esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Preliminaries  
**Definition 1** ([20]).: _Consider a fixed-time stability system with explicit time parameter_  
\[\dot{\mathbf{x}}=-\frac{\mathbf{g}(\infty)-\mathbf{g}(\mathbf{0})}{T_{c}}(\frac{\partial\mathbf{g} (\mathbf{x}^{m})}{\partial\mathbf{x}})^{-1}, \tag{1}\]  
_where \(0<m<1\), \(T_{c}\) is a positive parameter and \(\mathbf{g}\) is a right-monotone-increasing continuous function with terminal property. \(\mathbf{x}=\left[\begin{array}{cc}x_{1}&\cdots&x_{n}\end{array}\right]^{T}\in R ^{n}\) and \(\mathbf{g}(\mathbf{x}):D\to R^{n}\) is bounded in an open neighborhood \(D\) of the origin \(\mathbf{x}=\mathbf{0}\), and \(\mathbf{g}(\mathbf{0})=\mathbf{0}\). (1) can be said to be a fixed-time stable system if (1) is globally finite-time stable and \(T_{c}\) is the upper bound of the convergence time._  
**Theorem 1**.: _Consider a novel system_  
\[\dot{\mathbf{x}}=-\frac{\frac{\pi}{2}+\arctan(\|\mathbf{x}_{0}\|)}{mT_{c}}(1+(\|\mathbf{x }\|^{m}-\|\mathbf{x}_{0}\|)^{2})\frac{\mathbf{x}}{\|\mathbf{x}\|^{m}}, \tag{2}\]  
(2) _is a fixed-time stable system and the input is smaller than one of the existing fixed-time stable system._  
**Proof of Theorem 1.** Consider a candidate Lyapunov function  
\[V=\|\mathbf{x}\|. \tag{3}\]  
Then, the time derivative of \(V\) can be deduced as:  
\[\begin{array}{l}\dot{V}=\frac{\mathbf{x}^{T}\mathbf{x}}{\|\mathbf{x}\|}\\ =-\frac{\mathbf{x}^{T}}{\|\mathbf{x}\|}\frac{\frac{\mathbf{x}}{\mathbf{x}}+arctan(\|\mathbf{x}_{0} \|)}{m_{\text{c}}}(1+(\|\mathbf{x}\|^{m}-\|\mathbf{x}_{0}\|)^{2})\frac{\mathbf{x}}{\|\mathbf{x }\|^{m}}\\ =-\frac{\mathbf{x}^{T}+arctan(V_{0})}{m_{\text{c}}}(1+(V^{m}-V_{0})^{2})V^{1-m}, \end{array} \tag{4}\]  
the upper bound of settling time can be solved to  
\[\begin{array}{l}T=\int\limits_{0}^{\infty}-\frac{\mathbf{x}^{T}+arctan(V_{0})}{ m_{\text{c}}}(1+(V^{m}-V_{0})^{2})V^{1-m}dV\\ =T_{\text{c}}\frac{arctan(\infty-V_{0})+arctan(V_{0})}{\mathbf{x}^{T}+arctan(V_{ 0}))}\\ \leq T_{\text{c}}.\end{array} \tag{5}\]  
In the end, it is clear that the proportional coefficient function of system (2) is related to the initial value rather than the infinity point value of function \(\mathbf{g}(\mathbf{x})=arctan(\|\mathbf{x}\|^{m})\) given by (1), so the input of (2) is smaller than the one of an ordinary fixed time stable system \(\frac{\mathbf{x}^{T}+arctan(\|\mathbf{x}_{0}\|)}{m_{\text{c}}}(1+(\|\mathbf{x}\|^{m}-\| \mathbf{x}_{0}\|)^{2})<\frac{\mathbf{x}}{2m_{\text{c}}}(1+\|\mathbf{x}\|^{2m})\) for \(\|\mathbf{x}_{0}\|>1\) in initial moment.
