esa-sceva/satcom-chunk-collection huggingface dataset:
# A VIKOR-Based Sequential Three-Way Classification Ranking Method
Creating a sequential three-way decisions model that combines three-waydecisions and granular computing is becoming more and more important in classification. [PERSON] et al. [21] proposed four three-way sequential classifiers in order to solve the issue of the coarse and fine granularity of objects potentially causing conflict and thus affecting the decision accuracy. S3 WD uses coarse-to-fine information granularity. [PERSON] et al. [22] addressed granularity construction and decision cost in the three-way sequential decision model, verified the model's correctness and algorithm's feasibility, and solved the double constraint problem. The sequential three-way decision method, enhanced by multi-level granularity, is proven effective for solving human problems. [PERSON] et al. [23] introduced a novel rational subspace classifier that outperforms advanced classifiers with fewer attributes. Combining granularity and multi-levels, this method efficiently handles uncertainty and dynamics in decision making. The aforementioned researchers proposed improvements and extensions to the VIKOR method and three-way decisions to tailor them to their research fields. However, these enhancements did not integrate VIKOR with three-way decisions; VIKOR improvements focused solely on prioritization without classification. Similarly, three-way decision enhancements neglected ranking alternatives. This paper combines sequential three-way decisions with an improved VIKOR method, incorporating decision-makers' subjective tendencies and considering both maximizing team utility and minimizing individual regret. It argues that relying solely on team utility or individual regret for classification and judgment can lead to significant errors. Instead, it constructs a sequential three-way decision model considering both values. VIKOR classifies schemes into three regions using three-way sequential decisions. Ranking rules and formulas based on intradomain and cross-domain comparisons are proposed, and their correctness and applicability are demonstrated through an example. Section 2 introduces the basics of three-way sequential decisions and multi-attribute decisions. Section 3 proposes the sequential three-way VIKOR method based on individual regret or group utility values, studying ordering rules within and across different areas. Section 4 introduces the sequential three-way VIKOR method considering both individual regret and team utility values, verifying its feasibility. Section 5 assesses the method's reliability and usefulness using a real-world engineering investment case study. Section 6 concludes the paper.
## 3 Inverse Kinematics
### Closed-Form Solution for Multiple-GSJ Section
#### 3.3.3. GSJ Angles for Multiple-GSJ Section  
Based on a list of locations provided by the distance-based algorithm in Section 3.3.1, the corresponding list of \(\mathbf{a}_{i}^{i-1}\) (\(i=1,\cdots,n\)) can be obtained through the following derivation:  
From Equation (4), the component \(\mathbf{a}_{i}\) of rotation matrix is given by  
\[\mathbf{a}_{i}=\frac{\mathbf{p}_{i}-\mathbf{p}_{i-1}}{l_{i}}. \tag{17}\]  
For given \(\beta_{1},\gamma_{1},\cdots,\beta_{i-1},\gamma_{i-1}\), the component \(\mathbf{a}_{i}\) of rotation matrix \(\mathbf{R}_{i}\) can also be expressed by  
\[\mathbf{a}_{i}=\mathbf{R}_{i-1}(\beta_{1},\gamma_{1},\cdots,\beta_{i-1},\gamma_{i-1}) \cdot\mathbf{a}_{i}^{i-1}. \tag{18}\]  
Combining Equations (17) and (18) gives  
\[\mathbf{a}_{i}^{i-1}=(\mathbf{R}_{i-1}(\beta_{1},\gamma_{1},\cdots,\beta_{i-1},\gamma_ {i-1}))^{-1}.\frac{\mathbf{p}_{i}-\mathbf{p}_{i-1}}{l_{i}}. \tag{19}\]  
Applying the inverse kinematics of single-GSJ section expressed in Equation (6) gives the closed-form solution for GSJ angles. Set the value of \(i\) equal to \(1,\ldots,n\) successively, and the solution of \((\beta_{1},\gamma_{1},\cdots,\beta_{n},\gamma_{n})\) can be computed by Equations (6) and (19). The combination of Equations (6) and (19) provides the closed-form solution for the studied \(2n\)-DOF serial manipulator with \(n\) identical UJs.  
