esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Proposed Method  
### Overlapping Group Sparsity with L1 Norm (OGS-L1) Model  
To reduce the staircase effect of the ATV model, [PERSON] and [PERSON] proposed the overlapping group sparsity regularization term [5; 6; 7] in 2006, which expands the vertical and horizontal gradient of pixels to the group gradient of \(N\) adjacent points (\(N\) is the size of the group). Setting a reasonable threshold, the individual noise points and image edge points can be distinguished. This model preserves the edge information of the image and mitigates the disadvantages of the staircase effect. With reference to the work of [PERSON] and [PERSON], [PERSON] et al. extended the overlapping group sparsity regularizer from one-dimensional to two-dimensional cases, then substituted it in the anisotropic total variation model for the deconvolution and removal of salt and pepper noise [8].  
This model is centered at the pixel \(x_{i,j}\) and extends into all directions, forming multiple staggered and overlapped squares. The variable \(\widetilde{\boldsymbol{X}}_{i,j,N,N}\in\mathbb{R}^{N\times N}\) is the \(N\times N\) pixel matrix, centered at the coordinates \((i,j)\), as shown in Equation (3):  
\[\widetilde{\boldsymbol{X}}_{i,j,N,N}=\left[\begin{array}{cccc}x_{i-N_{i},j-N _{l}}&x_{i-N_{l},j-N_{l}+1}&\cdots&x_{i-N_{l},j+N_{r}}\\ x_{i-N_{l}+1,j-N_{l}}&x_{i-N_{l}+1,j-N_{l}+1}&\cdots&x_{i-N_{l}+1,j+N_{r}}\\ \vdots&\vdots&\ddots&\vdots\\ x_{i+N_{r},j-N_{l}}&x_{i+N_{r},j-N_{l}+1}&\cdots&x_{i+N_{r},j+N_{r}}\end{array} \right], \tag{3}\]  
where \(N_{l}=\left\lfloor\frac{N-1}{2}\right\rfloor\), \(N_{r}=\left\lfloor\frac{N}{2}\right\rfloor\). and \(\lfloor\ \rfloor\) is the rounding-down operators. We define \(\varphi(\boldsymbol{X})\) to represent the overlapping group sparsity functional of the two-dimensional array:  
\[\varphi(\boldsymbol{X})=\sum\limits_{i=1}^{N}\sum\limits_{j=1}^{N}\left\| \widetilde{\boldsymbol{X}}_{i,j,N,N}\right\|_{2}. \tag{4}\]  
The ATV model can then be extended to embody overlapping group sparsity regularization (called OGS-L1 model for short), as shown in Equation (5):  
\[\boldsymbol{F}=\underset{\boldsymbol{F}}{\text{argmin}}\|\boldsymbol{F}- \boldsymbol{G}\|_{1}+\mu\big{[}\varphi(\boldsymbol{K}_{\boldsymbol{h}}* \boldsymbol{F})+\varphi(\boldsymbol{K}_{\boldsymbol{v}}*\boldsymbol{F})\big{]}, \tag{5}\]  
where the regularization term \(\varphi(\boldsymbol{X})=\sum\limits_{i=1}^{N}\sum\limits_{j=1}^{N}\left\| \widetilde{\boldsymbol{X}}_{i,j,N,N}\right\|_{2}\). is the group gradient. Equation (4) shows that the OGS-TV model takes into full consideration the gradient information close to a pixel, so it strengthens the dissimilarity between the smooth and edge regions of the image.
