esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results
### Performance Comparison
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{2}{c}{**Valve**} & \multicolumn{2}{c}{**Fan**} & \multicolumn{2}{c}{**Pump**} & \multicolumn{2}{c}{**Slider**} & \multicolumn{2}{c}{**ToyCar**} & \multicolumn{2}{c}{**ToyConveyor**} & \multicolumn{2}{c}{**Average**} \\ \cline{2-13}  & **AUC** & **pAUC** & **AUC** & **pAUC** & **AUC** & **pAUC** & **AUC** & **pAUC** & **AUC** & **pAUC** & **AUC** & **pAUC** & **AUC** & **pAUC** \\ \hline \multirow{2}{*}{**AE Baseline**[52] & 66.28 & 50.98 & 65.83 & 52.45 & 72.89 & 59.99 & 84.76 & 66.53 & 78.77 & 67.58 & 72.53 & 67.58 & 73.51 & 65.85 \\ \hline \multirow{2}{*}{**GMADE [7]**} & 99.07 & 96.20 & 83.06 & 79.55 & 87.87 & 82.38 & 97.62 & 89.70 & **95.57** & **91.54** & 81.46 & 66.62 & 90.77 & 84.33 \\ \hline \multirow{2}{*}{**MobileNetV2**[53] & 88.65 & 87.98 & 80.19 & 74.40 & 82.53 & 76.50 & 95.27 & 85.22 & 87.66 & 85.92 & 69.71 & 56.43 & 84.34 & 77.74 \\ \hline \multirow{2}{*}{**Glow\_AFF [8]**} & 91.40 & 75.00 & 74.90 & 65.30 & 83.40 & 73.80 & 94.60 & 82.80 & 92.20 & 84.10 & 71.50 & 59.00 & 85.20 & 73.90 \\ \hline \multirow{2}{*}{**STgram-MFN**[39] & **99.64** & **98.44** & 94.04 & **88.97** & 91.94 & 81.75 & **99.55** & 97.61 & 94.44 & 87.68 & 74.57 & 63.30 & 92.36 & 86.34 \\ \hline \multirow{2}{*}{**AADCL [2]**} & 68.62 & 55.03 & 85.27 & 68.93 & 86.75 & 70.85 & 77.74 & 61.62 & 88.79 & 75.95 & 71.26 & 57.40 & 79.74 & 64.96 \\ \hline \multirow{2}{*}{**Our Method**} & 99.52 & 98.37 & **95.12** & 88.10 & **92.82** & **83.25** & 99.10 & **97.84** & 95.02 & 91.35 & **84.80** & **68.70** & **94.39** & **87.93** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparing RC-MAE with SOTA methods. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **RC-MAE without DDA (pAUC)** & **RC-MAE with DDA (pAUC)** \\ \hline
**Valve** & 98.01 & **98.37** \\ \hline
**Fan** & 87.44 & **88.10** \\ \hline
**Pump** & **83.89** & 83.25 \\ \hline
**Slider** & 97.16 & **97.84** \\ \hline
**ToyCar** & 90.10 & **91.35** \\ \hline
**ToyConveyor** & 65.38 & **68.70** \\ \hline
**Average** & 86.99 & **87.93** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparing RC-MAE with and without Diffusion-Based Data Augmentation (DDA). Figure 4: The t-SNE visualizations of fine-tuned model output features on the Train and Test datasets for the different machine IDs (**a**–**f**); different colors represent different machine IDs. The shape “**a**” and shape “**x**” denote normal and anomalous classes, respectively. Figure 3: The t-SNE visualizations of pre-trained model output features on the Train and Test datasets for the different machine IDs. Different colors represent different machine IDs. The shape “**e**” and shape “**x**” denote normal and anomalous classes, respectively.
