esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Axis TF in the Area Coordinate System  
### Area Coordinate System  
In Figure 3, three sub-triangles (_Pjm_, _Pmi_ and _Pij_) are formed by connecting any point \(P\) in the triangle _ijm_ with its three vertexes \(i,j\) and \(m\).  
Location of point \(P\) in the triangle _ijm_ can be determined by either the Cartesian coordinate system O-XY or three sub-triangles. Areas of three sub-triangles (_Pjm_, _Pmi_ and _Pij_) are \(\Delta_{Pjm}\), \(\Delta_{Pmi}\) and \(\Delta_{Pij}\), respectively. The ratios between areas of three sub-triangles and the area of the triangle _ijm_ (\(\Delta_{Pjm}/\Delta\), \(\Delta_{Pmi}/\Delta\) and \(\Delta_{Pij}/\Delta\)), can be expressed as \(L_{i}\), \(L_{j}\) and \(L_{m}\):  
\[\left\{\begin{array}{l}L_{i}=\frac{\Delta_{Pjm}}{\Delta}=\frac{\Delta_{i}}{ \Delta}\\ L_{j}=\frac{\Delta_{Pmi}}{\Delta}=\frac{\Delta_{j}}{\Delta}\\ L_{m}=\frac{\Delta_{Pij}}{\Delta}=\frac{\Delta_{m}}{\Delta}\end{array}\right. \tag{3}\]  
\(L_{i}\), \(L_{j}\) and \(L_{m}\) are area coordinate values of \(P\). In Figure 3, the area coordinate value of any point on relative sides of each vertex of the triangle is 0. Generally, the relationship between area coordinate values is:  
\[L_{i}+L_{j}+L_{m}=1 \tag{4}\]  
The mapping relation of \(P\) from \(O\)-\(XY\) to the area coordinate system is:  
\[\left\{\begin{array}{l}L_{i}\\ L_{j}\\ L_{m}\end{array}\right\}=\frac{1}{2\Delta}\left[\begin{array}{cccc}a_{i}&b_{i }&c_{i}\\ a_{j}&b_{j}&c_{j}\\ a_{m}&b_{m}&c_{m}\end{array}\right]\left\{\begin{array}{l}1\\ x\\ y\end{array}\right\} \tag{5}\]  
Figure 3: Area coordinate system of triangles.  
where \(a_{i}\), \(b_{i}\), \(c_{i}\), \(a_{j}\), \(b_{j}\), \(c_{j}\), \(a_{m}\), \(b_{m}\) and \(c_{m}\) are algebraic cofactor of elements in the first, second and third rows at the right determinant of the calculation formula of triangle in Equation (6):  
\[2\Delta=\left|\begin{array}{ccc}1&x_{i}&y_{i}\\ 1&x_{j}&y_{j}\\ 1&x_{m}&y_{m}\end{array}\right| \tag{6}\]  
According to properties of the determinant and Equation (4), the mapping relation of \(P\) from \(O\)-\(XY\) to the area coordinate system is:  
\[\left\{\begin{array}{c}1\\ x\\ y\end{array}\right\}=\left[\begin{array}{ccc}1&1&1\\ x_{i}&x_{j}&x_{m}\\ y_{i}&y_{j}&y_{m}\end{array}\right]\left\{\begin{array}{c}L_{i}\\ L_{j}\\ L_{m}\end{array}\right\} \tag{7}\]  
It can be known from Equations (5) and (7) that locations of \(P\) in \(O\)-\(XY\) correspond to \(\Delta_{Pjm}\), \(\Delta_{Pmi}\) and \(\Delta_{Pij}\).
