esa-sceva/satcom-chunk-collection huggingface dataset:
# Blind Interleaver Parameters Estimation Using Kolmogorov-Smirnov Test
## 2 Materials and Methods
### Rank Distributions of Square Matrices and Linear Dependence of Codewords  
Assume that there is \(l\times l\) square matrices, \(\Lambda\), whose elements follow a uniform distribution. The rank distributions of the \(\Lambda\) are computed as described in [14]. As \(l\) increases, the rank distribution quickly converges to a specific distribution.  
The rank distributions can be calculated as shown in Table 1 when \(l\to\infty\)[15]. \(P_{s}\) is the probability that the rank of a random binary square matrix is \(l-s\). It decreases steeply with increasing \(s\) (\(s>1\)). In Table 1, when \(s>4\), \(P_{s}\) is relatively very small and has no significant effect, so we consider \(P_{s}(s=4)\) as \(P_{s}(s\geq 4)\).  
A totally different probability distribution from that given in Table 1 is obtained when the elements of matrices are not random signals but codewords. In channel coding, an \((n,k)\) linear block code has a generator matrix that has a full rank, where \(n\) is the codeword length and \(k\) is the length of the message. The block code generates codewords and there is linear dependence among codewords because they form a vector space [16].  
Since block codes are typically specified for correcting wide-spread i.i.d. errors over the block, the performance of the receiver deteriorates when burst errors occur. To spread burst errors over the received bitstream, the encoded bits are interleaved by every certain period of time. The interleaving interval is typically a multiple of the codeword length. In other words, the interleaver period can be represented as \(S=\beta n\) where \(\beta\in N+\).  
Given the intercepted symbols, we can divide the bitstream by the length of \(l\) and construct \(\Lambda\). If \(l=S\), the rows of the \(\Lambda\) have a linear dependence because the row elements are composed of codewords. Therefore, the rank distributions of the \(\Lambda\) are far different from that shown in Table 1.  
Based on the linear dependence of the codewords, the ranks of the \(\Lambda\) can be used as a criterion for estimating interleaver periods. This can be used to distinguish the two distributions from matrices consisting of random binary signals and codewords [4; 5; 6].  
\begin{table}
\begin{tabular}{c c} \hline \hline \(\mathbf{s}\) & \(\mathbf{P_{s}}\) \\ \hline
0 & 0.288788 \\
1 & 0.577576 \\
2 & 0.128350 \\
3 & 0.005238 \\
4 & 0.000048 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Rank distribution of the random binary square matrices.  
Figure 2: Illustration of block interleavers when the period of block interleaver \(l_{s}=4\).
## 5 Implementation
### Case Study for First Architecture: Collaborative Virtual Reality with Hand Recognition  
For the first reference architecture mentioned in the previous section, an application was implemented to verify its proper functioning. It is a virtual space where different users can interact with each other or virtual objects. The user's hand represents the connection point between the real and virtual worlds. The operation is as follows: the user places his or her hand, left or right, in front of the camera. This captures the video stream and sends it in real time to the cloud. Here, the Object Creation component deals with virtual hand reconstruction using a rule-based approach, leveraging the Reconstruction of Data component, which identifies 21 different hand landmarks through a specific model called the Hand Landmarks Detection Model [24; 25; 26] (Figure 10).  
Depending on the number of connected users, the arrangement of individual hands within the virtual space changes, as described in the architecture. Collaboration was implemented through two different approaches: the possibility for each user to interact with virtual objects, which, in this scenario, are simple geometric figures embedded in the environment, and the possibility of interaction between multiple users (Figure 11).  
Figure 10: This figure conceptually illustrates the division of the hand into 21 points, allowing real-time tracking of the independent movements of each finger or the entire hand.  
Figure 9: This figure shows the three reference architectures mapped with the most appropriate technologies to implement.
