esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Results and Discussion
### PlanetiQ-COSMIC Profiles Comparison
#### 4.2.2 Multi-Profile Comparison
These results are consistent with the noted disparities, underscoring the critical role of accurate observational data in comprehending atmospheric dynamics. Table 1 summarizes the assessment of differences between variances and observations within the context of G1 observations, considering a temporal difference less than 15 min and a spatial deviation of 0.25\({}^{\circ}\) in latitude and longitude. The f-test is employed to evaluate the significance of variance differences, with a \(p\)-value greater than 0.05 indicating no substantial variance distinction between profiles. On the other hand, the \(t\)-test assesses the significance of divergence in observation profiles, with a t-stat value below the critical threshold signifying no noteworthy variation. Figure 14: Mean diff., mean diff.% and RMSE between PlanetiQ and COSMIC profiles for G2 for all variables. Figure 15: Mean diff., mean diff.% and RMSE between PlanetiQ and COSMIC profiles for G3 for all variables. The f-test results for the four profile variables across the nine checkpoints reveal a lack of significant disparity in variances among the compared profiles. Furthermore, the t-stat values from the \(t\)-test analysis are consistently below the critical threshold for all observation variables. This substantiates the conclusion that there is no significant dissimilarity between the PlanetQi and COSMIC profiles across all the examined checkpoints.
## 2 Proposed Method
### The Main Network
#### 2.1.2 Loss Function  
We quantized the continuous scale of the pitch range into a discrete set of values to form the output layer in a classification setting. They are often represented as a one-hot vector to incorporate it into the categorical cross entropy (CE) loss function [15; 16]. One problem of the loss function is that, unless the predicted pitch is close enough to the ground-truth pitch within the quantization size (6.25 cents in our case), it is regarded as the \"wrong class\". In order to mitigate excessive loss for neighboring pitches of the ground truth, a Gaussian-blurred version of one-hot vector was proposed [17; 34]. We also adopted this  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Components**} & \multicolumn{2}{c}{**Output Size**} \\ \cline{2-4}  & _Main_ & _Main + AUX_ & _Main_ & _Main + AUX_ \\ \hline Input & - & & 31 \(\times\) 513 \\ Conv block & [\(3\times 3\), 64] \(\times\) 2 & & 31 \(\times\) 513, 64 \\ ResNet Block 1 & [\(3\times 3\), 128] \(\times\) 2 & & 31 \(\times\) 128, 128 \\ ResNet Block 2 & [\(3\times 3\), 192] \(\times\) 2 & & 31 \(\times\) 32, 192 \\ ResNet Block 3 & [\(3\times 3\), 256] \(\times\) 2 & & 31 \(\times\) 8, 256 \\ Pool block & - & & 31 \(\times\) 2, 256 \\ Bi-LSTM & 256 & 256 + 32 & 31 \(\times\) 512 & 31 \(\times\) (512 + 64) \\ FC & 722 & 722 + 2 & 31 \(\times\) 722 & 31 \(\times\) (722 + 2) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Model configurations of the main and joint networks. ConvBlock and ResBlock have two convolutional layers; [\(n\times n\), \(k\)] denotes a convolutional operator of \(n\) filters and a kernel size of \(k\).  
version, so the loss function of the main network (\(L_{pitch}\)) was defined between the prediction \(\hat{\mathbf{y}}\) and the Gaussian-blurred labels \(\mathbf{y}_{g}\) as below:  
\[L_{pitch}=CE(\mathbf{y}_{g},\hat{\mathbf{y}}) \tag{1}\]  
\[y_{g}(i)=\begin{cases}exp(-\frac{(c_{i}-c_{true})^{2}}{2\sigma_{g}^{2}})&\text {if $c_{true}\
eq 0$ and $|c_{i}-c_{true}|\leq M$,}\\ 0&\text{otherwise,}\end{cases} \tag{2}\]  
where \(CE(\mathbf{y}_{g},\hat{\mathbf{y}})\) is the cross-entropy loss for the pitch prediction. \(c_{true}\) is the constant index of the true pitch, and \(c_{i}\) is a variable index. \(M\) determines the number of non-zero elements. We set \(M\) to three and \(\sigma_{g}\) to one in our experiment.
# Design and Analysis of a Novel Variable Stiffness Joint Based on Leaf Springs
## 4 Dynamics Modeling and Simulation Analysis
### Dynamic Modeling  
The dynamic model of the reconfigurable VSJ is shown in Figure 13. It contains two links: the position driving chain and the stiffness adjustment chain.  