## 3 Results
Assuming that \((y_{n})\) follows locally a logistic function \(y_{n}\approx y(n)=\frac{u_{max}}{1+\exp(-\frac{n-b}{a})}\) and since by definition it holds  
\[y^{\prime\prime}(x)=\frac{u_{max}}{a^{3/2}}y_{2}^{a,b}(x),\]  
then by (12) we get successively \[\sum_{n} \Delta^{2}y_{n}\phi_{2}^{a,b}(n)\approx\sum_{n}\Delta^{2}y(n)\psi_{2 }^{a,b}(n)\approx\int_{-\infty}^{\infty}y^{\prime\prime}(x)\phi_{2}^{a,b}(x)dx= \int_{-\infty}^{\infty}\frac{u_{max}}{a^{3/2}}\psi_{2}^{a,b}(x)\psi_{2}^{a,b}(x )dx\] \[=\frac{u_{max}}{a^{3/2}}\int_{-\infty}^{\infty}(\psi_{2}^{a,b}(x)) ^{2}dx=\frac{u_{max}}{30a^{3/2}}. \tag{21}\]  
Using (21) we can estimate the saturation level \(u_{max}\) as follows  
\[u_{max}\approx 30a^{3/2}\sum_{n}\Delta^{2}y_{n}\psi_{2}^{a,b}(n), \tag{22}\]  
Parameters \(a\) and \(b\) in (20) can also be estimated by maximizing locally the integral (i.e., the CWT coefficient) on the left-hand side of (21). Hence, we find in the sequence \(\Delta^{2}y_{n}\) the best pattern corresponding to the wavelet \(\psi_{2}^{a,b}\). The saturation level of a logistic wave can also be estimated as twice the value of the sequence \((y_{n})\) at the point where \((\Delta^{2}y_{n})\) changes signs (inflection point) or its maximal value multiplied by \(1/0.211\) (zero of the third derivative). This approach is especially important for the last wave of the multilogistic function (20), when it is still in its initial or middle stage and has not yet terminated. After this we use the non-linear generalized reduced gradient method, minimizing the RMSE error, to optimize the parameters, mainly saturation levels. All data were collected from the Our World in Data website [27]. We will use the theory to build models for the total cumulative number of individuals reported to be infected by COVID-19 successively in Germany, Italy, Poland, the United Kingdom, the United States, and in the world.
# 3 GPP Evolution from 5G to 6G: A 10-Year Retrospective
## 9 Conclusions  
The evolution of 3 GPP from Release 15 to Release 20 has been a decade-long journey of innovation and collaboration, transforming the promise of 5G into reality and setting the stage for 6G. Each release has contributed uniquely to building a robust and versatile ecosystem that has advanced connectivity, expanded possibilities, and prepared the groundwork for the next generation of mobile networks. One of the most significant take-aways from this decade-long journey is the importance of adaptability and collaboration. 3 GPP's ability to align diverse stakeholders has been instrumental in driving consensus and progress.  
As we look ahead to the 6G era, the lessons learned and foundations built over the past ten years will serve as invaluable guideposts. 6G envisions a hyper-connected world where communication, sensing, and AI converge to create seamless and immersive experiences. The journey to 6G is already underway. The formal 6G requirements process, led by ITU in collaboration with 3 GPP, will define the benchmarks for IMT-2030 technologies. These requirements will encompass not only traditional metrics such as data rate, latency, and reliability, but also new dimensions like sustainability, sensing, and AI. The convergence of AI, edge computing, and cloud technologies will further enhance the adaptability and intelligence of 6G networks, enabling them to anticipate and respond to user needs in real-time. With continued dedication to innovation, inclusivity, and sustainability, 6G has the potential to reshape our world in ways we are only beginning to imagine.  
This research received no external funding.  
**Data Availability Statement:** No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
**Acknowledgments:** The process of 3 GPP standardization is a collaborative, international effort. I am thankful to my peers throughout the wireless industry, with special recognition to those engaged in 3 GPP RAN activities. Their commitment, expertise, and continued contributions to shaping the standards have been fundamental. Without their work, this review article would not have been possible.  
