esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 GMDH Network
The smaller the \(w\) calculated by the external criterion, the better the neuron and the better the K-G polynomial fitting effect. The poorer neurons are rejected, and the excellent neurons  
Figure 1: Group method of data handling (GMDH) network architecture. are preserved and become the input of the next layer. Meanwhile, the minimum \(w_{min}\) of this layer is recorded. When the \(w_{min}\) of this layer is no longer reduced relative to the previous layer, it indicates that the prediction error of the network is no longer decreasing; then, the network stops expanding, and the result of the previous layer is output. \(P\) is the number of test sets. \[w=\frac{{\sum\
olimits_{n=1}^{P}{\left({{\dot{y}}_{n}}-{y_{n}}\right)^{2}}}}{ \sum\
olimits_{n=1}^{P}{\left({{y_{n}}}\right)^{2}}}, \tag{4}\]  
Traditionally, the coefficient of the K-G polynomial is estimated by the least square method, and the calculation process is as follows:  
\[\left\{{ \begin{array}{*{20}{l}}{{\dot{y}}_{n}}={{a_{0}}+{a_{1}}{x_{in}}+{a_{2 }}{x_{jn}}+{a_{3}}{x_{in}}{x_{jn}}+{a_{4}}{x_{in}^{2}}+{a_{5}}{x_{jn}^{2}}}\\ {{e}=\sum\
olimits_{n=1}^{N}{\left({{y_{n}}-{\dot{y}}_{n}}\right)^{2}}}\\ {\frac{{{\partial{\mathbf{x}}}}}{{{\partial{a_{k}}}}}=0\;k=0,1,2,3,4,5}}\end{array}  }\right., \tag{5}\]  
In order to facilitate the analysis, the results are expressed in matrix form:  
\[{\mathbf{a}}={{\left({{\mathbf{X}}^{T}{\mathbf{X}}}\right)^{-1}}}{{\mathbf{X}}^{T}}{\mathbf{y}}, \tag{6}\]  
where,  
\[{\mathbf{X}}=\left\{{ \begin{array}{*{20}{l}}1&{{x_{i1}}}&{{x_{j1}}}&{{x_{i1}}}&{ {x_{i1}^{2}}}&{{x_{i1}^{2}}}\\ 1&{{x_{i2}}}&{{x_{i2}}}&{{x_{i2}}}{{x_{i2}}}&{{x_{i2}^{2}}}&{{x_{i2}^{2}}}\\ 1&{{x_{i3}}}&{{x_{j3}}}&{{x_{i1}}}{{x_{j2}}}&{{x_{i3}^{2}}}&{{x_{i3}^{2}}}\\ \vdots&\vdots&\vdots&\vdots&\vdots&\vdots\\ 1&{{x_{in}}}&{{x_{jn}}}&{{x_{in}}}{{x_{jn}}}&{{x_{in}^{2}}}\end{array} }\right\}, \tag{7}\]  
and \({\mathbf{a}}\) is polynomial coefficient, \({\mathbf{a}}=({a_{0}},{a_{1}},{a_{2}},{a_{3}},{a_{4}},{a_{5}})\). \({\mathbf{y}}\) is the observed value, \({\mathbf{y}}=({y_{1}},{y_{2}},\ldots,{y_{N}})\). This calculation process requires the least square method to meet the basic assumption of the linear regression model. One of the important assumptions is that there is no linear relationship between variables in the regression model [28]. In short-term load forecasting, when the input variable has multicollinearity, \({\mathbf{X}}^{T}{\mathbf{X}}\) does not have an inverse matrix, so Equation (6) cannot be solved. This results in severe distortion of the parameter estimation and a decrease in GMDH prediction accuracy. Therefore, this paper uses elastic net instead of the least square method to estimate the K-G polynomial coefficient and thereby solve the problem of multiple multicollinearity and overfitting in the estimation of the least square method. Moreover, the elastic net uses the L1 norms and L2 norms as prior regular terms to obtain a more stable and practical regression equation through the compression regression coefficient.
