esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results and Discussion
### Particle Transport and Deposition
#### 3.2.1 Calculation of Contact Efficiency  
After calculating the contact efficiency as a function of the size distribution (\(d_{10}\), \(d_{50}\), \(d_{90}\)), we can see that the main factors controlling particle-sand contact are sedimentation and interception (Figure 4a). While \(\eta_{1}\) and \(\eta_{\text{G}}\) significantly increased with the increasing particle size, \(\eta_{\text{D}}\) showed the reverse trend. Using Equation (9), we calculated \(\eta_{0}\) between the suspended and collected particles with size distributions of \(d_{10}\), \(d_{50}\), and \(d_{90}\) (0.007, 0.908, and 1.98, respectively). A previous report found that graphene oxide was retained  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Suspension**} & \multicolumn{6}{c}{**Mass Deposited in Each Section (\%)**} & \multirow{2}{*}{\(M_{\text{d}}\) (\%)**} & \multirow{2}{*}{\(M_{\text{eff}}\) (\%)} & \multirow{2}{*}{\(M_{\text{in}}\) (\%)} \\ \cline{2-2} \cline{6-9}  & **1** & **2** & **3** & **4** & **5** & & \\ \hline
1.84 NTU & 55.0 & 20.9 & 4.96 & 3.17 & 1.67 & 85.7 & 11.1 & 96.8 \\
1.09 NTU & 30.3 & 28.3 & 8.42 & 3.92 & 2.26 & 73.2 & 20.8 & 94.0 \\
0.540 NTU & 33.8 & 30.5 & 9.79 & 7.65 & 4.53 & 86.3 & 21.3 & 108.0 \\
0.160 NTU & 3.63 & 5.27 & 5.32 & 5.04 & 3.22 & 22.5 & 82.3 & 105.0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Spatial mass distribution of differently sized particles in the columns (or mass balances), including mass percentages retrieved in the effluent (\(M_{\text{eff}}\)), deposition in each of the five column sections as a whole (\(M_{\text{d}}\)), and injection mass (\(M_{\text{in}}=M_{\text{eff}}+M_{\text{d}}\)).  
by collected particles in a Na-Ca electrolyte background, and \(\eta_{0}\) was calculated to be less than 0.050 [30]. In contrast, [PERSON] et al. reported an \(\eta_{0}\) value of less than 0.019 when aluminum oxide nanoparticles were retained in saturated sand at different ionic strengths (0.00-100 mM) [31]. [PERSON] et al. showed that straining is an important mechanism for particles with a particle size of 3.20 \(\upmu\)m to be retained in a porous medium with a median diameter of 0.700 mm in the process of studying the physical factors affecting particle transport, where \(\eta_{0}\) is less than 0.029 [32]. The collision efficiency of particles in this study is significantly higher than that in the above study, and we calculated that the particle-sand contact efficiency is greater than 0.050 when the size distributions are 32.4 \(\upmu\)m and 96.6 \(\upmu\)m. Therefore, this study obtained higher contact efficiencies, and we can infer that the particles easily collided with sand grains during percolation.
# A Denoising Method for Multi-Noise on Steel Surface Detection
## 1 Introduction
[21; 22; 23; 24] used an image denoising technique based on nonlocal Bayesian singular value thresholding and the Stein unbiased risk estimator. [PERSON] et al. [25; 26; 27; 28] proposed a fusion denoising method for laser blood flow speckle imaging based on homomorphic transform and three-dimensional transform domain synergistic filtering, which is widely used, but only in medical species. [PERSON] et al. [29; 30] apply deep learning and generative networks to process noise, but real-time performance needs to be improved. The detection algorithm is not robust and real-time detection is difficult to realize. [PERSON] et al. [31; 32; 33] proposed a method using convolutional neural networks to remove noise. However, this method requires a large amount of data and has some limitations. The traditional method can only illuminate part of the surface of the steel plate, and the quality inspection personnel cannot see the whole steel plate, which makes it not only easy to cause leakage detection, but quality inspection personnel, for some time and due to the high frequency and high intensity flash irradiation, will be affected by physical and mental health issues to varying degrees, so there is a certain degree of safety hazard. Most of the methods based on deep learning are artificially designed for a specific set of functions for specific defects, are not universal, and not accurate enough to locate the defects. In most cases, this can only locate defects in the rough position, the detection method is inefficient, real-time is poor, and the method is mixed with personal subjective factors and lack of scientific standardization; therefore, there cannot be a production process for multiple surfaces of steel at the same time in order to carry out real-time detection. The research in this paper studies a denoising method for multi-noise in steel surface detection. These noises may include Gaussian noise, pretzel noise, streak noise, color noise, artifacts, blurring and distortion, pressure noise, and other interfering information, which usually needs to be processed and removed in order to accurately analyze the steel surface image to obtain clearer and more accurate image data.