# An Observer-Based Active Fault Tolerant Controller for Vehicle Suspension System
## 2 System Modelling and Problem Statement
### Generalized Fault Model of Active Suspension System
\begin{array}{l}\dot{\mathbf{x}}(t)=\mathbf{A}\mathbf{x}(t)+\mathbf{B}\mathbf{u}(t)+\mathbf{B} _{d}\mathbf{d}(t)\\ \mathbf{y}(t)=\mathbf{C}_{1}\mathbf{x}(t)\\ \mathbf{z}(t)=\mathbf{C}_{2}\mathbf{x}(t)+\mathbf{D}_{2}\mathbf{u}(t)\end{array} \right. \tag{3}\]  
where \(\mathbf{A}\), \(\mathbf{B}\), \(\mathbf{B}_{d}\), \(\mathbf{C}_{1}\), \(\mathbf{C}_{2}\), and \(\mathbf{D}_{2}\) were the matrices with appropriate dimensions to be determined, which are expressed in Appendix A. It is widely accepted that the fault has the characteristic of randomness, fuzziness, and unpredictability. The common faults like actuator jam or offset in sensor outputs were firstly tested in the experiment bench and were then modeled in a finite parameter family as a constant gain fault or slow drift fault [29]. Without loss of generality, the following exosystem was used to describe the actuator fault model as [30; 31]  
\[\left\{ \begin{array}{l}\dot{\mathbf{x}}_{f}(t)=\mathbf{A}_{wf}\mathbf{x}_{f}(t)+\mathbf{B}_ {wf}\delta(t)\\ \mathbf{f}(t)=\mathbf{C}_{wf}\mathbf{x}_{f}(t)\end{array} \right. \tag{4}\]  
where \(\mathbf{x}_{f}\in R^{n_{f}}\) denotes the state vector of the fault model, \(\delta(t)\) denotes the virtual input signal with the bounded \(L_{2}\) norm. It should be noted that the auxiliary fault diagnosis system was needed to confirm the value of the coefficient matrix and \(\delta(t)\). In brief, this paper adopted the random ramp signal to describe the actuator fault \(\mathbf{f}(t)\). Let the coefficient matrix be \(\mathbf{A}_{wf}=0\), \(\mathbf{B}_{wf}=\mathbf{I}\), \(\mathbf{C}_{wf}=\mathbf{I}\) and \(\delta(t)\) satisfying:  
\[\delta(t)=\left\{ \begin{array}{l}0,t<t_{f}\\ \beta_{f},t\geq t_{f}\end{array} \right. \tag{5}\]  
where \(t_{f}\) and \(\beta_{f}\) stand for the occurring time and the amplitude of the suspension fault. It is noted that an arbitrarily random ramp signal could be generated by tuning the value of \(t_{f}\) and \(\beta_{f}\). Combining (3) and (4) yields the state-space equations of the half-vehicle suspension system with the generalized actuator faults as:  
\[\left\{ \begin{array}{l}\dot{\mathbf{x}}(t)=\mathbf{A}\mathbf{x}(t)+\mathbf{B}\mathbf{u}(t)+\mathbf{ B}_{d}\mathbf{d}(t)+\mathbf{B}_{f}\mathbf{f}(t)\\ \mathbf{y}(t)=\mathbf{C}_{1}\mathbf{x}(t)\\ \mathbf{z}(t)=\mathbf{C}_{2}\mathbf{x}(t)+\mathbf{D}_{2}\mathbf{u}(t)+\mathbf{D}_{2}\mathbf{f}\mathbf{f}(t) \end{array} \right. \tag{6}\]  
where \(\mathbf{B}_{f}\) and \(\mathbf{D}_{2f}\) are the known matrices with appropriate dimensions, and there exists a known gain matrix \(\mathbf{M}\) satisfying \([\mathbf{B}_{f}^{T}\mathbf{D}_{2f}^{T}]^{T}=[\mathbf{B}^{T}\mathbf{D}_{2}^{T}]^{T}\mathbf{M}\)[26]. It is noted that when \(\mathbf{f}(t)=0\), the active suspension system works under normal operations, and when \(\mathbf{f}(t)\
eq 0\), it can be confirmed that there occurs some actuator faults in the active suspension system.
# Intelligently Counting Agricultural Pests by Integrating SAM with FamNet
## 4 Discussion and Conclusions  
### Conclusions  
This study makes several contributions. Firstly, it proposes a system called segment anything method (SAM) for counting with the assistance of FamNet. By exploring the limitations of FamNet in different environments and combining it with the SAM auxiliary layer, preliminary semantic feature extraction is performed. This leverages the powerful unsupervised semantic segmentation capability of FamNet to enhance the perception of object features in the counting small model. Secondly, it introduces the use of TopK vector matching to refine the counting process, transforming it into a two-stage process to address domain adaptation issues when dealing with samples and tests of the same type but different scenes. This is beneficial for better handling the long-tail effect in the data and reducing the impact of lighting and other scene factors. Finally, inspired by the use of historical dialogue in GPT to improve performance, this research proposes an architecture that can enhance performance through prompt learning during use. This architecture helps the model automatically expand rare datasets and allows for convenient manual adjustment of model prompts. Overall, this work contributes to the application of large models in downstream agricultural tasks.