# Energy-Efficient Power Scheduling Policy for Cloud-Assisted Distributed PV System: A TD3 Approach
## 5 Simulation Results and Analysis
### Convergence Performance Comparison with Benchmark Algorithms  
In order to verify the superior convergence performance of the power scheduling strategy based on the TD3 algorithm, experiments are conducted with different algorithms set to the same lr and gamma \(\gamma\) with a number of six parks and the random seed is fixed to ensure that the time sequence of electric load and power generation is the same. The parameter comparison table of TD3 algorithm, DDPG algorithm and Soft Actor-Critic (SAC) algorithm is shown in Table 2. We set the learning rate to a low value to ensure stability and convergence, the discount factor to a high value to enhance long-term planning ability, the target update rate to a low value to maintain the smoothness and stability of the target network parameters, the replay buffer size to a large value to increase sample diversity and utilization efficiency, and the batch size to a moderate value to balance sampling efficiency and training efficiency.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **TD3** & **DDPG** & **SAC** \\ \hline Number of critic networks & Two & One & Two \\ Target value calculation & Minimum of two target critics & Single target critic & Minimum of two target critics \\ Action selection & Target actor output plus noise & Actor output & Reparametrized stochastic actor output \\ Exploration noise & Gaussian noise & Ornstein-Uhlenbeck & None \\ Target update rate & 0.005 & 0.001 & 0.005 \\ Entropy regularization & No & No & Yes \\ Learning rate \(\alpha\) & \(10^{-4}\) & \(10^{-4}\) & \(10^{-4}\), \(3\times 10^{-4}\) \\ Discount factor \(\gamma\) & 0.9 & 0.9 & 0.9 \\ Replay buffer size & \(10^{6}\) & \(10^{6}\) & \(10^{6}\) \\ Batch size & 256 & 256 & 256 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The parameter comparison table of TD3 algorithm and benchmark algorithm.  
Figure 4: Convergence performance of different parameters. The episode is the \(t\) in Algorithm 2.  
Figure 5 shows the convergence performance of TD3, DDPG and SAC algorithms. From Figure 5, it is observed that the reward of TD3 is much higher than DDPG and SAC when it reaches stability and TD3 has lower fluctuation, which means the performance of TD3 is relatively stable.
# Multi-Level Feature Dynamic Fusion Neural Radiance Fields for Audio-Driven Talking Head Generation
## 4 Experiments
### Quantitative Evaluation

Table 1: The quantitative results of head reconstruction on different methods. The best values are in **bold**. the model's fairness, we refrain from selecting methods like SSP-NeRF, whose code is not publicly available. In Table 2, our proposed method has excellent generalization ability for lip movements in the audio-driven talking head generation task. AD-NeRF has lower confidence in SyncNet due to the smooth transition of lip movements. Although GeneFace uses prior knowledge landmarks to alleviate this problem, the method cannot stably synthesize complex lip movements due to its reliance on previous knowledge, resulting in unsatisfactory scores in lip sync. Our proposed approach consistently outperforms the baselines in terms of lip sync and LMD scores. (3) We use four image quality indicators in the NeRF-based method to evaluate the quality of the entire image after rendering in the audio-driven talking head generation because accurate head and torso matching can make the content the model generates more natural. In addition to PSNR, LPIPS, and LMD, we also compare the Frechet inception distances (FIDs) [57] of different methods. Compared to other baselines shown in Table 3, our method obtains the best scores in three indicators (PSNR, LMD, and FID) for matching head and torso. LPIPS scores are not optimal compared to ER-NeRF, which could be because we calculate fewer details for the torso reconstruction. Among them, the rendering speed was also tested. Using CUDA acceleration, audio-driven talking head videos with a resolution of 512 x 512 can achieve a rendering rate of 32 FPS on an NVIDIA RTX A5000 GPU. This capability allows for the real-time creation of video streams, as it exceeds the typical 25 FPS video input speed.
