esa-sceva/satcom-chunk-collection huggingface dataset:
# Design, Implementation, and Analysis of a Block Cipher Based on a Secure Chaotic Generator
###### Abstract  
This work proposes a new secure chaos-based encryption/decryption system, operating in cipher block chaining (CBC) mode, and analyze its performance. The cryptosystem includes a robust pseudorandom number generator of chaotic sequences (PRNG-CS). A strong chaos-based S-box is proposed to perform a circular substitution operation (confusion process). This PRNG-CS consists of four discrete 1-D chaotic maps, weakly coupled by a predefined coupling matrix M, to avoid, on the one hand, the divide-and-conquer attack and, on the other hand, to improve the generated sequence's randomness and lengths. The noun is also used in the construction of the S-box. Moreover, a 2-D modified cat map and a horizontal addition diffusion (HAD) preceded by a vertical addition diffusion (VAD) are introduced to perform the diffusion process. The security analysis and numerous simulation results of the main components (PRNG-CS and S-box) as well as the whole cryptosystem reveal that the proposed chaos-based cryptosystem holds up against various types of statistical and cryptographic attacks.  
chaos-based encryption/decryption system; PRNG-CS; S-box; modified 2-D cat map; performance; security analysis Article Design, Implementation, and Analysis of a Block Cipher Based on a Secure Chaotic Generator. 2022, 12, 9952. [[https://doi.org/10.3390/app1299952](https://doi.org/10.3390/app1299952)]([https://doi.org/10.3390/app1299952](https://doi.org/10.3390/app1299952))
## 2 Related Works
### Deterministic Methods  
Some works use deterministic methods to determine the excitation current weights of array elements. For instance, [PERSON] et al. [10] proposed an iterative algorithm for sparse antenna arrays which introduces a compressive sensing approach for transforming the original non-convex optimization problem into a convex problem. Moreover, the authors in [11] proposed a deterministic approach to the optimal power synthesis of mask-constrained shaped beams through the CCAAs. Additionally, [PERSON] et al. [12] formulated a unified sparse array design framework for beam pattern synthesis based on this design metric. The authors in [13] discussed a novel technique for sparse array synthesis in which the synthesis strategy was based on a sparse forcing algorithm using an improvement of reweighted minimization. In [14], a novel analytical approach to the synthesis of linear sparse arrays with non-uniform amplitude excitation was presented and thoroughly discussed. [PERSON] et al. [15] presented an iterative algorithm for the synthesis of the 3D radiation pattern generated by an antenna array of arbitrary geometry. However, these methods often require a relaxation of certain key constraints, leading to a degradation of the optimization performance.
## 6 Microstructural Analysis of Cement Paste with Water Reducer  
### Microstructural Characterisation of Cement Paste with Water Reducer  
Scanning electron microscope (SEM) images of hydrated cement paste are shown in Figure 12. SEM images of hydrated cement pastes (CO\({}_{2}\) AA is 1.76%) before and after water reducer addition are shown in Figure 12a,b (the enlargement factor is 500\(\times\)). It can be seen from Figure 12a that before adding water reducer, flocculants of cement paste show relatively complicated distributions and the diameter-size distribution differs greatly (diameter = 10-50 \(\upmu\)m).  
It can be seen from Figure 12b that for cement paste with water reducer, the flocculant distribution is relatively uniform and the particle size also decreases. The flocculant particles become tighter. Finally, it can be seen from Figure 12a,b that porosity decreases significantly after adding water reducer.  
SEM images at 5000\(\times\) magnification before and after adding water reducer are shown in Figure 12c,d. Smaller-sized hydration structures can be clearly observed. It can be seen from Figure 12c that cement-particle sizes are uneven before adding water reducer and flocculants look like the shape of the cotton, accompanied by high porosity. There are needle-like AFt crystals produced by the hydration of C\({}_{3}\)A, as well as CaCO\({}_{3}\) crystals formed by carbonation of the cement paste.  
Additionally, it can be seen from Figure 12d that the cement-particle distribution with water reducer is more uniform and the pores are smaller. The main sizes in the system change. Except for some large cement particles, particles 2-4 \(\upmu\)m in diameter dominate.  
