esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Materials and Methods
### Regression Model II  
In the next step, we observe the dependence of the apparent sound reduction index on the frequency, the excitation interval and the type of noise. In this case, we consider the output variable \(R^{\prime}\) as a function  
\[R^{\prime}=f(F,I,N) \tag{7}\]  
where \(R^{\prime}\) is the apparent sound reduction index, \(F\) is the frequency (Hz), \(I\) is the excitation interval (dB), and \(N\) is the type of noise used (white or pink noise).  
It is apparent that, for the frequency Interval I (frequency from 50 to 100 Hz), the best regression model has the form (Model IIa)  
\[R^{\prime}=b_{0}+b_{1}F+b_{2}I+b_{3}N \tag{8}\]  
For the frequency Interval II (frequency from 125 to 500 Hz), the best regression model has the form (Model IIb)  
\[R^{\prime}=b_{0}+b_{1}F+b_{2}I \tag{9}\]  
For the frequency Interval III (frequency from 630 to 1000 Hz), the best regression model has the form (Model IIc)  
\[R^{\prime}=b_{0}+b_{1}F \tag{10}\]  
Point estimates of parameters of multiple regression models and values of determination indices are given in Table 4. In all cases, the observed regression model is statistically significant. The parameters of the model are statistically significant as well.  
A graphical representation of the residuals, i.e., the differences between the theoretical values obtained from Regression Model II (Model IIa, Model IIb, Model IIc) and the experimental (measured) values for all excitation intervals, is shown in Figure 8. The most significant differences are in the frequency band up to 100 Hz.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \(\mathbf{b_{0}}\) & \(\mathbf{b_{1}}\) & \(\mathbf{b_{2}}\) & \(\mathbf{b_{3}}\) & \(\mathbf{r^{2*}100\%}\) \\ \hline
**Interval I** & & & & & \\
**Model IIa** & \(-\)12.827 & 0.213 & 0.198 & 2.541 & 77.1 \\ \hline
**Interval II** & & & & & \\
**Model IIb** & 24.511 & 0.024 & 0.033 & - & 75.5 \\ \hline
**Interval III** & & & & & \\
**Model IIc** & 29.810 & 0.008 & - & - & 78.8 \\ \hline \end{tabular}
\end{table}
Table 4: Parameters of Regression Model II.  
The summary of the effect of parameters on the apparent sound reduction index in individual frequency intervals is shown in Table 5.
## 6 Limitations and Future Work  
During this study, several limitations were encountered. First, a small sample size was used to train the algorithms. Despite an imbalance in the number of patients per groups in our study, the incidence of LOS in this high risk population (14/39 patients = 36%) has been reported in number of other papers; thus, we feel that it is not likely to influence the current results as the current analysis does not predict whether an infant has a high risk of getting a LOS, but if vital parameters can predict LOS at an early stage and which technique (linear or non-linear) is superior to detect a LOS. For instance, [PERSON] et al. (2020) used a sample size of 49 patients and [PERSON] et al. (2019) [9] used a sample size of 79 patients. Second, in the same vein as the study of [PERSON] et al. (2020) [8], we found significant differences for gestational age and birthweight. Although we attempted to correct for these significant features using a calibration period of 48 h, it was not ruled out that these significant characteristics still influenced the predictive performance on the models. Third, although we aimed to overcome the class imbalance using the stratified version of K-fold cross-validation, it might still be the case that our algorithm was slightly biased towards the majority class (i.e., the control group). Nevertheless, [PERSON] et al. (2019) [9; 11] also dealt with a similar class imbalance, so, from that perspective, our findings are externally validated. Fourth and related to the previous, it must be noted that our findings are best compared with the work of [PERSON] et al. (2019) [9], who used a similar cross-validation method (i.e., repeated stratified cross-validation).  
On the contrary, [PERSON] et al. (2020) [8] and [PERSON] et al. (2021) [7] used leaving-one-out cross validation, which is known to yield more conservative results. Lastly, not all vital parameters and other LOS related factors that are available were assessed in this study; for instance, blood pressure, motion, clinical signs, and laboratory tests. Therefore, we encourage future scholars to also investigate the effect of other factors when predicting LOS using ML. A future direction is to explore the mean diagnosis of all AI algorithms including hybrid classifier-based particle swarm optimization (PSO) and neural network while keeping and preserving interpretability [34; 35; 36] for the early diagnosis of late onset sepsis.