# Settlement Prediction and Differential Settlement Criterion for Heightening and Thickening Leveee
## 3 Case Study
### Differential Settlement Control Criterion
#### 3.3.1 Horizontal Stress of Pavement  
Figure 13 shows the horizontal stress distribution of pavement at the top of the HTL. The pavement cracking is caused by the horizontal tensile stress exceeding the ultimate tensile strength. Therefore, the horizontal stress distribution of the pavement is a very important factor to prevent pavement cracking.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Monitoring Points**} & \multicolumn{1}{c}{**Prediction Models**} & \multicolumn{1}{c}{**Sum of Squares of Errors**} \\ \hline \multirow{3}{*}{G1} & GSPM & **0.32** \\  & Logistic model & 0.34 \\  & Hyperbolic model & 0.4 \\ \hline \multirow{3}{*}{A} & GSPM & **0.43** \\  & Logistic model & 0.65 \\  & Hyperbolic model & 0.81 \\ \hline \multirow{3}{*}{G2} & GSPM & **0.93** \\  & Logistic model & 1.36 \\  & Hyperbolic model & 1.53 \\ \hline \multirow{3}{*}{B} & GSPM & **3.71** \\  & Logistic model & 4.48 \\  & Hyperbolic model & 10.20 \\ \hline \multirow{3}{*}{L} & GSPM & **4.43** \\  & Logistic model & 4.90 \\  & Hyperbolic model & 11.91 \\ \hline \multirow{3}{*}{Depth 0.5 m at top} & GSPM & **3.93** \\  & Logistic model & 5.30 \\  & Hyperbolic model & 12.37 \\ \hline \multirow{3}{*}{Depth 1 m at top} & GSPM & **5.89** \\  & Logistic model & 6.70 \\  & Hyperbolic model & 13.15 \\ \hline \multirow{3}{*}{Depth 6 m at top} & GSPM & **4.02** \\  & Logistic model & 7.36 \\  & Hyperbolic model & 4.53 \\ \hline \multirow{3}{*}{Depth 0.5 m at half} & GSPM & **0.22** \\  & Logistic model & 0.30 \\  & Hyperbolic model & 0.42 \\ \hline \multirow{3}{*}{Depth 1 m at half} & GSPM & **0.19** \\  & Logistic model & 0.29 \\  & Hyperbolic model & 0.51 \\ \hline \multirow{3}{*}{Depth 4 m at half} & GSPM & **2.68** \\  & Logistic model & 3.07 \\ \cline{1-1}  & Hyperbolic model & 2.87 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Sum of squares of errors for different settlement–time models unit:mm\({}^{2}\).  
From Figure 13a, it can be seen that the maximum horizontal tensile stress appears at the junction of the backfill and the old levee, which is basically consistent with the crack location in the actual project.  
The main reason for pavement cracking is the compressibility difference between the backfill and the old levee owing to the insufficient compaction of backfill. This insufficient compaction of backfill may come from rolling during construction.  
The time-space relationship of the horizontal stress of the pavement is shown in Figure 13b. It can be seen from Figure 13b that the horizontal stress of the pavement presents an asymmetric W-type in space. The horizontal stress on one side of the old levee is lower than that on the side of backfill, and the maximum tensile stress appears at the joint of the backfill and the old levee.
## 4 Procedure of Compound Faults Diagnosis  
This method is applied to separate and extract the compound fault of the inner and outer race of the bearing. Firstly, the input measured signal is preprocessed by the parallel dual-Q-factor base sparse decomposition to obtain a low resonance component, and the compound failure impacts of the inner and outer rings are clearly extracted. Then the IMCKD is used to separate and extract the compound fault feature according to different fault periods. The specific process of the proposed method is illustrated in the flow chart shown in Figure 5, and the method is described as follows:  
1. Input the vibration signal \(x(t)\), including noise, random vibration generated by normal parts of the rolling bearing and shock vibration generated by composite faults.