Figure 12: SEM images of cement pastes before and after adding water reducer: (**a**) before (500\(\times\)); (**b**) after (500\(\times\)) (**c**) before (5000\(\times\)); (**d**) after (5000\(\times\)).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**CO\({}_{2}\) AA/\%** & **30 L/s** & **60 L/s** & **90 L/s** & **120 L/s** & **150 L/s** \\ \hline
0 & 0.15 \(\pm\) 0.05 & 0.16 \(\pm\) 0.04 & 0.17 \(\pm\) 0.06 & 0.16 \(\pm\) 0.08 & 0.19 \(\pm\) 0.08 \\
0.44 & 0.19 \(\pm\) 0.07 & 0.12 \(\pm\) 0.05 & 0.13 \(\pm\) 0.05 & 0.14 \(\pm\) 0.06 & 0.2 \(\pm\) 0.09 \\
0.88 & 0.36 \(\pm\) 0.16 & 0.2 \(\pm\) 0.09 & 0.26 \(\pm\) 0.06 & 0.3 \(\pm\) 0.17 & 0.38 \(\pm\) 0.11 \\
1.32 & 0.85 \(\pm\) 0.03 & 0.47 \(\pm\) 0.12 & 0.44 \(\pm\) 0.08 & 0.49 \(\pm\) 0.12 & 0.55 \(\pm\) 0.12 \\
1.76 & 1.31 \(\pm\) 0.07 & 0.68 \(\pm\) 0.13 & 0.63 \(\pm\) 0.12 & 0.6 \(\pm\) 0.229 & 0.61 \(\pm\) 0.13 \\
2.20 & 2.11 \(\pm\) 0.09 & 1.12 \(\pm\) 0.05 & 1.06 \(\pm\) 0.35 & 0.88 \(\pm\) 0.23 & 0.90 \(\pm\) 0.26 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Viscosity values of fresh carbonated cement pastes before and after PS addition (Pa-s).  
The particle size decreases and the structure is relatively loose. The results demonstrate that after adding water reducer, flocculation particles are dispersed effectively and the liquidity of the cement paste increases accordingly.
# Tensor Rank Regularization with Bias Compensation for Millimeter Wave Channel Estimation
## 5 Computational Complexity Analysis  
We analyze the computational complexity of the proposed CP decomposition-based joint estimation method and the baseline \(l1\) regularization LS method.  
The major computational task of the proposed joint rank and component matrices estimation method involves solving the three least squares problems (32)-(34) at each iteration. Considering the calculation of \(\mathbf{A}^{\left(n+1\right)^{\mathrm{T}}}\), we have (32). The complexity of calculating \(\mathbf{A}^{\left(n+1\right)^{\mathrm{T}}}\) consists of three steps:  
\[\text{To calculate}\left(\left(\mathbf{C}^{\left(n\right)}\odot \mathbf{B}^{\left(n\right)}\right)^{\mathrm{H}}\!\left(\mathbf{C}^{\left(n \right)}\odot\mathbf{B}^{\left(n\right)}\right)+\lambda\mathbf{I}\right)^{-1} \text{,the complexity is }\mathcal{O}\left(M_{bs}K\widetilde{R}^{2}+\widetilde{R}^{3}\right)\text{,} \tag{1}\] \[\text{To calculate}\left(\left(\mathbf{C}^{\left(n\right)}\odot \mathbf{B}^{\left(n\right)}\right)^{\mathrm{H}}\!\left(\mathbf{C}^{\left(n \right)}\odot\mathbf{B}^{\left(n\right)}\right)+\lambda\mathbf{I}\right)^{-1} \!\left(\left(\mathbf{C}^{\left(n\right)}\odot\mathbf{B}^{\left(n\right)} \right)^{\mathrm{H}}\!\mathbf{Y}_{\left(1\right)}^{\mathrm{T}}+\lambda \gamma\mathbf{I}\mathbf{A}^{\left(n\right)^{\mathrm{T}}}\right)\text{,} \tag{2}\]  
The complexity is \(\mathcal{O}\left(M_{ms}\widetilde{R}^{2}\right)\).  
Thus, the total number of flops required to compute \(\mathbf{A}^{\left(n+1\right)^{\mathrm{T}}}\) is of order \(\mathcal{O}\left(M_{ms}M_{bs}K\widetilde{R}+M_{bs}K\widetilde{R}^{2}+ \widetilde{R}^{3}+M_{ms}\widetilde{R}^{2}\right)\).  
