esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Experiments
### Box-Type vs. Ball-Type Gradient Constraint  
The performance of our methods depend on the variation of the luminance and color in a reference image. Accordingly, we studied the sensitivity of our methods with respect to a reference image by conducting an experiment on Gaussian noise removal.  
We generated a noisy image, which is shown in Figure 3b, by adding zero-mean Gaussian noise with standard deviation \(\sigma=5.0\times 10^{-3}\) to the ground truth image shown in Figure 3a. Then, four types of images, shown in Figure 4(a-1) ground truth image, a-2 horizontally flipped image of a-1, a-3 hue shift image of a-1, and a-4 horizontally flipped and hue shift image of a-1, were prepared, each of which was used as a reference image of our proposed gradient constraints. For the quality metric, we used the peak signal-to-noise ratio (PSNR). For the smoothing parameter setting, the balancing weight \(\lambda\) was set to maximize PSNR. Note that the purpose of this experiment is not to evaluate the pure performance of noise removal but to clarify the sensitivity of the method.  
Figure 4 shows the noise removal results and their PSNR values. One can see from Figure 4b,c that our images with the ball-type constraint have higher PSNR and visually better results than the box-type image for all cases. The results of Figure 4(b-2,b-4) are over-smoothed because the reference images have luminance variations that are considerably different from those of the input image (there are flipped relationships between the luminance variations of the input and reference images in the horizontal direction). This is because the sign of the gradients of the reference images is often reversed from the ideal one around the edges. The box-type constraint does not prevent the smoothed image from having the gradients whose sign is reversed from that of the reference image, thus yielding blurred images. In Figure 4(b-1,b-3), this constraint generates a better smooth result with sharper edges similar to those of the ground truth image; however, pseudo-color artifacts often occur around edges as shown in Figure 4(b-3). Thus, this constraint is very sensitive  
Figure 4: Noise removal results and their PSNR values [dB]: (from left to right) (**a1–4**) reference images, (**b1–4**) our image with the box-type constraint, and (**c1–4**) our image with the ball-type one.  
Figure 3: Ground truth and input images on zero-mean Gaussian noise removal (\(\sigma=5.0\times 10^{-3}\)). (**a**) Ground truth. (**b**) Input image.  
to the sign of image gradients unless an input image is used as a reference. In contrast, the ball-type constraint robustly generates a better smooth result with sharper edges that is the same as that in the input image, even if the reference images have luminance and color variations considerably different from those in the input image.
# Improved Block Element Method for Simulating Rock Failure
## 3 Constitutive Model Considering Coupled Normal and Shear Stress Behavior
The initial damage surface and the failure damage surface are illustrated in Figure 4 and can be written as follows:  
\[\text{Initial damage surface}:\ \left(\frac{\langle\delta_{n}\rangle}{\delta_{n}^{0 }}\right)^{2}+\left(\frac{\delta_{s}}{\delta_{s}^{0}}\right)^{2}=1 \tag{14}\]  
\[\text{Failure damage surface}:\ \left(\frac{\langle\delta_{n}\rangle}{\delta_{n}^{f }}\right)^{2}+\left(\frac{\delta_{s}}{\delta_{s}^{f}}\right)^{2}=1 \tag{15}\]  
In these equations, \(\delta_{n}^{0}\) and \(\delta_{s}^{0}\) represent the initial damage relative displacement in the normal and tangential directions, respectively, while \(\delta_{n}^{f}\) and \(\delta_{n}^{f}\) denote the failure damage relative displacement in the normal and tangential directions, respectively. These values are calculated as follows:  
Figure 3: Schematic diagram of bilinear damage model. \[\delta_{\rm m}=\sqrt{\left\langle\delta_{\rm n}\right\rangle^{2}+\left(\delta_{\rm s }\right)^{2}} \tag{26}\]  