# Statistical Power Analysis in Reliability Demonstration Testing: The Probability of Test Success
## 3 Calculation of the Probability of Test Success
### General Calculation Procedure  
Due to the possibly very complex sampling schemes and the great variety among reliability tests and their configurations, any general calculation procedure must be very flexible. In order to guarantee such flexibility, a bootstrap [49] approach is used here, as it does not require analytical effort or equation solving prior to the actual calculation taking place. The bootstrap approach is used to estimate the sampling distributions of (6) and  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline Null hypothesis & \(H_{0}:t_{R_{r}}<t_{\text{r}}\) & The reliability requirement is not met \\ \hline Alternative hypothesis & \(H_{1}:t_{R_{r}}\geq t_{\text{r}}\) & The reliability requirement is met \\ \hline Confidence level & \(C=1-\alpha\) & Probability of correctly accepting \(H_{0}\) & Probability of the reliability statement of the test to be correct \\ \hline Probability of Test Success & \(P_{\text{bs}}=1-\beta\) & Probability of correctly accepting \(H_{1}\) & Probability of the test to be successful in demonstrating the reliability requirement \\ \hline \end{tabular}
\end{table}
Table 1: Interpretationof Confidence Level, Probability of Test Success, and Hypotheses in the context of Reliability Demonstration Testing.  
Figure 1: Null distribution \(f_{H_{0}}\), alternative distribution \(f_{H_{1}}\), confidence level \(C\), and Probability of Test Success \(P_{\text{bs}}\) as functions of the test statistic, \(\tau=t_{R_{r}}-t_{\text{r}}\).  
(7) from Figure 1. Because \(f_{H_{0}}\) and \(f_{H_{1}}\) are obtained in empirical form from the bootstrap iterations and used in a parameter-free way, the variance and the entire shape and all of the statistical moments [10; 50] of the distributions are captured. Therefore, no assumption as to the distribution type has to be made.
## 2 System Model
### Channel Model  
We assume that \(H\in\mathbb{C}^{N_{R}\times N_{T}}\) denotes the flat Rayleigh fading channel matrix with two-channel taps that are independent and identically distributed (i.i.d.) and obey Gaussian distribution with unit variance and zero mean, and the elements in noise vector \(\mathbf{n}\) are i.i.d. and have complex Gaussian distribution \(\mathcal{CN}\big{(}0,\sigma^{2}\big{)}\).  
At the BS, the task of the detector is to estimate the transmitted signal vector \(\mathbf{s}\) from the received signal vector \(\mathbf{y}\). According to [20], the conventional linear MMSE detection algorithm has been proven, which is near-optimal for uplink MIMO systems. In addition, the estimate of the transmitted signal vector \(\mathbf{s}\) can be expressed as  
\[\mathbf{s}=\left(H^{H}H+\sigma^{2}I_{N_{T}}\right)^{-1}H^{H}\mathbf{y}=W^{-1} \mathbf{y}^{MF}, \tag{3}\]  
where \(\sigma^{2}\) denotes the variance of the noise vector, \(W\) is the filtering matrix of conventional MMSE, and \(\mathbf{y}^{MF}\) is the output of the matched filter. Within Equation (3), we can observe that the matrix inversion operation is contained in the conventional MMSE detection. Therefore, the computational complexity of conventional MMSE is too high to realize in the MU-MIMO systems, not to mention the massive antennas.  
To estimate the flat Rayleigh fading matrix at the BS, we used a comb-type pilot structure [34], with pilot tones at periodically located subcarriers. Then, we used the least square (LS) channel estimation method [35] to find the channel estimate \(\hat{H}_{LS}\) by pilot tones. The result of LS channel estimation is given by [7]  
\[\hat{H}_{LS}=\left(X^{H}X\right)^{-1}X^{H}Y=X^{-1}Y, \tag{4}\]  
where \(X\) and \(Y\) denote the transmitted signal's pilot tones and the received signal's pilot tones at the subcarriers, respectively.
## 5 Discussion
### Model Limitations and Future Perspectives  
The results indicate that the AUC values for Scenario 2 (0.979) and Scenario 3 (0.986) were significantly higher than the best value for Scenario 1 (0.914), with Scenario 3 achieving the highest AUC. Typically, AUC values ranging from 0.85 to 1 are considered to reflect strong model performance [19]. However, such particularly high values can raise concerns about potential overfitting, which is a common issue in predictive modeling, as highlighted by some researchers' studies [14; 35].  