Conflicts of Interest: Author [PERSON] was employed by the company NVIDIA. The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
## 3 Numerical Study
### Material Model and Input Parameters
#### 3.2.4 Interface Constitutive Model and Parameters  
During the interaction between the structure and the soil, the deformation of both is not the same due to the existence of the interface. Therefore, in order to accurately simulate the deformation of the structure and the soil, the numerical model sets up interface elements at the junction of the structure and soil, and the stiffness and strength of the interface elements are obtained from the shear modulus of the adjacent soil. In PLAXIS\({}^{\text{3D}}\), the most important parameter of the interface element is the reduction factor \(R_{\text{inter}}\). It is generally considered that the strength and stiffness of the interface are smaller than the parameters of the surrounding soil body, so this property of the interface can be reacted by setting \(R_{\text{inter}}\)[29]. The elastic deformation of the interface element obeys Equations (11)-(15).  
\[s_{\text{n}}=\frac{\sigma}{K_{\text{n}}}=\frac{\sigma t_{\text{i}}}{E_{\text{ oed,i}}} \tag{11}\]  
\[s_{\text{s}}=\frac{\tau}{K_{\text{s}}}=\frac{\tau t_{\text{i}}}{G_{\text{i}}} \tag{12}\]  
\[E_{\text{oed,i}}=2G_{\text{i}}\frac{1-v_{\text{i}}}{1-2v_{\text{i}}} \tag{13}\]  
\[G_{\text{i}}=R_{\text{inter}}^{2}G_{\text{soil}}\leq G_{\text{soil}} \tag{14}\]  
\[v_{\text{i}}=0.45 \tag{15}\]  
where \(G_{\text{i}}\) is the shear modulus of the interface, \(E_{\text{oed,i}}\) is the one-dimensional compression modulus of the interface, \(t_{\text{i}}\) is the virtual thickness of the interface, generally taken as 0.1 m, \(K_{\text{n}}\) is the normal stiffness of the interface, \(K_{\text{s}}\) is the tangential stiffness of the interface, \(R_{\text{inter}}\) is taken as 0.75 in this study [27; 30], \(G_{\text{soil}}\) is the shear modulus of the adjacent soil, and \(v_{\text{i}}\) is Poisson's ratio of the interface, which is a fixed value of 0.45. The strength parameters of the interface are determined by Equation (16).  
\[\begin{array}{c}c_{i}=R_{\text{inter}}c_{\text{soil}}\\ \tan\varphi_{\text{i}}=R_{\text{inter}}\tan\varphi_{\text{soil}}\leq\tan \varphi_{\text{soil}}\end{array} \tag{16}\]  
where \(c_{\text{i}}\) is the interface cohesion, \(c_{\text{soil}}\) is the adjacent soil cohesion, \(\varphi_{\text{i}}\) is the interface internal friction angle, and \(\varphi_{\text{soil}}\) is the adjacent soil internal friction angle.
# Optimization of Slotted Steel Plate Shear Walls Based on Adaptive Genetic Algorithm
## 3 Optimization Analysis of SSPSWs  
### Experimental Design  
The experimental steel frame-SSPSW model adopts the SF10S specimen configuration from [PERSON]'s seminal work [1], with geometric parameters detailed in Figure 3. Key specimen specifications include the following: steel plate dimensions: 800 \(\times\) 800 \(\times\) 4.5 mm\({}^{3}\) (SS400 steel grade); edge stiffener profile: 50 \(\times\) 4.5 mm\({}^{2}\); frame member sections: 100 \(\times\) 100 \(\times\) 6 \(\times\) 8 mm\({}^{4}\) (beams/columns); slot configuration: n = 17 slots arranged in m = 2 rows; inter-slot column dimensions: l = 235 mm, b = 42; and slot width: d = 3 mm. The test setup employs high-strength steel bar connections to reaction frame beams, incorporating lateral restraint devices to prevent out-of-plane displacements. Horizontal loading is applied via a hydraulic jack under displacement-controlled conditions, with inter-story displacement defined as the relative movement between base beam surfaces and specimen beam axes. The loading protocol initiates with a 0.25% drift cycle, followed by 0.5% incremental increases per cycle until achieving 5% drift capacity.