# Fast Segmentation Algorithm for Cytoid Macular Edema Based on Omnidirectional Wave Operator
## 2 Methods
### Algorithm Overview  
When the OCT system acquires fundus images, scattered light waves with random phases are coherently superimposed to produce speckle noise. Speckle noise appears as an irregular speckle pattern, which is randomly distributed in the image [18]. When directly processing the pixels in the image, speckle greatly affects the segmentation accuracy. For the contour extraction algorithm using gradient information, speckle will cause wrong segmentation. In order to reduce the influence of speckle noise, the first step of the omnidirectional wave operator in this paper is to construct a working environment. Through denoising and contrast stretching, the speckle noise is weakened and the contrast between the target and the background area is enhanced. The second step of the algorithm is image segmentation. As CME is located at a specific level of the retina, by determining the ROI area, segmentation results from other areas can be avoided, and the calculation speed can be greatly increased. The algorithm firstly performs ROI division in the second part, and then uses the omnidirectional wave operator to segment the CME. The third step of the algorithm is contour integration. After the results of the four directions are aggregated, the connected domain is processed to obtain the final CME contour. The algorithm flow chart is shown in Figure 1.
# Microseismic Electronic Fencing for Monitoring of Transboundary Mining in Mines
## 2 Factors Affecting Localization Accuracy  
The monitoring of cross-border mining is, as the name suggests, an effort to locate mining activities occurring at the boundaries of the mine. This allows for accurate and timely supervision, effectively preventing illegal activities such as poaching and theft of mineral resources. This necessitates accurate localization of vibration events around the mine boundary. As outlined in the preamble, the localization accuracy of the vibration source depends on several factors, including the source localization algorithm, velocity structure model, first arrival time pickup, and sensor deployment methods.  
Therefore, this section investigates the effects of the localization method, sensor deployment scale, and velocity model on the accuracy of seismic source localization at the mine boundary using numerical simulation. The numerical simulation uses the 3D finite difference method, employing a model sized 1500 m \(\times\) 1500 m \(\times\) 500 m. As shown in Figure 1a, the grid spacing is 5 m, and the sampling interval is 0.1 ms. Since the study focuses on the effect of sensor distribution on localization accuracy, the model was configured as a homogeneous isotropic medium with a velocity of 3500 m/s. The sensors were deployed on the surface and within the wells. In the forward simulation, the source is excited underground, and the received vibration signals are recorded to extract the first arrival times. Finally, the localization algorithm is used to locate the source. The subsequent sections investigate the results of the numerical simulation with respect to the localization method, observation system, and number of sensors.
# A Dual-Adaptive Approach Based on Discrete Cosine Transform for Removal of ECG Baseline Wander
## 2 Methods
### The Proposed Dual-Adaptive Scheme  
It has been repeatedly emphasized that the determination of the cut-point between BW and inherent ECG components is of great importance in order to fully eliminate BW and preserve the original clinical information. To illustrate this, a 20 s ECG (Figure 1a) from the PTB Diagnostic Database [25] was considered. There were 30 heartbeat occurrences in the 20 s ECG signal. We then calculated the cardiac fundamental frequency (CFF), which is the counterpart of heart rate and indicates the frequency of heartbeat occurrence in units of time. The accurate calculation of CFF is important because it is recommended to have a cutoff frequency that does not exceed CFF when filtering BW in the ECG signal [26]. In Figure 1a, CFF is 1.5 Hz approximately. Unfortunately, no visible peak exists (Figure 1b) around 1.5 Hz in the Fourier spectrum because it is obscured by severe BW.  
To overcome this drawback, we developed a novel scheme, called a dual-adaptive scheme (DAS), which can remove BW adaptively with the optimal cut-point not only adjusted to CFF, but also adjusted to the degree of BW existence. The proposed DAS contains three major steps as shown in Figure 2.  
Figure 1: Comparison of CFF detection by the previous method [20] and the proposed method (PTB record 801301 rem, lead I, 00:00\(-\)00:20). (**a**) Raw ECG signal contaminated with severe BW. (**b**) Amplitude of raw ECG in the Fourier domain. (**c**) Waveform of the extracted QRS complexes \(|x_{QRS}(n)|\). (**d**) Amplitude of \(|x_{QRS}(n)|\) in the DCT domain, the red ‘triangle’ and red ‘square’ denote the position of CFF and its higher harmonic, respectively.  