Next, the closed-form property of the proposed inverse kinematics solution is analyzed. The closed-form is determined by two parts, i.e., the determination of the two distances and the resolution of GSJ angles for multiple-GSJ section. Using a finite number of standard operations [24], Equation (14) gives the closed-form solution of the two distances after judging whether they satisfy the constraints in Equations (10) and (16). This ensures the first part's closed-form property. The closed-form of the inverse kinematics solution formed by Equations (6), (9), and (19) is obvious. Hence, closed-form property of the proposed inverse kinematics solution for the \(2n\)-DOF hyper-redundant manipulator is ensured.
## 2 Two-Row ESPAR Antenna  
### Antenna Design  
The proposed antenna concept has been discussed in [31] and is presented in Figure 1. It was aimed to achieve a low-cost reconfigurable antenna that is able to provide maximal angular radiation coverage by steering the beam in elevation and azimuth. The active quarter-wave monopole is located in the center of the metallic ground plane realized on the top of a dielectric substrate and surrounded by 12 passive radiators symmetrically arranged in two circular rows. The active radiator is fed coaxially with RF signal, while the passive radiators can be open or shorted to the ground plane by changing the state of the SPDT switches. Forming the radiation pattern is realized by setting proper configuration of the passive elements that become reflectors when shorted to the ground or directors when opened. Such an approach simplifies the beam steering control that can be realized with external microcontroller or transceiver having its general purpose input/output (GPIO) lines connected to the RF switches. As a result, each radiation pattern corresponds to a steering vector \(V=[v_{1},\,v_{2},\dots,v_{s},\dots,v_{12}]\), in which \(v_{s}\) denotes the state of \(s\)th passive element: \(v_{s}=1\) for open and \(v_{s}=0\) for the shorted one. The antenna was optimized to provide three sets of directional radiation patterns with different inclination angles \(\theta_{max\_up}=46^{\circ}\), \(\theta_{max\_down}=56^{\circ}\), and \(\theta_{max\_mid}=52^{\circ}\) obtained for three different steering vectors sets. The symmetrical design allows rotating each beam by \(360^{\circ}\), which means that it is possible to steer the radiation pattern in both, azimuth and elevation. Therefore, for each elevation direction, 6 directional radiation patterns having maximum in azimuth at \(30^{\circ}\), \(90^{\circ}\), \(150^{\circ}\), \(210^{\circ}\), \(270^{\circ}\), \(330^{\circ}\) are available for steering vectors \(V_{UP}^{\varphi_{max}}\), \(V_{DOWN}^{\varphi_{max}}\), and \(V_{MID}^{\varphi_{max}}\), where \(\varphi_{max}=\{30,\,90,\,150,\,210,\,270,\,330\}\) degrees. The antenna was designed and optimized in Altair FEKO simulation tool to operate at center frequency 2.44 GHz and the detailed design procedure including optimization goals was described in [31].
## 3 Results and Discussions
### Tissue Thickness  
The thicknesses of tissues, which may affect the ultrasound thermal therapy, are different from person to person. As a result, the effects of the hydrogel phantom thickness on the temperature variation were investigated. The three-layer composite systems were simulated for ultrasound diathermy with 30 s at a power of 15 W and 12 W using 1 MHz and 3 MHz, respectively. Figures 8 and 9 show the simulated results of the temperature profiles in the composite specimens with a stainless steel implant and different thicknesses hydrogel phantom under 1 MHz and 3 MHz ultrasound operation frequencies.  
For the cases of 1 MHz, the peak temperature location predicted by the analytical solution occurs at the middle region of the hydrogel phantom in the composite system. It is worth noting that the peak temperature does not change depending on different hydrogel thickness. However, the region with the peak temperature in the hydrogel has greater expansion with increasing thickness of the hydrogel in  
Figure 8: Temperature distribution within the three-layer composite bio-system for different hydrogel thickness at 30 s using 1 MHz ultrasound.  
