esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Results and Discussion
### Dynamic Mechanical Properties of Polyurea
#### 4.1.4 Effects of Excitation Frequency  
Figure 10a presents the force-displacement characteristics of a \(\phi\)80 mm \(\times\) 10 mm polyurea sample subjected to a 300 N preload and 0.2 mm excitation amplitude at varying frequencies. The resulting dynamic stiffness and damping properties are plotted in Figures 10b and 10c, respectively.  
Figure 10a shows that as the excitation frequency increases, the area enclosed by the force-displacement curve expands, indicating enhanced energy dissipation capacity. Correspondingly, Figure 10c demonstrates a progressive rise in the damping coefficient with frequency, with the rate of increase accelerating. Simultaneously, the slope of the force-displacement curve steepens, reflecting an increase in the dynamic stiffness of the polyurea sample. As depicted in Figure 10b, when the excitation frequency increases from 0.1 Hz to 2 Hz, the dynamic stiffness grows from 1270.19 N/mm to 1732.17 N/mm, yet the rate of stiffness augmentation gradually declines. Consequently, to ensure accurate prediction of damping performance and the vibration isolation system's shock resistance and isolation effectiveness, polyurea samples should be tested under low-frequency excitation conditions.
## 3 Problem Definition  
Services provided in MANET are afforded by the broker available in the middle. Based on the cluster head algorithm, a single broker can be selected to transfer the benefits to the service requester and provider in a centralized system. As a result, it is more prone to a single point of failure. However, a multiple broker-selection mechanism converts the centralized system into a decentralized system that might eradicate the single point of failure. The service traffic will increase with respect to the link failure between the requester or provider and the broker. By using ZRP [27], a region can be formed and transfer services to different zones in a network. The zones in the architecture become overlapped, while the clusters will not become overlapped in the network. The ZRP requires more control messages to be transmitted for updating the routing table. So, we need cluster-based architecture and a dynamic broker based on QoS metrics to avoid and overcome link failure as well as balance the network load.  
The cluster-based dynamic broker architecture is required to recover from link failure and provide reliability to the network. More than one dynamic broker is selected, which provides the decentralized model. When the link fails between brokers, it automatically redirects to another broker. The dynamic broker in our proposed architecture is selected based on the QoS metrics. We need a protocol based on the QoS metrics to choose the broker in a cluster architecture. The dynamic broker is determined based on the QoS metric's value calculated by each mobile node, providing a secure transfer of services from one cluster to another cluster by the AODV protocol. The proposed system architecture using QoSSDSB consists of four modules:  
1. Cluster formation of mobile nodes;
2. Routing protocol;
3. Dynamic broker selection;
4. Secure broker selection.  
The working process of the proposed methodology with four modules is discussed in detail in Section 5.
## 3 Experimental Results and Analysis  
### Microstructure Analysis  
Figure S1 (in Supplementary Material) illustrates the surface morphology of 20 steel subjected to laser cleaning at varying laser energy densities and spot overlap rates. Figure 2c-f depict the micromorphology of the surfaces cleaned at a spot overlap rate of 75% with different laser energy densities. The uncleaned original sample displays a non-smooth corrosion layer surface (Figure 2a) characterized by an abundance of protruding oxides (Figure 2b). At a laser energy density of 1.42 J/cm\({}^{2}\) (Figure 2c), there is a notable reduction in surface roughness, leaving only a few small pits. Increasing the laser energy density to 2.84 J/cm\({}^{2}\) results in the detachment of parts of the corrosion layer (Figure 2d), although metal oxides remain on the surface. Further escalation of the laser energy density to 4.26 J/cm\({}^{2}\) (Figure 2e) smoothens the material surface, effectively removing noticeable oxides and demonstrating superior cleaning efficacy. However, at a laser energy density of 5.68 J/cm\({}^{2}\), the excessive energy inflicts damage to the substrate, which is evidenced by a clear melting phenomenon and the formation of irregular craters on the sample's surface.  