2. Use the parallel dual-Q-factor bases sparse decomposition to obtain the high resonance components (random vibration generated by the normal part and strong noise) and the low resonance components (composite fault impact component and a small amount of noise): 1. Set the appropriate decomposition parameters: The quality factor Q\({}_{1}\), Q\({}_{2}\), the redundancy \(r_{1}\), \(r_{2}\), and the number of layers \(J_{1}\), \(J_{2}\); 2. Decompose the input signal \(x(t)\) using the parallel dual-Q-factor; 3. Extract the low resonance component \(x_{L}\);
3. The low resonance components of the signal are deconvoluted and filtered with the optimal parameters by IMCKD: 1. Calculate the \(T_{*}\) (\(*\) is \(i\), \(o\); \(i\) represents inner, \(o\) represents outer), and pre-select the scope of MCKD parameters (\(M\), \(L\)); 2. Calculate \(M_{best-i}\), \(L_{best-i}\) and \(M_{best-o}\), \(L_{best-o}\) based on Section 3.2.2; 3. The low resonance component \(x_{L}\) is deconvoluted and filtered with the optimized parameters [\(T_{o}\), \(M_{best-o}\), \(L_{best-o}\)] and [\(T_{i}\), \(M_{best-i}\), \(L_{best-i}\)] respectively to obtain the time domain signals \(y_{1}\) and \(y_{2}\);
4. Extract the fault feature frequency from the envelope spectrum calculated by Hilbert Transform (HT).
# Chaotic Image Encryption: State-of-the-Art, Ecosystem, and Future Roadmap
## 2 Existing Surveys
### Surveys on AI-Assisted Image Processing  
Reviewing existing AI-assisted image processing methods has been of interest to many researchers. For example, a survey reported in [28] focused on the interactions between machine learning and binocular stereo for depth estimation from images. Depth estimation has many practical purposes in fields such as 3D image reconstruction and autonomous driving. Included in the many techniques for estimating depth, stereo matching compares two images for pixel disparity and utilizes triangulation to determine the depth of the pixel. Data-driven and learning-based techniques have been applied to stereo matchingwith outstanding success, but the reverse has also yielded promising advances in using stereo matchingto develop new methodologies based on deep networks.  
Another relevant review studied deep learning-based Multi-Focus Image Fusion (MFIF) methods [29]. MFIF is an image processing technique for fusing multiple images with differing depths of fields to create a single in-focus image. Propositions for solving the MFIF problem using deep learning techniques have been growing at a rapid rate since 2017, although none yet have shown any advantages or performance improvements over traditional methods. The applications of deep learning in image segmentation were studied in another survey [30]. Image segmentation, the process of partitioning an image into two or more segments, has a wide range of use cases in fields such as video surveillance, image compression, augmented reality, and scene interpretation. Algorithms based on deep learning models have demonstrated very impressive results, often outperforming traditional segmentation algorithms on many popular benchmarks.
## 3 Observations
### Digisonde Measurements
#### 3.1.4 Ionospheric Absorption Investigation  
During the above listed periods of the \"fade-out\", not only the F1 and F2 layers disappeared from the ionograms at the investigated stations but the E layer as well. A known reason for the fade-out phenomena, especially in the lower frequency range (1-5 MHz), is the increased absorption occurring in the lower ionosphere caused by enhanced X-ray or proton flux (see e.g., [56; 57]). During this Mother's Day storm period, the background X-ray flux was quite high. Furthermore, several strong solar flares were registered, consequently the ionospheric absorption is probably also increased (see the article of [58] for the list of the incident flares). To investigate the reason for the fade-out in the current case, the \"amplitude method\" [38] has been applied for the ionosonde data recorded at SO and VT during the studied period (Figures 5 and A9). Figure 5 shows the X-ray and proton flux, furthermore, the absorption detected at 3 MHz at SO during 3 consecutive reference days (upper 3 subplots) and during the time of the geomagnetic storm (lower 3 subplots). The daily variation of the absorption can be clearly recognized in the data measured during the reference days (Figure 5c). The time of the \"fade-out\" is indicated by dark grey, while the periods when the maximum frequency of the F layer (foF2 or foF1) was below 3 MHz are indicated by faint grey shadow. Increased values of the absorption can be seen in the early morning hours and before the \"fade-out\" (02-06 UT) on 11 May (Figure 5f). The period of enhanced absorption agrees well with the time when the integrated proton flux increased according to the GOES data (Figure 5e). It is also important to note that the X-ray flux was increased as well throughout the day on 11 May (Figure 5d, time of terminators are indicated by black dashed lines). In summary, according to the results of the current analysis, we cannot exclude that the increased absorption caused by the enhanced proton and X-ray flux (during the early morning hours and the whole day, respectively) has an important role in the disappearance of the E-layer from the ionograms during the fade-out period.
