esa-sceva/satcom-chunk-collection huggingface dataset:
# Nonlinear and Linear Equation of Gas Diffusion in Coal--Theory and Applications
## 4 Numerical Solution of the Nonlinear Diffusion Equation  
In order to solve the nonlinear diffusion equation, the numerical finite difference method was applied. By deriving the Laplace operator to spherical coordinates--while taking into account the angular symmetry--and by making the substitution \(\eta=\xi^{2}\), we shall receive the following formula:  
\[\frac{\partial\eta}{\partial t}=2\sqrt{\eta}\cdot D\cdot\left(\frac{\partial^ {2}\eta}{\partial r^{2}}+\frac{2}{r}\frac{\partial\eta}{\partial r}\right) \tag{19}\]  
Below, the boundary-initial values under which Equation (19) will be solved are specified:  
\[\left\{\begin{array}{ccc}\eta(r,0)=1&\rightarrow&0\leq r\leq r_{0}\\ \eta(r_{0},t)=0&\rightarrow&t\geq 0\\ \frac{\partial\eta}{\partial r}=0&\rightarrow&t\geq 0,r=0.\end{array}\right. \tag{20}\]  
The differential scheme for Equation (19) shall look as follows:  
\[\eta_{i,j+1}=\left(1-2\cdot\chi\sqrt{\eta_{i,j}}-\frac{2\chi}{i}\sqrt{\eta_{ i,j}}\right)\cdot\eta_{i,j}+\left(\chi\sqrt{\eta_{i,j}}+\frac{2\cdot\chi}{i} \sqrt{\eta_{i,j}}\right)\cdot\eta_{i+1,j}+\chi\sqrt{\eta_{i,j}}\cdot\eta_{i-1,j} \tag{21}\]  
where:  
\(\chi=\frac{D\cdot k}{h\eta}\) is the parameter related to the stability of the solution;  
\(h_{r}=\frac{r_{0}}{n}\) is the step of the spatial grid (m);  
\(k_{t}=\frac{\chi\cdot h^{2}}{D}\) is the step of the temporal grid (s).  
The stability of the solution to Equation (21) depends on parameter \(\chi\). For the parabolic equation, a stable (oscillation-free) solution for condition \(\chi<0.5\) is obtained. In the case of the nonlinear equation, there is no definite value of parameter \(\chi\), which would guarantee the stability of the solution.  
The calculation scheme involves using the known density of gas in a particular time step in a whole coal grain in order to calculate the density in the next step. For the sake of the calculations, it was assumed that \(\chi=0.4\). For such parameter \(\chi\), the solution of the diffusion equation is monotonic and compatible with the course of the curves in the experiment.  
The grain radius was divided into 24 parts (\(n=24\)). The initial value of the relative density distribution is equal to 1. In each temporal step, the distribution of density inside a grain was calculated and then averaged:  
\[\overline{\gamma}=\frac{3}{h_{r}^{3}\cdot r_{0}^{3}}\sum_{i=1}^{n}\sqrt{\gamma_ {i}}\cdot i^{2} \tag{22}\]  
The diagram of the spherical grain division adopted for the calculation of changes in gas density within its individual parts during gas emission is shown in Figure 2.
## 4 Simulation Experiment and Analysis
### Performance Evaluation of Multipath Routing Algorithms
#### 4.1.2 Packet Loss Rate  
The simulation results in Figure 9 show that before the sending rate is less than 40 packets/s, both packet loss rates are extremely low because the amount of data does not reach the bandwidth capacity. With the increase in the service sending rate, the loss rate of both algorithms increases, but the loss rate of multipath algorithm is significantly lower than single-path algorithm, because the increase of data volume puts pressure on bandwidth capacity, and single-path transmission is difficult to guarantee the delivery of data and is prone to large-scale loss of packets.