According to the bilinear damage factor formulation [30; 31], the equivalent damage index \(\omega\) under coupled stress conditions has the following expression:  
\[\omega= \begin{cases}0&\delta_{m}\leq\delta_{m}^{0}\\ \frac{\delta_{m}^{\prime}(\delta_{m}-\delta_{m}^{0})}{\delta_{m}(\delta_{m}^{ \prime}-\delta_{m}^{0})}&\delta_{m}^{0}<\delta_{m}<\delta_{m}^{f}\\ 1&\delta_{m}\geq\delta_{m}^{f}\end{cases}  \tag{27}\]  
After obtaining the damage factor, the stress in the nonlinear stage can be expressed as follows:  
\[\sigma_{n}= \begin{cases}(1-\omega)k_{n}\delta_{n}&\delta_{n}>0\\ k_{n}\delta_{n}&\delta_{n}\leq 0\end{cases}  \tag{28}\]  
\[\sigma_{\rm s}=(1-\omega)k_{s}\delta_{s} \tag{29}\]  
Equation (28) indicates that the damaged region is still capable of transmitting normal stress under compressive normal stress. In view of the nonlinear behavior exhibited by rock materials during the softening phase, this study adopts the total iteration algorithm proposed by [PERSON] et al. [32] for computational analysis. In the initial loading stage, the displacement-controlled loads are applied based on the initial elastic modulus of the material, and the principal strain field for each element is calculated. According to the proposed damage constitutive model, the secant modulus of each element is updated based on the current strain state. The structure is then reloaded using the updated secant modulus to update the strain field until the convergence criterion is satisfied. The converged secant modulus is used as the initial parameter for the next loading increment, and the process is repeated until the entire loading procedure is completed. It should be noted that this direct iteration method is only applicable to material nonlinear problems that are path-independent. For conditions involving path-dependent deformation history, a more complex incremental iterative algorithm should be employed.
## 2 Route Generation Methodology
### Lower-Level Path Generation: Ant Colony Optimization (ACO)
#### 2.2.2 Modifications for the Coverage Salesman Planning Problem (CSP)  
Since the ACO algorithm is being used to find the shortest distance path that covers the desired area, there are some changes required to the traditional ACO algorithm. Specifically, the traditional ACO algorithm can be used to find the shortest path from point \(a\) to point \(b\). However, this is not the case for this research. Since the sensors onboard the surveillance vehicles have a specific scanning radius, a portion of the surrounding area is scanned at each instance. In graph theory, this is modeled as the CSP, where only a portion of nodes should be traversed to cover the desired area.  
To make this modification in the ACO algorithm, the set \(A\) in Equation (1) can be modified. Typically, \(A\) would contain all nodes that are adjacent to node \(i\). However, \(A\) was modified to include only adjacent nodes that have not been covered by the sensor. This means that the set of scanned nodes should be updated after each selection made by the ants. Additionally, the termination condition is the desired area coverage. Therefore, the ants will continue to travel through the target area until the desired area coverage is  
Figure 2: A simple ACO example. After several iterations, the shortest path is exploited through a pheromone reward/evaporation scheme.  
met. One of the challenges with this approach is finding an appropriate coverage ratio input. When the desired coverage input is 100%, the ants travel significantly more to cover every node. However, when the coverage is near 100% (around 95%), the ants yield more efficient paths with less overlapping. This highlights the tradeoff between the desired area coverage and the path distance. Therefore, the coverage ratio should be selected such that an appropriate coverage ratio is obtained in a relatively short path. The node coverage scheme is visualized in Figure 3, where a hypothetical sensor radius is highlighted in yellow.