## 3 Optical Error Analysis  
The theoretical analysis in Section 2 is based on the idealized assumptions of FTIS and FPI performance. However, in practical implementations, positional and alignment errors in optical components within the FTIS and FPI systems inevitably introduce deviations between measured data and theoretical predictions. The foundational principle of MJI-HI relies on establishing a linear relationship between \(I_{2}\) and \(I_{0}\) in Equation (6) through FPI modulation, which enables the reconstruction of the original interferogram via this linear dependency. It is, therefore, critical to systematically evaluate whether these optical errors compromise the integrity of this linear relationship. In the interferogram \(I_{2}\), the frequency-shifted components can be expressed as follows: \(a_{m}I_{0}(\Delta\pm m\Delta_{FPI})=I_{0}(\Delta)*a_{m}\mathcal{S}(\Delta\pm m \Delta_{FPI})\). Here, \(a_{m}\mathcal{S}(\Delta\pm m\Delta_{FPI})\) serves as the response function for each frequency-shifted component. Analyzing the deviations caused by various optical errors in the response function provides a more intuitive understanding of their impact on the linear relationship and the overall effect on each frequency-shifted component. In the following sections, the interferograms \(I_{0}\), \(I_{1}\), and \(I_{2}\) under different error conditions are denoted as \(I_{0\text{-error}}\), \(I_{1\text{-error}}\), and \(I_{2\text{-error}}\), respectively.
## 3 Case Study
### Assessment Index  
In order to evaluate the several prediction models proposed in this paper effectively, performance evaluation is indispensable. In this study, four commonly used indicators are selected to effectively evaluate the five proposed machine learning models. They are: mean absolute error (\(MAE\)), mean square error (\(MSE\)), root mean square error (\(RMSE\)), and coefficient of determination (\(R^{2}\)), and can be defined by Equations (15)-(18):  
\[MAE=\frac{1}{n}{\sum_{1}^{n}}|y_{i}-p_{i}| \tag{15}\]  
\[RMSE=\sqrt{\frac{1}{n}{\sum_{1}^{n}}(y_{i}-p_{i})^{2}} \tag{16}\]\[MSE=\frac{1}{n}\frac{\sum\limits_{1}^{n}{(y_{i}-p_{i})^{2}}}{1} \tag{17}\] \[R^{2}=1-\frac{\frac{\sum\limits_{i}^{n}{(y_{i}-p_{i})^{2}}}{\sum \limits_{1}^{n}{(y_{i}-\overline{y_{i}})^{2}}}} \tag{18}\]  
where, \(y\) is the actual advance rate value; \(p\) is the predicted value of AR; \(n\) is the ring number; \(y\) is the average value of the AR of each ring; _MAE_, _MSE_, and _RMSE_ are used to calculate the loss between the true value and the predicted value. The smaller they are, the better the model is, and \(R^{2}\) reflects the degree of matching between the predicted value and the true value, and its target value is close to \(1\).
## 4 Experimental Setup and DSP Stack  
### Experimental Setup  
Figure 5a shows the experimental setup. At the transmitter, a continuous wave light was generated by an external cavity laser (ECL) at 1550.2 nm with 15 dBm optical power. The light was then fed into DDMZM (Fujistu FTM7937) with 25 GHz bandwidth. Two channels from the arbitrary waveform generator (AWG, Keysight M8195A) were used to emulate the imbalances of MZM. The sampling rate and bandwidth of AWG were 64 GSa/s and 25 GHz, respectively. For differential driven mode, the peak-to-peak voltage (Vpp) was typically set as 250 mV. For fair comparison, the sum of the Vpp of two channels were kept the same with single-arm driven mode in this experiment. Afterwards, the output waveforms were amplified by a dual-input-dual-output electrical amplifier (EA, CENTELLAX OA4 SMM4). The amplitude ratio or time skew were set through the software. The inset showed the measured optical spectrum of 34 Gbaud Nyquist PAM-6 signals at 0.02 nm resolution. With the help of digital Nyquist shaping, the rectangular spectrum could be observed with symmetric double sidebands. The signal occupied approximately 0.29 nm optical bandwidth, which was equivalent to \(\sim\)36 GHz, including the RRC roll-off. The transmitted fiber link was 20 km SSMF without optical dispersion compensation.  
Figure 4: Calculated transfer function of differential driven mode with (**a**) positive and (**b**) negative skew values \(\tau\) after 20 km SSMF transmission and with (**c**) positive and (**d**) negative skew values \(\tau\) at BTB.  