# On the Local and String Stability Analysis of Traffic Collision Risk
## 3 Introduction of Traffic Collision Risk Stability  
Conventional traffic stability analysis focuses on the stability of vehicle motion, e.g., speed, acceleration, and position. In this section, we extend the analysis of traffic stability to safety and introduce collision risk local and string stability.  
In traffic safety research, to assess the rear-end collision risk of vehicles on the road, safety surrogate measures (SSMs) are widely adopted [33]. SSMs are usually derived from the currently available measures, such as the position, velocity, and acceleration of the subject vehicle and the preceding vehicle [34]. There are various SSMs, such as the gap time (GP), which characterize the time to collision by assuming the leading vehicle suddenly stops while its follower keeps traveling at the current speed [35], and the crash index (CI), which goes further to cover the momentum information of the vehicles to characterize the severity of the accident [36].  
In this study, we define the collision risk, \(r_{n}(t)\), referenced from a general SSM, as follows:  
\[r_{n}(t)=f_{SSM}(\Delta x_{n}(t),\dot{x}_{n}(t),\dot{x}_{n-1}(t),\ddot{x}_{n}(t ),\ddot{x}_{n-1}(t)) \tag{9}\]  
It is worth noting that we would further characterize a positive relationship between \(r_{n}(t)\) and the collision risk; i.e., a higher value of \(r_{n}(t)\) signifies higher collision risk. The variable \(r_{n}(t)\) can be based on any SSM. If a chosen SSM is inversely correlated with collision risk (e.g., GP), the reciprocal can be applied to ensure that the measure aligns with the notion that a higher value correlates with a greater collision risk.  
Stability analysis regards the equilibrium state as the baseline and investigates the variation between the current state and the equilibrium state. The variation between the current risk state and the equilibrium risk is defined as the risk disturbance, denoted by \(\Delta r_{n}(t)\), which is expressed as  
\[\Delta r_{n}(t)=r_{n}(t)-r_{n}^{eq}(t) \tag{10}\]where \(r_{n}^{eq}(t)\) represents the collision risk at an equilibrium state, where \(x_{n}-x_{n+1}=d^{eq}\), \(\dot{x}_{n}=\dot{x}_{n+1}=v^{eq}\) and \(\dot{x}_{n}=\dot{x}_{n+1}=0\), with \(v^{eq}\) and \(d^{eq}\) denoting the velocity and relative space between two neighbor vehicles in the equilibrium state. In other words, \(r_{n}^{eq}(t)=f_{SSM}(d^{eq},v^{eq},v^{eq},0,0)\).
# A Predefined-Time Control for the Laser Acquisition in Space Gravitational Wave Detection Mission
## 5 Numerical Simulations
### Initial Conditions
The comparison between the proposed predefined-time controller which is denoted as PTC and the traditional proportional-integral-derivative controller which is denoted as PID is shown in Figure 23.  
Figure 10:0 Ponting Angle of T1 on SC. Figure 10:1 Comparison for the Pointing Angle Error of T1 on SA. Figure 10:2 Ponting Angle Error of T1 on SC. It can be observed that the PTC controller could guarantee the settling time within 5 s while PID controller could not at some points. This simulation indicates that the PTC controller has an advantage in prescribed-time convergence for the acquisition phase over the PID controller. Another obvious advantage is that the predefine time of PTC controller can be changed as a parameter according to the requirements of the actual scheme.
## 4 Mechanical Design and Thermal Modelling of 6U CubeSat
### Environmental Load Studies and Orbit Parameters
RAAN and \(i\) are dependent on the satellite's orbit but \(\Gamma\) is a function of earth's position in orbit around the sun [42]. Two factors that affect the beta angle are the change of seasons and perturbation of the orbit due to earth oblateness. As the beta angle varies, there are two consequences of interest to be considered [41]. * Planet shadow varies: Fraction of sunlight reaching the satellite reduces. This is illustrated in Figure 12.
* The incident solar intensity varies. Variation of solar intensity ranges from 0 to 90 degrees and it is clearly seen from the variations plotted using System Tools Kit (STK) tool. The relationship between the sun season and beta angles is also shown in Figure 13.  