# Efficient Control of a Non-Linear System Using a Modified Sliding Mode Control
###### Abstract  
Trajectory tracking is an essential requirement in robot manipulator movement and localization applications. It is a current research topic of interest, and several researchers have proposed different schemes to achieve the task accurately. This research proposes efficient control of a hydraulic non-linear robot manipulator using a modified sliding mode control, named proportional derivative sliding mode control with sliding perturbation observer (PDSMCSPO), to overcome parameter uncertainties and non-linearity. The proposed new control strategy achieves higher accuracy and better time convergence than the previous one. A positive derivative gain, which has a value less than one, is multiplied with the velocity error term of the sliding surface. The proposed control (PDSMCSPO) also achieves robustness. Results show that by introducing the derivative gain, the chattering from the system has been reduced more than classical sliding mode control (SMC). The reason is that during reaching phase this small gain multiplies with the perturbation and minimizes the effect of perturbation on the system. A smaller value of switching gain K is required as compared to SMC, and the transfer function between sliding surface and perturbation in proportional derivative sliding mode control (PDSMC)has low pass filter characteristics. The proposed PDSMCSPO has a faster response than previous sliding mode control with sliding perturbation observer (SMCSPO), and the output and sliding surface convergence to the desired value is much quicker than conventional logic. Some other characteristics such as error in the output are small because of more attenuation of the perturbation signal. Simulation and experimental results are presented for a link between the hydraulic robot manipulator and the mass damper system.  
s 2019; 9, 1284; doi:10.3390/app9071284
# Detecting Axial Ratio of Microwave Field with High Resolution Using NV Centers in Diamond
## 2 Principle
Simply by turning over the permanent magnet to apply bias magnetic fields in reversed direction, the strength of both \(\sigma^{-}\) and \(\sigma^{+}\) circularly-polarized components of the MW magnetic field at a certain frequency perpendicular to the NV axis that rotate in different directions can be extracted by detecting Rabi frequencies. Therefore, the axial ratio of the MW magnetic field at the location of the NV center perpendicular to the NV axis can be deduced. Figure 2: (**a**) The ground electron spin triplet state of the NV center with zero field splitting of \(D=2.87\) GHz between the \(m_{s}=0\) state and \(m_{s}=\pm 1\) state. A magnetic field of \(B_{z}\) along the direction of the NV axis leads to an energy level splitting of \(2\gamma_{e}B_{z}\), where \(\gamma_{e}=2.8\) MHz/G is the gyro-magnetic ratio of NV electron spin. The spin transition \(m_{s}=0\leftrightarrow m_{s}=-1(+1)\) can be selectively addressed by the \(\sigma^{-}(\sigma^{+})\) polarized MW field. (**b**) Scanning picture of a diamond sample containing a single NV center. The marked bright spot is the single NV center used for MW field detection in this experiment. The other bright signals below are from ensemble NV centers. (**c**) Optically-detected magnetic resonance spectra of nitrogen vacancy (NV) center under a bias magnetic field of about 500 G. The data are fitted with the Gauss function. The first (second) dip at \(f_{1}=1.44\) GHz (\(f_{2}=4.30\) GHz) corresponds to the transition \(m_{s}=0\leftrightarrow m_{s}=-1\) (\(+1\)) state.
# Finite Differences on Sparse Grids for Continuous-Time Heterogeneous Agent Models
## 2 Heterogeneous Agent Models as Optimal Control Problems
### Optimal Control Problems in Economics
We use in (4a) the transaction cost function \(\chi\) from [16] given by  
\[\chi(d,a)=\chi_{0}|d|+\frac{\chi_{1}}{2}\bigg{(}\frac{d}{a}\bigg{)}^{2}a+\chi _{2}\mathds{1}_{\{d\
eq 0\}},\]  
with the derivative with respect to \(d\) given by  
\[\partial_{d}\chi(d,a)=\chi_{0}\mathds{1}_{\{d>0\}}-\chi_{0}\mathds{1}_{\{d<0 \}}+\chi_{1}\frac{d}{a}.\]  
Here, the linear component \(\chi_{0}>0\) generates inaction in optimal deposit decisions. The quadratic term with \(\chi_{1}>0\) ensures that deposit rates \(d/a\) are finite, so that households' asset holdings never jump. By using standard arguments, one obtains the HJB equation  