In this study, Energy-Dispersive X-ray Spectroscopy (EDS) was employed to quantify the oxygen content on metal surfaces, serving as an indicator of the extent of corrosion layer removal. As depicted in Figure 3a, the oxygen content of samples subjected to laser cleaning at varying laser energy densities and spot overlap rates was analyzed. The findings demonstrate that an elevation in both laser energy density and spot overlap results in a reduction in oxygen content. This reduction is attributed to the enhanced capability of the laser in removing the corrosion layer due to the increased parameters. However, excessively high energy densities and spot overlap rates can cause laser-induced damage to the substrate. Particularly in an air environment, such damage is further exacerbated by oxidation of the substrate material. Consequently, it is observed that an increase in laser energy density from 4.26 to 5.68 J/cm\({}^{2}\) paradoxically increases the surface oxygen content. A similar trend is noted when the spot overlap rate is raised from 75% to 80%.  
Figure 2: Micomorphology of 20 steel surfaces cleaned by changing the laser fluence: (**a**,**b**) Untreated sample surface, (**c**) 1.42 J/cm\({}^{2}\), (**d**) 2.84 J/cm\({}^{2}\), (**e**) 4.62 J/cm\({}^{2}\), (**f**) 5.68 J/cm\({}^{2}\).
# Evaluating Novel Speech Transcription Architectures on the Spanish RTVE2020 Database +
## 5 Results and Resources
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**TV Program** & **Multistream CNN** & **CNN-TDNN-F** & **Q15\(\times\)5** & **Q5\(\times\)5** & **Wav2 vec2.0** \\ \hline \hline \multicolumn{1}{l}{See programa del que Ud. habla} & 23.64 & 25.67 & 29.65 & 36.15 & 26.81 \\ \hline \hline \multicolumn{1}{l}{Los desayunos de RTVE} & 9.26 & 10.11 & 12.14 & 14.68 & 11.08 \\ \hline \hline \multicolumn{1}{l}{Neverfilms} & 19.81 & 24.21 & 29.03 & 37.82 & 28.05 \\ \hline \hline \multicolumn{1}{l}{Si fueras tti} & 24.57 & 29.31 & 36.76 & 46.73 & 36.43 \\ \hline \hline \multicolumn{1}{l}{Bajo la red} & 22.41 & 33.31 & 32.99 & 41.06 & 32.33 \\ \hline \hline \multicolumn{1}{l}{Comando actualidad} & 22.58 & 24.68 & 27.34 & 32.70 & 25.6 \\ \hline \hline \multicolumn{1}{l}{Boca norte} & 32.07 & 37.94 & 43.16 & 52.92 & 40.37 \\ \hline \hline \multicolumn{1}{l}{Wake-up} & 30.87 & 33.96 & 40.81 & 47.71 & 38.19 \\ \hline \hline \multicolumn{1}{l}{Version espanola} & 16.14 & 18.10 & 19.15 & 25.66 & 18.06 \\ \hline \hline \multicolumn{1}{l}{Aqui la tierra} & 14.90 & 16.48 & 19.69 & 24.68 & 17.67 \\ \hline \hline \multicolumn{1}{l}{Mercado central} & 16.44 & 17.83 & 25.43 & 34.05 & 21.91 \\ \hline \hline \multicolumn{1}{l}{Vaya crack} & 19.22 & 19.96 & 28.43 & 30.16 & 20.80 \\ \hline \hline \multicolumn{1}{l}{Cómo nos reaimos} & 46.17 & 48.53 & 54.33 & 61.41 & 53.20 \\ \hline \hline \multicolumn{1}{l}{Impresciindibles} & 30.44 & 34.45 & 37.12 & 44.94 & 29.52 \\ \hline \hline \multicolumn{1}{l}{Millenium} & 16.02 & 15.98 & 17.30 & 18.82 & 17.57 \\ \hline \hline \multicolumn{1}{l}{**Global**} & **17.60** & 19.27 & **22.96** & 28.42 & **20.68** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Total WER of the ASR systems on each TV program of the RTVE2020 test set. compared to the other TV shows. In contrast, in more complicated contents like _Como nos Reiamos, Boca Norte_ or _Wake-up_, which include many segments with spontaneous and acted speech, acoustically adverse conditions and overlapping, the results degrade appreciably in all ASR engines.