At the receiver, the erbium-doped fiber amplifier (EDFA) was employed only to compensate for the initial loss of the following attenuator. The noise figure and output power of the EDFA were 5.5-6.0 dB and 2 dBm. The optical-to-electrical conversion was realized by a PD (Picometrix PT-40A) with 40 GHz bandwidth, which was integrated with a trans-impedance amplifier (TIA). Finally, a real-time digital storage oscilloscope (DSO, Lecroy 845 Zi-A), operating at 40 GSa/s, was utilized to capture the received waveform for offline processing later.
## 1 Introduction
### Isotopic Fractionation
The volatilization of ammonia will lead to the enrichment of \(\delta^{15}\)N-NH\({}_{4}\)+ in the remaining ammonium salt, followed by nitrification that may result in the formation of which will further nitrate with enriched \(\delta^{15}\)N [30]. The assimilation process, in which plants utilize ammonium salt, nitrate, and nitrite, will result in extensive isotopic fractionation (usually ranges from \(-27\%\) to \(0\%\)). Theoretically, the fractionation ratio of \(\delta^{15}\)N to \(\delta^{18}\)O caused by assimilation is 1:1 [31]. Biological nitrogen fixation is a major source of nitrogen of surface water. During biological nitrogen fixation process, the molecular nitrogen is converted to ammonia. The \(\delta^{15}\)N value of the nitrogen substances generated by nitrogen fixation is close to that of atmospheric N\({}_{2}\) (\(0\%\)) [32]. However, the organic substances produced by diazotrophs will undergo mineralization or nitrification, which eventually indirectly affect the concentration and \(\delta^{15}\)N value of nitrate. The above-mentioned biochemical processes are easily affected by land-use types, climate, hydrological conditions, and migration pathways. It is important to quantify the influence of these factors on the identification of pollution sources and transformation of tracer nitrogen. The fractionation produced by denitrification is relatively high, while the nitrogen isotopic fractionation is relatively low during nitrification, ammonia volatilization, mineralization, assimilation, and nitrogen fixation. Approximately 72% of the nitrogen entering the river is removed during processes like biological absorption, atmospheric deposition, leakage to the bottom aquifer, and microbial denitrification [33; 34]. Denitrification is the only way to permanently remove nitrogen in the rivers, and it can directly and significantly change the isotope values of nitrates. The denitrification determination and the attenuation mechanism of nitrate are applicable to specific geological and hydrological conditions. The mechanisms of isotopic fractionation would be influenced by land use, vegetation, soils, industry, agriculture, mixed-degree of different sources, and complex transformation processes of the nitrogen cycle. The current researches of isotopic fractionation are limited to qualitative level and they lack a quantitative basis. That is, they can only determine whether isotopic fractionation has occurred, but they cannot analyze the degree of fractionation caused by various biochemical reactions. Therefore, the mechanisms of the related process are still unclear.
## 3 Problem Formulation  
We use \(\alpha=\{\alpha_{1},\,\alpha_{2},...,\,\alpha_{t}\}\) to represent the sequence set of \(T\) positive weights. Furthermore, we introduce a weighting factor for each maritime user \(t\). Then, we analyze the property of the objective function according to the weight value. By introducing the weight value, we can solve the performance optimization and user fairness based on multiple resource blocks [13]. The issue \(W\) aims at maximizing the WAR of the NOMA maritime system:  
\[W=max\sum_{t\in T}\alpha_{t}\sum_{s\in S}C_{t}^{s}(\mathbf{P}_{s}). \tag{7}\]  
\[w1:\sum_{t\in T}P_{t}^{s}\leq P_{max}^{s}; \tag{8}\]  
\[w2:\sum_{t\in T}\sum_{s\in S}P_{t}^{s}\leq P_{max}; \tag{9}\]  
\[w3:|A_{s}|\leq A; \tag{10}\]  
\[w4:P_{t}^{s}\geq 0. \tag{11}\]  
It is noteworthy that Condition \(w1\) restricts the upper power limit of each resource block. In Condition \(w2\), \(P_{\max}\) represents the upper bound of the total power provided by coastal BS. Condition \(w3\) reflects the finite multiplexed maritime users carried by each resource block: \(\mid A_{s}\mid\leq A\). Additionally, Constraint \(w4\) ensures that the offshore user obtains a non-negative allocated power.  
