esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Experiments and Results
### Effect of Swarm Size
Markedly, when the swarm size (P) is 50, the \(SSA_{(P=50)}\) outperformed the other variants and attained the best error rate results, while when (P = 80), the algorithm performed the worst performance regarding the error rate. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Population Size** & **Accuracy** & **Recall** & **FPR** & **TNR** & **Precision** & **G-Mean** & **AUC** \\ \hline  & **avg**\(\pm\)**std** & **avg**\(\pm\)**std** & **avg**\(\pm\)**std** & **avg**\(\pm\)**std** & **avg**\(\pm\)**std** & **avg**\(\pm\)**std** & **avg**\(\pm\)**std** \\ \hline
50 & **0.980**\(\pm\) 0.022 & 0.980 \(\pm\) 0.021 & **0.020**\(\pm\) 0.028 & **0.980**\(\pm\) 0.028 & **0.980**\(\pm\) 0.027 & **0.980**\(\pm\) 0.022 & **0.980**\(\pm\) 0.022 \\
60 & 0.973 \(\pm\) 0.015 & 0.978 \(\pm\) 0.018 & 0.032 \(\pm\) 0.027 & 0.968 \(\pm\) 0.027 & 0.969 \(\pm\) 0.026 & 0.973 \(\pm\) 0.015 & 0.973 \(\pm\) 0.015 \\
70 & 0.970 \(\pm\) 0.012 & 0.970 \(\pm\) 0.014 & 0.030 \(\pm\) 0.030 & 0.970 \(\pm\) 0.030 & 0.971 \(\pm\) 0.029 & 0.970 \(\pm\) 0.013 & 0.970 \(\pm\) 0.012 \\
80 & 0.967 \(\pm\) 0.016 & 0.974 \(\pm\) 0.019 & 0.040 \(\pm\) 0.016 & 0.960 \(\pm\) 0.016 & 0.961 \(\pm\) 0.016 & 0.967 \(\pm\) 0.016 & 0.967 \(\pm\) 0.016 \\
90 & 0.975 \(\pm\) 0.007 & 0.982 \(\pm\) 0.022 & 0.032 \(\pm\) 0.010 & 0.968 \(\pm\) 0.010 & 0.969 \(\pm\) 0.009 & 0.975 \(\pm\) 0.007 & 0.975 \(\pm\) 0.007 \\
100 & 0.974 \(\pm\) 0.018 & **0.982**\(\pm\)**0.018** & 0.034 \(\pm\) 0.034 & 0.966 \(\pm\) 0.034 & 0.968 \(\pm\) 0.032 & 0.974 \(\pm\) 0.019 & 0.974 \(\pm\) 0.018 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The performance evaluation of the SSA at (50%) of the ratio of leaders at different population sizes, in terms of average accuracy, recall, FPR, TNR, precision, g-mean, and AUC. Figure 10: Box plots presentation of the SSA algorithm at different population sizes. Nonetheless, Figure 11 shows the convergence plots of the SSA algorithm at various population sizes. It can be noticed that at all the experimented population sizes, the SSA algorithm exhibits similar, good convergence rates that eventually could reach such best fitness values. For instance, \(SSA_{(P=50)}\) at iteration (22), it reached a minimal fitness of (0.00059), while at \(SSA_{(P=100)}\), the algorithm optimally minimized the fitness to (0.00045). Generally speaking, the SSA algorithm has a successful convergence trend toward optimal solutions over the course of iterations with slight difference in relation to the population size effect.