# Cracking and Toughening Mechanisms in Nanoscale Metallic Multilayer Films: A Brief Review
## 3 Basic Mechanical Properties
### Experiment Methods
#### 3.1.2 Uniaxial Tensile  
Since nanoindentation has been the primary mechanical test method, the nominal strain to failure data for NMMFs is limited, Uniaxial tensile testing can cover this shortage [46; 47; 48; 12; 48]. During tensile testing, the strain and stress were automatically recorded by machine and then Young's modulus of the film/substrate system (\(E_{total}\)) and the substrate (\(E_{s}\))), and the yield strength of the film/substrate system (\(\sigma_{total}\)) and the substrate (\(\sigma_{s}\)) are calculated from the \(\sigma\)-\(\varepsilon\) curve [49; 50; 51]. The yield strength (\(\sigma_{y}\)) is determined as the 0.2% offset. Accordingly, [PERSON]'s modulus (\(E_{f}\)) and the yield strength (\(\sigma_{f}\)) of the NMMFs can be determined from the following equations [51]:  
\[E_{f}=(t_{sb}/t_{f})(E_{total}-E_{s}) \tag{9}\]  
and:  
\[\sigma_{f}=(t_{sb}/t_{f})(\sigma_{total}-\sigma_{s}) \tag{10}\]  
Figure 7: (**a**) SEM images of indents on Ag/Co multilayer. (**b**) Typical indentation load-displacement data defining key experimental quantities [37; 44].  
A macroscopic strain (\(\epsilon_{c}\)) obtained from the \(R\)-\(\epsilon\) curves [49] is used to characterize the ductility. Respective SEM images are often shown thereafter to characterize the fracture behavior, as shown in Cu/Nb NMMFs in Figure 8[52]. The cracking of brittle films is described analytically with a 2-D steady-state models [53], in which the steady-state energy release rate \(\xi\) can be described as [53]:  
\[\xi=\frac{\pi\sigma^{2}t}{2E}(1-v^{2})g(\alpha_{1},\alpha_{2}) \tag{11}\]  
where \(E\) is the Young's modulus of the NMMFs; \(\sigma\) is the tensile stress of NMMFs at \(\epsilon_{c}\); \(t\) is the multilayer thickness; and \(g(\alpha,\beta)\) is calculated from the elastic mismatch between the film and substrate, with \(\alpha_{1}\) and \(\alpha_{2}\) being the two Dundurs' parameters [54]. The fracture toughness (\(K_{IC}\)) of the NMMFs is generally expressed as [55]:  
\[K_{IC}=\sqrt{\frac{E_{\xi}^{\xi}}{1-v^{2}}} \tag{12}\]
## 3 Proposed Algorithm of Protection Scheme
### ALN-Index  
The alienation index (ALN-index) is evaluated using sample-based alienation coefficients of current signals. The sampling frequency used for the study was 3.84 kHz. The selection of this sampling frequency is explained in the case studies section. The following relation was utilized for the evaluation of the ALN-index:  
\[ALNindex=1-r^{2} \tag{5}\]  
where \(r\) is used to indicate the correlation coefficient between variables \(x\) and \(y\). The following relation expresses these variables:  
\[r=\frac{N_{s}\sum xy-(\sum x)(\sum y)}{\sqrt{[N_{s}\sum x^{2}-(\sum x)^{2}][N_{ s}\sum y^{2}-(\sum y)^{2}]}} \tag{6}\]  
where \(N_{s}\) indicates the sample numbers in a cycle (64 samples in this study), \(x\) represents the current samples recorded at \(t_{0}\) time, \(y\) represents the current samples recorded at \(-T+t_{0}\) time where T is the current signal time period [20; 21]. The ALN-index is computed using the moving window approach using quarter-cycle samples. This is implemented by comparing the data of the present quarter cycle with the data of the previous cycle with the help of a moving window (one sample step) with a quarter-cycle width. The ALN-index has the merit of a sharp change at the time of fault incidence, which helps to reduce the fault detection time and make the protection scheme fast.