Problem \(W\) can be solved by polynomial decomposition to be equivalent to \(W^{*}\):  
\[W^{*}=max\sum_{s\in S}\sum_{n=1}^{T}\widetilde{o}_{n}^{s}(\widetilde{p}_{n}^{ s})+C. \tag{12}\]  
\[w1^{*}:\widetilde{p}_{1}^{s}\leq P_{max}^{s}; \tag{13}\]  
\[w2^{*}:\sum_{s\in S}\widetilde{p}_{1}^{s}\leq P_{max}; \tag{14}\]  
\[w3^{*}:|A_{s}*|\leq A; \tag{15}\]  
\[w4^{*}:\widetilde{p}_{n}^{s}\geq\widetilde{p}_{n+1}^{s},n\in\{1,\dots,T\}; \tag{16}\]  
\[w5^{*}:\widetilde{p}_{T+1}^{s}=0. \tag{17}\]  
where \(C\) refers to a constant term formula separated from \(W\):\(C=\sum\limits_{s\in S}\alpha_{\beta_{s}(T)}log_{2}(\frac{1}{\widetilde{p}_{s(T)} ^{s}})\). In the following discussion, we leave the constant \(C\) aside and investigate the influence of function \(\sigma_{n}^{s}\) on the optimization results. The modification problem \(W^{*}\) displays a detachable target function in dimensions \(n\in\{1,2,\ldots,T\}\) and \(s\in\{1,2,\ldots,S\}\), respectively. In addition, function \(\varphi_{n}^{s}(\widetilde{p}_{n}^{s})\) depends on the variable of \(\widetilde{p}_{n}^{s}\) only to simplify the optimization workload.  
\[\widetilde{p}_{n}^{s}=\left\{\begin{array}{c}\sum\limits_{m=n}^{T}P_{\beta_{ s}(m)}^{s},n\in\{1,\ldots,T\}\\ 0,n\geq T+1\end{array}\right., \tag{18}\]  
\[\varphi_{n}^{s}(\widetilde{p}_{n}^{s})=\left\{\begin{array}{c}log_{2}(( \widetilde{p}_{1}^{s}+\widetilde{\sigma}_{\beta_{s}(1)}^{s})^{\alpha_{\beta_{s }(1)}})^{B_{S}},n=1\\ log_{2}(\left(\frac{(\widetilde{p}_{n}^{s}+\widetilde{\sigma}_{\beta_{s}(n)}^{ \alpha_{\beta_{s}(n)}})^{\alpha_{\beta_{s}(n)}})^{B_{S}}}{(\widetilde{p}_{n}^ {s}+\widetilde{\sigma}_{\beta_{s}(n-1)}^{\alpha_{\beta_{s}(n-1)}})^{B_{S}}} \right)^{B_{S}},n>1\end{array}\right.. \tag{19}\]  
A detailed description of the equivalent transformation process from Equation (7) to Equation (12) is presented in Appendix A.
## 3 Results and Discussion  
### Event 1 (3 July 2021)  
The event on 3 July 2021 took place in region AR12838, located in zone N24 W88, reaching a higher intensity in the X1.59 type flare, starting at 14:18 UTC and reaching its maximum intensity at 14:29 UTC, ending at 14:34 UTC. Although the event occurred in a location that was not favorable for its study, alterations in the ionosphere can still be found due to the implemented methodology. During the event time period, we have information from six GNSS stations (UTEO, UNPM, OXUM, SPIG, SSNX and UCOE), with an average of five satellites' information for each station during the event hour, with a window from 13:00 UTC to 15:00 UTC. Figure 4 shows the results of the event for only OXPE station (PRN 14), including X-ray irradiance measurements, vTEC, and wavelet details at different levels over a 2-hour period in UTC time. On the other hand, Figure 5 shows the wavelet results for the same event utilizing all six stations. In these, it is possible to identify the event in question; however, at the SSNX station, despite identifying the event, there are signal alterations that are not shown in other receivers, even though they interact with the same satellites. Therefore, for this station, it could be said that this is due to disturbances independent of the solar flare, or even noise from the receiver. Satellite 30 presented alterations at the beginning of the time window for all receivers; nevertheless, it is possible to identify the alterations that occurred due to the solar flare. Satellites 15 and 19 of the SPIG station had a poorer response, making it difficult to clearly identify the event. A possible cause of this could be the location of the station, which is further north than the other stations studied.  