Figure 7: Temperature profiles in the composite bio-system from the proposed analytical solution in the first five seconds using 3 MHz ultrasound.  
Figure 9: Temperature distribution within the three-layer composite bio-system for different hydrogel thickness at 30 s using 3 MHz ultrasound.  
the composite system. Approaching the interface between the hydrogel and the stainless implant, the temperature decreases and continues to decrease in the bone of the composite system as shown in Figure 8.  
Alternatively, the peak temperature location predicted by the analytical solution is always in the bone for the case of 3 MHz as shown in Figure 9. Similarly, the peak temperature in each layer does not change with different hydrogel thicknesses. However, the region of the peak local temperature in the hydrogel expands more with increasing thickness of the hydrogel. Close to the interface between the hydrogel and the stainless implant, the temperature decreases, but the temperature keeps increasing in the bone of the composite system.  
These results can be explained by the pressure distribution curves, as shown in Figure 5, where the pressure oscillation does not change in the composite system media. In addition, the amplitude of the heat source in each medium, according to Equations (A1) and (A2), is related to the thickness of the implant, and not to the thickness of the hydrogel. As a result, the highest temperature in the media remains the same with different hydrogel thicknesses.
## 3 Results
### Data Synthesis
#### 3.6.2 Photobiomodulation Therapy for Managing QoL in Fibromyalgia Patients  
Localized PBMT has shown moderate improvements by targeting tender points and modulating central sensitization mechanisms in Fibromyalgiagia. However, its effects on broader functional outcomes remain inconsistent. In a randomized, single-blinded trial, [PERSON] et al. (2019) [47] assessed the impact of ten PBMT sessions on QoL in Fibromyalgiagia patients. While the intervention led to a significant reduction in pain intensity (a reduced VAS from 6.9 to 3.5, \(p\) < 0.001), no significant differences in QoL measures were observed when compared to local anesthetic injections.  
Similarly, a double-blinded RCT by [PERSON] et al. (2013) [50] investigated Class IV laser therapy (LiteCure(r) LCT-1000, 810 nm and 980 nm, 10 W, 7 min per session, two times for 4 weeks) applied to seven tender points. The study reported a moderate reduction in Fibromyalgiagia Impact Questionnaire (FIQ) scores from 62 to 55 (\(p\) < 0.05); however, the improvement in QoL was less pronounced than that observed in whole-body PBMT interventions.  
In contrast, whole-body PBMT has demonstrated more substantial and sustained improvements in QoL for Fibromyalgiagia patients. [PERSON] et al. (2023) [36] conducted a single-arm feasibility study evaluating whole-body PBMT over 18 sessions across 6 weeks using the NovoTHOR(r) full-body PBMT system (660-850 nm, 967 W total power output, 25.2 J/cm\({}^{2}\) fluence, 20 min per session). The study reported a significant improvement in FIQR scores from 63.2 to 45.6 (\(p\) < 0.001), with benefits sustained at 24 weeks, suggesting long-term efficacy in regard to both functional and psychological well-being.  
Similarly, in a triple-blinded, randomized controlled trial, [PERSON] et al. (2023) [38] administered whole-body PBMT (12 sessions, three times per week, 20 min per session) using the NovoTHOR(r) system, delivering near-infrared and red-light therapy (660-850 nm, power density \(\sim\)40 mW/cm\({}^{2}\)). This intervention resulted in a significant improvement in SF-36 QoL scores from 38.1 to 55.4 (\(p\) < 0.001), with effects persisting at a 2-week follow-up, reinforcing the sustained impact of PBMT on Fibromyalgiagia-related disability. Further supporting these findings, [PERSON] et al. (2022) [41] demonstrated that whole-body PBMT improved FIQR scores from 62.5 to 47.3 (\(p\) < 0.001), confirming its effectiveness in enhancing physical, emotional, and functional aspects of a patient's daily life.  