## Appendix A Overview of the SkySat and PlanetScope Push-Frame Imaging System
### SkySat
During the fusion, a super-resolution process is used to increase the resolution from 0.9 m to \(\sim\)0.72 m. Downstream of the super-resolution step, a pan-sharpening process combines the panchromatic and the multispectral bands to create high-resolution 4-band images [5; 47]. The composite L1B imagesare delivered with RPCs derived from external high resolution DEMs and GCPs extracted from ortho-images (i.e., using the terrain-dependent approach, Figure 1). SkySat is an on-demand collection data (i.e., require tasking). Users can specify the collection angles through a web service application \"Tasking Dashboard\" [4].
## 2 Methods and Tools
### Combined Geophysical Methods  
Integrated approaches combining different geophysical methods have proven highly effective for understanding and mitigating sinkhole hazards. For example, the combination of TEM methods with magnetic resonance sounding (MRS) resolves interpretational ambiguities, while integrating MASW with MRS enables the assessment of in situ salt karstification by correlating shear wave velocities with hydraulic conductivity [52]. Similarly, coupling FDEM with TEM enhances the interpretation of resistivity variations, thereby improving the delineation of hazardous zones [53]. These comprehensive geophysical applications have significantly advanced insights into sinkhole mechanisms and facilitated improved hazard assessments.  
Given the complexity of the Dead Sea's geological setting, the integration of multiple geophysical techniques is often indispensable for a thorough understanding of subsurface processes [23; 54]. Ground-based LiDAR surveys, continuous water level monitoring, and geophysical logging have been successfully combined to investigate the formation and drainage mechanisms of submerged sinkholes along the western Dead Sea shores [13; 14]. This multidisciplinary approach has elucidated the intricate links between sinkhole formation, subsurface cavity development, and the mechanical failure of overlying impermeable layers [2; 16].  
The integration of geophysical data with LiDAR-derived surface models and water level monitoring has provided a robust framework for understanding the dynamic processes driving sinkhole evolution [15; 55]. Such studies underscore the importance of employing diverse geophysical methodologies to address the unique challenges posed by the extreme environmental and geological conditions of the Dead Sea [16; 17; 23]. These integrated approaches not only enhance the accuracy of subsurface interpretations but also contribute to more effective risk mitigation strategies.
# DDL R-CNN: Dynamic Direction Learning R-CNN for Rotated Object Detection
## 3 Method
### Dynamic Directional Learning (DDL) Module  
Previous detectors typically rotate convolutional kernels at fixed angles based on prior knowledge, which presents difficulties in dynamically adjusting to targets with diverse orientations. To enable the detector to automatically perceive arbitrary changes in the target direction, a DDL module is proposed. This module has \(n\) kernels \((w_{1},\ldots,w_{n})\), each with the shape \([C_{out},C_{in},k,k]\). It uses the \((\theta,\lambda)\) generated by the routing function to guide the rotation of the convolutional kernels at different angles, thereby extracting more refined spatial features of the target. Finally, the spatial features extracted by these differently rotated convolutional kernels are fused through weighting. Referencing Figure 2, the detailed operations are delineated below:  
Firstly, a set of predicted rotation angles \(\theta=[\theta_{1},\theta_{2},\ldots,\theta_{n}]\) obtained from the routing function is used to rotate each of the \(n\) kernels individually.  
\[w^{\prime}_{i}=\text{Rotate}(W_{i};\theta_{i}),\quad i=1,2,3,\ldots,n,;\quad Rotate (\theta)=\begin{bmatrix}\cos(\theta)&-\sin(\theta)\\ \sin(\theta)&\cos(\theta)\end{bmatrix} \tag{5}\]  
For Equation (5), \(\theta_{i}\) represents the rotation angle of \(w_{i}\), and \(w^{\prime}_{i}\) is the rotated kernel. The Rotate() function rotates the kernel \(w_{i}\) by the predicted angle \(\theta_{i}\). This function defines the counterclockwise (clockwise) direction as positive and uses bilinear interpolation to fill in the sampling locations missing due to rotation.  