## 4 Beamforming Based on INCM Reconstruction
### INCM Reconstruction  
The ICM can be reconstructed using the SVs of the DME signals obtained above  
\[\hat{\mathbf{R}}_{i}=\sum_{m=1}^{L}\hat{P}_{c}\big{(}\hat{\theta}_{m}\big{)}\hat{ \mathbf{a}}_{m}\hat{\mathbf{a}}_{m}^{H}=\sum_{m=1}^{L}\frac{\hat{\mathbf{a}}_{m}\hat{\mathbf{ a}}_{m}^{H}}{\hat{\mathbf{a}}_{m}^{H}\hat{\mathbf{R}}_{x}^{-1}\hat{\mathbf{a}}_{m}}. \tag{25}\]  
However, in the Capon power spectrum of the DME sector, the residual noise power exists, and direct reconstruction will result in a larger error. According to [PERSON]'s statement that the power of the residual noise is \(\frac{1}{M}\) times the actual, the ICM can be corrected as [26]  
\[\hat{\mathbf{R}}_{i}=\sum_{m=1}^{L}\left(\frac{1}{\hat{\mathbf{a}}_{m}^{H}\hat{\mathbf{R} }_{x}^{-1}\hat{\mathbf{a}}_{m}}-\overline{\sigma}_{n}^{2}\right)\hat{\mathbf{a}}_{m} \hat{\mathbf{a}}_{m}^{H}, \tag{26}\]  
where \(\overline{\sigma}_{n}^{2}\) represents the average power of the noise sector  
\[\overline{\sigma}_{n}^{2}=\frac{1}{F}\sum_{f=1}^{F}\frac{1}{\bar{\mathbf{a}}^{H} \big{(}\theta_{f}\big{)}\mathbf{R}_{x}^{-1}\bar{\mathbf{a}}\big{(}\theta_{f}\big{)}}. \tag{27}\]  
\(F\) represents the number of sampling points in the noise sector.  
Define the estimated signal SV matrix \(\hat{\mathbf{A}}=[\hat{\mathbf{a}}_{0},\hat{\mathbf{a}}_{1},\ldots,\hat{\mathbf{a}}_{L}]\). According to \(\mathbf{x}=\mathbf{A}\mathbf{s}\), the signal vector \(\hat{\mathbf{s}}(k)\) is obtained using the least squares method  
\[\hat{\mathbf{s}}(k)=\left(\hat{\mathbf{A}}^{H}\hat{\mathbf{A}}\right)^{-1}\hat{\mathbf{A}}^{H} \mathbf{x}(k). \tag{28}\]  
Noise can be expressed as  
\[\hat{\mathbf{x}}_{n}(k)=\mathbf{x}(k)-\hat{\mathbf{A}}\hat{\mathbf{s}}(k)=\left[\mathbf{I}-\hat{ \mathbf{A}}\Big{(}\hat{\mathbf{A}}^{H}\hat{\mathbf{A}}\Big{)}^{-1}\hat{\mathbf{A}}^{H}\right] \mathbf{x}(k). \tag{29}\]Furthermore, the NCM can be reconstructed as  
\[\mathbf{\hat{R}}_{n}=\frac{1}{K}\sum_{k=1}^{K}\hat{\mathbf{x}}_{n}(k)\hat{\mathbf{x}}_{n} ^{H}(k)+\overline{\sigma}_{n}^{2}\mathbf{I}. \tag{30}\]  
Therefore, the INCM obtained from the reconstruction is  
\[\mathbf{\hat{R}}_{i+n}=\mathbf{\hat{R}}_{i}+\mathbf{\hat{R}}_{n}. \tag{31}\]
# Equatorial Plasma Bubbles: A Review
## 2 Observations of EPBs and Associated Irregularities  
It has already been described in the Introduction how ionosonde observations of range and frequency spread indicated the presence of irregularities in the equatorial and off-equatorial low-latitude ionosphere during post-sunset hours and gave rise to the generic term 'Equatorial Spread F' (ESF). However, there has been no theoretical investigation towards establishing a relationship between the features of ESF observed by an ionosonde and the characteristics of irregularities that give rise to spread F on ionograms. As such, scale sizes of the irregularities that produce range or frequency spread on ionograms have not been established, unlike the situation with coherently backscattered radar signals or ionospheric scintillations, where it is known theoretically that irregularities of certain scale sizes are involved in their production. Nevertheless, ionosonde observations are still widely used to indicate the presence of irregularities in the post-sunset equatorial and low-latitude ionosphere [13]. While in situ measurements by rocket- or satellite-borne instruments yield information about the various scale sizes present in the plasma density structures encountered in their trajectories, steerable radars are also capable of providing a large-scale picture of EPBs. Ground-based observations of ionospheric scintillations on VHF to L-band trans-ionospheric radio signals have been used to extract information about EPB irregularities of intermediate-scale (100 m to a few km). Observations of EPBs using different techniques have established that the plasma density structures associated with EPBs span a large range of scale sizes, extending from sub-meter measurements to hundreds of kilometers.