# Landslide Displacement Prediction Based on Variational Mode Decomposition and GA-Elman Model
## 4 Application Research and Method Comparison
### Model Comparison  
After determining the prediction model for the Shuizhuyuan area in the Three Gorges, this paper further compares the results of this model with other landslide displacement prediction models. In order to verify the validity and feasibility of VMD, the results of the model are compared with the results of the GA-Elman model, and, to verify the practicability of the GA-Elman algorithm, the model is compared with the Elman model. The comparison results are shown in Table 7. It can be seen that the MAPE values of the Elman and GA-Elman models were both greater than 100%; the prediction effect of the model was poor, and not as good as the prediction effect of the combined model. The model proposed in this paper had the advantage of higher prediction accuracy.
# Evaluation of Optimal Visible Wavelengths for Free-Space Optical Communications
## 4 Results and Discussion
### Summary of Findings
#### 4.4.2 Theoretical Consistency with Fog Attenuation Models
The consistency between our experimental findings and theoretical attenuation trends further validates the suitability of 650 nm wavelengths for energy-efficient, short-range FSO communication, particularly in environments with moderate visibility challenges.
## 4 Training Methodology  
In this work, the predictive ability of deep learning models, which are known for their ability to extract spatio-temporal information from data, was evaluated. The experiments were divided into three scenarios based on the input characteristics of the models. Scenario 1 included only irradiance from the target and neighboring stations, Scenario 2 included astronomical data (solar elevation angle and azimuth angle) in addition to the irradiance used in Scenario 1, and the third scenario added meteorological variables (temperature, humidity, wind speed, wind direction, and precipitation for each station) in addition to the variables used in Scenario 2.  
Considering that the temporal resolution of the data is half an hour, 48 lags representing 24 h in the past are used for each of the variables in order to predict the next instant of time, which in this case would be the next half hour (30 min). The data are prepared using the sliding window method and then flattened to enter to the model. This selection  
Figure 5: Description of the architecture of the ST_Dilated_CNN model.  
of features ensures that the models have as much information about their environment as possible. Because low solar incidence angles tend to affect the quality of the measurements, only measurements for solar elevation angles greater than 5\({}^{\circ}\) were considered.  
The methodology used is shown in Figure 6. Specific features tailored to each station's particular scenario were chosen. The data for each fold of the dataset were then scaled and reshaped to prepare it for model training and fitting. Once the data were prepared, the model was trained and fitted. Error metrics were then calculated to assess model performance for each station. Finally, the results of these error metrics were combined to obtain an overall picture of the model performance for all selected stations.  
The predictive model is defined as \(f(\cdot)\), which aims to predict a target variable \(y\) based on a set of input variables \(X\). The target variable \(y\) represents the spatio-temporal phenomenon of solar irradiance.
## 5 Discussion
### Algorithm Operability  
The method presented in this paper has been designed in order to not require any specific tuning at the target level, meaning that it can be implemented and operated in a fully unsupervised way. Future work should hence easily involve a much larger collection of targets to assess its precision and accuracy at a world-wide level.
# Reinforcement Learning Based Resource Management for Network Slicing
## 6 Performance Evaluation
### Adaptive Resource Trading Based on the Market Price.  
Finally, we investigated the effects of the pricing adjusted by the provider on the resource trading. We assumed that the buying price \(p^{buy}\) is relative to the total allocated resource amount of all slices in Equation (1). This is a consideration of the following two concerns in our business model. One concern is in terms of tenants: what should be done if sudden physical resource shortages arise due to increased traffic and increased resource requirements. It is reasonable to allow tenants to determine their resource amounts before a resource shortage occurs. The other concern is in terms of a provider, who pursues its profits as an independent business entity. As can be noticed in Figure 9, only the proposed algorithm adjusted the purchase amount of the resource according to the buying price change. The change of the buying price may be caused by an increase in the total traffic volume of all slices. Since we set the selling price to $200, purchasing resources at a buying price larger than $200 would lead to a serious profit loss. Considering this fact, we can observe that our algorithm minimized the damage by reducing the amount of purchased resource when the unit buying price exceeded $200. This result also indicates that the provider is able to manage and balance the allocation of limited resources through the price adjustments.  