The dynamic equations of the joint are defined as follows:  
\[\left\{\begin{array}{l}{J\ddot{q}+D\dot{q}+\tau_{ext}=K_{s}(q_{1}-q)}\\ {J_{1}\dot{q}_{1}+D_{1}\dot{q}_{1}+K_{s}(q_{1}-q)=u_{1}}\\ {J_{2}\dot{q}_{2}+D_{2}\dot{q}_{2}+\tau_{r}=u_{2}}\end{array}\right. \tag{17}\]  
where \(J\), \(D\), and \(q\) represent the inertia, damping, and position of the output shaft, respectively. \(J_{1}\), \(J_{2}\), \(D_{1}\), \(D_{2}\), \(q_{1}\), \(q_{2}\), \(u_{1}\), and \(u_{2}\) represent the inertia, damping, position, and control torque of the input shaft and the VSM, respectively. \(\tau_{r}\) and \(\tau_{ext}\) represent the stiffness adjustment resistant torque and load torque, respectively.  
Based on Equation (17), the following relations are derived:  
\[\left\{\begin{array}{l}{\ddot{q}=\frac{K_{s}}{J}(q_{1}-q)-\frac{D}{J}\dot{q}- \frac{\tau_{ext}}{J}}\\ {\ddot{q}_{1}=\frac{u_{1}}{J_{1}}-\frac{D_{1}}{J_{1}}\dot{q}_{1}-\frac{K_{s}}{ J_{1}}(q_{1}-q)}\\ {\ddot{q}_{2}=\frac{u_{2}}{J_{2}}-\frac{\tau_{1}}{J_{2}}\dot{q}_{2}-\frac{ \tau_{r}}{J_{2}}}\end{array}\right. \tag{18}\]  
Based on Equation (18), the dynamic model of the VSJ is built using Matlab/Simulink (R2019a), as shown in Figure 14.  
Figure 13: Dynamic model of the VSJ.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Items** & **Proposed** & **vsJ** & **resat-II [20]** & **REGT-VSA [23]** & **RVSA** & **CLSM-VSA [29]** \\ \hline \multirow{2}{*}{Regulation principle} & beam & \multirow{2}{*}{pivot of lever} & \multirow{2}{*}{pivot of lever} & \multirow{2}{*}{pivot of lever} & \multirow{2}{*}{beam length} & \multirow{2}{*}{section moment of inertia} \\  & length & & & & & inertia \\ Stiffness (Nm/rad) & \(N\times\) (9-inf.) & 0.7–948 & 20–2362 & 20-inf. & 50–946 \\ Range of motion (\({}^{\circ}\)) & \(\pm\)360 & \(\pm\)28.6 & \(\pm\)180 & \(\pm\)360 & \(\pm\)180 \\ Regulation Time (s) & 0.34 & 0.9 & 0.5 & 0.09 & 0.49 \\ Nominal torque (Nm) & \(N\times\) 14.6 & 15 & 22 & 11 & 21 \\ Size (mm) & \(\Phi\)140 \(\times\) 114 & / & \(\Phi\)128 \(\times\) 257 & \(\Phi\)130 \(\times\) 122 & \(\Phi\)80 \(\times\) 155 \\ Weight (kg) & 4 & 2.5 & 4.5 & 2.08 & 1.78 \\ Stiffness adjustment & only rotating the & planetary gear & \multirow{2}{*}{rocker linkage} & \multirow{2}{*}{only rotating} & \multirow{2}{*}{ball screw} \\ mechanism & disc & & & spring \\ Reconfigurable/ & & & & yes/ & yes/ \\ without disassembly & yes & no & no & disassembly. & disassembly. \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparisons of the specifications of the variable stiffness joint.