# Nonlinear Finite Element Analysis Formulation for Shear in Reinforced Concrete Beams
## 9 Results  
Figure 9 compares the predicted and observed curves of load versus midspan deflection relations. The prediction by using the Bernoulli-Euler beam element is denoted as predicted without shear, and the one by using the proposed element as predicted with shear. In the test results, it can be observed that when no stirrup is present, the strength drops. The strength reduction was significant, especially in the members with a small shear span ratio.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Specimen** & _f\({}^{\prime}\)c_ **(MPa)** & **Span (m)** & _a/d_ & **Spacing of Stirrups (mm)** & **Failure Mode** \\ \hline OA-1 & 22.5 & 3.66 & 3.97 & - & Diagonal tension failure \\ OA-2 & 23.7 & 4.57 & 4.90 & - & Diagonal tension failure \\ OA-3 & 37.6 & 6.40 & 6.94 & - & Diagonal tension failure \\ A-1 & 24.1 & 3.66 & 3.92 & 210 & Shear compression failure \\ A-2 & 24.3 & 4.57 & 4.93 & 210 & Shear compression failure \\ A-3 & 35.0 & 6.40 & 6.91 & 210 & Flexure-compression failure \\ \hline \end{tabular}
\end{table}
Table 1: Dimensions and material properties of test specimens.  
Figure 9: Load versus mid-span deflection.  
The predictions without shear present the flexural response only; therefore, there was no effect of the stirrups. This explains why the predictions without shear in series OA were similar to the counterparts in series A. As shown in the figure, the predictions without shear showed a higher member strength and stiffness and higher ductility than those with shear. The discrepancy between the two predictions, which represents the shear contribution to the deflection, increased proportionally as the applied load increased. Generally speaking, the curves of the test results corresponded well to those without shear up to the point of half of the ultimate strength but became closer to them with shear afterwards. For most cases, the proposed model predicted the strength of the actual beams satisfactorily, while the model without shear consideration predicted twice as much as the actual shear strength, depending on the problem. For specimen A-1 and 2, the analysis with the proposed model was terminated shortly before it reached the actual strength. However, as can be seen in the figure, the termination points were closely related to the points where the slope of the curve of test changes abruptly.
## 3 Inhomogeneous Broadening  
### The Urbach Line Shape  
In bulk solid materials, the exponential low energy spectral tail may span several orders of magnitude down in the bandgap. It arises from the disorder in the periodic crystal potential [23; 24] that is either frozen in the material during the fabrication or created by phonon vibrations at the instance of the e-h pair recombination or creation in the optical emission or absorption, respectively. Therefore, at usual ambient temperatures, Urbach tails can exist even in perfect crystals. It has been shown that with a Gaussian disorder depth distribution, the original (disorder free) band states disperse in energy with an exponentially decreasing deviation probability. At the same time, the original abrupt band edges disperse outlined by the convolution with this probability distribution. Since the disorder originates from local variations, the emerging DOS tails are classified as inhomogeneous and are correlated in the conduction and valence bands (disorder related charge carrier scattering is examined in Section 4).  
