum angle so that the CoM and CoG of the robot lie within the polygon.  
Assume the initial position to be \(X_{0}\ (x_{0},\ y_{0})\) and target position to be \(X_{t}\ (x_{t},\ y_{t})\). A PSO particle is given by \(Q_{i}=\{\theta_{1},\theta_{2}\}\), Where \(Q_{i}\) is a set of possible joint angles subjected to the following constraints.  
\[\theta_{1}\in\ [\theta_{1 min}\,\ \theta_{1 max}]\ \text{and}\ \theta_{2}\in\ [ \theta_{2 min}\,\ \theta_{2 max}] \tag{14}\]  
After applying the joint angles in the forward kinematic equation, the robot position in a reference frame can be obtained as, \(X_{i}\ (x_{i},\ y_{i})=(X_{1},\ X_{2}.....X_{n})\) This position is compared with the target position, \(X_{t}\). Hence, the fitness function, f is given as the Euclidean distance between the target position and the obtained robot position.  
\[f\ =||X_{t}-X_{i}||=\sqrt{\left(x_{t}-x_{i}\right)^{2}+\left(y_{t}-y_{i} \right)^{2}} \tag{15}\]
## Appendix A Monte Carlo Simulations for Different Coin Size  
In Figure 11, Monte Carlo simulations' results are shown of the probability to find solution \(p(\phi,\zeta,m)\) of the QRWS algorithm with a coin constructed by an HR and an additional phase multiplier. Simulation parameters are both phases \(\phi\) and \(\zeta\). Different images correspond to different size of the coin \(m\). The images in the first row represent QRWS with coin size \(m=2,3,4\) (Figure 11a-c), on the second--with \(m=5,6,7\) (Figure 11d-f) and on the third--with \(m=8,9,10\) (Figure 11g-i).  
For coin size 2, areas with high probability \(p(\phi,\zeta,m)\) are chess-like arranged rhomboids. For coin size 3, those rhomboids begin to merge in the direction of the line \(\zeta=-2\phi+3\pi\). At coin size 4, the merged rhomboids became parallel stripes. From this point on, the stripes' width begins to decrease with increasing the size of the coin.
# Backstepping Based Formation Control of Quadrotors with the State Transformation Technique
## 4 Simulation Results and Analysis  
### Simulation Environment Settings  
We perform simulations to verify the effectiveness of the proposed backstepping-based formation controller of the quadrotor system using the state transformation technique. In these simulations, the quadrotor dynamics in (5) is employed. In addition, we do not consider the rotor dynamics of a quadrotor. Instead, as defined in (6), the control inputs of the \(i\)-th follower quadrotor \(u_{i,1}\), \(u_{i,A}\), derived as in (15), (40) and (41), are used. The simulations gain parameters are chosen as follows: \(k_{i,1}=1.5\), \(k_{i,2}=1.5\), \(k_{i,3}=1.5\), \(k_{i,4}=1.5\), \(k_{i,7},k_{i,9},k_{i,11}=5\), \(k_{i,8},k_{i,10},k_{i,12}=5\). In this paper, these gains are selected by changing slightly based on gains of the controller used in [20], and these gains are tuned to ensure acceptable tracking performance with minimizing the overshoot and the undershoot error signals. In addition, the simulations are performed with the model parameters presented in Table 1.  
In this simulation, a total of three quadrotors is considered to verify the proposed quadrotor formation controller. That is, we consider a formation consisting of one leader and two follower quadrotors. First, the leader tracks the predefined trajectory. In this simulation, the ascending circular trajectory is set as the reference trajectory. Since the circular trajectory is a complex trajectory used to move the quadrotors, it is appropriate to verify the validity of the controller proposed in this paper.  
Next, each follower quadrotor keeps constant distance \(d_{i,(x,y,z)}\) and tracks the leader. In this simulation, the relative distances \(d_{i,x}\), \(d_{i,y}\) and \(d_{i,z}\) between the leader and the \(i\)-th follower are set as follows:  
\[d_{1,x}= 1,\qquad\quad d_{1,y}=1,\qquad\quad d_{1,z}=0.2,\] \[d_{2,x}= -1,\qquad d_{2,y}=-1,\qquad d_{2,z}=0.4.\]  
In Section 4.2, the results and analysis of two kinds of simulations are covered. First, the formation control simulation for the ascending circular trajectory using the formation controller applying the state transformation technique proposed in this paper is performed. Second, is the performance comparison simulation comparing the proposed formation controller and PID, a backstepping control technique not applying the state transformation technique. We verify the superiority and effectiveness of the proposed formation control method using the state transformation technique especially when the attitude angles change is large and sudden disturbance occurs.
# Spatial Data Reconstruction via ADMM and Spatial Spline Regression +
## 3 Patched Estimation and Spatial Spline Regression
### Spatial Spline Regression
The estimator \(\hat{f}(x,y)\) for \(f\) can then be derived from (9) as  
\[\hat{f}(x,y)=\hat{\mathbf{f}}_{K}^{\mathsf{T}}\psi(x,y).\]  
It is worth noting that commodity triangulation software for finite element analysis is readily available in many free and commercial finite element packages. For example, Delaunay triangulations of a set of data location points (e.g., [27]) \(V\) are such that no point in \(V\) is inside the circumcircle of any triangle; they maximize the minimum angle of all the triangle angles, avoiding stretched triangles. Now, we can see that if \(l=n\) and we plug \(h_{j}=\tilde{f}(\mathbf{p}_{j})\), \(j=1,\ldots,n\) into problem (8), we will get a new density surface \(\hat{f}\) as a solution to the SSR problem (8) that is a smoothened approximation of the patched estimates \(\tilde{f}(\mathbf{p}_{j})\). However, SSR given by (8) can not accommodate any constraints, which is the major limitation in solving our problem. Specially, in our case, SSR does not enforce the aggregated volume constraint (1) (or \(\mathbf{z}=\mathbf{Af}\) in (4)). Therefore, SSR gives no guarantee that the estimated densities in each patch \(\Omega_{B_{i}}\) will sum up to the observed volume \(z_{i}\) on the point \(B_{i}\). In this way, SSR would likely cause large estimation errors as it violates the constraint.
## 4 Early Warning of Rockburst Based on Microseismic Indices
### Commonly Used Microseismic Indices
#### 4.1.2 Apparent Volume  
The volume of a rock mass in which microseisms produce a corresponding inelastic strain under the action of the apparent stress is measured using the apparent volume [59]. The calculation formula is as follows:  
\[V_{\rm A}=\frac{M}{2\sigma_{\rm A}} \tag{4}\]  
The physical unit of the apparent volume is m\({}^{3}\); therefore, it can be easily accumulated or analyzed in the form of a cloud map. Because of this accumulative advantage, many scholars have established a relationship between the cumulative apparent volume and the risk of rockbursts. They believe that a rockburst may occur when the cumulative apparent volume increases rapidly. By analyzing the microseismic evolution law of the rockburst in the diversion tunnel of the Jinping II Hydropower Station, [PERSON] et al. [14] and [PERSON] et al. [60] found that the cumulative apparent volume evidently increased a few days before the rockburst, which is related to the occurrence of large-scale cracks in the rock mass. [PERSON] et al. [17] found a similar phenomenon in the study of rockburst evolution of the Hanjiang-to-Weihe River Diversion Project. However, from Equation (4), we find that the apparent volume is more sensitive to the change in the seismic moment, and if the seismic moment of the microseism increases, the apparent volume will increase accordingly. The increase in the seismic moment is only a necessary condition for increased rockburst risk. Therefore, the evaluation of rockburst risk using a single index based on the volume may lead to a misjudgment.