The major computational task of \(I1\) regularization LS joint rank and component matrices estimation method involves solving three least squares problems (15)-(17) at each iteration. The complexity of the \(\mathbf{A}^{\left(n+1\right)^{\mathrm{T}}}\) calculation in (15) is the same as the computational complexity (32) above because the calculations of matrix sum, matrix transpose, matrix conjugate, and matrix multiplication by a constant can be ignored in the complexity evaluation.  
Similarly, we can analyze the complexity of \(\mathbf{B}^{\left(n+1\right)^{\mathrm{T}}}\) (33) and \(\mathbf{C}^{\left(n+1\right)^{\mathrm{T}}}\) (34) as above.
## 2 Materials and Methods
### System Implementation
#### 2.3.1 Signal Preprocessing  
EEG data were bandpass filtered from 0.5 to 35 Hz using a 4 th-order Butterworth filter. Common average referencing was applied. Alpha rhythms show high amplitudes at occipital and parietal areas; thus, only channels PO8 and PO7 are used in the rest of the pipeline. The training data were divided into non-overlapping 1-second epochs, and 80% were used for training the classifier, while 20% were used for testing (the collection of training data is outlined in Section 2.4).  
Figure 1: Schematic of the proposed system. EEG is recorded, followed by feature extraction. The classifier detects high power alpha waves and sends the selected commands to the robotic arm while providing feedback primarily through auditory cues.
## 3 Filter-Level Pruning Based on RL
### Optimization of Pruning Rate with DDPG  
RL is rather effective in dealing with the sequential decision-making problem. The target of the RL agent is to find an optimal policy \(\pi(a_{t}|s_{t})\) to maximize the expected cumulative rewards, which is expressed as:  
\[R_{t}=\sum_{i=t}^{\infty}\gamma^{(i=t)}r_{i}, \tag{3}\]  
where \(\gamma\) denotes the discount factor that represents the attenuation of the future rewards. Let \(Q(s,a)\) denote the state-action evaluate function, which measures the expected accumulative return by taking action \(a=a_{t}\) following policy \(\pi\) in state \(s=s_{t}\) as follows:  
\[Q(s,a)=E[R_{t}|s=s_{t},a=a_{t}]. \tag{4}\]  
The \(Q\)-value can be obtained in a recursive manner as in the Bellman Equation (5), which sets the foundation of RL.  
\[Q(s,a)=E(r_{t}+\lambda\underset{a_{t+1}}{\text{max}}Q(s_{t+1},a_{t+1})|s_{t}= s,a_{t}=a) \tag{5}\]  
In this paper, the DDPG algorithm is applied to solve the MDP problem, which is composed of an actor network and a critic network. The actor network \(\pi(s|\theta^{\pi})\) parametrized by \(\theta^{\pi}\) defines the policy, which maps the state to the action, i.e., \(a=\pi(s|\theta^{\pi})\). The critic network \(Q(s,a|\theta^{Q})\) parametrized by \(\theta^{Q}\) approximates the \(Q\)-value function.  
In deep reinforcement learning, the policy \(\pi\) determines the agent's action \(a\). Considering the deterministic policy, denoted as \(\mu\), the \(Q\)-value function can be written as  
\[Q(s_{t},a_{t})=E[(r(s_{t},a_{t})+\gamma Q(s_{t+1},\mu(s_{t+1}))], \tag{6}\]  
where \(\gamma\) denotes the discount factor in the Bellman equation.  
The critic net approximates the \(Q\)-value function. The loss of the critic net in (7) is adopted to minimize the difference in the \(Q\)-value.  
\[L(\theta^{Q})=E\Big{[}(Q(s_{t},a_{t}|\theta^{Q})-y_{t})^{2}\Big{]} \tag{7}\]  
where \(\theta^{Q}\) represents the parameters in the deep \(Q\)-network and \(y_{t}\) is defined as follows:  
\[y_{t}=r_{t}(s_{t},a_{t})+\gamma Q(s_{t+1},\mu(s_{t+1})|\theta^{Q}) \tag{8}\]  
The actor net updates the policy with the aid of the critic net. The policy gradient in (9) is used for the optimization of actor network parameters, which strives to boost the \(Q\)-value [30].  
\[\
abla_{\theta^{\pi}}J=E(\
abla_{a}Q(s,a|\theta^{Q})|_{s=s_{t},a=\mu(s_{t})} \
abla_{\theta^{\pi}}\mu(s|\theta^{\mu})|_{s=s_{t}}) \tag{9}\]  
where \(\theta^{\pi}\) represents the parameters of the online actor net.  