In the first step, CFF is calculated using a 20 s long portion of the ECG that is to be processed. In the second step, the optimal cut-point before CFF is investigated by analyzing the lower order DCT-coefficients. Finally, BW is reconstructed by applying IDCT to those DCT coefficients before the optimal cut-point, and the BW-free ECG is retrieved by subtracting BW from the original ECG. The detailed procedure is described in the sections below.  
Figure 2: Block diagram of the Dual-Adaptive Scheme.
## 2 Pull-Out Test Setup  
### Pull-Out Specimens  
Three kinds of pull-out test specimens were proposed to investigate the mechanical performance of PBL connectors with different embedded depths. The embedded depth indicated the distance between the nearest perforated rebar and the concrete surface in the pull-out direction. For the first type of specimen (PA1, PA2, and PA3), the embedded depth was 300 mm, as shown in Figure 1a, while an embedded depth of 150 mm was employed in the second type (PB1, PB2, PB3), as shown in Figure 1b. The third type of specimen (PC1, PC2, PC3) was similar to the first type but without perforated rebars. Specim PC3 was not considered due to a manufacturing error. The three-dimensional view of a pull-out specimen is shown in Figure 1c. The PA and PC specimens consisted of the concrete member (1000 \(\times\) 650 \(\times\) 1000 mm), steel plate (2000 or 1850 \(\times\) 200 \(\times\) 24 mm), perforated rebars (22 mm in diameter), and reinforcing bars (16 mm in diameter). Preformed holes 65 mm in diameter were drilled through the steel plate, except in PC specimens. In addition, no perforated rebar was installed in PC specimens. The material strength tests were carried out according to TB 10002.3-2005 [40]. The mechanical properties of the concrete C50 were obtained from standard cube samples (150 \(\times\) 150 \(\times\) 150 mm). The average compressive strength and Young's modulus of the standard cubes after 28 days of curing were 59.2 MPa and 34.5 GPa, respectively. In addition, tensile tests were performed for the structural steel and reinforcing bars. The mechanical properties of the materials are listed in Table 1. C50 concrete was adopted in the concrete member. Q345 qE low-alloy high-strength bridge structural steel was used for all steel plates. The perforated rebars and reinforcing bars were made of HRB335 steel.  
Figure 1: _Cont._
# The Effect of Antagonist Abiotic Stress on Bioactive Compounds from Basil (_Ocimum basilicum_)
## 3 Results
### The Influence of Stress on Volatile Organic Compounds Emission  
Different green leaf volatile compounds (GLV) and monoterpenes (MT) have been identified in the blend of volatile emission from _O. basilicum_ leaves (Figure 3). The GLV identified in plants subjected to abiotic stresses were 3-methyl-pentane and 1-hexanol, and the MT identified were: alpha-pinene, camphene, sabinene, beta-pinene, 3-carene, D-limonene, gamma-terpinene, linalool, camphor, and alpha-terpineol.  
The green leaf volatile emission for control plants is close to zero over all of the experiments. In the plants under flooding and drought stresses, the emission increases at a maximum of 2.43 \(\pm\) 0.14 nmol m\({}^{-2}\) s\({}^{-1}\) on day 15 without statistically significant differences between first flooding or drought (Figure 3a). The emission for plants that were watered normally in the second treatment decreases close to zero on day 29. In contrast, the plants which were subject to the second treatment (flooding or drought stress) first decrease the emission (for one day in case of drought\(-\)flooding and three days for flooding-drought) followed by an increase until 2.48 \(\pm\) 0.44 nmol m\({}^{-2}\) s\({}^{-1}\).  
The leaves from _O. basilicum_ emit different monoterpenes (MT) constitutively. The total average emission of MT from control leaves is 2.00 \(\pm\) 0.34 nmol m\({}^{-2}\) s\({}^{-1}\). For plants under drought and flooding stress (as first treatment), the MT emissions increase until 5.10 \(\pm\) 0.60 nmol m\({}^{-2}\) s\({}^{-1}\) and 6.29 \(\pm\) 0.57 nmol m\({}^{-2}\) s\({}^{-1}\) respectively. For plants that were watered normally in the second treatment, the emission decreases until the level of control plants. In contrast, the emission from leaves from drought\(-\)flooding and flooding\(-\)drought plants decreases initially, followed by a sharp increase until 7.37 \(\pm\) 0.07 nmol m\({}^{-2}\) s\({}^{-1}\) (Figure 3b).