Figure 8: Trading resource amount with respect to the QoS weight  
Figure 9: Purchase amount with respect to unit buying price.
## 4 Conclusions  
This paper presents a low-profile antenna array that considers 16 miniaturized patch antennas for CubeSat applications. The innovation of this research lies in the high gain of a microstrip antenna array with FN and its assembly on a CubeSat structure. The main design challenge was the development of an antenna array to operate at low 5G frequencies whilst keeping the overall antenna size smaller than 10 cm \(\times\) 10 cm. The array was simulated in CST Studio Suite(r) software and fabricated for performance testing. Due to its reduced dimensions, this design is an excellent alternative for mounting on CubeSat since it combines efficient performance and a low profile. Future work will be focused on the optimization of antenna excitations and the use of aperture couple antennas to increase the gain even more.  
Conceptualization, A.R. and D.A.J.; methodology, A.R. and D.A.J.; software, D.A.J. and L.I.B.; validation, A.R., L.I.B. and M.A.P.; formal analysis, D.A.J. and A.R.; investigation, D.A.J.; resources, A.R. and L.I.B.; data curation, D.A.J. and A.R.; writing--original draft preparation, D.A.J. and A.R.; writing--review and editing, D.A.J. and A.R.; visualization, D.A.J., A.R. and M.A.P.; supervision, A.R.; project administration, A.R.; funding acquisition, A.R. and M.A.P. All authors have read and agreed to the published version of the manuscript.  
The research presented in this paper was supported by CONACYT under grant number 785782 and by UAT under the project number PEI2018-UAT-2022.  
Not applicable.  
The authors declare no conflict of interest.
# Modulus Waveform Design Based on Manifold ADMM Idea in Dual-Function Radar-Communication System
## 3 DFRC Waveform Design by Alternating Sequential Optimization Manifold-ADMM Idea
### DFRC Waveform Design
 \tag{40}\]  
its closed-form solution has  
\[\widetilde{\mathbf{Y}}^{(m+1)}=\Big{(}\frac{\rho}{2}\mathbf{I}\Big{)}^{-1} \Big{(}\frac{\rho}{2}\Big{(}\mathbf{X}^{(m)}-\boldsymbol{\lambda}^{(m)}\Big{)} -\mathbf{D}\mathbf{X}\text{+}\mathbf{2}\mathbf{G}\Big{)}. \tag{41}\]Then the updating of each point of (41) can be expressed as  
\[\mathbf{Y}^{(m+1)}=\sqrt{\frac{P_{0}}{NL}}\left[\frac{\widetilde{y}_{n,l}}{\left\| \widetilde{y}_{n,l}\right\|_{2}^{2}}\right],n=1,2,\ldots,N;l=1,2,\ldots,L. \tag{42}\]  
Combining (38) with (18), we have  
\[\mathbf{X}^{(m+1)} :=\arg\!\min_{\mathbf{X}\in S_{X}}\!F\!\left(\mathbf{X},\mathbf{Y }^{(m+1)}\right)+\frac{\rho}{2}\!\left\|\mathbf{Y}^{(m+1)}\!-\!\mathbf{X}+ \boldsymbol{\lambda}^{(m)}\right\|_{2}^{2}\!\!\!. \tag{43}\] \[\
abla_{\mathbf{X}}L\!\left(\mathbf{X},\mathbf{Y}^{(m+1)} \boldsymbol{\lambda}^{(m)}\right)\] \[= \
abla_{\mathbf{X}}F\!\left(\mathbf{X},\mathbf{Y}^{(m+1)}\right) +\frac{\rho}{2}\