Equation (3) includes the abrupt JDOS, and two convolution operations would be needed to add the conduction and valence band tails separately. A detailed analysis of the broadened JDOS should also include the oscillator strengths in these band tail states [24] and the contribution of excitonic states in the bandgap. However, exciton peaks are absent in the LED spectra, and Urbach tails recorded on bulk semiconductor materials at usual ambient temperatures. Starting from the abrupt JDOS, we can, at the moment, reach only semiempirical broadening functions to combine the conduction and valence band tails. This does not turn down their value in the disorder analysis with experimental absorption and emission spectra.  
Equations (6) and (7) are the simplest lineshapes that in convolution with the original bulk material and quantum well \(\rho_{Jdos}(E)\) functions produce the observed exponential tails. A detailed microscopic analysis would be needed to study the spectral symmetry of the JDOS broadening and the correlations between the conduction and valence band tail states. Without it, we can examine the symmetry effects by comparing the fully symmetric, Equation (6), and maximally asymmetric, Equation (7), Urbach tail functions:  
\[L_{Jdos}(E)=\exp[-|E-\epsilon|/E_{u}]. \tag{6}\]  
\[L_{Jdos}(E)=\frac{1}{2}(1-sgn(E-\epsilon))\cdot\exp[-(E-\epsilon)/E_{u}]. \tag{7}\]  
Here \(E-\epsilon\) is the deviation from the unbroadened band state energy \(\epsilon\), and \(E_{u}\) is the Urbach broadening parameter. In convolution integrals, both functions produce the requested exponential Urbach tails in the bandgap. However, the asymmetric lineshape of Equation (7) produces abnormally sharp-peaked emission lines, as is seen in Figure 2. This leads to the conclusion that the Urbach broadening in the JDOS is more or less symmetric and only Equation (6) is used in the further analysis, though the sharp peak somewhat softens after including the lifetime broadening examined in Section 4.
## 5 Verification of Measurements  
The data of measured currents and voltages using a power five-phase analyzer were recorded during all measurements. These data were then entered into a Matlab environment to test the correctness and efficacy of using new fault-tolerant control in the following manner:  
* First, the data from the measured stator currents were entered into Matlab and plotted as a function of time;
* Following that, a five-phase transformation was demonstrated, in which was converted the currents from the _abcde_ system to the stationary reference frame _dq_;
* Finally, a circle diagram of currents \(i_{d}\) and \(i_{q}\) was created.  
In all four cases, the procedure is the same. The distribution of the MMF can be seen using circle diagrams.
# Presenting a Human Pupil Orbit Model (HPOM) for Eye-Gaze Tracking
## 4 Discussion  
We confirmed in the first experiment that the HPOM can be estimated by using the proposed method and the ES had an effect on the HPOM estimation process. The minimum amount of accurate data required for the estimation of HPOM was found to be three in this paper. However, when the ES was three, the estimation of the HPOM failed. This is due to the random sampling characteristics of RANSAC and the fact that half of the TS consists of error data. The RANSAC method relies on probability because it randomly selects a sample in order to estimate the best fit model. Therefore, the probability of estimating a suitable model is determined in proportion to the error data ratio and the number of estimation iterations. When, the ES is 3, the probability that all data selected for estimating the HPOM does not contain errors is less than 1.3%. The number of iterations is also determined by the ES. The maximum number of iterations when ES is 3 is 35. The means that HPOM estimation was impossible when the ES was 3, as the probability of estimating the HPOM accurately is less than 1.3%, and this is unlikely to occur once over the maximum 35 iterations. Consequently, HPOM estimation is almost impossible according to the probabilities at play when the ES is 3. In addition, when the ES was set excessively high, the processing time increased while the accuracy decreased. The increase in processing time is an expected result of the ORCP inference because the number of straight lines generated is proportional to the ES. Increasing the ES also causes a growth in the possibility an error is included in the data sample. Therefore, the ORCP of the estimated HPOM has a wide spread, as the error proportion of the samples included in the ES increases. Conversely, when the ES is minimized, the ORCP distribution becomes wide because the mathematical model of the initial HPOM is only weakly acquired in the RANSAC process.