# Image Encryption Algorithms: A Survey of Design and Evaluation Metrics
## 3 Evaluation Metrics
### Resistance Against Differential Attacks
#### 3.6.1 Avalanche Effect  
In image encryption, the avalanche effect refers to the phenomenon that occurs where a slight change to the key or the plaintext image results in an image encryption algorithm producing a significantly different cipher image. An encryption algorithm is considered safe against differential attacks when one pixel change in the plaintext image or key results in a change of more than 50% of the pixels in the cipher image [57]. The avalanche effect can be analyzed using the MSE metric by modifying Equation (23) to calculate the mean-squared difference between the two cipher images, which are produced by encrypting a plaintext image and the same plaintext image with only one pixel modified. The avalanche effect MSE (\(MSE_{av}\)) can be calculated as follows:  
\[MSE_{av}=\frac{1}{H\times W}\sum_{i=1}^{H}\sum_{j=1}^{W}[C_{1}(i,j)-C_{2}(i,j) ]^{2}, \tag{28}\]  
where \(C_{1}\) and \(C_{2}\) are the two cipher images produced by encrypting two plaintext images, where the two plaintext images differ in only one pixel, with the remaining pixels being the same. \(C_{1}(i,j)\) and \(C_{2}(i,j)\) represent the pixel values at position \((i,j)\) of \(C_{1}\) and \(C_{2}\), respectively. The minimum value of \(MSE_{av}\) is 0, and the maximum value is 65,025, the same as the MSE minimum and maximum values, which are calculated in Section 3.5.1.
## 4 Result  
### Comparison of Forest Burned Area Detection Performance  
The classification performance for three Schemes in Site A and B is summarized in Tables 4 and 5, respectively. The values in the tables were averaged with 10 times repetitions of the results. In the case of binary classification of Scheme 3, a simple threshold value was applied to the dNBR image to extract the burned area for the comparison point of view. To this end, the threshold value applied for the extraction of the forest fire burned area was classified into the burned area and the unburned area based on the burn severity standard proposed by the USGS [37]. As a result, the dNBR binary classification map was constructed by mapping the values of low severity (\(<\)+0.1) or higher to the wildfire burn area and the values below (\(>\)+0.1) to the unburned area. The results from U-Net showed the highest accuracies (OA and Precision) among the three machine learning approaches in both Sites A and B. However, all Schemes in Site B have lower Recall values in U-Net compared to other methods. It is considered that LightGBM and RF tend to over detect burned areas compared to U-Net. As mentioned above, F1-Score and Kappa are much appropriate metrics in the unbalanced dataset. U-Net exhibits an enhanced Kappa and F1-Score in both multiclass and binary classification when compared to LightGBM and RF, indicating that the deep learning model was successful in identifying forest burned regions. The LightGBM, RF, and U-Net classification results also compared with the dNBR result, and showed the better classification performance for three Schemes in site A and B. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Multiclass Classification**} \\ \hline  & - & **OA** & **Recall** & **Precision** & **F1-Score** & **Kappa** \\ \hline \multirow{3}{*}{Scheme 1} & LightGBM & 0.85 & 0.78 & 0.60 & 0.68 & 0.73 \\  & RF & 0.85 & 0.74 & 0.62 & 0.67 & 0.74 \\  & U-Net & 0.93 & 0.87 & 0.89 & 0.88 & 0.88 \\ \hline \multirow{3}{*}{Scheme 2} & LightGBM & 0.86 & 0.80 & 0.68 & 0.73 & 0.76 \\  & RF & 0.86 & 0.78 & 0.67 & 0.72 & 0.75 \\  & U-Net & 0.93 & 0.88 & 0.89 & 0.88 & 0.88 \\ \hline \multirow{3}{*}{Scheme 3} & LightGBM & 0.88 & 0.81 & 0.71 & 0.76 & 0.78 \\  & RF & 0.87 & 0.81 & 0.70 & 0.75 & 0.77 \\  & U-Net & 0.93 & 0.89 & 0.88 & 0.89 & 0.88 \\ \hline \multicolumn{6}{c}{Binary Classification} \\ \hline  & - & **OA** & **Recall** & **Precision** & **F1-Score** & **Kappa** \\ \hline \multirow{3}{*}{Scheme 1} & LightGBM & 0.92 & 0.78 & 0.60 & 0.68 & 0.63 \\  & RF & 0.92 & 0.74 & 0.62 & 0.67 & 0.62 \\  & U-Net & 0.97 & 0.87 & 0.89 & 0.88 & 0.86 \\ \hline \multirow{3}{*}{Scheme 2} & LightGBM & 0.94 & 0.80 & 0.68 & 0.73 & 0.69 \\  & RF & 0.93 & 0.78 & 0.67 & 0.72 & 0.68 \\  & U-Net & 0.98 & 0.88 & 0.89 & 0.89 & 0.87 \\ \hline \multirow{3}{*}{Scheme 3} & LightGBM & 0.94 & 0.81 & 0.71 & 0.76 & 0.73 \\  & RF & 0.94 & 0.81 & 0.70 & 0.75 & 0.71 \\  & dNBR & 0.92 & 0.56 & 0.63 & 0.59 & 0.55 \\  & U-Net & 0.98 & 0.89 & 0.88 & 0.89 & 0.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of the burned area detection results for Site A.