## 3 Aggressive Control of Quadrotors with Extended Finite-Time Observer
### Nonlinear-Flatness Based Decoupling Control
Under Assumption 1, we can assume that \(\tan\theta_{i}\approx\theta_{i}\), \(\tan\phi_{i}\approx\phi_{i}\), \(\cos\theta_{i}\approx 1\), and \(\cos\phi_{i}\approx 1\). The desired yaw angle is zero. Using controller (11), \(\psi_{i}\approx 0\). Then, \(\cos\psi_{i}\approx 1\) and \(\sin\psi_{i}\approx 0\). We also assume that the altitude is stabilized and keep constant, such that \(Z_{i}\approx Z_{i}^{d}\) and \(Z_{i}\approx 0\). Then we have, \(\dot{Z}_{i}\approx 0\). Therefore, according to the analysis in Appendix A.2, we consider  
\[ \begin{array}{c}\ddot{X}_{i}=\theta_{i}g\\ \ddot{Y}_{i}=-\phi_{i}g\end{array}  \tag{16}\]  
Then, the controllers in (14) becomes  
\[ \begin{array}{c}v_{i1}=\dddot{X}_{i}^{d}-k_{4X}(\dot{\theta}_{i}g-\dddot{X} _{i})-k_{3X}(\theta_{i}g-\dddot{X}_{i}^{d})-k_{2X}(\dot{X}_{i}-\dddot{X}_{i}^ {d})-k_{1X}(X_{i}-X_{i}^{d})\\ v_{i2}=\dddot{Y}_{i}^{d}-k_{4Y}(-\phi_{i}g-\dddot{Y}_{i}^{d})-k_{3Y}(-\phi_{i}g- \dddot{Y}_{i}^{d})-k_{2Y}(\dot{Y}_{i}-\dddot{Y}_{i}^{d})-k_{1Y}(Y_{i}-Y_{i}^{d })\end{array}  \tag{17}\]  
Then, we obtain  
\[ \begin{bmatrix}\tau_{\phi_{i}}\\ \tilde{\tau}_{\phi_{i}}\\ \tilde{\tau}_{\phi_{i}}\end{bmatrix} = \begin{bmatrix}-\frac{1}{g}v_{i2}\\ \frac{1}{g}v_{i1}\\ \ddot{\psi}_{i}^{d}-k_{2\tilde{\tau}_{i}}(\dot{\psi}_{i}-\dot{\psi}_{i}^{d})- k_{1\psi_{i}}(\psi_{i}-\psi_{i}^{d})\end{bmatrix}  \tag{18}\]  
The control strategy in (18) is based on the knowledge of high-order derivatives of the planar positions \(X_{i}^{d}\) and \(Y_{i}^{d}\) in guidance vector, which are normally not measurable. Note that, for each quadrotor, the guidance vector depends on neighbors states (and the reference formation trajectory (RFT), if the quadrotor is a leader). If the quadrotors move slowly and the RFT varies slowly, we can assume that the higher-order derivatives are null. However, the performance will not be satisfactory for aggressive formations. The fast convergence of the observer is crucial in aggressive formation. Therefore, we will propose in the next subsection an extended finite-time observer to estimate these high-order derivatives.