In DDPG, it is important to balance exploration and exploitation for agent training. Hence, the exploration policy by adding Gaussian noise as in (10) is applied.  
\[a=\pi(s|\theta^{\pi})+N(0,\sigma^{2}I) \tag{10}\]To facilitate the training of DDPG, an experience reply [31] is considered whereby at each time step a mini-batch of samples is uniformly sampled for the update of network parameters. To stabilize the training process, target networks are used to evaluate target \(Q\)-values, and a soft update strategy [32] is used to update the parameters of target networks.
# Performance Evaluation Model of Landport and Seaport Collaboration Using the Support Vector Machine
## 5 Case Analysis
### Result Analysis  
(1) Zhengzhou  
Zhengzhou is the hub of China; the multimodal transport of railway transportation, sea transportation, and road transportation within its radius range of 1500 km covers three-quarters of China's provinces, and extends to the Asia-Pacific region. Relying on the cooperation agreements between the Zhengzhou Economic Development Zone, Zhengzhou Materials Group and Lianyungang Port Group, Zhengzhou has further attracted Lianyungang Port, Tianjin Port, Shanghai Port, and Qingdao Port to establish themselves there. Zhengzhou set up dry port customs as well as inspection and quarantine departments to provide convenient customs clearance services, which attracted freight forwarders, shipping agents, and shipping companies to set up branches in the dry port, thus improving the transit capacity of international goods. Therefore, Zhengzhou has the highest score in the performance evaluation for the cooperation between dry ports and Shanghai Port. Consequently, Shanghai Port is preferred for cooperation with Zhengzhou.  
(2) Ningbo  
Ningbo has strategically established a port economic circle, leveraging its inherent port strengths. The establishment of dry ports will amplify Ningbo's port advantages within the framework of the Silk Road Economic Belt, consequently catalyzing the progress of inland cities along this economic corridor. Capitalizing on its own inland port, Suzhou possesses three distinct advantages: a customs inspection linkage function, a secure logistics mode, and a favorable logistics cost structure. Furthermore, Suzhou's proximity to Shanghai Port bolsters the competitiveness of the Suzhou dry port.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**City** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **Accumulated Value Score** \\ \hline
1 & - & \(-1\) & 1 & 1 & 1 & 1 & \(-1\) & 1 & 10 \\
2 & 1 & - & 1 & 1 & 1 & 1 & \(-1\) & 1 & 12 \\
3 & \(-1\) & \(-1\) & - & 0 & 1 & 1 & \(-1\) & 0 & 4 \\
4 & \(-1\) & \(-1\) & 0 & - & 1 & 1 & \(-1\) & \(-1\)Xi'an Xi'an  
Xi'an International Port Zone relies on the connecting facilities for Xi'an Comprehensive Free Trade Zone, Xi'an Railway Container Central Station, Xi'an Highway Wharf, and airports, and is building China's largest international land port and important modern international logistics center and business hub on the Eurasia Land Bridge. Through the strategic cooperation of Xi'an with China's eastern coastal ports and western Khorgos port, as well as with Central Asian countries, a new pattern of regional integration of logistics has gradually formed.  
Jinhua, Xiaoshan, Shaoxing, and Lishui Jinhua, Xiaoshan, Shaoxing, and Lishui are all located in Zhejiang Province. They are close to each other, so there is direct competition among them. Their sources of goods can be diverted to a certain extent by each other, and their separate competitiveness is weak at present. Despite this, their geographical positions and traffic conditions are superior, and these cities have broad development prospects.