Satellite in low earth circular orbits spends approximately 37% in eclipse and 63% in sunlight for low inclination orbits. Satellite at 408 km altitude, eclipse duration gradually reduces until when the beta angle approximately equals to 70 degrees as shown in Figure 12 [41]. Figure 12: Fraction of time spent in sunlit and eclipse.
# Optical Flow-Based Fast Motion Parameters Estimation for Affine Motion Compensation
## 2 Related Works
### Motion Parameter Prediction and Entropy Coding  
To achieve optimal efficiency when using affine motion prediction, it is important to signal the affine motion parameters with as few bits as possible. Every method uses the same coding as HEVC for the translational parameters, making full use of the motion vector prediction coding.  
Reference [9] improves the translational motion vector coding by estimating the change in the translation parameter between blocks. Block-to-block translational shift compensation (BBTSC) corrects the translational shift, allowing merge mode to be used much more often as there is no need to signal the motion vector difference. This results in an improvement of 6% in the tested sequences.  
Coding the affine motion parameters is difficult, as it is more difficult to predict them from neighboring blocks. The first limitation is not all blocks are going to use affine prediction, so it may be often necessary to code them without a prediction, but even in the case where a neighbor uses affine prediction, it may use a different reference picture, and scaling the motion parameters is challenging, as simply multiplying every value by the distance ratio does not work. Reference [11] tackles this problem by allowing motion scaling to work on affine parameters. They propose decomposing the transform into separate transforms, for example a rotation and a zoom operation, and scale each matrix appropriately, then combine them again to get the new parameters.  
For the quantization, the most common, used in References [3,8,9], is a quantization step of \(1/512\). Reference [10] evaluates different quantization step sizes, from \(1/16\) to \(1/512\). They find that using such a fine quantization step gives no coding efficiency benefit, and that \(1/256\) is enough to get the best efficiency. As their method is a semi-exhaustive search, reducing the number of possible values is also good for encoding speed. They also choose to limit the maximum quantized parameter to 16, as higher values are too rare and seldom used.
## 5 Conclusions
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Deletion Strategy** & **Algorithm** & **Model Accuracy** & **Unlearning Efficiency** & **Residual Influence** & **Communication Overhead** & **Convergence Time** & **Unlearning Accuracy** & **Computational Cost** \\ \hline \multirow{3}{*}{Random Deletion} & FedEraser & 0.85 & 0.9 & 0.05 & 0.6 & 0.8 & 0.88 & 0.7 \\  & EG-FedUnlearn & 0.89 & 0.91 & 0.04 & 0.55 & 0.78 & 0.9 & 0.68 \\  & OFU-Conology & **0.92** & **0.92** & **0.03** & **0.52** & **0.75** & **0.93** & **0.65** \\  & VeFi & 0.81 & 0.85 & 0.06 & 0.65 & 0.82 & 0.87 & 0.72 \\ \hline \multirow{3}{*}{Class-based Deletion} & FedEraser & 0.87 & 0.91 & 0.04 & 0.58 & 0.79 & 0.92 & 0.68 \\  & EG-FedUnlearn & 0.91 & 0.93 & 0.03 & 0.53 & 0.76 & 0.94 & 0.65 \\  & OFU-Conology & **0.93** & **0.94** & **0.02** & **0.50** & **0.74** & **0.96** & **0.6** \\  & VeFi & 0.83 & 0.87 & 0.05 & 0.62 & 0.80 & 0.9 & 0.7 \\ \hline \multirow{3}{*}{Feature-based Deletion} & FedEraser & 0.86 & 0.90 & 0.05 & 0.57 & 0.77 & 0.90 & 0.70 \\  & EG-FedUnlearn & 0.90 & 0.92 & 0.04 & 0.54 & 0.75 & 0.92 & 0.66 \\ \cline{1-1}  & OFU-Onology & **0.93** & **0.93** & **0.03** & **0.49** & **0.72** & **0.95** & **0.62** \\ \cline{1-1}  & VeFi & 0.82 & 0.86 & 0.06 & 0.64 & 0.79 & 0.88 & 0.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparison of federated unlearning algorithms using three deletion strategies for the UCI Adult dataset.