###### Abstract  
The soft and fractured strata can cause significant deformation of surrounding rock during tunnel excavation. This study analyzes field monitoring test results and compares numerical simulations from the third bid project of the Dali I section construction within the water diversion project in central Yunnan to address the issue of significant deformation following tunnel excavation in soft and fractured strata. It proposes an optimized support scheme consisting of a densified steel arch and enhanced initial support strength and stiffness. In addition, the research investigates support effectiveness considering varying support strengths and steel arch ring spacing. The study findings indicated the following: (1) The tunnel traverses soft and fractured strata, causing unevenly distributed vertical convergence deformation around the cavern. The maximum settlement occurs at the crown, showing pronounced nonlinearity. (2) The maximum stress in the steel arch is concentrated at the arch crown, measuring \(-19.02\) MPa. The arch remains compressed, with stress decreasing from the crown to the waist. (3) The axial force in the anchor bolt reduces from the crown to the arch's waist on both sides. As the depth of the rock mass increases, the axial force in each anchor bolt decreases and the tension state is maintained. The maximum axial force reaches 46.57 kN. (4) The maximum displacement decreases from 4.21 to 0.15 cm after the optimized support structure is implemented, demonstrating the optimization scheme's effectiveness. Future constructions can refer to this scheme and make necessary adjustments based on various terrain conditions to ensure safety.  
Keywords:diversion tunnel; softly fractured strata; surrounding rock deformation monitoring; steel arch stress; numerical simulation +
Footnote †: journal: Applied sciences
# Research on a Time Series Data Prediction Model Based on Causal Feature Weight Adjustment
## 2 Related Work
[31] proposed an improved additive noise model with conditional probability to solve the problem of many-to-one causality discovery in high-dimensional dynamic stock markets and successfully mined the relationship between multiple factors and returns. [PERSON] et al. [32] proposed the causal feature selection (CFS) algorithm by using the constraint-based causal discovery algorithm, which can select the feature set with the best effect on stock market prediction. The importance of each feature to the predicted objective is different and the features that have a causal relationship with the stock price should be more critical to the forecast. Therefore, we propose that the weight of these features should be different from other features. We propose a method to adjust the feature weights, which combines the causal discovery algorithm based on the structural causal model, feature weight adjustment, and deep neural network to improve the accuracy of stock price prediction. Our work is different from existing methods.
# Quantum Synchronization and Entanglement of Dissipative Qubits Coupled to a Resonator
## 2 Model Description
In the RWA formulation, Lindblad Equation (4) takes the following form:  
\[\partial_{t}\hat{\rho}_{\mathcal{R}}=-\frac{i}{\hbar}[\hat{H}_{\mathcal{R}}, \hat{\rho}_{\mathcal{R}}]+\mathcal{L}_{d}(\rho_{\mathcal{R}}) \tag{6}\]  
Since the Hamiltonian \(\hat{H}_{\mathcal{R}}\) is stationary, the steady-state value of \(\hat{\rho}_{\mathcal{R}}\) can be found by setting the left-hand side of Equation (6) to zero. The advantage is that finding the steady state does not require numerically integrating the equations of motion Equation (4) and can be found more directly by solving the matrix equation, as follows:  
\[-\frac{i}{\hbar}[\hat{H}_{\mathcal{R}},\hat{\rho}_{\mathcal{R}}]+\mathcal{L}_ {d}(\rho_{\mathcal{R}})=0 \tag{7}\]  
The described model is an extension of the Jaynes-Cummings model, which appears in various fields of physics describing the most natural coupling between the oscillator and two-level atom (spin-half). The extensions we use include the dissipation of qubits and cavities and also the monochromatic driving of cavities. Such a situation naturally appears for superconducting qubits coupled to a driven cavity (see [6; 7; 8; 9; 10; 11]) and, thus, we believe that our model is suited for the study of the synchronization of dissipative qubits coupled to a driven resonator (cavity).