## 3 Analysis of Torque Performance
### Analysis of Torque  
Due to the fact that the Bingham model can only effectively describe the rheological properties of the post-shear yield region and cannot describe the shear thinning phenomenon, in order to describe the phenomenon of the shear thinning or thickening of the MRF viscosity during shear rheology more accurately, the 1-D flow model of the MRF can be described by the Herschel-Bulkley model [8]  
\[\left\{\begin{array}{ll}\tau_{2\theta}=\Big{[}\tau_{y}+k\big{|}\dot{\gamma} \big{|}^{m}\Big{]}\text{sgn}(\dot{\gamma})&\tau_{2\theta}\geq\tau_{y}\\ \dot{\gamma}=0&\tau_{2\theta}<\tau_{y}\end{array}\right. \tag{20}\]  
where \(m\) and \(k\) are constants greater than zero, which are determined experimentally, and \(m\) is the flow behavior index of the MRF. When \(m=1\), the Herschel-Bulkley model degenerates to the Bingham model; when \(m<1\) (or \(m>1\)), the shear thinning (or thickening) of the reacting liquid is observed. The equivalent zero-field viscosity in the Herschel-Bulkley model is  
\[\eta_{0}=k\big{|}\dot{\gamma}\big{|}^{m-1} \tag{21}\]  
For the flow of the MRF between two discs, assume that the working area of the disc is a ring of radius from \(r_{3}\) to \(r_{2}\), and take a micro-circular area \(\text{d}A\) at radius \(r\); since \(\text{d}A=2\pi\text{d}r\), the torque \(M\) transferred by the whole disc can be expressed as  
\[M=\int_{r_{3}}^{r_{2}}2\pi r^{2}\tau_{z\theta}\text{d}r \tag{22}\]  
From the Herschel-Bulkley model shown in Equation (20), the torque \(M\) generated by the magnetorheological fluid after yielding can be composed of two parts, which are the magnetic torque \(M_{\text{H}}\) generated by the MRF magnetic shear-yielding stress and the viscous torque \(M_{\text{n}}\) generated by the MRF viscosity.  
Combining Equations (20) and (22), the torque \(M_{\text{H}}\) transferred due to the shear yield stress generated by the chain-formation mechanism of the MRF is  
\[M_{\text{H}}=\int_{r_{3}}^{r_{2}}2\pi r^{2}\tau_{y}\text{d}r=\frac{2\pi}{3} \Big{(}r_{2}^{3}-r_{3}^{3}\Big{)}\tau_{y} \tag{23}\]  
Combining Equations (20)-(22), the viscous torque \(M_{\text{n}}\) transferred due to the shear yield stress generated by the viscosity of the MRF is  
\[M_{\text{n}}=\int_{r_{3}}^{r_{2}}2\pi r^{2}k\dot{\gamma}^{m}\text{d}r=\int_{r _{3}}^{r_{2}}2\pi r^{3}k\bigg{(}\frac{\text{d}\omega(z)}{\text{d}z}\bigg{)}^{ m}\text{d}r=\int_{r_{3}}^{r_{2}}2\pi r^{3}k\bigg{(}\frac{\Delta\omega}{h} \bigg{)}^{m}\text{d}r\]  
\[M_{\text{n}}=\frac{2\pi k}{m+3}\Big{(}r_{2}^{m+3}-r_{3}^{m+3}\Big{)}\bigg{(} \frac{\omega_{2}-\omega_{1}}{h}\bigg{)}^{m} \tag{24}\]  
Therefore, the torque \(M\) transferred by the MRF between the two discs can be expressed as  
\[M=M_{\text{H}}+M_{\text{n}}=\frac{2\pi}{3}\Big{(}r_{2}^{3}-r_{3}^{3}\Big{)} \tau_{y}(H)+\frac{2\pi k}{m+3}\Big{(}r_{2}^{m+3}-r_{3}^{m+3}\Big{)}\bigg{(} \frac{\omega_{2}-\omega_{1}}{h}\bigg{)}^{m} \tag{25}\]
## 2 Materials and Methods
### Characterization  
Infrared (FT-IR) spectra of samples in powder form, dispersed in KBr pellets, were measured with a Perkin-Elmer GX, Fourier transform spectrometer in the frequency range 400-4000 cm\({}^{-1}\). Spectra were the average of 32 scans with a 2 cm\({}^{-1}\) resolution.  
Thermogravimetric (TGA) and differential thermal (DTA) analysis were performed using a Perkin-Elmer Pyris Diamond TG/DTA. Samples of approximately 5 mg were heated in nitrogen from 25 to 800 \({}^{\circ}\)C, at a rate of 5 \({}^{\circ}\)C/min.  
Raman spectra were recorded with a RM 1000 Renishaw micro-Raman system using a laser excitation line at 532 nm (Nd:YAG) in the range of 400-3500 cm\({}^{-1}\). A laser power of \(\sim\)10 mW was used with a 2 \(\upmu\)m focus spot.  