## 3 Results
### Doping of HA Nanoparticles
#### 3.3.3 Magnesium-Doped Nano-Hydroxapatite (Mg-Nano-HA)  
Magnesium (Mg) is a vital element in the human body, with 60-65% stored in bones and teeth and the remaining distributed across other tissues [46]. Magnesium ions (Mg\({}^{2+}\)) are critical for early cartilage and bone development, though their concentration decreases as bones mature [12]. Mg plays a central role in bone regeneration by promoting the proliferation of osteoblasts and fibroblasts, which support osteogenesis. Magnesium deficiency can significantly impact bone health, leading to reduced stiffness, lower osteoblast activity, and increased oxidative stress, ultimately resulting in bone fragility and loss.  
In synthetic hydroxyapatite, magnesium influences crystal size, strength, and structural integrity [11]. Incorporating magnesium into hydroxyapatite (Mg-HA) combines the beneficial properties of both materials, making Mg-based composites highly relevant in orthopedic applications due to their biocompatibility and biodegradability [47]. When applied as a coating on titanium implants, Mg-HA demonstrates superior mineralization and greater osseointegration compared to pure or natural HA [12]. These properties enhance the performance of implants, facilitating stronger integration with surrounding bone tissue.  
Magnesium doping also modifies the surface characteristics of HA, increasing surface roughness, which contributes to antibacterial properties. Porous Mg-containing implants create an environment where new bone can grow within the pores, forming a stable bond between the implant and adjacent tissue [50]. However, the relationship between porosity and mechanical strength must be carefully managed. Excessive porosity can weaken the scaffold's structure, but controlled doping of Mg\({}^{2+}\) ions ensures an optimal balance between structural integrity and biological performance [45].  
These multifunctional benefits of Mg-nano-HA, including enhanced osteogenesis, improved antibacterial activity, and superior implant integration, underscore its potential for advanced applications in bone tissue engineering and orthopedic implants [50].
# Optimization of the Position and Stiffness of Passive Walking Assistance Devices
## 2 Methods
### Optimal Location and Stiffness of Passive Walking Assistance System  
The design parameters of the passive walking assistance system were the stiffness, free length, and location of the spring. The tension spring that was used in the device generated forces depending on the stiffness when the length of the spring exceeded the free length of the spring. The placement of the walking assistance system was determined by using the position of both ends of the spring, (\(x_{1}\), \(y_{1}\)) and (\(x_{2}\), \(y_{2}\)). The positions (\(x_{1}\), \(y_{1}\)) and (\(x_{2}\), \(y_{2}\)) were defined on the \(u\)-\(v\) coordinate system, which was aligned to the distal-proximal direction of the human body. The definition of the position of the spring on the human body is shown in Figure 3. The \(u\)-axis describes the location on the distal-proximal direction. The value of \(u\) was between 0 and 1. A value of \(u\) between 0 and 0.2 described the location on the foot from toe to heel. Similarly, the ranges of 0.2-0.4, 0.4-0.6, 0.6-0.8, and 0.8-1 determined the positions on the shank, thigh, pelvis, and trunk, respectively. The \(v\)-axis was perpendicular to the \(u\)-axis, and the range of the \(v\)-axis was defined as \(\pm\) 5 cm.  
Figure 2: Ankle, knee, hip, and pelvis-trunk joint angles at walking speeds of 0.9, 1.1, 1.3. and 1.5 m/s.  