## 2 Mechanical Model
### Model of the Frame Structure Connected to Vibrating Mass and an Inerter Device
\begin{split}& T=\frac{1}{2}(I_{e}+I_{M})\dot{\theta}_{e}^{2}(t)+ \frac{1}{2}(I_{s}+I_{1}+I_{2})\theta_{s}^{2}(t)+\frac{1}{2}m_{e}\hat{x}_{e}^{2} (t)+\frac{1}{2}M_{r}\hat{x}_{M_{r}}^{2}(t)+\\ &\frac{1}{2}M_{I}\hat{x}_{M_{l}}^{2}(t)+\frac{1}{2}m_{s}\hat{x}_{ s}^{2}(t)+\frac{1}{2}m_{1}\hat{x}_{1}^{2}(t)+\frac{1}{2}m_{2}\hat{x}_{2}^{2}(t), \end{split}  \tag{2}\]  
where \(\hat{x}_{M_{l}}(t)=\dot{u}_{e}(t)+\dot{u}_{M}(t)-\dot{\theta}_{e}(t)h_{e}\) represents the relative velocity between the two terminals of the inerter device, characterized by the virtual mass \(M_{l}\), the quantities \(I_{e}\) and \(I_{s}\) denote the polar inertia of the foundation platforms, and their masses, \(m_{e}\) and \(m_{i}\), also account for the virtual contribution of the soil below the platforms. The explicit definition of these four quantities is provided in Section 2.2. The polar inertia of the oscillating mass (\(I_{M}\)) and the two stories of the 2-DOF equivalent system (\(I_{1}\) and \(I_{2}\)) are deemed negligible (\(I_{M}=I_{1}=I_{2}=0\)). The potential energy, needed to apply the Lagrangian approach, reads based on Equation (3):  
\[ \begin{split}& U=\frac{1}{2}k_{e}u_{e}(t)^{2}+\frac{1}{2}k_{s}u_{s}(t) ^{2}+\frac{1}{2}k_{\theta e}\theta_{e}(t)^{2}+\frac{1}{2}k_{\theta s}\theta_{s }(t)^{2}+\frac{1}{2}k_{M}u_{M}(t)^{2}+\\ &\frac{1}{2}k_{1}u_{1}(t)^{2}+\frac{1}{2}k_{2}(u_{2}(t)-u_{1}(t)) ^{2}+\frac{1}{2}k_{es}(u_{s}(t)-u_{e}(t))^{2}+\frac{1}{2}k_{es}(\theta_{s}(t) -\theta_{e}(t))^{2},\end{split}  \tag{3}\]  
where the stiffness of the Kelvin-Voigt devices representing the soil are defined in Section 2.2. Furthermore, to take into account the viscous non-conservative forces, the effect of such forces has to be considered. This effect, denoted as \(W\), is formulated according to Equation (4):  
\[ \begin{split}& W=-[c_{e}\dot{u}_{e}(t)u_{e}(t)+c_{s}\dot{u}_{s}(t)u _{s}(t)+c_{\phi}\dot{\phi}_{e}(t)\phi_{e}(t)+c_{\delta s}\dot{\theta}_{s}(t) \theta_{s}(t)+c_{M}\dot{u}_{M}(t)u_{M}(t)+\\ & c_{1}\dot{u}_{1}(t)u_{1}(t)+c_{2}(\dot{u}_{2}(t)-\dot{u}_{1}(t) )(u_{2}(t)-u_{1}(t))+c_{es}(\dot{u}_{s}(t)-\dot{u}_{e}(t))(u_{s}(t)-u_{e}(t))+ \\ & c_{\theta e}(\dot{\theta}_{s}(t)-\dot{\theta}_{e}(t))(\theta_{ s}(t)-\theta_{e}(t)),\end{split}  \tag{4}\]  
where, \(c_{1}\), \(c_{2}\), and \(c_{M}\) are the damping coefficients that refer to the 2-DOF system and the oscillating mass. The other coefficients provide the viscous damping of the Kelvin-Voigt devices representing the soil and are defined in Section 2.2. By introducing the Lagrangian function \(L=T-U\) and letting \(\{q_{1},q_{2},q_{3},q_{4},q_{5},q_{6},q_{7}\}=\{u_{e},\theta_{e},u_{M},u_{s}, \theta_{s},u_{1},u_{2}\}\), the seven Lagrangian equations of motion are obtained according to Equation (5):  
\[ \begin{split}\bigg{[}\frac{\delta}{\delta t}\bigg{(}\frac{\delta L }{\delta q_{i}}\bigg{)}-\frac{\delta U}{\delta q_{i}}-\frac{\delta W}{\delta q _{i}}\bigg{]}dq_{i}=0,\ \ \forall dq_{i}\
eq 0,\ \ (i=1,\ldots,7).\end{split}  \tag{5}\]  
Such equations of motion read based on Equation (6):  
\[