Additionally, the combination of PBMT with exercise has shown synergistic effects in improving a patient's QoL. In a double-blinded RCT, [PERSON] et al. (2024) [35] applied PBMT to 18 muscle groups (810 nm, 100 mW, 4 J per point, three times per week for 12 weeks) in conjunction with an aerobic exercise program. The study reported a significant increase in SF-36 scores from 38.4 to 55.7 (\(p\) < 0.05), suggesting that PBMT enhances the benefits of physical activity in Fibromyalgiagia patients. Further details are available in Figure 3.
## Materials and Methods
### Statistical Data Analysis  
All four system were well calibrated following the radiometric calibration protocol using the reference light sources of HL-3 (Ocean Optics Inc., Dunedin, FL, USA) to calibrate the hemispherical sensor and an integrated sphere to calibrate the conical sensor in the lab, ensuring that synchronously measured incident irradiance and reflected radiance have no systematical difference obtained from these four systems. After preprocesses, such as dark current correction, quality checking, and the calculation of irradiance and radiance from digital numbers, data were then used to calculate reflectance and to retrieve SIF. In total, data observing grey reference and bare soil background, four days measuring _E. aureus_ with four systems and another four days measuring lawn plot with two systems were collected and analyzed in this study.  
IT and reflectance were chosen to be the indicators for the comparison of the four systems and different configurations (i.e. hemi-con and bi-hemi configurations). In the test for FOV of CC-3, the \"true\" footprint of hemispherical sensor (CC-3) was tested by moving a potted _E. aureus_ away from the center of the sensor FOV. Diurnal patterns of instantaneously acquired SIF from different systems and configurations were also compared to evaluate the consistency of SIF obtained from a variety of devices when observing the same target, something which has not yet been reported. Statistical analyses were performed using MATLAB and Microsoft Excel software.  
Figure 5: Diagram of measuring the field of view (FOV) of cosine corrector (CC-3).
# Line-of-Sight Initial Pointing Model of Space Dynamic Optical Network and Its Verification
## 3 Multi-Link LOS Pointing Model
### The Principle of LOS Pointing
#### 3.1.3 Pointing Angle Calculation  
After the above coordinate conversion, the coordinates \((x_{i},y_{i},z_{i})\) of the \(i\)-th opponent (coordinates in the WGS-84 coordinate system) in one's own sight-axis coordinate system can be obtained. The calculation formula is as follows:  
\[\begin{pmatrix}x_{i}\\ y_{i}\\ z_{i}\end{pmatrix}=C_{bi}^{a}C_{n}^{b}C_{e}^{a}\begin{pmatrix}X_{o}-X_{i}\\ Y_{o}-Y_{i}\\ Z_{o}-Z_{i}\end{pmatrix} \tag{5}\]  
Figure 2: Coordinate conversion and transfer process.  
In the formula, \(X_{o},Y_{o},Z_{o}\) and \(X_{i},Y_{i},Z_{i}\) are the master-slave terminal geodetic rectangular coordinate values obtained by substituting the longitude, latitude, and elevation values into Equation (1).  
The initial pointing angle of the visual axis is defined in the visual-axis coordinate system and can be calculated by the following formula:  
\[\left\{\begin{array}{l}\alpha_{i}=\arctan(x_{i}/y_{i})\\ \beta_{i}=\arctan(z_{i}/\sqrt{x_{i}^{2}+y_{i}^{2}})\end{array}\right. \tag{6}\]  
In the formula, respectively, the \(i\)-th visual axis needs to rotate around the azimuth angle and elevation angle. The formula shows the coordinates of the opponent's coordinate point (coordinates under WGS-84) in relation one's own \(i\)-th visual-axis coordinate system.
## 3 Validation of the Restrictions
### Multisampled Average Current Control (MACC)  
The multisampled average current control for the bidirectional buck-boost converter was presented in [33]. The MACC stage generates the control variable (\(u\)) that is processed by a dual digital PWM to obtain the discrete control signals (\(u_{1}\) and \(u_{2}\)) that activate the converter half-bridges. The external loop regulates the output voltage by providing the MACC with the output current reference through a discrete proportional-integral control transfer function \(G_{ppi}(z)\), as it is seen in Figure 3. An important element of the MACC loop is the ripple filter processing the error between output current \(i_{L}[n]\) and its desired reference \(i_{Lref}[n-1]\). The ripple filter averages two consecutive samples per switching period (\(f_{samp}=2f_{s}\)) of the output current error. This strategy eliminates the switching ripple in the current loop without significant phase loss [34].  