These rotated kernels are generally computed by performing convolutions with the input feature map and then summing the resulting feature maps element by element.  
\[y=\lambda_{1}(w^{\prime}_{1}*x)+\lambda_{2}(w^{\prime}_{2}*x)+\cdots+\lambda_{ n}(w^{\prime}_{n}*x), \tag{6}\]  
\(\lambda=[\lambda_{1},\lambda_{2},\ldots,\lambda_{n}]\) are the combination weights predicted by the routing function, \(*\) denotes the convolution operation, and \(y\) is the combined output feature map. However, this approach requires individual convolution operations for each kernel, followed by an addition step, potentially resulting in reduced computational efficiency. Consequently, we reformulate the aforementioned Equation (6) as follows:  
\[y=(\lambda_{1}w^{\prime}_{1}+\lambda_{2}w^{\prime}_{2}+\cdots+\lambda_{n}w^{ \prime}_{n})*x, \tag{7}\]  
This implies that convolving the input features separately and summing their outputs (Equation (6)) is equivalent to multiplying these kernels with their respective combination weights (as shown in Figure 2a) and summing them before performing a single convolution operation (Equation (7)). In Equation (7), the re-convolution calculation occurs only once, whereas in Equation (6) it does not. This strategy significantly reduces computational complexity while maintaining the same feature expression capability of the model.
## 3 Results
### Method Validation for Quantitative Analysis  
Calibration curves for astragalin, ellagic acid, fisetin, fustin, and sulfuretin were plotted using standard concentrations in the x-axis and respective peak areas in the y-axis. The correlation coefficients (\(R^{2}\)) of the standard calibration curves were \(\geq\)0.9995, showing good linearity in injected ranges. The LOD and LOQ were determined based on the SD of y-intercepts of regression lines and slope (S). The LOD and LOQ were shown to have values of 3.24 to 8.64 and 9.81 to 26.17, respectively for the standard compounds. The regression equation, correlation coefficients (\(R^{2}\)), SD of Y-intercepts, LOD, and LOQ values for each standard compound are listed in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Standard** & **Regression Equation \({}^{\star}\)** & \(R^{2}\) & **SD\({}_{\textbf{Y-intercept}}\)** & **LOD (\(\upmu\)g/mL)** & **LOQ (\(\upmu\)g/mL)** \\ \hline Astragalin & y = 41.092x + 8.9667 & 0.9996 & 72.57 & 5.83 & 17.66 \\ Fustin & y = 43.41x \(-\) 27.017 & 0.9999 & 113.61 & 8.64 & 26.17 \\ Fisetin & y = 46.419x \(-\) 204.05 & 0.9995 & 51.75 & 3.68 & 11.15 \\ Sulfuretin & y = 37.027x \(-\) 28.963 & 0.9997 & 53.76 & 4.79 & 14.52 \\ Ellagic acid & y = 59.779x \(-\) 484.89 & 0.9995 & 58.65 & 3.24 & 9.81 \\ \hline \hline \end{tabular} \({}^{\star}\) y: peak area, x: sample concentration (\(\upmu\)g/mL).  
\end{table}
Table 1: The UPLC analyzed regression data, LODs, and LOQs for the marker compounds (n = 3).  
Figure 1: UPLC chromatograms of Formulation F2 along with standard compounds (ellagic acid, fustin, astragalin, fisetin, sulfuricin) and plant ingredients (_O. japonica, R. verniciflua_, and _G. thunbergii_) [22].  
The specificity was evaluated by comparing the peak purity of five marker compounds of the formulation F2 with that of standard compounds. Figure 2 showed that peaks of the marker compounds in F2 were pure and there was no interference by impurities.  
The precision of the developed method was determined by intra- and inter-day variability assessment. The analyzed data showed that the RSD of intra-day and inter-day were in the range of 0.64 to 3.95 and 0.94 to 4.34%, respectively (Table 2). None of the precision data exceeded 5%. These data revealed that the described method maintained an acceptable degree of precision.