# Synthetic Fog Generation Using High-Performance Dehazing Networks for Surveillance Applications
###### Abstract  
This research addresses visibility challenges in surveillance systems under foggy conditions through a novel synthetic fog generation method leveraging the GridNet dehazing architecture. Our approach uniquely reverses GridNet, originally developed for fog removal, to synthesize realistic foggy images. The proposed Fog Generator Model incorporates perceptual and dark channel consistency losses to enhance fog realism and structural consistency. Comparative experiments on the O-HAZY dataset demonstrate that dehazing models trained on our synthetic fog outperform those trained on conventional methods, achieving superior Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) scores. These findings confirm that integrating high-performance dehazing networks into fog synthesis improves the realism and effectiveness of fog removal solutions, offering significant benefits for real-world surveillance applications.  
s _article_2025_15_, 6503
## 3 Case Study
### Calculation of Diesel Engine with Shock Absorbers in Impact Condition
#### 3.3.2 Crankshaft Stress of Diesel Engine with Shock Absorbers in Impact Condition  
As shown in Figure 16, it is the peak crankshaft stress curve in impact condition within 0 to 0.9 s. In Figure 16, it can be noticed that between 0 and 0.05 s, there are two peak crankshaft stresses, 432 MPa and 442 MPa, which are significantly higher than the peak crankshaft stress within 0.05 to 0.9 s. This abnormal results are caused by insufficient convergence in the initial stage of 0-0.05 s of the simulation. After the subsequent calculation time, the crankshaft stress curve gradually becomes stable.  
Within 0.05-0.9 s, the maximum crankshaft stress in impact conditions is 363 MPa at 0.17778 s at the eighth crank pin, as shown in Figure 17. That does not exceed the yield limit of the crankshaft material (650 MPa) with a large safety margin.  
Figure 16: Peak crankshaft stress curve under impact condition within 0 to 0.9 s.  
Figure 15: Distribution map of the average oil film pressure and the average asperity contact pressure of the ninth main bearing in shock condition in 0 to 0.12 s. (**a**) Distribution map of the average oil film pressure of the ninth main bearing. (**b**) Distribution map of the average asperity contact pressure of the ninth main bearing.  
In short, in 0-0.9 s, the crankshaft stress in impact conditions does not exceed the yield limit of the crankshaft material with a large safety margin, so the crankshaft of the diesel engine with shock absorber is safe under external impact.  
Through the calculation results, it can be found that when the shock absorber is installed, the main bearing can maintain the normal lubrication state, and the crankshaft stress does not exceed the yield limit, so the diesel engine with shock absorbers can work normally in impact conditions.  
It can also find that, when the diesel engine equipped with shock absorbers, the main bearing lubrication results and crankshaft stress results in the external shock condition are very similar to the one in normal conditions. That means the shock absorbers can protect the diesel engine from external shock.
# Intersection-Based Link-Adaptive Beaconless Forwarding in Urban Vehicular Ad-Hoc Networks
## 2 Background
### Specific Characteristics of Remote Monitoring in Urban VANETs  
Wireless communication for the remote monitoring applications in an urban environment has unique characteristics. Some of the characteristics specific to remote monitoring in urban VANETs are explained next.
## 3 Methodologies
### Logistic Map
#### 3.1.2 Bifurcation Diagram of the Logistic Map  
Along with sensitive dependence, a characteristic that must be present in a chaotic function is randomness or topological transitivity. This property can be observed using a bifurcation diagram.  
Figure 4 shows the bifurcation diagram for the logistic map in the range \(0\leq r\leq 4\). For some small values of \(r\), there is always a fixed point, namely, \(0\) for \(r<1\) and a non-zero value for \(1<r<3\). This image only shows attractors, the set of \(x\) values where their iterations converge, for different values of \(r\). There are also unstable fixed points and limit cycles that are not visible here. For example, the stable fixed point for \(r<1\) continues for \(r>3\) but becomes unstable, so its iteration does not persist and is not visible for \(r>3\). Instead, a stable attractor, with a cycle length of \(2\), emerges for \(r\) slightly greater than \(3\).  
Figure 4: Bifurcation diagram of the logistic map growth rate for the range \(0\leq r\leq 4\).  
Figure 3: Lyapunov exponent graph of the logistic map growth rate for the range \(0\leq r\leq 4\).  