The manually refined datasets in Scenarios 2 and 3 tend to be more conservative, predicting more high-susceptibility areas. To address the possibility of overfitting, we plan to validate the model further by using cross-validation techniques and external validation datasets in future research. If the model's performance remains consistent across different datasets, the high AUC values could be considered reasonable and indicative of its strong predictive power. On the other hand, if the model significantly underperforms on new data, it would suggest the need for further refinement, such as simplifying the model or incorporating regularization techniques to improve its generalizability. This conservative approach may still be appropriate in specific scenarios--such as route planning for critical infrastructure projects--as it better ensures that high-susceptibility areas are not overlooked.
# Solution for the Mathematical Modeling and Future Prediction of the COVID-19 Pandemic Dynamics
## 4 Prediction of Future Pandemic Evolution
### Identification Model  
#### 4.1.1 Continuous Transfer Function Model  
The next five equations were determined based on real data collected through the National Committee for Special Emergency Situations, as follows:  
\[\mathrm{H_{1}(s)}=\frac{0.08897\mathrm{s}-0.0003917}{\mathrm{s}^{4}+0.7874 \mathrm{s}^{3}+0.01296\mathrm{s}^{2}+0.0003136\mathrm{s}+1.395\mathrm{\cdot}10^ {-5}}, \tag{25}\]  
\[\mathrm{H_{2}(s)}=\frac{0.0087\mathrm{s}+7.098\mathrm{\cdot}10^{-5}}{\mathrm{ s}^{4}+0.004978\mathrm{s}^{3}+0.01069\mathrm{s}^{2}+2.571\mathrm{\cdot}10^ {-5}\mathrm{s}+1.345\mathrm{\cdot}10^{-5}}, \tag{26}\]  
\[\mathrm{H_{3}(s)}=\frac{-0.004716\mathrm{s}+9.113\mathrm{\cdot}10^{-5}}{\mathrm{ s}^{4}+0.01741\mathrm{s}^{3}+0.0108\mathrm{s}^{2}+0.0001057\mathrm{s}+2.951 \mathrm{\cdot}10^{-6}} \tag{27}\]  
\[\mathrm{H_{4}(s)}=\frac{-0.0009913\mathrm{s}+5.405\mathrm{\cdot}10^{-5}}{ \mathrm{s}^{4}+0.01583\mathrm{s}^{3}+0.01108\mathrm{s}^{2}+8.476\mathrm{\cdot }10^{-5}\mathrm{s}+7.494\mathrm{\cdot}10^{-6}} \tag{28}\]  
\[\mathrm{H_{5}(s)}=\frac{-0.0003472\mathrm{s}-8.991\mathrm{\cdot}10^{-5}}{ \mathrm{s}^{4}+0.04924\mathrm{s}^{3}+0.02067\mathrm{s}^{2}+0.0003081\mathrm{s }+5.897\mathrm{\cdot}10^{-5}} \tag{29}\]  
The significance of the transfer functions is:  
* \(\mathrm{H_{1}(s)}\)--transfer function correlating inside temperatures with the number of new cases.
* \(\mathrm{H_{2}(s)}\)--transfer function correlating outside temperatures with the number of new cases.
* \(\mathrm{H_{3}(s)}\)--transfer function correlating humidity with the number of new cases.
* \(\mathrm{H_{4}(s)}\)--transfer function correlating number of tests with the number of new cases.
* \(\mathrm{H_{5}(s)}\)--transfer function correlating quantified values of COVID-19 measures with the number of new cases.  
Each of these transfer functions provides relevant distinct information between a specific input affecting the spread of the disease and the outcome, the number of new cases.