In the present study, the reduction in energy cost was the main aim of the walking assistance system. The power of the ith joint, \(P_{i(t)}\), was calculated by the multiplication of the moment, \(\tau_{i(t)}\), and angular velocity of the ith joint. The positive energy of the ith joint was obtained by the integral of the positive power with respect to time, \(t\), and it was divided into the duration of the gait cycle, \(T\). The objective function is the summation of the positive energy of all joints as given in Equation (2), where \(n_{joints}\) is the total number of joints.  
\[f=\sum_{i=1}^{n_{joints}}\left(\frac{\int_{0}^{T}\max\left(0,P_{i(t)}\right) \text{dt}}{T}\right) \tag{2}\]  
The generated assistive moments around the joints depend on the moment arm and the generated force on the spring. A proportional increase in force and a decrease in moment arm, or vice versa, result in equivalent results in terms of the assistive moment. Therefore, the optimization of the position and stiffness was conducted in two steps. First, the optimal positions of the walking assistance system were found. Then, the optimal stiffness depending on the walking speed was investigated.
# Robust Damage Estimation of Typhoon Goni on Coconut Crops with Sentinel-2 Imagery
## 5 Results
### Baseline Comparisons
However, it does return also non-coconut changes on certain urban structures, as in Figure 10 (bottom). Overall this more recent method delivers more consistent results than the other baselines. Across all compared methods we observe a high level of agreement on unchanged areas (Figure 10, middle), even though unsupervised methods can of course fail to recognise whether an unchanged area shows coconut plantings. Overall, it was to be expected that the main problem of unsupervised change detection for damage assessment are false alarms due to land-cover changes not associated with coconut trees. But we also observe a significant volume of false negatives (missed changes). Figure 10: Comparison of our method with unsupervised change detection methods DSFA [61], \(k\)-means [60] and S2-CGAN [62] in northern Albay (**top**) and Quezon (**bottom**).
# Validation of Drifting Buoy Data for Ocean Wave Observation
## 2 Data and Methods  
### Drifting Buoy Data and Analysis  
Data from the JMA drifting buoys by December 2018 were used for comparison herein. The JMA buoy data can be downloaded from [[http://www.data.jma.go.jp/gmd/kaiyou/db/vessel_obs/data-report/html/buoy/buoy_e.php](http://www.data.jma.go.jp/gmd/kaiyou/db/vessel_obs/data-report/html/buoy/buoy_e.php)]([http://www.data.jma.go.jp/gmd/kaiyou/db/vessel_obs/data-report/html/buoy/buoy_e.php](http://www.data.jma.go.jp/gmd/kaiyou/db/vessel_obs/data-report/html/buoy/buoy_e.php)) (accessed on 30 June 2021). The shape and weight distribution of the drifting buoy were designed to follow the sea surface at any time. The wave properties were measured by an accelerometer. The accelerometer was placed at the center of gravity of the buoy. The accelerometer was supported by a gimbal. Therefore, even if the buoy is tilted by waves, the axis to be measured is always in the vertical direction. The sampling interval of the surface displacements was 0.5 s, and the measurement time was 512 s. The significant wave height and period measured by the drifting buoy are the wave height and period determined by the zero-up crossing method. They are obtained from 1024 sea surface displacements. The drifting buoy-measured significant wave height and period are denoted by \(H_{b}\) and \(T_{b}\), respectively. The significant wave height and period obtained by the zero-up crossing method are denoted as \(H_{1/3}\) and \(T_{1/3}\). The buoy position was obtained from the GPS receiver [11; 12].  
The buoys usually observed significant wave height and period at 3 h intervals, but sometimes observed them at 1 h intervals. The wave height resolution measured by the drifting buoy is 0.1 m, and the period resolution is 1 s. The buoy was almost spherical. The diameter, disc diameter, and height of the buoy were 0.46 m, 0.64 m, and 0.54 m, respectively. The buoy weight was approximately 30 kg. The specification of the drifting buoy is described in [[http://www.data.jma.go.jp/kaiyou/db/buoy/buoy-info.html](http://www.data.jma.go.jp/kaiyou/db/buoy/buoy-info.html)]([http://www.data.jma.go.jp/kaiyou/db/buoy/buoy-info.html](http://www.data.jma.go.jp/kaiyou/db/buoy/buoy-info.html)) (accessed on 30 June 2021). The buoy data were transmitted by a satellite communication system. The satellite altitude was approximately 800 km. Therefore, the distance from the satellite earth station to the buoy position was limited to a few thousand kilometers [12].