In addition, the period-doubling cascade, a bifurcation event within bifurcation [23], can also be observed starting from \(r=3\) up to about \(r=3.5688\), where chaos occurs. Therefore, based on the analysis of the Lyapunov exponent and bifurcation diagram of the logistic map, the range of \(r\) values indicating chaotic behavior is estimated to be \(3.5688<r<4\).
## Materials and Methods
### Experimental Set-Up  
The laboratory-scale, dead-end PMR is shown in Figure 1. The experimental set-up consisted of a membrane module integrated with a UV lamp, feed reservoir, and data acquisition system. A Congo red dye solution (100 mg\(\cdot\)L\({}^{-1}\)) was used to simulate the dye wastewater. The feed solution was prepared by diluting a stock solution of 500 mg\(\cdot\)L\({}^{-1}\). The test solution was placed in a 5 L feed reservoir under continuous stirring at a constant pressure of 1.5 bar applied by a pressurized oxygen tank to push the feed solution toward the membrane module equipped with a disk-type ceramic membrane (effective surface area of 4.5 cm\({}^{2}\)). The aim of oxygen gas was to enhance the photocatalytic activity as it can act as an electron acceptor and thus can reduce the probability of electron hole recombination. A UV-C lamp (\(\lambda_{\text{max}}\) = 254 nm, Philips TUV 4W SLM, Seoul, Korea) was installed inside the membrane module to irradiate UV light on membrane surface directly. The thickness of water channel between UV lamp and membrane surface was approximately 2 cm. The permeate water produced by the membrane module was collected in a permeate vessel and weighed on an electronic balance (Ohaus Corporation, Pine Brook, NJ, USA). The data acquisition system was used to monitor the permeate weight on the electronic balance with the filtration time. The permeate flux (LMH) (L m\({}^{-2}\) h\({}^{-1}\)) was calculated by the permeate volume (L) divided by the effective membrane surface area (m\({}^{2}\)) and filtration time (h). The concentration of Congo red in the membrane permeate was analyzed by measuring its absorbance (\(\lambda_{\text{max}}\)) at 496 nm using a UV-Visible spectrophotometer (SCINCO, S-3100, Seoul, Korea). Pure deionized water from an ultrapure water production system (STS-8l, Human Science, Seoul, Korea) was used in all the experimental work performed in this study.  
Figure 1: Experimental setup of the photocatalytic membrane reactor (PMR) with direct ultraviolet (UV) irradiation on membrane surface.
## 4 Materials and Methods
### Electrical Resistivity Tomography (ERT)
#### 4.1.1 ERT Data Acquisition  
Fourteen ERT profiles were surveyed to collect the resistivity data for the 2D sections in the study site (Figure 4), utilizing the pole-dipole configuration with 2.5 m electrode spacing, to provide more in-depth information on the subsurface. The pole-dipole arrangement was chosen for this inquiry because it has a substantially greater signal to noise ratio [40]. An automatic resistivity system (ARES GF instrument) was used to conduct this survey using a multielectrode cable for implementing the automatic resistivity measurements. A depth of around 21 m was achieved in this survey by the selected (a) and (n) spacing.
## 2 Design of Components and Fabrication
### Experimental Setup
#### 2.1.1 Key Parameters  
The innovative spring-driven universal impact testing setup, as depicted in Figure 1, introduces a sophisticated experimental configuration with extensive adaptability. This configuration offers enhanced control over the main impact parameters--specifically, impact velocity (\(v\)) in meters per second (m/s) and impact energy (\(E\)) in joules (J). This control is facilitated by Equation (1), which relates the elastic potential energy stored in the tension springs to the kinetic energy, in which the fundamental variables are the spring constant (\(k\)) in newtons per meter (N/m), extension distance (\(x\)) in meters (m), and mass of the impactor (\(m\)) in kilograms (kg). Equation (1) serves as the bedrock for precise experimental control over the impact conditions.  