The solar flare occurred on 3 July 2021, but according to the magnetic field and GOES 17 satellite data, the previous day (2 July 2021) was calm (without external disturbances in the ionosphere). Therefore, for comparative purposes, we applied the same algorithms to this quiet day, yielding random and nonsensical alterations as results. This is in contrast to when a solar flare occurs, resulting in disturbances across all stations at a specific time (during the solar flare event). For each of the events, we followed the same procedure, generating a graph for a calm day and another for the event day. In the case of Event 1, Figure 6 presents the obtained results.  
Figure 3: Variations of the Dst index during the events.
## 2 Design of the Permanent Magnet TCV
### Design of the Magnet Coil Winding  
The electromagnetic force can be expressed as (3) as the product of the number of rotations N of the magnetic coil generating magnetic flux and the current I flowing through the magnetic coil.  
\[U=NI \tag{3}\]  
Figure 7 is a simplified representation of a bobbin and a magnetic coil wound around the bobbin. If the inner diameter of the bobbin is B\({}_{i}\), the outer diameter is B\({}_{o}\), the height h, and the diameter of the enamel wire is c\({}_{d}\), the number of coil winding stacks in the bobbin axial direction, n\({}_{c}\), and the number of coil winding stacks in the bobbin radial direction, m\({}_{c}\), are as shown in (4) and (5). The number of coil turns can be expressed as (6) as the product of the number of stacks in the radial and axial directions.  
\[n_{c}=\left(\frac{h}{c_{d}}\right)-1 \tag{4}\]  
\[m_{c}=\frac{w}{c_{d}} \tag{5}\]  
\[N=n_{c}m_{c} \tag{6}\]  
The current flowing in the magnetic coil can be expressed as (7) using the copper wire diameter N\({}_{d}\) excluding the insulating layer of the enamel wire, the resistivity \(\rho\), and the average length l\({}_{ca}\) of the one-turn coil winding [31].  
\[I=\frac{V}{4\rho\left(\frac{laN}{\pi N_{d}^{2}}\right)} \tag{7}\]  
In the magnetic coil design, the design conditions that affect the TCV electromagnetic force are the inner diameter, outer diameter, bobbin height, applied voltage, and the diameter of the enameled wire. Magnetic coil rotation is a factor that affects the electromagnetic force when voltage and resistance are fixed. The conducting and overall diameter were chosen to fill the magnetic coil to the maximum within the bobbin space. Therefore, the design elements of the magnetic coil assembly are shown in Table 1.  
Figure 6: Schematic of the permanent magnet TCV.
# Enhancing Design for Additive Manufacturing Workflow: Optimization, Design and Simulation Tools
## 4 Optimization Strategy
### Numerical Instabilities of TO  
Main numerical instabilities of TO problems are defined in [43] as checkerboard patterns, mesh dependence and local minima solution. The checkerboard pattern describes a periodic pattern of low and high values for the design variable arranged as a checkerboard. This result is undesirable since the material layout is not appropriate. It was shown in [44] that a finite discretized domain with a patch arrangement of average density of \(\
icefrac{{1}}{{2}}\) provides artificial high stiffness when applied to the TO for minimizing compliance. Additionally, [45] concludes that this numerical instability is caused by FEM where the equilibrium equations are only referred to element nodes. Moreover, the use of lower-order elements promotes checkerboard patterns, while higher-order discretization schemes reduce the global effect. In this case, finite-volume theory accomplishes the task to eliminate checkerboards.  
The mesh dependence problem appears when mesh-refinement of the design domain results in different topology instead of better description for boundaries [46]. The solution to both checkerboard-patterns and mesh dependency is the regularization of the domain design by filtering techniques. From the wide spectrum of filtering schemes the most valuable for easy implementation and efficiency are density and sensitivity filters [47]. In the former, the element density is calculated as a weighted average of the neighborhood elements included in the characteristic filter radius; in the latter, standard calculus of element density is used to calculate a weighted average of the neighborhood sensitivities [48].  