Atomic force microscopy (AFM) images were obtained in tapping mode with a Multimode Nanoscope 3D using Tap-300G silicon cantilevers with a tip radius \(<\)10 nm and a force constant of \(\sim\)20-75 N m\({}^{-1}\).  
Transmission electron microscopy (TEM) images of polystyrene nanocomposites deposited on carbon-coated copper grids (CF300-CU-UL, carbon square mesh, CU, 300 mesh from Electron Microscopy Science) were obtained using the instrument JEM HR-2100, JEOL Ltd., Tokyo, Japan operated at 200 kV in bright-field mode. The mechanical performance of all films was evaluated using a miniature material tester with a 50 N load cell. Three to five \"dog bone\" tensile specimens (ASTM 638/95 Type V) were clamped between the grips (30 mm initial distance) and tensioned at a crosshead speed of 1 mm/min according to ASTM D638. Force (N) and deformation (mm) were recorded during the test and converted into stress (MPa) and strain (%), based on the cross-sectional area and the initial length data, respectively. The results obtained from the mini-tester can only be used for comparison, because the strain values are based on the rotational movement of the drive shaft. Baseline samples (not containing CNW) were tested at the beginning of each set of samples for comparison.  
A NETZSCH DMA 242C apparatus was used to evaluate the thermomechanical response of selected samples under tensile mode at a frequency of 1 Hz, and temperatures ranging from 20-120 \({}^{\circ}\)C (rate 2 \({}^{\circ}\)C/min). The amplitude of the deformation was 60 \(\upmu\)m.
# Optimization of Protection Level of GBAS with Gaussian Mixture Model
## 3 Appling Solution Separation Method to the GMM
The anomaly monitoring of GBAS and SBAS is mainly done by the server side, and the protection level is usually under a fault-free hypothesis, i.e., that there is no need to implement the monitoring algorithm here and no continuity risk at the protection level. The direct use of the solution separation algorithm results in the loss of continuity and protection level. 2. As the existing solution separation algorithm is applied to RAIM, which usually only needs to consider the situation of 2-3 satellite failures, the number of the solutions is controllable. But the tail part of the Gaussian mixture distribution has a high probability that almost all assumptions need to be considered, and the number of the solutions is particularly large, which results in a high computational complexity.
## 3 Implementation of the Model-Based Algorithm and the Experimental Setup
### Numerical Implementation of the Algorithm
Using each template, the weighted correlation with the turbulence wedge at the position \(x_{i}\) is calculated. To calculate the weighted correlation, the top left corner of the current template matrix is placed at \((x_{i}-w_{k}^{\prime}/2)\) along the natural transition line at \(y_{i}=y_{\text{NT}}(x_{i})\), resulting in the top right corner of the template to be positioned at \((x_{i}+w_{k}^{\prime}/2)\). The columns (i.e., the width) of the thermogram section are selected from the \(x\)-position \((x_{i}-w_{k}^{\prime}/2)\) of the thermogram to \((x_{i}+w_{k}^{\prime}/2)\). The rows (i.e., the height) of the thermogram section are determined from the \(y\)-position \(y_{\text{NT}}(x_{i})\) to \(y_{\text{NT}}(x_{i})+h_{k}^{\prime}\). Thus, the thermogram section and the template have the same size. The weighted correlation is chosen as a measure of similarity so that the intensity gradient near the leading edge of the thermogram is counteracted, which is implemented through the weights \(\gamma\) in the weight matrix. Thus, the weighting emphasizes a good match at the base of the template to the turbulence wedge. Therefore, the weights are larger near the base of the turbulence wedge, with \(\gamma_{\text{base}}=10\), and linearly decrease row by row to smaller weights near the tip, \(\gamma_{\text{tip}}=1\). The number of steps for the linear decrease, which was implemented with the _linspace_ function of _Python's numpy_, is equal to the height \(h_{j}^{\prime}\) of the current template. The linear decrease is repeated in each matrix column for \(w_{j}^{\prime}\) columns. The weight matrix, the thermogram section and the template therefore all have the same size, and the weighted correlation is calculated using Equation (7). The calculations result in a phase space of correlation values, i.e., one value for each height-width combination, see Figure 6. The size of the template which attains the highest correlation value, see red x in Figure 6, is the size \((h_{i},w_{i})\) of the turbulence wedge at position \(x_{i}\), from which the area \(A_{i}\) can be calculated with Equation (6).