\[E=\frac{1}{2}kx^{2}=\frac{1}{2}mv^{2} \tag{1}\]
## 3 Results  
A total of 41 QRLs [20] and 41 SDSCs [21] were answered through Google forms. The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) [25] was used to guide this cross-sectional study. Figure 1 shows the detailed development of this study through the STROBE flowchart. Table 1 presents the most relevant characteristics of the DS children and adolescents of the current study (\(n=41\)). The information was provided by the guardians of the DS children and adolescents during the completion of the form on personal data. Table 2 presents a profile of the population investigated through the QRL. The number (\(n\)) of participants in each category is shown between parentheses, followed by the corresponding percentage (%). The total sample of DS children and adolescents is 41. Regarding the prevalence of the sleep behavior, it is possible to verify that most children (36.58%) wake up at least once during the night, sleep during the day (56%) and fall asleep within 15 to 30 min (36.58%). \begin{table}
\begin{tabular}{l l} \hline Gender & Girls (18) 43.90\%, age range 1–14 years \\  & Boys (23) 56.09\%, age range 1–17 years \\ \hline Age (years) & 1–3 (17) 41.46\% \\ \hline  & 4–6 (16) 39.02\% \\ \hline  & 7–9 (3) 7.31\% \\ \hline  & 10–12 (3) 7.31\% \\ \hline  & 14–17(2) 4.87\% \\ \hline Relation of respondent to child or adolescent & Mother (40) 97.56\% \\  & Father (1) 2.43\% \\ \hline Obesity (BMI \(\geq\) 30) & (3) 7.31\% \\ \hline Daytime sleepiness & (23) 56.09\% \\ \hline OSA diagnostic & Yes (9) 21.95\% \\  & Unaware of the diagnosis (12) 29.26\% \\ \hline BMI—body mass index; OSA—obstructive sleep apnea. (\%) percentage. \\ \hline \end{tabular} \begin{tabular}{l l} \hline Excluded \\ The answers were \\ incomplete: \\ QRL - (\(n=5\)) \\ SDSD - (\(n=0\)) \\ \hline \end{tabular} \
\begin{tabular}{l l} \hline Included in the study and according to study criteria \\ girls (\(n=18\)) and boys (\(n=23\)) with DS (1 to 17 years) \\ \hline \end{tabular}
\begin{tabular}{l l} \hline \multicolumn{1}{c}{SD children analyzed (\(n=41\))} \\ \hline \end{tabular}
\end{table} 
Table 1: DS child and adolescent characteristics. Figure 1: Flowchart of the study. Table 3 shows the answers referring to the sleep pattern and presence of sleep disorders, obtaining information about the structural, temporal and physiological organization of the sleep\(-\)wake cycle. The number (\(n\)) of participants in each category is shown between parentheses, followed by the corresponding percentage (%). The total sample is 41 DS children.
# Practical Performance Assessment of Water Vapor Monitoring Using BDS PPP-B2b Service
## 2 Data Description
### GNSS Satellite Ephemeris  
Satellite ephemeris in this study include three products. First, orbit and clock offset corrections provided by the BDS PPP-B2b service are directly captured and decoded by the Hexagon FangZhou receiver in the State Space Representation (SSR) format. The B2b ephemeris can be obtained with the combination of SSR and navigation message. Second, the final multi-GNSS ephemeris from Wuhan University (WUM) are collected and applied for the post-processing [32], which will serve as the reference for the following evaluation. In addition, the real-time multi-GNSS ephemeris generated by the China Academy of Science (CAS) are also collected and applied for processing for comparison [33]. Except for the B2b ephemeris, satellite products from WUM and CAS can both be obtained from the IGS ([[https://igs.org/products/#about](https://igs.org/products/#about)]([https://igs.org/products/#about](https://igs.org/products/#about)), accessed on 12 June 2025).
## 3 Proposed Method
### Global Feature Attention Module
#### 3.2.1 Channel Attention Module  
The main idea of this module is to establish correlations between channels and dynamically adjust the channel weight of the input features, resulting in enhanced model performance and improved generalization capability.  
First, formally, given an input feature map\(f\in\mathbb{R}^{C\times H\times W}\), where \(H\), \(W\), and \(C\) denote its height, width, and the channel numbers, respectively, we propose a Channel Attention module to calculate the channel attention vector. The structure of this module is show in Figure 5a.  