## 2 Stability Analysis of Haptic Interaction
### Virtual Spring  
The simplest haptic effect involves the implementation of an elastic force with stiffness coefficient \(K\), which is \(C(z)=K\). In this case, the characteristic equation of the system will be a second-order polynomial in the complex variable \(z\):  
\[1+K\frac{z(e^{-\delta}-1+\delta)+1-(1+\delta)e^{-\delta}}{(z-1)(z-e^{-\delta} )\frac{b^{2}}{m}}=0 \tag{4}\]  
\[(z-1)(z-e^{-\delta})\frac{b^{2}}{m}+K\left[z(e^{-\delta}-1+\delta)+1-(1+ \delta)e^{-\delta}\right]=0 \tag{5}\]  
The Routh-Hurwitz criterion is applied following a bilinear transformation in order to analyze the stability of the system [14]. Consequently, the range of stable values of \(K\) will be:  
\[0<K<\frac{b^{2}(e^{\delta}-1)}{me^{\delta}-m-Tb} \tag{6}\]  
This expression contains two conditions that stiffness \(K\) must satisfy as upper and lower limits. The dimensionless parameter \(\delta\) is very low in haptic systems [15] and, thus, the following Taylor series can be used in order to obtain some approximations as follows:  
\[e^{\delta}=1+\delta+\frac{1}{2}\delta^{2}+\frac{1}{6}\delta^{3}+O(\delta^{4}) \tag{7}\]  
Using the Taylor series (7), a good approximation of the previous stability condition (6) is:  
\[0<K<\frac{2b}{T} \tag{8}\]  
\[0<\alpha<2\delta \tag{9}\]  
where _dimensionless virtual stiffness_\(\alpha\) is defined, as follows:  
\[\alpha=\frac{KT^{2}}{m} \tag{10}\]  
The results that are obtained from this section are very well known in literature [14; 16; 17]. If physical damping \(b\) is low, then the upper limit in (8) will also be relatively low. In this case, there is little room to simulate rigid virtual springs without the addition of other virtual effects.
# A Low-Light Sensor Image Enhancement Algorithm Based on HSI Color Model
## 4 Experiments Results
### Comparison with State-of-the-Art Methods
#### 4.4.2 Evaluation on Real-Word Dataset
However, according to the three objective parameters, except the information entropy in comparison with LIME algorithm, the proposed approach outperforms other methods for image enhancement. Now, for further verification and comparing the performance of the proposed algorithm and the algorithm for direct RGB image enhancement, we implement two groups of control experiments on the test dataset LIVE1 after training 50 Epochs under the condition of BN and without BN. And then we record the average PSNR and SSIM obtained during the network testing in each Epoch as shown in the Figure 10.  
As seen in Figure 10, the HSI training method converges rapidly in comparison with direct enhancement of the RGB image and it gets the greater values in average for PSNR and SSIM with BN or without BN. At the same time, it can also be seen that the batch normalization can also improve the convergence speed of the network training as well. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline Method & HE & Dong & SRIE & LIME & Ours \\ \hline entropy & 7.1412 & 6.9541 & 6.9542 & 7.2612 & 7.1425 \\ Chromaticity change & 0.2474 & 0.0313 & 0.0045 & 0.0124 & 0.0032 \\ LOE & 571 & 1484 & 972 & 1390 & 378 \\ VIF & 0.4782 & 0.4262 & 0.6153 & 0.3444 & 0.7356 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Objective evaluation index of different algorithms for real low-light images.