# Design and Evaluation of Steganographic Channels in Fifth-Generation New Radio +
## 4 Protocol Analysis and Covert Channel Design
### Design
#### 4.5.6 Covert Channel Properties  
The proposed covert channel is robust against normal traffic noise due to the reliability measures of the PDCP and the underlying protocols. However, it can be limited or even completely eliminated by traffic normalization of the reserved bits in the PDCP header. Regarding detectability, it is not feasible to easily place a warden on the air interface. This is mainly because communication over the air interface is very dynamic. The physical properties of the carrier channel often change during data transmission. In addition, hardening on the air interface only makes sense if the UE in which the covert sender or receiver is located does not change location. Otherwise, the UE would force a handover to another cell in the mobile network, and the warden would not be able to detect the covert channel anymore. However, detection may be simple within the base station or the UE if a network analyzer is used. The covert capacity is evaluated in the next section.
# GPU Parallel Implementation for Real-Time Feature Extraction of Hyperspectral Images
## 2 Hyperspectral Image Feature Extraction Based on INAPC  
Aiming at transforming the original hyperspectral image data into a feature space, PCA obtains the principal component information according to the magnitude of the variance, while NAPC determines the principal component information by the magnitude of the signal-to-noise ratio, which reduces the influence of noise, but needs external noise processing [26]. This method is essentially an overlap operation of two PCA, which means more massive computational overhead taking account of the characteristics of hyperspectral data, as stated above. The INAPC algorithm, also considered as a complete CPU-GPU collaborative computing solution, mainly whitens the noise in each band before performing the principal component analysis, so we directly deploy two singular value decompositions (SVDs) on the noise whitening process and the adjusted observation matrix (the data after noise reduction), which can reduce calculation steps and eliminate uneven noise distribution. In the noise whitening process, the noise covariance matrix calculation is a key step, so we put the noise estimation into the entire data processing, where noise is estimated by the minimum/maximum autocorrelation factors method (MAF) [21]. After the second SVD for the adjusted observation matrix, we propose a choosing rule to determine the \(k\) value (the number of principal components). Spectral feature extraction is also a process of dimensionality reduction. Through the choosing rule, a clear superiority is established that there is no need to manually input the value of k or set it to a fixed value on different input data anymore, so we can more adaptively and flexibly perform feature extraction on different hyperspectral datasets, which is also more conducive to the deployment of real-time applications. The details of our choosing rule are as follows. At first, put all singular values into a vector \(V\ =\ [\sigma_{1},\sigma_{2},\cdots,\sigma_{r}]\), and calculate the gradient vector G of the singular value vector V, denote \(G\ =\ [g_{1},g_{2},\cdots,\sigma_{r}]\). Then, we find the first \(\sigma_{k}\) while satisfying the following choosing rules:  
\[1-\ \frac{\sigma_{\mathbf{k}}}{\sigma_{1}}\ \geq 94\%\ \ \ \ \ \ \&\&\ \ \ \ \ \ \frac{\mathbf{g_{k}}}{\mathbf{g_{1}}}\ \leq 1\% \tag{1}\]  
The fixed values 94% and 1% are derived by mathematical induction based on eigenvalue and accuracy [27; 28]. Algorithm 1 shows the pseudocode and the annotations of the INAPC algorithm, and the calculation matrix of each step are described in Algorithm 1. The fourth step is noise estimation. \(\Delta_{1}\) and \(\Delta_{2}\) represent the neighborhood estimation in the horizontal and vertical directions, respectively. Since the hyperspectral image can consider as a three-dimensional data cube (which has been reshaped to a two-dimensional matrix), a three-layer loop needs to be set up.