Secondly, we perform a \(1\times 1\) convolution to reduce the channel numbers of the input feature map to \(f_{c1}\in\mathbb{R}^{C/4\times H\times W}\), and next we reshape\(f_{c1}\) to\(f_{c1}\in\mathbb{R}^{C/4\times(HW)}\). Meanwhile, we can obtain \(f_{c2}\in\mathbb{R}^{1\times H\times W}\) by performing a \(1\times 1\) convolution to reduce the channel numbers of \(f\). Next, we reshape and transpose \(f_{c2}\) to \(f_{c2}\in\mathbb{R}^{(HW)\times 1\times 1}\). After that, we perform a matrix multiplication between \(f_{c1}\) and \(f_{c2}\) to obtain \(f_{c}\in\mathbb{R}^{C/4\times 1\times 1}\). The process can be described by  
\[f_{c}=RS(\mathcal{W}_{1\times 1}\odot f+b)\otimes\sigma(RT(\mathcal{W}_{1 \times 1}\odot f+b)), \tag{1}\]  
where \(\otimes\) and \(\odot\) indicate element-wise multiplication and the convolution operation, respectively, and \(RS(\cdot)\), \(RT(\cdot)\), and \(\sigma(\cdot)\) denote the reshape operation, reshape and transpose operation, and sigmoid activation, respectively. \(W_{1\times 1}\) denotes the filter value, and \(b\) indicates the bias value.  
Finally, the input feature map is calculated according to Equation (1), then, we can obtain the result\(f_{c}\in\mathbb{R}^{C/4\times 1\times I}\). Next, we use a \(1\times 1\) convolution to make the channel number of \(f_{c1}\) the same as the input feature map, then, we employ a sigmoid activation to make it nonlinear. After that, we can obtain the output \(y_{c}\in\mathbb{R}^{C\times 1\times 1}\), which can be described by  
\[y_{c}=\sigma(\mathcal{W}_{1\times 1}\odot f_{c}+b). \tag{2}\]  
Figure 3: Details of the RRD module, where © and © are concatenate and add operations, respectively. DW denotes depth-wise convolution with a kernel size of \(3\times 3\) and a padding size of \(1\).
# A Linear Strong Constraint Joint Solution Method Based on Angle Information Enhancement
## 5 Experimental Performance Verification
### Performance of the Fusion Localization Algorithm
However, in complex scenarios, not all regions have a lot of redundant observation information. In region one, there are fewer redundant observations, and the number of effective particles will accelerate decay. After resampling, the diversity of particles will decrease, and the ability to explore the state space will weaken, making it easy to fall into local optima and resulting in a decrease in localization performance. At this point, the algorithm proposed in this article fully explores the relationship between angle and distance, and has high positioning robustness. Even with less redundant observation information, it can provide high positioning accuracy. Figure 11: The layout of the base station.
# Reduced Complexity Detection in MIMO Systems with SC-FDE Modulations and Iterative DFE Receivers
## 3 Multiuser Detection
For this purpose, we can consider the example of a matrix \(\mathbf{M}\), made of invertible blocks with appropriate dimensions, and its inverse \(\mathbf{M}^{-1}\) as:  
\[\mathbf{M}= \begin{bmatrix}\mathbf{I}&\mathbf{A}\\ -\mathbf{B}&\mathbf{D}\end{bmatrix} \quad\text{and}\quad\mathbf{M}^{-1}= \begin{bmatrix}\mathbf{X}&\mathbf{Y}\\ \mathbf{W}&\mathbf{Z}\end{bmatrix} , \tag{22}\]  
with \(\mathbf{I}\) and \(\mathbf{D}\) being diagonal matrices (\(\mathbf{I}\) indicates an identity matrix). It can be shown that \(\mathbf{M}\mathbf{M}^{-1}\) and \(\mathbf{M}^{-1}\mathbf{M}\) correspond to:  
\[ \begin{split}\mathbf{M}\mathbf{M}^{-1}=\begin{bmatrix}\mathbf{I}& 0\\ 0&\mathbf{I}\end{bmatrix}&=\begin{bmatrix}\mathbf{I}&\mathbf{A}\\ -\mathbf{B}&\mathbf{D}\end{bmatrix}\begin{bmatrix}\mathbf{X}&\mathbf{Y}\\ \mathbf{W}&\mathbf{Z}\end{bmatrix}\\ &=\begin{bmatrix}\mathbf{X}+\mathbf{A}\mathbf{W}&\mathbf{Y}+\mathbf{A} \mathbf{Z}\\ -\mathbf{B}\mathbf{X}+\mathbf{D}\mathbf{W}&-\mathbf{B}\mathbf{Y}+\mathbf{D} \mathbf{Z}\end{bmatrix}\end{split}  \tag{23}\]