## 4 Results
### Application of FR Model
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Factors** & **Class** & **Percentage of Domain** & **Percentage of Landslides** & **FR** & **Wj** \\ \hline STI & \textless{}10 & 55.157 & 63.830 & 1.157 & 0.024 \\  & 10–20 & 22.491 & 22.695 & 1.009 & \\  & 20–30 & 9.447 & 4.255 & 0.450 & \\  & 30–40 & 4.524 & 3.546 & 0.784 & \\  & \textgreater{}40 & 8.381 & 5.674 & 0.677 & \\ Distance to roads (m) & \textless{}300 & 11.010 & 23.404 & 2.126 & 0.065 \\  & 300–600 & 8.951 & 11.348 & 1.268 & \\  & 600–900 & 7.852 & 5.674 & 0.723 & \\  & 900–1200 & 7.036 & 10.638 & 1.512 & \\  & \textgreater{}1200 & 65.151 & 48.936 & 0.751 & \\ Distance to rivers (m) & \textless{}200 & 16.686 & 19.149 & 1.148 & 0.003 \\  & 200–400 & 14.837 & 15.603 & 1.052 & \\  & 400–600 & 13.695 & 12.766 & 0.932 & \\  & 600–800 & 12.002 & 13.475 & 1.123 & \\  & \textgreater{}800 & 42.781 & 39.007 & 0.912 & \\ Distance to faults (m) & \textless{}1000 & 21.510 & 22.695 & 1.055 & 0.022 \\  & 1000–2000 & 16.106 & 12.766 & 0.793 & \\  & 2000–3000 & 13.198 & 14.894 & 1.129 & \\  & 3000–4000 & 11.168 & 5.674 & 0.508 & \\  & \textgreater{}4000 & 38.019 & 43.972 & 1.157 & \\ Lithology & Group 1 & 11.627 & 19.149 & 1.647 & 0.117 \\  & Group 2 & 0.054 & 0.000 & 0.000 & \\  & Group 3 & 4.383 & 1.418 & 0.324 & \\  & Group 4 & 12.756 & 4.255 & 0.334 & \\  & Group 5 & 0.239 & 0.000 & 0.000 & \\  & Group 6 & 3.453 & 0.000 & 0.000 & \\  & Group 7 & 7.231 & 3.546 & 0.490 & \\  & Group 8 & 10.228 & 7.092 & 0.693 & \\  & Group 9 & 8.846 & 6.383 & 0.722 & \\  & Group 10 & 1.254 & 0.709 & 0.566 & \\  & Group 11 & 13.945 & 22.695 & 1.627 & \\  & Group 12 & 25.982 & 34.752 & 1.338 & \\ Rainfall (mm/yr) & \textless{}900 & 6.069 & 5.674 & 0.935 & 0.111 \\  & 900–1000 & 18.642 & 20.567 & 1.103 & \\  & 1000–1100 & 9.029 & 16.312 & 1.807 & \\  & 1100–1200 & 10.544 & 24.823 & 2.354 & \\  & 1200–1300 & 8.680 & 11.348 & 1.307 & \\  & 1300–1400 & 20.159 & 12.766 & 0.633 & \\  & 1400–1500 & 11.247 & 4.965 & 0.441 & \\  & 1500–1600 & 8.670 & 2.128 & 0.245 & \\  & 1600–1700 & 4.343 & 0.709 & 0.163 & \\  & \textgreater{}1700 & 2.618 & 0.709 & 0.271 & \\ Soil & \textless{} Atc & 11.538 & 14.184 & 1.229 & 0.326 \\  & CMd & 3.647 & 2.837 & 0.778 & \\  & CMe & 7.992 & 21.986 & 2.751 & \\  & FLc & 1.186 & 0.000 & 0.000 & \\  & LVh & 70.808 & 56.738 & 0.801 & \\  & LVv & 0.322 & 0.000 & 0.000 & \\  & PLe & 0.475 & 2.128 & 4.479 & \\  & RGc & 2.630 & 0.709 & 0.270 & \\  & RGe & 1.403 & 1.418 & 1.011 & \\ NDVI & \textless{}0.21 & 0.21 & 2.161 & 2.837 & 1.313 & 0.128 \\  & 0.21–0.36 & 6.660 & 7.092 & 1.065 & \\  & 0.36–0.44 & 20.845 & 44.681 & 2.144 & \\  & 0.44–0.52 & 34.881 & 39.716 & 1.139 & \\  & 0.52–0.65 & 35.454 & 5.674 & 0.160 & \\ Land use & Farmland & 28.826 & 60.993 & 2.116 & 0.311 \\  & Forestland & 30.974 & 2.837 & 0.092 & \\  & Forestland & 38.500 & 36.170 & 0.939 & \\  & Water & 0.603 & 0.000 & 0.000 & \\  & Residential areas & 1.075 & 0.000 & 0.000 & \\  & Bare land & 0.022 & 0.000 & 0.000 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._
# Train-Induced Vibration Analysis and Isolation Trench Measures in Metro Depot Structures
## 4 Study on Vibration Isolation Trench Measures for Depot
### The Effect of Open Trench Width on Vibration Isolation  
The width of open trenches in the depot is restricted by the distance between the track and adjacent structural columns. Therefore, without altering the normal structural layout of the depot, the trench widths in this study were set to 0.5 m, 1 m, and 1.5 m. The trench depth and distance were uniformly set to 6 m and 2.4 m, respectively. The effect of different trench widths on the vibration isolation performance was investigated. Figure 21 shows the vibration acceleration attenuation coefficients of slab 1 on the 1 st, 4 th, 6 th, and 9 th floors under the three trench widths. It can be seen from Figure 21 that, as the trench width increases, the acceleration attenuation coefficients in the 1-10 Hz vibration frequency range remain nearly the same. In the 10-200 Hz frequency range, the acceleration attenuation coefficients show slight fluctuations but do not exhibit a clear trend of enhancement or reduction. The vibration isolation effects of the trenches under the three conditions show little difference.  