\[ \begin{split}\rho v(b,a,z_{i})=&\max_{c,d}u(c)\\ &+\partial_{b}v(b,a,z_{i})(wz+r^{b}(b)b-d-\chi(d,a)-c)\\ &+\partial_{a}v(b,a,z_{i})(r^{a}+d)\\ &+\sum_{j=1}^{2}\lambda(i,j)(v(b,a,z_{j})-v(b,a,z_{i})),\end{split}  \tag{6}\]for \(i=1,2\) for the two state Poisson process. The first order conditions with respect to \(c\) and \(d\) yield  
\[\partial_{c}u(c) =\partial_{b}v(b,a,z), \tag{7a}\] \[\partial_{a}v(b,a,z) =\partial_{b}v(b,a,z)(1+\partial_{d}\chi(d,a)) \tag{7b}\]  
and thus we can simply compute the optimal consumption and optimal deposits given the value function derivatives. The optimal consumption is then given by  
\[c=(v_{b}(b,a,z))^{-\frac{1}{7}}.\]  
Using our cost function, we obtain the optimal deposits for illiquid assets  
\[ \begin{split} d&=\underbrace{d^{+}}_{\text{case }d>0}+\underbrace{d^{-}}_{\text{case }d<0}\\ &=\left((\frac{v_{a}}{v_{b}}-1-\chi_{0})\frac{a}{\chi_{1}}\right) ^{+}+\left((\frac{v_{a}}{v_{b}}-1+\chi_{0})\frac{a}{\chi_{1}}\right)^{-}.\end{split}  \tag{8}\]  
Both can be collected per state to obtain the policy function given the value function. In (4), the productivity \(z_{t}\) follows a Poisson process with intensities \(\lambda(z,z^{\prime})\). The setting can be easily extended to diffusion type stochastic processes. Thus, _productivity_, which is a measure for the output per unit of input, is modeled such that it influences the households income as \(wz_{t}\). For the same model setup, one could also interpret \(z\) as a specific skill that influences the income. Note that all agents face different productivity shocks and thus this is an example of an economic model featuring heterogeneity.
###### Abstract  
The basic system of the BeiDou global navigation satellite system (BDS-3) with 18 satellites has been deployed since December 2018. As the primary frequency standard, BDS-3 satellites include two clock types with the passive hydrogen maser (PHM) and the rubidium atomic frequency standard (RAFS). Based on the final precise orbit and clock product from Xi'an Research Institute of Surveying and Mapping (XRS), the atomic clock performance of BDS-3 satellites is evaluated, including the frequency accuracy, frequency drift rate, and frequency stability, and compared with GPS block IIF satellites with RAFS, Galileo satellites with PHM, and BDS-2 satellites. A data auto-editing procedure to preprocess clock data and assess the clock performance is developed, where the assessed results are derived at each continuous data arc and the outliers are excluded properly. The stability of XRS product noise is given by using some stations equipped with high-precision active hydrogen masers (AHM). The best stability is \(8.93\times 10^{-15}\) and \(1.85\times 10^{-15}\) for the averaging time of 10,000 s and 1 day, which is basically comparable to one-third of the in-orbit PHM frequency stability. The assessed results show the average frequency accuracy and drift rate of BDS-3 with RAFS are slightly worse while the stability is better than BDS-2 medium earth orbit (MEO) satellites. The 10,000 s stability is better but the 1-day stability is worse than GPS, which may be related to the performance of the BDS-3 RAFS clock. As for BDS-3 with PHM, the frequency accuracy is slightly worse than Galileo PHM satellites; the drift rate, when excluding C34 and C35, is basically comparable to Galileo and significantly better than GPS satellites; the stability is comparable to Galileo, where the 10,000 s stability is slightly worse than Galileo and better than GPS. The 1-day stability among BDS-3 PHM, GPS IIF RAFS, and Galileo PHM satellites is basically comparable.  
BDS-3; Clock performance; PHM; RAFS; Hadamard deviation 2019 11 2895 2019 12895 2019 11 2895 2019 2019
## 2 Background
### Author Contribution  
In addition to providing the reader with assistance in selecting a clustering method tailored to their particular application's requirements, this paper's primary objective is to provide a concise review of several clustering methodologies [22]. In order to accomplish this goal, we conducted a comprehensive analysis of the most up-to-date optimized clustering solutions [40]. As a result, multiple performance parameters are utilized to compare and assess them. LEACH is a fascinating routing system for WSNs, yet it is plagued with several flaws that adversely impair its performance. These deficiencies result from many variables connected to its operation, some of which are highlighted below.  