## 4 Protocols Protecting Terminal Devices in Zero-Trust Networks
### Description of the Protocols with CRP Mechanisms
#### 4.1.2 Verification Cycle  
The terminal device can verify the authenticity of C by recovering Pk with Kr and \(\mathrm{Kc}\), in which Kr: \(\left\{r^{\prime}1,\ldots,r^{\prime}_{j},\ldots,r^{\prime}_{f}\right\}\) and \(\mathrm{Kc}\): {S, \(\omega\), M*}.  
* The first part of Algorithm 7 shown below is a replay of the enrollment cycle to generate the responses \(\left\{r_{1},\ldots,r_{i},\ldots,r_{N}\right\}\) that each have a length equal to P-bit.
* The key K is recovered by comparing the full sequence of responses with the subset, as shown in module 4.  
The injection of bad bits in the subset of the response, a process that can also be called \"noise injection\", has no effect on the outcome of the protocol provided the noise level is below the threshold T that can disturb the recovery of K.  
```
0: Up to \(T\) bad bits are injected in \(Kr\)
1: Variable input data: C, Kc and the noisy \(Kr\)
2:\(\rightarrow\) Use Module 1: Generate a set of N responses with \(C\), and {\(\omega\),S}: * Static input data: Positive integers \(d\), \(N\), \(P\), \(\alpha\), \(\beta\) * Output data: the \(N\), \(P\)-bit long, responses {\(r_{1},\ldots,r_{i},\ldots,r_{N}\)}
3:\(\rightarrow\) Module 4: Decrypt \(M\) from \(M^{*}\) and the \(f\) noisy responses {\(r^{\prime}_{1},\ldots,r^{\prime}_{j},\ldots,r^{\prime}_{f}\)}, \(j\in\){1, P}: 3.1: Enter both sets {\(r^{\prime}_{1},\ldots,r^{\prime}_{j},\ldots,r^{\prime}_{f}\)}, {\(r_{1},\ldots,r_{i},\ldots,r_{N}\)}, and \(T\) 3.2:\(j=1\), \(i=1\) * While \(i<N+1\): * Measure hamming distance H(\(r^{\prime}_{i}\), r): * If \(H(r^{\prime}_{i}r_{i})\leq T\): \(k_{i}=1\); increment \(i\), \(j\) by \(1\) * Else: \(k_{i}=0\); increment \(i\) by \(1\) * (\(M=Pk)\leftarrow\) Decrypt(\(M^{*}\), \(K\))
4:\(F\leftarrow\) Decrypt(\(C\), \(Pk\))
6: Output \(F\), \(Pk\)
```  
**Algorithm 7**Decrypt file \(F\) with subkey \(Kc\) and noisy subkey \(Kr\)  
The example shown in Tables 2 and 3 illustrates how the scheme operates. With the sequence {\(r_{1},\ldots,r_{8}\)} and key K {0,1,1,0,1,0,0,1}, Kr is {\(r^{\prime}_{1}=r_{2},r^{\prime}_{2}=r_{3},r^{\prime}_{3}=r_{5},r^{\prime}_{4 }=r_{8}\)}. The key K is recovered by comparing the Kr and the full sequence.