## 4 Network Architecture and Parameter Optimization  
### Data Pre-Processing  
The input parameters of the neural network have varying dimensions, so it makes sense to normalize the input parameters in order to increase the predicting precision of the neural network [28,29]. The input parameters are mapped to a range from 0 to 1 using the normalization formula below:  
\[x_{norm}=\frac{x-x_{min}}{x_{max}-x_{min}} \tag{4}\]  
where \(x_{norm}\) stands for the normalized input, \(x\) stands for the current original input, \(x_{min}\) stands for the minimum value for all inputs, and \(x_{max}\) stands for the maximum value.
# A Novel Scheme for MIMO-SAR Systems Using Rotational Orbital Angular Momentum
The RDE of vortex EM waves brings a novel scheme for MIMO-SAR systems. By transmitting the rotational OAM beams, the transmitted signals of different OAM modes are fixed into specific center frequencies in the azimuth. Therefore, the echo signals of different OAM modes can be separated without ambiguities in the range-Doppler domain using bandpass filtering. Since the orthogonal separation is realized by filtering rather than decoding, the performance of the proposed scheme can avoid the impacts of the time-variant channel responses [7]. Besides, compared with plane EM waves, vortex EM waves have a wider beam width, which brings better performance in terms of swath width and azimuth resolution under the same antenna aperture size [12]. Based on the added DOF, the OAM-based scheme may greatly enhance the performance of MIMO-SAR applications, including high-resolution wide-swath remote sensing, 3-D imaging [17], stealth target detection [10], and radar-communication integration [18]. To our knowledge, there exist no public papers concerning the OAM-based MIMO-SAR system. In this article, a novel scheme for MIMO radar systems using the rotational OAM is proposed. Different OAM signals are mapped into different frequency shifts at the receiving end, and thus the orthogonal and spiral properties of OAM beams can be utilized in MIMO-SAR systems. The rest of this paper is organized as follows. In Section 2, the OAM-based MIMO-SAR system model is established. In Section 3, a novel OAM-based MIMO-SAR scheme using RDE is proposed, together with the processing progress. In Section 4, proof-of-concept experiments are presented to verify the scheme. In Section 5, a discussion is given. Finally, in Section 6, a conclusion of this work is provided.
## 3 Results and Discussion
### Mechanical Properties  
Figure 5 shows the hardness and impact toughness plots of CS_QAT and CS_IQAT. CS_QAT has a hardness of 274 HV and an impact toughness of 100 J/cm\({}^{2}\). CS_IQAT has a hardness of 306 10 HV and an impact toughness of 192 J/cm\({}^{2}\). Compared to CS_QAT, the hardness of CS_IQAT improved by a factor of 32 HV and a 1.9 times higher impact toughness. An improved impact toughness of workpieces has multiple benefits: firstly, it significantly improves the safety and durability of workpieces when subjected to impacts or collisions, reducing the risk of accidents; secondly, high-impact toughness materials prolong the service life of workpieces because they can effectively absorb energy and withstand the effects of the external environment; and lastly, this property helps to improve the stability and efficiency of the machining process, reducing the incidence of cracks and deformations.  
Figure 4: XRD images of CS_QAT and CS_IQAT.  
Figure 3: SEM images of CS_QAT and CS_IQAT (**a**) CS_QAT; (**c**) CS_QAT; (**b**)CS_IQAT; (**d**) CS_IQAT.  
Figure 6 shows the stress-strain curves of CS_QAT and CS_IQAT. It can be observed that there is a difference between the stress-strain curves of the two specimens. The yield strength of CS_IQAT (657 MPa) is higher than that of CS_QTA (506 MPa). The elongation of CS_IQAT (9.8%) is also higher than that of CS_QTA (8.8%).  
The strength of CS_QAT and CS_IQAT is affected by the number and size of Fe\({}_{3}\) C particles, while plasticity is mainly provided by ferrite. According to [PERSON]'s theory [27], the strength is proportional to the number of hard particles and inversely proportional to the size of the particles. In CS_IQAT, the number of Fe\({}_{3}\) C particles is higher and the size is smaller. It helps to increase the strength of CS_IQAT.