Nerveless, it is worth noting that regularization schemes fail in mitigating solutions with a grayscale interface. To obtain pure black and white designs, with a minimum interface, post-processing on the design domain is required through projection schemes like the Heaviside threshold [49]. For example, commercial software Comsol Multiphysics (Comsol Inc., Stockholm, Sweden) englobes filtering and projection schemes in the so-called three-field density representation [50]. The chain of transformations starts from the design domain, then a PDE density filter scheme is applied and the last operation includes a Heaviside projection function to improve the contour boundaries.  
Solving TO problems with penalized interpolation schemes results in non-convex problems, hence obtaining local minima solutions [51]. To prevent this, continuation schemes are typically employed on material and filter parameters. For the SIMP scheme, the continuation strategies solve an initial convex problem, characterized with uniqueness solution, with low value of the penalization parameter. This solution is used as input for consecutive cycles, where this parameter is increased in steps until arriving at adequate values.
## 4 Simulation of Non-Stationary Turbulent Wind Fields for the RSB
### Turbulent Wind Field Simulation for the Main Girder  
The Davenport exponential function model is adopted to be the coherence function for the turbulence simulation of main girder [3]:  
\[\gamma_{ij}(\omega)=\exp\left(-\frac{\lambda\omega\Delta\big{|}i-j\big{|}}{2\pi \overline{U}(Z)}\right)=\xi^{|i-j|} \tag{42}\]  
where  
\[\xi=\exp\left(-\frac{\lambda\omega\Delta}{2\pi\overline{U}(Z)}\right) \tag{43}\]  
In Equations (42) and (43), \(\lambda\) represent the decay factor; \(\Delta\) is the distance between the successive simulated points; \(\overline{U}(Z,t)\) represents the mean wind speed, which can be obtained by averaging the \(\overline{U}(Z,t)\). The mean wind speed profile at the RSB site is consistent with the power law:  
\[\frac{U_{2}}{U_{1}}=\left(\frac{Z_{2}}{Z_{1}}\right)^{\alpha} \tag{44}\]  
where \(U_{1}\) and \(U_{2}\) denote wind speeds at altitude \(Z_{1}\) and \(Z_{2}\), respectively, and \(\alpha\) is a dimensionless exponent which depends on roughness of terrain, taken as measured value 0.12 herein [35]. Based on Equation (36), the explicit form of the lagged decomposed EPSD matrix \(\Lambda\) can be expressed as [36]:  
\[\mathbf{\Lambda}(\omega,t)=\sqrt{S(\omega,t)}\left[\begin{array}{cccc}1&0&0& 0\\ \xi&\sqrt{1-\xi^{2}}&\cdots&0\\ \vdots&\vdots&\ddots&\vdots\\ \xi^{n-1}&\xi^{n-2}\sqrt{1-\xi^{2}}&\cdots&\sqrt{1-\xi^{2}}\end{array}\right] \tag{45}\]  
Here, the Davenport coherence function is adopted and the decay factor is taken as seven. Table 2 lists the detailed information in the simulation.  
Figure 7: Spectrum snapshots of the decomposed EPSD (vertical).  
As shown in Figure 8, 5000 samples (both in Along-wind and Vertical direction) are simulated using the measured EPSDs. Then, the auto-/cross-correlation functions are estimated using the generated samples. The generated wind fields are validated by comparing the estimated correlation functions and the target ones at various time differences \(\tau\), as shown in Figure 9.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Overall length, L (m) & 1490 & Height of simulated points, Z (m) & 69.3 \\ Number of simulated points, n & 19 & Cutoff frequency, \(\omega\)u (rad/s) & 4\(\pi\) \\ Frequency segmentations, N & 4096 & Sample time interval, \(\Delta t\) (s) & 0.25 \\ Number of generated samples & 5000 & Time duration, Tu (s) & 2048 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Details for non-stationary turbulent wind field simulations of main girder.  
Figure 8: The generated samples for the main girder.  
Figure 8 shows that the generated wind samples in along-wind and vertical directions exhibit prescribed non-stationary features. In Figure 9, the estimated auto-correlation functions fit well with the target one, while the discrepancy between the cross-correlation function and the target one is relatively wide. This phenomenon will be improved if many more samples are considered.