## 4 Experiments and Analysis of Results
### Interpretability Analysis  
In order to further elucidate the hierarchical characterization mechanism of the MDFT-GAN discriminator in fault pattern recognition, the feature responses of Class 4 and Class 7 samples in the CWRU dataset at each discriminative layer are visualized based on the Grad-CAM method in this paper, as shown in Figure 26.  
The results show that in the shallow stage (Figure 26a,e), the model mainly responds to the low-frequency periodic structure, which reflects its effective suppression of background noise and the modeling ability of spectral prior; the activation of the intermediate layer (Figure 26b,f) is significantly enhanced, and the model begins to perceive the local non  
Figure 26: Visualization of Grad-CAM Responses for Fault Pattern Recognition in MDFT-GAN Discriminator—Class 4 and Class 7. (**a–d**) Class 4. (**e–h**) Class 7.  
Figure 25: The influence of ablation modules on fault diagnosis.  
stationary features, in which the activation of Class 4 samples concentrates in the amplitude mutation points, while Class 7 shows a multi-region sparse distribution, revealing the differential sensitivity mechanism of the model to local degradation features under different fault patterns.  
In the high-level semantic space (Figure 26c,d,g,h), the feature responses of the two classes of samples are further focused and show the trend of increasing intra-class consistency, with the activation of Class 4 expanding to the edge region to integrate extensive fault information, while Class 7 forms the discriminative core of center contraction, indicating that the model realizes the local nonsmooth features at the deeper level, with the activation of Class 4 concentrated at the amplitude mutation point, while Class 7 shows multi-region sparse distribution, which reveals the model's differential sensitivity mechanism to local degradation features under different fault patterns.  
This indicates that the model realizes class-specific semantic embedding and spatial aggregation at a deep level. The above activation evolution process systematically reveals the structural path of MDFT-GAN from low-level perception to high-level discrimination and demonstrates its discriminative robustness and semantic interpretability for complex fault types.  
Overall, these results demonstrate the effectiveness and robustness of MDFT-GAN in modeling complex vibration signals and performing fault diagnosis. The model excels in both generation and classification tasks, providing a reliable solution for challenging diagnostic applications.
## 2 Materials and Methods
### Simulation Method Description  
The modelling procedure is based on the Lamb waves modal analysis results. The basic AE signal waveform \(u_{A0,S0}(z,t)\) is calculated analytically as a reaction of the waveguide on a point excitation, which is set as a \(\delta\)-function. The \(A_{0}\) and \(S_{0}\) modes are modeled separately. The transmission coefficient and sensor transfer functions are set in the frequency domain and could be interpreted as a linear frequency filter with a transfer function \(H_{A0,S0}(f)\) equal to the production of three functions--the transfer coefficient \(K_{A0,S0}(f)\), the frequency dependent part of the normal component of displacement vector \(\delta_{A0,S0}\), and the sensor frequency response \(S(f)\)  
\[H_{A0,S0}(f)=K_{A0,S0}(f)\cdot\delta_{A0,S0}(f)\cdot S(f). \tag{14}\]  
The frequency-sampling method has been applied to transform the transfer function \(H_{A0,S0}\) into a finite impulse response, which could be represented in a discrete form using Equation (15):  
\[h_{A0,S0}(t)=\frac{1}{N}\left[\sum\
olimits_{k=1}^{\frac{N}{2}-1}2H_{A0,S0}(k \Delta f)\cdot\cos\left(2\pi k\left(\frac{t-\left(\frac{N-1}{2}\right)}{N} \right)\right)+H_{A0,S0}(0)\right], \tag{15}\]  
where \(\Delta f\) is the sampling frequency interval, and \(N\) is the number of frequency samples [19].  