Figure 22 shows the Z-vibration levels of slab 1 on floors 1-9 under three different trench widths. When the trench width is 0.5 m, the Z-vibration levels of the slabs decrease by 11.0-17.2 dB. When the trench width is 1.0 m, the Z-vibration levels decrease by 13.9-18.4 dB. When the trench width is 1.5 m, the Z-vibration levels decrease by 12.3-16.7 dB. The available space within the depot area is limited, making it impossible to set excessively large trench widths. Based on the attenuation of floor acceleration and the reduction in Z-vibration levels under three working conditions, it can be observed that changes in trench width within the range of 0.5-1.5 m have a relatively minor effect on vibration isolation performance. Therefore, in practical engineering trench excavation, the trench width should be determined by balancing economic excavation costs and construction difficulty.  
Figure 21: Influence of open trench width on floor acceleration: (**a**) 1 st floor; (**b**) 4 th floor; (**c**) 6 th floor; (**d**) 9 th floor.
## 4 Results and Discussion
### Chemical Partitioning
The proportions of As, Cr, Pb, and Sb linked to reducible soil components (F2) of the amended plot were found to be significantly low relative to the control soil (\(p<0.01\)), while those of Cu, Zn, Ni, and Cd showed a significant increase (\(p<0.01\)). These findings indicate that iron oxyhydroxides were potentially responsible for retention of considerable levels of contaminants in soil after amendment, either by adsorption or coprecipitation processes [11]. In general, the percentages of PHE extracted from the treated soil sample under oxidizing conditions (F3) were significantly higher (\(p<0.01\)) than those of the control sample, with the exception of Pb and Tl. The increase was particularly noteworthy for Cu and Ni, suggesting that a considerable proportion of them (up to 22%) seem to be bound to naturally occurring organic substances derived from plants growing on the amended soil. In brief, most Pb, As, Sb, Tl, and Cr were found accumulated in the residual fraction (F4) of both treated and untreated soil; the fractionation patterns of Cu and Ni were fairly similar as they appear more or less evenly distributed among F2, F3, and F4 fractions; and Cd and Zn seemed preferentially partitioned among the most labile compartments (F1 and F2).
# LoRaWAN Base Station Improvement for Better Coverage and Capacity
## 3 Design of LoRaWAN Base Station  
### Standard LoRaWAN Base Station  
The implementation of the LoRaWAN base station is based on [33] where a Raspberry Pi is used as a microcomputer and certified LoRaWAN board iC880A [34] as a concentrator. Raspberry Pi 4B is high-performance microcomputer with large support community, while iC880A concentrator is able to receive messages sent with different spreading factors on up to 8 channels in parallel. In the model, an omnidirectional antenna [35] with a frequency  
Figure 1: Correlation of LoRa spreading factor and symbol duration is given with 2\({}^{SF}\)/BW. Using higher spreading factor means longer symbol duration which provides better transmission, but decreases data rate.  
range between 824 and 896 MHz (for EU868 region) is connected to the concentrator, and concentrator to the microcomputer using Serial Peripheral Interface (SPI). The developed base station is registered to The Things Network (TTN) Server [36]. The radiation pattern of the omnidirectional antenna used in standard single antenna base station is given in Figure 2a).