abla_{\mathbf{X}}\!\left\|\mathbf{Y}^{(m+1)}\!-\!\mathbf{X}+ \boldsymbol{\lambda}^{(m)}\right\|_{2}^{2}\] \[= \frac{\rho}{2}\mathbf{X}-\left(\frac{\rho}{2}\!\left(\mathbf{Y} ^{(m+1)}+\boldsymbol{\lambda}^{(m)}\right)-\mathbf{D}^{H}\mathbf{Y}\right)\] \[= \boldsymbol{0},\]  
The closed-form solution has  
\[\widetilde{\mathbf{X}}^{(m+1)}=\left(\frac{\rho}{2}\mathbf{I}\right)^{-1} \!\left(\frac{\rho}{2}\!\left(\mathbf{Y}^{(m+1)}+\boldsymbol{\lambda}^{(m)} \right)-\mathbf{D}^{H}\mathbf{Y}\right), \tag{45}\]  
\[\mathbf{X}^{(m+1)}=\sqrt{\frac{P_{0}}{NL}}\left[\frac{\widetilde{x}_{n,l}}{ \left\|\widetilde{x}_{n,l}\right\|_{2}^{2}}\right],n=1,2,\ldots,N;l=1,2,\ldots,L. \tag{46}\]  
Once we have obtained each point \(\left(\mathbf{X}^{(m+1)}\boldsymbol{Y}^{(m+1)}\right)\in S_{(X,Y)}\) on a given product manifold, we could update \(\boldsymbol{\lambda}\) by  
\[\boldsymbol{\lambda}^{(m+1)}=\boldsymbol{\lambda}^{(m)}\!+\!\mathbf{Y}^{(m+1) }\!-\!\mathbf{X}^{(m+1)}. \tag{47}\]  
We summarize the DFRC Algorithm 2 based on manifold-ADMM (named DFRC-MA) as follows. ```
Initialize:\(\mathbf{X}^{(0)},\mathbf{Y}^{(0)},\boldsymbol{\lambda}^{(0)}\rho\), and the tolerance \(\varepsilon\). While the termination criteria are not satisfied do. Update \(\mathbf{Y}^{(m+1)}\) using (42). Update \(\mathbf{X}^{(m+1)}\) using (46). Update \(\boldsymbol{\lambda}^{(m+1)}\) using (47). \(m=m+1\). Endwhile
```  
**Algorithm 2**Applying manifold-ADMM to solve the problem (36).
## 4 Multiple Objective Motion Optimization Problem
### Combining the Acceleration Constraints
#### 4.2.3 A Greedy Velocity Optimization Algorithm  
To solve Problem (2), a greedy algorithm is proposed to optimize the motion plan of the MASS. It contains two steps: (1) The MASS updates the VO model based on surrounding information using Algorithm 1. (2) Then, the MASS adjusts its velocity in a greedy manner to solve Problem (2). This algorithm helps the MASS adjust its velocity to approach the target while avoiding collisions. The details of the Algorithm are given in Algorithm 2.  
```
Input:\(X_{t}\), \(V_{t}\), \(VO\), \(T,\lambda_{1},\lambda_{2}\), interval length \(\Delta_{t}\) Output:\(V_{t+1}^{*}\), i.e., the optimized velocity at time \(t+1\)
1 Initialize \(A_{t}^{*}=0\); \(\mathcal{V}^{*}=\text{MaximumConst}\);
2 Generate the set of feasible accelerations \(\mathbf{A}_{t}\) based on the constraints of (5), (6), and (7);
3 foreach\(A_{t}\) in \(\mathbf{A}_{t}\)do
4 Calculate \(T_{E}(X,Target)\);
5 Calculate \(\frac{\langle V_{t}+A_{t},V_{t}\rangle}{\|V_{t}+A_{t}\|\|V_{t}\|}\) ;
6 Calculate \(\|V_{t}+A_{t}\|-\|V_{t}\|\);
7 Evaluate the objective function \(\mathcal{V}(X_{t})\) ;
8 if\((\mathcal{V}(X_{t})<\mathcal{V}^{*})\)then
9\(\mathcal{V}*=\mathcal{V}(X_{t})\);
10\(A_{t}^{*}=A_{t}\)
11 Update \(V_{t+1}^{*}=V_{t}+A_{t}^{*}\) ;
```  
**Algorithm 2**Greedy velocity optimization.