Ultimately, the modeled signal is obtained as a result of the convolution of \(u_{A0,S0}\) and \(h_{A0,S0}\). The scheme of the simulation algorithm is shown in Figure 3.  
Modeling was carried out for wall thicknesses from 3 to 40 mm, with propagation distances from 0.5 to 50 m. The acoustic parameters of carbon steel were used: \(\rho\) = 7800 kg/m\({}^{3}\), \(c_{L}\) = 5900 m/s, \(c_{T}\) = 3100 m/s. Signals arriving in the form of an \(S_{0}\) or \(A_{0}\) wave were modeled separately. An equal ratio of the energies of the \(S_{0}\) and \(A_{0}\) modes was set. The sampling frequency of the simulated signal was equal to 1000 kHz, and its duration ranged from 4096 to 16,384 us. A single impulse with a 1 us duration was used as the emitted signal.  
Figure 2: (a) Dependence of the transmittance on frequency for different thicknesses (from 5 to 30 mm) of the object and the distance \(l\) = 6 m: red for mode \(A_{0}\) and blue for mode \(S_{0}\); (b) The frequency response of the sensor.
## 4 Construction of Ellipsoidal Particle Unit in Particle-Flow Software
### Basis for the Construction of Ellipsoid Particles  
When the ellipsoidal model is compared with the pre-ellipsoidal model, the volume of the ellipsoidal pattern must be equal to the volume of the spherical particles to ensure that the model's porosity remains unchanged during the transformation of the particles into ellipsoids. As shown in Figure 9, a particle with radius \(r\) in the original model was transformed into a model characterized by a long axis \(a\) and a short axis \(b\).  
Let the ratio of the long axis to the short axis be \(a/b=\lambda\). This method for constructing the ellipsoid unit must satisfy \(1\leq\lambda\leq 2\). If \(\lambda\) exceeds 2, the ellipsoid unit must be reconstructed. Otherwise, errors will occur in the calculation of particle volume in PFC, which will alter the porosity of the model.  
The radii of the large and small circles required to construct the ellipse are determined by the values of \(a\) and \(b\). Consequently, an elliptical particle model with constant porosity can be approximately constructed in PFC.  
To construct ellipsoidal particles in PFC, the ratio of the long axis to the short axis, \(\lambda\), must be determined. In this study, tailings-sand particles with a size range of 2-5 mm were scanned to obtain their projection images. Particle shapes were analyzed using software ImageJ ([[https://ij.imjoy.io/](https://ij.imjoy.io/)]([https://ij.imjoy.io/](https://ij.imjoy.io/)), accessed on 17 April 2025) to obtain size information for each particle. Subsequently, the corresponding \(\lambda\) parameters were determined by calculating the ovalization of each particle. The mean value of \(\lambda\) for each particle was used as the basis for the \(\lambda\) parameter in the construction of ellipsoidal particles in PFC. The tailings used for scanning were screened from the Livigou tailings reservoir.
## 4 Discussion
### Impact of Soil Class and Soil Depth on Organic Carbon Content  
Although our findings indicate that the soil class is not a predominant factor influencing the SOC content, we did observe subtle variations in the TOC and carbon stock values across the three soil classes examined. For instance, the TOC accumulation rate in saturated soils such as Hidrisoils appears to be slightly higher than in other soil classes, likely due to the suppression of microbial activity in anaerobic conditions compared to aerobic environments [49]. Similarly, Chernozems (a type of Cernisoils) exhibit the highest carbon content, making them a significant SOC pool. Nevertheless, this is being compromised by the frequent tilling of these fertile soils [50; 51]. On a positive note, the restoration of impacted Chernozem soils has been shown to recover up to 91% of their original carbon stock [52]. Additionally, the highest TOC values were observed in Luvisoils, which can be attributed to the strong interaction between carbon and the significant clay fraction in these soils [53].  