The discrete-time ripple filter transfer function can be expressed as  
\[\hat{u}[n]=\frac{K_{pi}}{2}\left(3e_{i}[n]+2e_{i}[n-1]-e_{i}[n-2]\right). \tag{15}\]  
The proportional gain can be written in terms of the output current waveform slopes as  
Figure 3: Block diagram of the digital controller for the voltage regulation of the buck-boost converter. Bottom Left: Conventional voltage error subcircuit. Bottom Right: Proposed improved approach subcircuit.  
Figure 2: Power stage of a coupled-inductor buck-boost converter.  
\[K_{pi}=\frac{K_{n}}{(m_{1}+m_{2})T} \tag{16}\]  
where the output current has a periodic triangular waveform with rising and falling current slopes \(m_{1}\) and \(-m_{2}\), respectively. The expression \(m_{1}+m_{2}\) is obtained for each converter operation mode, yielding  
\[m_{1}+m_{2}=\left\{\begin{array}{ll}\frac{Mv_{o}[n]}{L^{2}-M^{2}}&\text{for boost mode}\\ \frac{LV_{g}}{L^{2}-M^{2}}&\text{for buck mode.}\end{array}\right. \tag{17}\]  
Parameter \(K_{n}\) has been adjusted to 0.35 to obtain a crossover frequency (CF) of approximately 11 kHz and a phase margin (PM) of 58\({}^{\circ}\) as in [33].  
The digital PI compensator in the z-domain added to the current control loop has been implemented using forward-Euler method as follows,  
\[G_{ipi}(z)=1+\frac{K_{i}}{2}\frac{1}{z-1} \tag{18}\]  
Figure 3 shows the implementation of the discrete-time PI compensator, whose integral gain can be chosen as in [33].
# Study of Subsidence and Earthquake Swarms in the Western Pakistan
## 2 Datasets and Methods
### One-Dimensional Differential Compaction Theory  
According to well-accepted theories [34], subsidence can be approximated by the following linear, simplified one-dimensional consolidation:  
\[\delta=\alpha\ \times\ \omega\ \times\ s\ \times\ \Delta h, \tag{1}\]  
Figure 5: **(Top)** Seismic profile 4 and 5 show the top of Shrinab Limestone (red horizons) and two thrust faults, shown on profile 4, dipping westward. **(Bottom)** Seismic profile 1, 2 and 3 show the top of Shrinab Limestone (red horizons) and many blind thrust faults. Only one thrust fault mapped on profile 3 serves as a boundary between the Shrinab and Chiltan Formations.  
where \(\delta\) (m) is subsidence, \(\alpha\) (kg\({}^{-1}\cdot\)m\({}^{-1}\)) is the compressibility of the soil, \(\omega\) (kg) is the weight of water, \(s\) (m) is the sediment layer thickness, and \(\Delta h\) (m) is the piezometric surface change.  
First approximation, piezometric surface change is a linear function of sediment thickness:  
\[\Delta h=c_{1}\ \times\ s \tag{2}\]  
where \(c_{1}\) is a constant.  
Second approximation, the sediment layer thickness is a linear function of the distance from the basin margin:  
\[s=c_{2}\ \times\ x \tag{3}\]  
where \(c_{2}\) is a constant, and \(x\) is the distance from the basin margin.  
Since the compressibility of the soil is constant, the weight of water is constant, and combines Equations (1)-(3):  
\[\delta=c_{3}\ \times\ x^{2} \tag{4}\]  
where \(c_{3}\) is a constant.  
Based on the above two approximations, it indicates when the gradient of sediment thickness is constant, yielding the ratio:  
\[\frac{d\delta}{dx}=c_{4}\ \times\ x \tag{5}\]  
where \(c_{4}\) is a constant.  