## 6 Simulation Results and Discussion
### FBS Power Consumption  
In Figure 6, we plot the FBS power consumption against the number of the active subscribers. In this scenario, the femtocell transmits under the aforementioned power control techniques in a radio-hostile environment. In order to carry out a candid comparison, the number of assigned resource blocks for a user were kept constant. We can see from Figure 6 that the proposed active power control technique outperforms its counterpart in reducing unnecessary power losses. Under the same scenario, the APC approach consumed 13.51% less power than the baseline. Whereas, the FUEAPCT, MUEAPCT and RBPCT, respectively, consumed 7.5%, 6.39% and 4.9% less power as compared to the baseline.
## 4 Experimental Results
### PVMM-Based Photo Watt-PWP 201  
For the PVMM, it can be observed from Table 6 that the best solutions were obtained from CO, ICO, SEDE, and WSO. However, in terms of the RMSE, the best result was related to the CO, and then the ICO, WSO, and SEDE were placed in the following ranks. Among the competitive algorithms, for \(n=40\) and \(n=80\), the CO, ICO, and WSO showed stable behavior in finding the best optimal solution. In Figure 8a,b, the I-V and P-V characteristics of the measured data were very similar to those obtained by the ICO and CO. It can be seen that the IAEI and IAEP in this example were less than 0.0048 and 0.0798, respectively (see Figure 8c,d). The results of this study demonstrate the high accuracy of the estimated parameters under the CO and ICO for the PVMM.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(n\) & **Algorithm** & \(I_{p}\)**(A)** & **I(A)** & \(R_{\text{alt}}\)**(O)** & \(R_{\text{t}}\)**(O)** & \(u\) & **RMSE** \\ \hline \multirow{4}{*}{40} & ICO & 1.03051 & 3.48 \(\times\) 10\({}^{-6}\) & 27.277 & 0.0334 & 1.3512 & 2.425074868095030 \(\times\) 10\({}^{-3}\) \\  & CO & 1.03051 & 3.48 \(\times\) 10\({}^{-6}\) & 27.277 & 0.0334 & 1.3512 & 2.425074868094980 \(\times\) 10\({}^{-3}\) \\  & DE & 1.02991 & 1.49 \(\times\) 10\({}^{-5}\) & 1065.617 & 0.0284 & 1.5261 & 5.266650305240960 \(\times\) 10\({}^{-3}\) \\  & PSO & 1.02677 & 5.98 \(\times\) 10\({}^{-6}\) & 88.261 & 0.0318 & 1.4111 & 2.86439166785901 \(\times\) 10\({}^{-3}\) \\  & GA & 1.02370 & 1.52 \(\times\) 10\({}^{-5}\) & 1944.805 & 0.0278 & 1.5294 & 6.099240455880790 \(\times\) 10\({}^{-3}\) \\  & TLBO & 1.02611 & 4.78 \(\times\) 10\({}^{-6}\) & 75.270 & 0.0325 & 1.3855 & 2.70040360152360 \(\times\) 10\({}^{-3}\) \\  & SEDE & 1.03051 & 3.48 \(\times\) 10\({}^{-6}\) & 27.277 & 0.0334 & 1.3512 & 2.425074868095090 \(\times\) 10\({}^{-3}\) \\  & JAYA & 1.02742 & 8.89 \(\times\) 10\({}^{-6}\) & 911.208 & 0.0305 & 1.4586 & 6.97656950234140 \(\times\) 10\({}^{-3}\) \\  & PGJAYA & 1.03052 & 3.48 \(\times\) 10\({}^{-6}\) & 27.250 & 0.0334 & 1.3511 & 2.4250730060160 \(\times\) 10\({}^{-3}\) \\  & WSO & 1.03051 & 3.48 \(\times\) 10\({}^{-6}\) & 27.277 & 0.0334 & 1.3512 & 2.425074868095050 \(\times\) 10\({}^{-3}\) \\  & GWO & 1.04843 & 5.00 \(\times\) 10\({}^{-5}\) & 3.016 & 0.0000 & 1.7509 & 5.384364616567090 \(\times\) 10\({}^{-2}\) \\  & SSA & 1.15116 & 5.00 \(\times\) 10\({}^{-5}\) & 2.191 & 0.0129 & 1.7224 & 5.130174319081860 \(\times\) 10\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Optimal parameters for PVMM by different algorithms with \(n=40\) and \(n=80\).  