The obtained results do not suggest that soil class alone is a decisive factor in SOC content. Furthermore, as this subject received limited attention in the scientific literature, it is difficult to define the precise way in which the soil type can influence the organic carbon sequestration capacity of soil.  
Regarding soil depth, the existing literature generally shows a decreasing trend in SOC with depth in undisturbed areas [54; 55]. In our study, this trend was observed in grasslands but not in arable lands. In arable soils, the TOC showed a notable decrease with depth, up to approximately 30 cm, across all three soil classes, followed by either a slight increase (in Cernisoils and Hidrisoils) or stagnation (in Luvisoils), as shown in Figure 4. This disruption is likely a result of ploughing, which typically occurs at depths of around 30 cm, redistributing organic matter. Additionally, factors such as the soil texture [56], root depth [57], water availability, and water movement through the soil profile [58] may influence the vertical TOC distribution [59].  
These findings highlight the critical role of grasslands in organic carbon sequestration and emphasize the importance of their conservation. Simultaneously, agricultural practices on arable land require careful evaluation, given their complex impact on the SOC content.
## 2 Steady-State Modeling of the Electricity-Gas-Heat IES
### Coupling Equipment  
CHP unit, P2G and P2H facilities are considered in this paper. Note that the electricity-driven compressor is also a particular kind of coupling equipment, since it inputs power from the electricity network and outputs power to the gas network.  
There are several kinds of CHP units (e.g., gas turbine CHP, reciprocating engine CHP and extraction steam turbine CHP). A gas turbine CHP unit, which produces electricity and heat power simultaneously by gas consumption, is considered in this paper. The model of a gas turbine CHP unit can be expressed as [13]  
\[\mathbf{\Phi}_{\mathrm{CHP}}=\epsilon_{\mathrm{HP}}P_{\mathrm{CHP}} \tag{11}\]  
\[F_{\mathrm{CHP}}=\frac{P_{\mathrm{CHP}}}{\epsilon_{\mathrm{GP}}}\]  
where \(\mathbf{\Phi}_{\mathrm{CHP}}\) and \(P_{\mathrm{CHP}}\) are the heat power and electrical power generated by the CHP unit; \(F_{\mathrm{CHP}}\) is the gas consumed by the CHP unit; \(c_{\mathrm{HP}}\) and \(c_{\mathrm{GP}}\) are the heat-to-power ratio and gas-to-power ratio of the CHP unit, respectively.  
P2G can convert electrical energy (usually excess renewable energy) to produce hydrogen, which is injected to the gas network or converted to synthetic natural gas. The simplified energy conversion relationship P2G can be found in [6]  
\[\mathbf{F}_{\mathrm{P2G}}=\mathbf{C}_{\mathrm{P2G}}P_{\mathrm{P2G}} \tag{12}\]  
where \(P_{\mathrm{P2G}}\) (MW) and \(F_{\mathrm{P2G}}\) (m\({}^{3}\)/h) are, respectively, the electrical power consumed and the gas generated by the P2G; \(C_{\mathrm{P2G}}\) is energy conversion coefficient of the P2G.  
P2H equipment, such as electrical boilers and heat pumps, can convert excess renewable energy to heat. This paper considers electrical boilers, and the electricity-heat conversion relationship of P2H is  
\[\mathbf{\Phi}_{\mathrm{P2H}}=\eta_{\mathrm{P2H}}P_{\mathrm{P2H}} \tag{13}\]  
where \(\mathbf{\Phi}_{\mathrm{P2H}}\) and \(P_{\mathrm{P2H}}\) are, respectively, the heat power generated and electrical power consumed by the P2H (MW); and \(\mathbf{\eta}_{\mathrm{P2H}}\) is the energy conversion efficiency, \(\eta_{\mathrm{P2H}}=98\%\)[24].  
It is worth mentioning that both P2G and P2H provide promising prospects for accommodating renewable energy.