# Ensemble-Based Knowledge Distillation for Video Anomaly Detection
## 4 Experimental Evaluation
### Comparison with State-of-the-Art Studies  
In this experiment, our best-performed model is quantitatively compared with other state-of-the-art (SOTA) weakly supervised approaches on the UCF-Crime dataset (Table 18). While for the previous experiments, the video-level AUC (V-AUC) metric is utilized to measure the performance of our models because the RWF-2000 dataset does not have frame-level annotations; the UCF-Crime dataset has frame-level annotations and other weakly supervised methods previously experimented on this dataset also use frame-level AUC (F-AUC) as a performance metric. Consequently, we repeat the testing process with our best ensemble-based student model trained on the UCF-Crime dataset with respect to frame-level AUC (F-AUC) metric for comparison with other SOTA studies. For this case, we select the student model trained with the CBMS method with \(\alpha=0.3\) which has the best overall performance as shown in Table 8.  
In Table 18, it can be concluded that the best ensemble-based student model (CBMS) we proposed exhibits comparable performance compared to the other state-of-the-art approaches. Besides, our CBMS-based student model also shows reassuring performance in the RWF-2000 dataset as shown in Table 8. Another important observation is that compared to the standard response-based method (Tables 3 and 4), our ensemble-based methods (Tables 5-10) have drastic performance increase regardless of the target dataset. This represents the increased generalization capability of our ensemble-based distillation methods.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**AR-Net Student (RWF-2000)** & **Actual Positive** & **Actual Negative** \\ \hline
**Predicted Positive** & 175 & 60 \\ \hline
**Predicted Negative** & 25 & 140 \\ \hline \hline \end{tabular}
\end{table}
Table 16: Confusion matrix of AR-Net student model with 0.5 threshold value on test set of Target Dataset (RWF-2000) with EWC approach.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Misclassification** & **GCN Teacher** & **AR-Net Teacher** & **Common** \\ \hline
**UCF-Crime** & 58 & 48 & 45 \\ \hline
**RWF-2000** & 169 & 164 & 157 \\ \hline \hline \end{tabular}
\end{table}
Table 17: Misclassified example statistics for both GCN and AR-Net-based teacher models for UCF-Crime (Source Dataset) and RWF-2000 (Target Dataset).  
In the case of the training case of AR-Net and GCN models on a specific dataset without knowledge distillation, it is observed that results are dramatically worse on the other dataset (RWF-2000, Tables 1 and 2 in Section 4.2). All SOTA models in Table 18 are trained without a knowledge distillation approach on the UCF-Crime dataset. Because they are trained on the UCF-Crime dataset without distillation, we conclude that while they have results better than our models on this specific dataset, their generalization performance will be lower than our models on another dataset, such as the RWF-2000 dataset as in Section 4.2.
# PID Control Assessment Using L-Moment Ratio Diagrams
## 2 Applied methods
### Statistical Moments  
We may utilize statistics in many different ways. We often calculate the data mean or standard deviation for some empirical data to show basic properties, i.e., its expected value and fluctuations. We may also address the problem in a different way using a theoretical approach. We fit an appropriate distribution model, a PDF function, to the data and then use its factors or moments (if they exist) to characterize the data.  