## 3 Results
### Inclination and Load Position Interaction  
The statistically significant interaction of incline factor and load position was found in the stance phase (\(F\) = 4.29, \(p\) = 0.02, \(\eta_{p}\)\({}^{2}\) = 0.10), swing phase (\(F\) = 4.18, \(p\) = 0.02, \(\eta_{p}\)\({}^{2}\) = 0.09), gait cycle (\(F\) = 12.67, \(p\) < 0.001, \(\eta_{p}\)\({}^{2}\) = 0.24) and cadence (\(F\) = 16.88, \(p\) < 0.001, \(\eta_{p}\)\({}^{2}\) = 0.30). The interactions are graphically presented in Figure 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Backpack in Hand**} & **Backpack** & **Without Backpack** \\  & & **on Shoulder** & **(Control Trial)** \\ \cline{2-4}  & **Mean** & **Mean** & **Mean** \\  & **(95\% CI)** & **(95\% CD)** & **(95\% CI)** \\ \hline
**Single Support [\%]** & & & \\ \hline Unloaded Side & 30.38 & 29.84 & 31.18 \\  & (29.65, 31.11) & (29.09, 30.59) & (30.46, 31.91) \\ \hline Loaded Side & 30.40 & 30.13 & 31.40 \\  & (29.68, 31.13) & (29.37, 30.88) & (30.61, 32.18) \\ \hline
**Double Support [\%]** & & & \\ \hline Unloaded Side & 39.46 & 40.31 & 37.43 \\  & (38.07, 40.85) & (38.92, 41.71) & (35.95, 38.91) \\ \hline Loaded Side & 39.44 & 39.86 & 37.45 \\  & (38.04, 40.84) & (38.39, 41.34) & (35.97, 38.93) \\ \hline
**Gait Cycle [s]** & & & \\ \hline Unloaded Side & 1.12 & 1.13 & 1.14 \\  & (1.08, 1.17) & (1.09, 1.18) & (1.09, 1.18) \\ \hline Loaded Side & 1.12 & 1.13 & 1.14 \\  & (1.08, 1.17) & (1.08, 1.17) & (1.09, 1.18) \\ \hline
**Cadence [step/min]** & & & \\ \hline Unloaded Side & 108.72 & 107.70 & 107.00 \\  & (104.49, 112.95) & (103.62, 111.77) & (103.21, 110.79) \\ \hline Loaded Side & 108.61 & 108.21 & 107.07 \\  & (104.58, 112.65) & (104.17, 112.26) & (103.29, 110.84) \\ \hline \hline \end{tabular}
\end{table}
Table 4: _Cont._The stance phase and swing phase were different (\(p<0.001\)) when comparing level walking and uphill walking in all three load positions. There were no statistically significant differences in terms of stance phase between hand position and no load when participants walked on the level treadmill. There were also no differences in terms of swing phase between hand position and shoulder position when participants walked uphill. Other comparisons of stance and swing phases between trials of different load positions, apart from those mentioned earlier, were statistically significant (\(p<0.05\)) (Figure 3).  
The gait cycle and cadence were different (\(p<0.05\)) when comparing level walking and uphill walking in all three load positions. There were no statistically significant differences in the gait cycle between the shoulder position and no load when participants walked on a level treadmill and with an incline. There were also no changes in terms of cadence between shoulder position and no load when participants walked on the level. The remaining comparisons of gait cycle and cadence between trials of different load positions, apart from those mentioned above, were statistically significant (\(p<0.05\)) (Figure 3).
## 2 LiCSAR System Architecture
### LiCSAR FrameBatch Processing
#### 2.3.2 FrameBatch Processing Chain  
After the data preparation step, we generate frame batch processing job definitions. First, epochs covering the requested time period are identified based on LiCSInfo database entries (selecting ingested files that contain bursts related to the frame definition). The epochs are then distributed into processing job definitions for LiCSAR processing steps: SLC generation, coregistration into RSLC, generating interferograms and unwrapping. A maximum of 5 job definitions per step are generated for cases where processing covers the last 3 months (i.e., covering up to 15 epochs, thus distributed into processing of up to 3 epochs per job); a maximum of 20 jobs per step are generated in case of larger requested time scales. A special LiCSBatch database interconnected to LiCSInfo is used--it contains tables allowing us to identify epochs related to each job definition and to keep track of the progress of jobs. The interferogram generation and unwrapping steps are set to create the standard set of combinations of every epoch with the four preceding epochs.  
After the LiCSBatch cache is ready, the processing jobs are started in parallel. Follow-up steps only begin once the preceding steps are finished for given epochs. The processing jobs are optimised to run for less than 24 h each. Only one processing core is requested per job. Though this approach does not take advantage of the increased effectiveness of parallel processing algorithms (e.g., GAMMA scripts or snaphu), it allows requesting a larger number of parallel jobs in the computing cluster environment.