Above is the first scenario, in which the gradient of sediment thickness is constant. The second scenario occurs when the gradient of sediment thickness is considered a second order polynomial:  
\[s=c_{5}\ \times\ x^{2} \tag{6}\]  
where \(c_{5}\) is a constant.  
By combining Equations (1), (2) and (6), we get,  
\[\delta=c_{6}\ \times\ x^{4} \tag{7}\]  
where \(c_{6}\) is a constant.  
Similarly, we get the ratio:  
\[\frac{d\delta}{dx}=c_{7}\ \times\ x^{3} \tag{8}\]  
where \(c_{7}\) is a constant.
## 4 Numerical Analysis of the Slope Stability of Coarse-Grained Soil Based on COMSOL Multiphysics  
In this study, numerical calculations are performed using COMSOL Multiphysics (V6.3), a multiphysics coupling analysis software developed by COMSOL, Sweden, based on the finite element method. This software solves the partial differential equations corresponding to multiple physical fields to achieve coupling calculations between them. It can accurately perform heat transfer and slope stability calculations on the slope soil.  
There are numerous formulas involved in this paper, and only the main equations are listed here. The governing equations for heat transfer calculations are shown in Equations (1) and (2) [33].  
\[\mathrm{d}_{x}\rho\mathrm{C}_{\mathrm{p}}\frac{\partial T}{\partial t}+\mathrm{ d}_{x}\rho\mathrm{C}_{\mathrm{p}}\mathrm{u}\cdot\
abla T+\
abla\cdot q=d_{z}Q+q^{0}+d_{ z}Q_{tot} \tag{1}\]  
\[q=-d_{z}k\
abla T \tag{2}\]  
In these equations, dz represents the thickness of the physical model, set to 1m in this study; \(\rho\) is the density, in kg/m\({}^{3}\); \(\mathrm{C}_{\mathrm{p}}\) is the specific heat at constant pressure, in J/(kg\(\cdot\)K); \(T\) is the temperature, in K; t is time, in hours; u is the velocity vector, in m/s; q is the conductive heat flux vector, in W/m\({}^{2}\); Q is the heat absorbed by the system, in J; q is the heat source term coefficient, in W/m\({}^{2}\); Qted is the thermal elastic damping, in J; and k is the thermal conductivity, in W/(m\(\cdot\)K) [33].  
\[\rho\mathrm{a}_{\mathrm{f}}=\
abla\cdot\mathrm{S}+\mathrm{F}_{\mathrm{v}} \tag{3}\]  
In this equation, \(\rho\) is the density, in kg/m\({}^{3}\); \(\mathrm{a}_{\mathrm{f}}\) is the multiphysics acceleration, in m/s\({}^{2}\); S is the second Piola-Kirchhoff stress tensor, in \(Pa\); and \(Fv\) is the body force density, in N/m\({}^{3}\).  
Using COMSOL Multiphysics software for modeling, the slope model adopts a two-dimensional model of a coarse-grained soil slope with a slope height of 35 m. The physical properties of the coarse-grained soil layer are shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameter** & **Density** & **Thermal** & **Specific Heat** & **Porosity** & **Young’s** & **Poisson’s** & **Cohesion** & **Internal Friction** \\
**(kg/m\({}^{3}\))** & **Conductivity** & **(W/(m\(\cdot\)K))** & **(J/(kg\(\cdot\)K))** & **(\%)** & **Modulus** & **Ratio** & **(kPa)** & **Angle (rad)** \\ \hline Initial Slope & 2150 & 3 & 1500 & 30 & 120 & 0.2 & 33.92 & 0.442 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Physical parameters for numerical calculations (based on available regional engineering reports).  
Considering the computational accuracy and time step, the model is automatically meshed into highly refined free triangular elements by COMSOL. The total number of mesh elements in the entire model is 8386, with different element masses. The minimum element mass is 0.6595, and the average element mass is 0.9538. The meshed coarse-grained soil slope model established is shown in Figure 14.