* In subsequent rounds, we will choose the CH without considering the excess energy of the sensor nodes;
* Therefore, a sensor node with low residual energy will pass away rapidly if it is picked to be the CH;
* Due to this, the network's resilience is diminished and its lifetime is shortened;
* Since they are placed near the edge of the clusters, the CHs would lose more energy, which would hurt the overall performance of the network;
* When it comes to data transmission, CHs that are further away from the BS use up more energy than CHs that are positioned closer to the BS. Due to this, the lifespan of the network may be reduced.  
We may sum up our primary contributions as follows.  
* Create a clustering protocol using weighted parameters. Review the state-of-the-art WSN clustering;
* Extensive comparison and assessment of the offered algorithms based on the parameters;
* Compared to state-of-the-art algorithms, the proposed one has significantly lower energy requirements while maintaining or improving performance.
# Full Field Inversion in Photoacoustic Tomography with Variable Sound Speed
## 3 Final Time Wave Inversion Problem for Variable Sound Speed
### Application of the Steepest 6 thhod  
We propose solving the finite time wave inversion problem (9) via gradient type methods applied to residual functional \(\Phi(f)\coloneqq\frac{1}{2}\left\|\mathbf{W}_{T}f-h\right\|^{2}\). Using standard PAT data, various iterative methods for PAT accounting for variable sound speed have been investigated in [36; 37; 38; 39; 40]. In particular, in [40] the steepest descent method has been demonstrated to be numerically efficient and robust. For the results shown in this paper we will therefore use the steepest-descent method. Our numerical experiments confirm that the steepest-descent method is also efficient for FFD-PAT and the final time wave inversion problem, where it reads as follows.  
Because of the injectivity and boundedness of \(\mathbf{W}_{T}\), the sequence of iterates generated by Algorithm 1 converges to the unique solution of (9). The stability result (11) even implies that the steepest descent method converges linearly for FFD-PAT. More precisely, the sequence \((f_{k})_{k\in\mathbb{N}}\) generated by Algorithm 1 satisfies the estimate \(\left\|f_{k+1}-f\right\|_{2}\leq c^{k}\,\left\|f_{0}-f\right\|_{2}^{2}\) for some constant \(c\in(0,1)\).  
```
(S1) Choose \(a_{*}\in(0,1]\) and initialize \(f_{0}=0\), \(k\gets 0\) (S2) While stopping criteria not satisfied, do \(\blacksquare\)\(\xi_{k}=\mathbf{W}_{T}^{*}(\mathbf{W}_{T}f_{k}-g)\) \(\blacksquare\)\(a_{k}=a_{*}\|\xi_{k}\|^{2}/\left\|\mathbf{W}_{T\xi_{k}}\right\|^{2}\) \(\blacksquare\)\(f_{k+1}=f_{k}-a_{k}s_{k}\) \(\blacksquare\)\(k\gets k+1\)
```  
**Algorithm 1**Steepest descent method for solving \(\mathbf{W}_{T}f=g\).
# Automatic Addition of Fault-Tolerance in Presence of Unchangeable Environment Actions +
## 6 Experimental Results
### Addition of Stabilization
#### 6.1.2 Two-Dimensional Stabilizing Shepherding Problem  
In this section, we consider the shepherding problem described in Section 6.1.1 in a two-dimensional space. Thus, instead of a single row of cells, we have a grid of cells where the sheep and the farmer can move. Thus, we have four variables \(r_{f}\), \(c_{f}\), \(r_{s}\) and \(c_{s}\) that represent the row and column of the farmer and the sheep, respectively (see Figure 6).  