In this approach, we use an empirical approach and consider appropriate estimators for basic statistical moments. Let us assume that \(\left\{X_{i}\right\}^{T}\) denotes a given time series with its expected value, mean \(\mu\) (the first statistical moment) and the \(r\)th central moment \(\gamma_{r}=E(X-\mu)^{r}\), where \(E(\cdot)\) represents the expectation operator. The mean \(\mu\) denotes the first moment \(\gamma_{1}\), while variance \(\sigma^{2}\) represents the second moment denoted as \(\gamma_{2}\), where \(\sigma\) indicates standard deviation.  
The first two moments are frequently supplemented in analyzes by the third \(\gamma_{3}\) moment called skewness and the fourth \(\gamma_{4}\)--the kurtosis. The data skewness factor reflects its asymmetry, with its value equal to zero for symmetrically distributed data. Kurtosis relates to the data concentration  
\[\gamma_{3} =\frac{1}{N\sigma^{3}}\sum_{i=1}^{N}(x_{i}-\mu)^{3}, \tag{3}\] \[\gamma_{4} =\frac{1}{N\sigma^{4}}\sum_{i=1}^{N}(x_{i}-\mu)^{4}-3. \tag{4}\]  
The above estimators can be used to evaluate the first four moments for a given empirical time series. The existence of data contamination in the form of outlying observations (those originating from different stochastic process) in data biases statistical analyzes and estimations.Outliers change the shape of a distribution function, increasing or extending its tails. They cause heavy or long tails in PDFs [32].  
This feature biases classical estimators of statistical moments, making them inappropriate. This fact causes artificially increased values of the standard deviation and biasedmean. To cope with this problem, we may use its robust counterparts like the median for the expected value, mean absolute deviation (MAD) for variance, trimmed estimators, and many others [33]. The other approach is to use L-moments, which are also robust against outliers and simultaneously introduce other advantages into the analyses.
## 2 High Diffraction Efficiency and Damage-Resistance Threshold Gratings
### Multilayer-Dielectric-Film Grating
#### 2.2.2 Multilayer Dielectric Film Transmission Grating  
All-dielectric transmission gratings with high diffraction efficiencies and anti-laser-damage thresholds have garnered a significant amount of attention in recent years and are widely utilized in DWDM, CPA systems, and SBC systems. [PERSON] and [PERSON] [47] created a transmission grating with a grating period of 330 nm, groove depth of 370 nm, and incidence angle of 42\({}^{\circ}\) in 1983. The diffraction efficiency of the transmission grating created by holographic exposure was better than 88% at 632.8 nm. [PERSON], [PERSON], et al. [48] devised and built a high-efficiency fused-silica transmission grating for high-power ultraviolet laser systems in 1997. The grating period was 350 nm, the Littrow blaze angle was 30\({}^{\circ}\), the duty cycle was 0.5, and the groove depth was 600 nm. The theoretical diffraction efficiency of \(-1\) order under TE polarization was 98%. Interference lithography and ion-beam etching were used to create the transmission grating. Except for a 4% shift near the peak, the grating diffraction efficiency was extremely close to the predicted efficiency. The grating diffraction efficiency was 94%. The transmission grating's anti-laser-damage threshold was evaluated using a 3 ns pulse Nd:YAG laser. The grating was positioned at a 30\({}^{\circ}\) angle to the TE polarized beam. The anti-laser-damage thresholds were 13.2 J/cm\({}^{2}\) from both the front and rear surfaces. The computed findings matched the experimental readings rather well. In 2003, [PERSON], [PERSON], et al. [49] designed and fabricated a high-efficiency fused-silica transmission grating in the 1064 nm band with a grating period of 800 nm, an incident angle of 41.5\({}^{\circ}\) under the Littrow structure, a groove depth of 1540 nm, and a duty cycle of 0.45. The highest diffraction efficiency was 97%. Manufacturing tolerances allowed