Figure 7: Estimated and measured data of the RTC France silicon solar cell based on DDM with the ICO: (**a**) I–V, (**b**) P–V, (**c**) IAEI, and (**d**) IAEP.
## 5 Conclusions  
Considering the application background of IR imagers and the brittle characteristics of IR materials, the freeform lens was used in an IR coaxial refractive optical system. In the design process, a 10-order XYP in one surface was used to balance various aberrations, especially for the distortion, and the effectiveness of the aberration correction and machinability of the IR material were considered at the same time. Aiming at the side-symmetric character of the NRFS, only the first quadrant FOVs need to be sampled to significantly reduce the optimization time. The uncooled IR imager of the freeform coaxial refractive optical system performed well. The distortion issue of the IR optical system in the 40\({}^{\circ}\)\(\times\) 30\({}^{\circ}\) FOV was corrected effectively by only one freeform surface. The testing results are consistent with the simulation. The surface type processing and detection method of the freeform surface is also reliable. Thus, the infrared freeform surface imager can be applied in engineering.  
The results indicate that the correction ability of the freeform lens is more powerful than that of the aspheric surface especially for high-order aberrations even if it is used in rotating axisymmetric systems. Fortunately, an NRFS requires less optimization time than traditional freeform surfaces and is more suitable for an FTS-processing mode of IR materials. Through the study of this system, the freeform lens design can be applied to more complex refractive IR imaging systems.  
The authors would like to express their sincere thanks to the Key Laboratory of Precision Measuring Technology & Instruments Centre of Micro-Nano Manufacturing Technology of Tianjin University and the Optics Testing Laboratory for the use of their equipment. The acknowledgements are extended to the supports of the Science Challenge Program and the National Natural Science Foundation (Grant No. 61635008).  
[PERSON] proposed the original idea, built the mathematical model and organized the paper. [PERSON] and [PERSON] developed the idea and improve the optical system. [PERSON] and [PERSON] manufactured the freeform optics and other IR lens and developed the paper. [PERSON] and [PERSON] carried out the assembly of the optical system and made the imaging tests. All authors carried out the data analysis, discussed the results and contributed to writing the paper.  
The authors declare no conflict of interest.  
Figure 13: Exhibition picture of the freeform IR un-cooled thermal imager.
## 4 Results and Discussion
### Evaluation of the Three-Phase Method  
In this study, we have presented a three-phase approach for understanding the early warning system for river health conditions, assuming that water quality and biotic integrity are fundamental to the health of an entire river system. In relation to model strength, we selected Shanxi Reservoir as the case reach. The root mean square error (_RMSE_) was utilized to characterize the accuracy of the forecasting model, while the correlation (\(R^{2}\)) was used as an indicator to evaluate the performance of the factor identification model. The _RMSE_s and \(R^{2}\)s for 24-h, 48-h, and 72-h prediction and identification, respectively, are shown in Table 2. The results show that the _RMSEs_ varied between 0.031 and 1.32 during the 72-h prediction. The _RMSEs_s of WQI for the three periods were the lowest during each period. This result indicated that the accuracy of the forecasting model was rather good. Additionally, the model for WQI was stronger than those for HI and IBI. However, the results also showed that the _RMSEs_ gradually decreased as the number of time steps ahead increased. In all predictive periods, the correlation \(R^{2}\) was higher than 0.85, which indicated that the correlation between the forecasting factors and the field observation factors was good. In other words, these identified factors sufficiently explained why the health risks or alarm signals were triggered. Based on this correlation, the model performed well and the characteristics made the model very suitable for implementation in practical situations.  