The upper right corner of the grid is the desired location. Thus, the invariant for this problem is \(\{s|r_{s}(s)=0\wedge c_{s}(s)=n-1\}\), where again \(n\) is the number of cells in a row. The sheep again tries to increases its distance with the farmer. The sheep and the farmer can only change either their row or  
Figure 6: An example state of a 2D shepherding problem with \(n=4\). In this example, \(r_{f}=2\), \(c_{f}=1\), \(r_{s}=1\) and \(c_{s}=2\).  
column by at most one at each step. As in Section 6.1.1, sheep stops moving once it is in the desired location. With this explanation, the set of environment transitions is  
\[\delta_{e}=\Big{\{}(s_{0},s_{1})|\
eg(r_{s}(s_{0})=0\wedge c_{s}(s_ {0})=n-1)\land\] \[(r_{f}(s_{0})=r_{f}(s_{1})\wedge c_{f}(s_{0})=c_{f}(s_{1}))\land\] \[(c_{s}(s_{0})=c_{s}(s_{1})\lor r_{s}(s_{0})=r_{s}(s_{1}))\land\] \[\Big{(}\big{(}c_{f}(s_{0})<c_{s}(s_{0})\wedge c_{s}(s_{0})<n-1 \wedge c_{s}(s_{1})=c_{s}(s_{0})+1\big{)}\lor\] \[(c_{f}(s_{0})>c_{s}(s_{0})\wedge c_{s}(s_{0})>0\wedge c_{s}(s_{1} )=c_{s}(s_{0})-1)\lor\] \[(c_{f}(s_{0})=c_{s}(s_{0})\wedge c_{s}(s_{0})<n-1\wedge c_{s}(s_{ 1})=c_{s}(s_{0})+1)\lor\] \[(c_{f}(s_{0})=c_{s}(s_{0})\wedge c_{s}(s_{0})>0\wedge c_{s}(s_{1} )=c_{s}(s_{0})-1)\lor\] \[(r_{f}(s_{0})<r_{s}(s_{0})\wedge r_{s}(s_{0})<n-1\wedge r_{s}(s_{ 1})=r_{s}(s_{0})+1)\lor\] \[(r_{f}(s_{0})>r_{s}(s_{0})\wedge r_{s}(s_{0})>0\wedge r_{s}(s_{1} )=r_{s}(s_{0})-1)\lor\] \[(r_{f}(s_{0})=r_{s}(s_{0})\wedge r_{s}(s_{0})<n-1\wedge r_{s}(s_{ 1})=r_{s}(s_{0})+1)\lor\] \[\big{(}r_{f}(s_{0})=r_{s}(s_{0})\wedge r_{s}(s_{0})>0\wedge r_{s}( s_{1})=r_{s}(s_{0})-1)\big{)}\Big{\}}\]  
Also, the set of program restrictions is  
\[\delta_{r}=\{(s_{0},s_{1})|\ |c_{f}(s_{0})-c_{f}(s_{1})|+|r_{f}(s_{0})-r_{f}(s_{1} )|>1\}.\]  
Like one-dimensional case discussed in Section 6.1.1, with a poorly designed farmer, here is also possible to chase the sheep forever and never reach the desired state. Table 1 shows the repair time using JavaRepair for this problem for different sizes.
# Estimating the Spectral Response of Eight-Band MSFA One-Shot Cameras Using Deep Learning
## 3 Materials and Methods
### Deep-Learning Algorithms  
Image reconstruction is a growing field in image processing, aiming to improve image quality with finer and more precise details. Deep-learning algorithms have progressed considerably, enabling more accurate and detailed image reconstructions. Among these algorithms, several innovative approaches stand out for their ability to exploit deep and complex architectures to improve images [19].  
In our study, we modify the architecture of three algorithms to meet our specific needs: very deep super-resolution (VDSR), Laplacian pyramid super-resolution network (LapSRN), and deeply recursive convolutional network (DRCN).  
Each of these algorithms provides a unique method for tackling the reconstruction problem by exploiting their architectures' specific characteristics to optimize the reconstructed images' quality. When these algorithms process images, they must understand and model how each spectral band contributes to the final image. The spectral response of the cameras plays a role in this process, as it directly influences the quality of the input data for these algorithms. An accurate and well-calibrated spectral response allows algorithms to capture better and restore spectral details, thereby improving the quality and fidelity of reconstructed images.