## 3 Results and Discussion  
### PLSR by Preprocessing Using Savitzky-Golay Smoothing  
Table 2 shows the results of PLSR analysis with SG smoothing applied to the dry and wet soil samples for the VIS and NIR spectral regions. In PLSR analysis, the number of factors affects the results, so the regression model of wet soil was developed with two  
factor counts: the number of appropriate factors and the same number of factors in the dry soil regression model. The evaluation of the regression model was performed based on the RPD value using the method created by [PERSON] et al. (2017) ([PERSON] et al., 2017) ([PERSON] et al., 2017). The results of PLSR analysis with preprocessing SG smoothing for dry clay showed RPD values of pH, EC, SOM, TN, TOC, and clay of 1.43-1.87, 1.30-1.60, 1.17-1.38, 1.26-1.43, 1.16-1.39, and 1.67-1.90, respectively, and all the properties except clay were evaluated as the best in the VIS spectral region. In addition, pH, EC, TN, and clay met the evaluation criteria for a fair model. The PLSR analysis of wet soil showed RPD values of pH, EC, SOM, TN, TOC, and clay of 1.09-1.16, 1.09-1.11, 1.05-1.06, 1.09-1.18, 1.01-1.03, and 1.12-1.15, respectively, which, with the exception of the SOM and clay, were the best values in the NIR region. With the right number of factors, the RPD values of pH, EC, SOM, TN, TOC, and clay were 1.13-1.26, 1.10-1.11, 1.06-1.07, 1.07-1.18, 1.03-1.07, and 1.15-1.23, respectively, while the predictive regression model for all the properties had the highest statistical value in the NIR region. However, both the regression models with the same number of factors as clay and the right number of factors were rated as poor models. The model with an appropriate number of factors showed increasing R\({}^{2}\) and RPD values for the soil properties, which were compared to those of the model with the same number of factors as dry soil, for which the RPD values increased by at least 1% and up to 9%. However, in the case of TN, the RPD
# Compact MIMO System Performances in Metallic Enclosures
## 4 Experimental Results and Discussions  
In this section, we present near-field MIMO BER and EVM measurement results in different scenarios. Measurements were performed in an empty enclosure in the presence of a static mode stirrer and the near-field MIMO BER and EVM results are presented from when the mode stirrer moved continuously. In the third scenario, we present near-field MIMO BER and EVM measurements in the presence of MIMO interference. MIMO interference is continuously generated using B210 USRP at sampling rates of 400 ksps. Baseband interference signals were generated in the GNU Radio and passed to B210 USRP for the repeated transmission.
# VR Sickness Evaluation Method Using Recurrence Period Density Entropy
## 2 Materials and Methods  
### Proposed VR Sickness Evaluation Method  
In this section, we describe the proposed method. The proposed method consists of two steps and an equation, as illustrated in Figure 1. Step (A) details the preprocessing steps for inputting the ECG data into the RPDE. In Step (B), the preprocessed data are introduced into the RPDE process to illustrate their manipulation. Finally, in Equation (C), the RPDE values are derived from the input of the processed data.  
The data preprocessing step (A) consisted of three processes: ECG feature detection, time-domain-based data binarization, and time series formation.  
First, (A)--1 ECG feature detection. ECG data represent the physiological activity with periodicity, which can be expressed as RR intervals. Various methods can be used to derive time series related to these intervals. However, in this study, we employed a windowing method to extract the maximum values within specific intervals, treating them as R peak points. We used ECG data from the 5 to 15 min period, during which VR sickness primarily occurs, and iteratively extracted R peak points every second from the data. Then, binarization was performed to calculate the heart rate.  
Second, (A)--2 involves time-domain-based data binarization. Once the R peak points were detected, we assigned a true value to the corresponding time points in the time series and a false value to areas where no peaks were detected, thereby binarizing the data.  
Third, (A)--3 is time series formation. We converted these data into a list format, allowing true/false values to be input according to the time series. This format was used as an input for the RPDE algorithm. The second step is RPDE (B), which consists of two processes: state-space embedding and recurrence-period density extraction.  
In (B)--3, we first continuously calculated the data distributions in R(t) and R(t + 1) from a single time series exhibiting periodicity. The calculated data columns were then mapped to the state space to determine when most of the repetitions occurred.  
In steps (B)--3, the number of cycles repeated within a certain time frame (T) was quantified to produce the cycle density value (P(t)). Subsequently, this calculated value was substituted into Equation (C) to derive the RPDE.