However, monitoring, assessment, and forecasting methods need to be developed in the context of an adaptive process to identify values and objectives, to guide management actions and to be responsive to changing user perceptions and values. [PERSON] et al. (2010) explained that linear models had limitation in modeling most ecosystem responses to stressors [35], and nonlinear models, such as artificial neural networks (ANN) [36], fuzzy logic [37], and the Bayesian method [38], have become more favorable. Therefore, further research could focus on testing nonlinear models with more cases at multiple temporal-spatial scales so that the approach could be further improved.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{2}{c}{**24-h**} & \multicolumn{2}{c}{**48-h**} & \multicolumn{2}{c}{**72-h**} \\ \cline{2-7}  & _RMSE_ & \(\mathbf{R^{2}}\) & _RMSE_ & \(\mathbf{R^{2}}\) & _RMSE_ & \(\mathbf{R^{2}}\) \\ \hline HI & 0.42 & 0.95 & 0.57 & 0.91 & 0.73 & 0.88 \\ WQI & 0.031 & 0.98 & 0.045 & 0.96 & 0.059 & 0.92 \\ IBI & 0.78 & 0.93 & 0.91 & 0.88 & 1.32 & 0.85 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary performance of the three-phase approach.  
Figure 7: _VIPs_ of different factors.
# Dimensioning of Reactive Power Compensation in an Autonomous Island System
## 5 Dynamic Security Analysis  
The results of the UC-ED analysis are complemented with further analysis of the system operational security. To this end, critical disturbances are simulated using a dynamic model developed in the PSS/E software that represents the particularities of the power system of Rhodes and is suitable for short-term stability analysis through fundamental frequency time domain simulations [32]. It consists of models from the PSS/E library [33] for:  
* Each synchronous generator of the two TPPs with its excitation and automatic voltage regulation system, as well as its turbine and governor. The modeling parameters used are based on available manufacturer data, test measurements, and disturbance recordings. A loss of excitation distance relay model is also included.
* Dynamic models with typical parameters for each WPP modeled with one equivalent generator.
* Frequency and voltage relay models for WPPs based on the settings as set by the corresponding independent power producers.
* Frequency-dependent loads, represented in dynamic simulation as frequency-dependent admittances (P = Pload V2 \(\Delta\)f). The reactive power load demand is assumed to be zero, per the conservative assumption of the static analysis.
* Under-frequency relay models according to the applied UFLS scheme, consisting of 13 stages, applied to 33 MV lines.  
This dynamic model has been used also in the post-mortem analysis of a Rhodes blackout event [12]. Its performance has been further verified for the analysis presented herein, by comparing the simulation results of a number of events that have occurred in the Rhodes system before the S. Rhodes TPP integration to the events' available recorded data, mainly the number of MV lines shed, i.e., the number of UFLS stages activated. As an example, Figure 12 shows the response of frequency as it results from the simulation of a trip of one diesel unit generating 16 MW at low load conditions (79 MW). This resulted in the activation of four UFLS stages, tripping eight MV lines, the same as recorded. Total load shedding amounted to 6.5 MW in the simulation.  
Based on the results of the UC-ED analysis, the feasibility of 4 MVAr, 8 MVAr, and 12 MVAr compensation is further examined with respect to dynamic security. In particular, minimum load conditions are examined (35 MW of system load) with the generators shown in Table 2 per case examined. RES generation is available from wind only, as minimum load conditions occur during the night.  
Next, results from the analysis of two critical disturbances are presented: (a) loss a single synchronous generator after a fault (G-1 contingency) and (b) loss of the S. Rhodes TPP after a fault, resulting in the loss of its double-circuit interconnection line (N-2).