# Dynamic Path Planning for Vehicles Based on Causal State-Masking Deep Reinforcement Learning
## 4 Causal State-Masking TD3 Algorithm
### Critic Networks  
The main function of the critic network is to evaluate the value of a given state and action, that is, to estimate the state-action value function \(Q(\mathbf{s},\mathbf{a})\). The design of the critic network follows the standard TD3 algorithm structure. We utilize a twin-value network architecture, employing two independent critic networks \(Q_{\phi_{1}}\) and \(Q_{\phi_{2}}\), represented by parameters \(\phi_{1}\) and \(\phi_{2}\), respectively [42]. The purpose of this is to reduce the bias in value estimation by using two independent estimates, enhancing algorithm performance. The inputs to the critic networks include the original state \(\mathbf{s}\) and action \(\mathbf{a}\), and the outputs are the corresponding Q-values \(Q_{\phi_{j}}(\mathbf{s},\mathbf{a})\), \(j=1,2\). During the update process of the value networks, we define target value networks \(Q_{\phi_{j}^{\prime}}\), whose parameters are obtained from the main network parameters \(\phi_{j}\) through a soft update method. We define the loss function of the value network \(L_{\text{critic}}^{j}(\phi_{j})\) as  
\[L_{\text{critic}}^{j}(\phi_{j})=\frac{1}{N}\sum_{i=1}^{N}\Bigl{(}Q_{\phi_{j}}( \mathbf{s}_{i},\mathbf{a}_{i})-y_{i}\Bigr{)}^{2} \tag{19}\]  
where \(y_{i}\) is the target Q-value:\[y_{i}=r_{i}+\gamma\min_{j=1,2}Q_{\phi_{j}}(\mathbf{s}_{i}^{\prime},\mathbf{a}_{i}^ {\prime}) \tag{20}\]  
where \(\gamma\) is the discount factor and \(\mathbf{\hat{a}}_{i}^{\prime}\) is the target action. The target Q-value \(y_{i}\) is based on the Bellman equation, which combines the current immediate reward \(r_{i}\) with the discounted cumulative future return, forming a robust learning signal. By taking the minimum value from the two target value networks, we further reduce the overestimation of Q-values.  
The update of the value network aims to minimize the value estimation error so that the critic network evaluates the actor network's policy accurately and reliably. To update the critic network's parameters \(\phi_{j}\), we use gradient descent to minimize the loss function \(L_{\text{critic}}^{j}(\phi_{j})\):  
\[\phi_{j}\leftarrow\phi_{j}-\eta_{\phi}\
abla_{\phi_{j}}L_{\text{critic}}^{j}( \phi_{j}) \tag{21}\]  
where \(\eta_{\phi}\) is the learning rate of the critic network, which determines the step size for each parameter update.
## 2 Design and Simulation Setup
### Design Evaluation  
The proposed design has a split ring resonator (SRR) and a circular ring resonator (CRR) which is shown in Figure 4a. Figure 4b shows the different layers of absorbance properties, whereas the SiO\({}_{2}\) dielectric layer shows there is no absorbance. As a result, all incident waves are transferred through the dielectric substance. Although the addition of a patch on metal results in approximately 63.7% absorbance and the highest incident wave continues to pass through the material. The patch and middle layer show 99.99% of maximum absorbance, but the average absorbance for the patch and middle layer is lower. An average absorbance level of 90.82% is attained throughout the working wavelength when the tungsten (W) is in both the top and bottom planes when a dielectric substrate layer (SiO\({}_{2}\)) is mounted between the top and bottom planes. It's inserted to block the transmission of the incident wave. Moreover, as seen in the design evolution, the geometrical shape of the patch is essential to achieve greater and broader absorbance levels of the suggested MMA. Figure 4c depicts the absorbance properties of different suggested MMA design progressions. The study delves into the vital role that the SRR and CRR of the unit cell perform. In the first step, This model has a peak absorbance of 95.37% at a visible spectrum of 557 nm with no other shape in the center of the unit cell. This configuration has an average bandwidth of 47 nm between 450 and 650 nm. In the meantime, the SRR is stuffed with another square ring resonator.  
Furthermore, the average absorbance between 450 nm and 650 nm is 80% due to the intervention of this square ring resonator, the peak absorbance is 96.02%, and the bandwidth is expanded from 47 to 82 nm. The peak absorbance was increased from 96.2% to 97.4% after the two-square ring resonator was split in the third step. After loading a circular ring resonator, the bandwidth was expanded from 75 nm to 119 nm, and peak absorbance was raised to 99.98% at 555 nm. In these scenarios, its average absorbance is significantly lower than expected. Finally, in the last step, the structure reaches maximum absorbance of 99.99% at a wavelength of 557 nm when two metallic splits are loaded with a circular ring resonator. In addition, the suggested model has an average absorbance of 97.82%, along with sensitivity to polarization and properties relating to the angle of incidence.  
Figure 2: (**a**) Tungsten’s and (**b**) Silicon dioxide’s excitation coefficient and refractive index in the visible optical range.  
Figure 3: Setup of boundary conditions (**a**) PEC and PMC for TEM mode (**b**) Array configuration for TM and TE mode (**c**) The characteristics of the tetrahedral mesh.