# Flutter of a Plate at High Supersonic Speeds
## 7 Results and Discussion
### Infinite Strip  
Figure 4 shows the non-dimensional flutter velocity as a function of the mass ratio. As expected, the flutter velocity decreased with increasing mass ratio. Since the curve in Figure 4 seems to have a simple structure, a mathematical expression between \(u_{f}\) and \(\mu\) could be developed by using curve fitting. This was done by using Matlab 2023b and the result was  
\[u_{f}=\frac{333.7+3.249\mu+0.1461\mu^{2}}{\mu-0.02} \tag{53}\]  
This equation gives the same points as in Figure 4 within an error of 1 percent.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Collocation Method**} & \multicolumn{2}{c}{**Analytical Results**} \\ \cline{2-5} \(\mu\) & **Before Flutter** & **After Flutter** & **Before Flutter** & **After Flutter** \\ \hline
1.006255 & 358.920571 & 359.571969 & 359.467520 & 359.571969 \\
1.242290 & 291.097486 & 291.372886 & 291.315280 & 291.372886 \\
1.572273 & 230.265826 & 230.461233 & 230.377137 & 230.461233 \\
2.053581 & 176.682416 & 176.762617 & 176.671744 & 176.762617 \\
2.795152 & 130.248788 & 130.299136 & 130.23840 & 130.299136 \\
4.025020 & 90.6746705 & 91.1957893 & 91.156960 & 91.195789 \\
6.289093 & 59.2604927 & 59.6428185 & 59.604512 & 59.642818 \\
11.18061 & 36.0023423 & 36.1616447 & 36.111424 & 36.161644 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Numerical results for a randomly chosen \(d=3\) value of the two methods.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Experimental Result** & **Theory** \\ \hline Steel & 254.7695 (panels with tension, clamped front and rear) & 263.5333 \\ Steel & 254.7695 (buckled panels, clamped front and rear) & 263.5333 \\ Brass & No flutter (panels with tension, clamped front and rear) & 919.6203 \\ Aluminum & No flutter (buckled panels, clamped on four edges) & 397.2558 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of some results with NACA report ([30]).
# A Dilemma-Based Learning-to-Rank Approach for Generative Design in Urban Architectural Regeneration
## 2 Proposed Methodology
### Evaluation Module
#### 2.2.3 Performance Metrics  
For evaluating the robustness of the learning-to-rank models, different metrics were used. Recall that the specific problem is based on a binary classification problem setup. Any two images, in the form of feature vectors, are fed to the classifier. The higher the output value, the more likely that the first image is more appropriate compared to the other, according to the user preferences. A short description of the evaluation metrics [28] is provided in the next paragraph.  
Following the model's outcomes, we may have four possible scenarios:  
* True Positive (TP): An image was correctly denoted as preferable, compared to the alternative, during the pairwise comparison, when fed to the classification model.
* False Positive (FP): An image was wrongly denoted as preferable, compared to the alternative, during the pairwise comparison, when fed to the classification model.
* (c) True Negative (TN): An image was correctly denoted as non-preferable, compared to the alternative, during the pairwise comparison, when fed to the classification model.
* (d) False Negative (FN): An image was wrongly denoted as non-preferable, compared to the alternative, during the pairwise comparison, when fed to the classification model.  
Using these values, the following evaluation metrics are calculated:  
* Accuracy (ACC): Indicates the number of correctly classified samples over the total number of samples, defined as \(\text{Acc}=\frac{TP+TN}{TP+FP+TN+FN}\).
* Precision (Pre): Refers to the proportion of true positives over the total predicted positives, given by \(\text{Pre}=\frac{TP}{TP+FP}\).
* Rec: Measures the model's ability to predict all true positives, calculated as \(\text{Rec}=\frac{TP}{TP+FN}\).
* F1-score (F1): Combines precision and recall to evaluate overall model performance, where a score closer to 1 indicates better performance. The formula is \(F1=2\times\frac{\text{Precision}\times\text{Recall}}{\text{Precision}+\text{Recall}}\).
## 3 System Model
### Task Processing Model  
#### 3.3.1 Computing on the Vehicle  
When the tasks of the vehicle \(un\) are computed locally (i.e., \(\eta_{un}=0\)), the tasks' computation delay is expressed as  
\[t_{un}^{vch}=\frac{d_{un}f_{un}\lambda_{un}}{C_{un}}, \tag{2}\]  
Figure 2: Task processing delay for different mechanisms.  
where \(C_{un}\) denotes the computing resource of vehicle \(un\).
## 3 Collective-Rotation Noise  
Collective-noise assumes that, when numerous qubits are transmitted simultaneously or near each other at least spatially, then the random unitaries or transformations due to noise on each qubit should be identical [42; 60; 61]. Various studies have recently reported on the influence of counter-clockwise and clockwise collective-rotation noise on the security of QKD [51; 62], respectively. Therefore, we analyze the impact of the clockwise collective-rotation noise in the channel, defined by the following unitary rotation matrix:  
\[U=\left(\begin{array}{cc}\cos\theta&\sin\theta\\ -\sin\theta&\cos\theta\end{array}\right), \tag{1}\]  
where \(\theta\) represents the rotation angle that characterizes the effect of the noise. The collective-rotation noise changes the four BB84 states according to the following:  
\[|0\rangle \rightarrow \cos\theta|0\rangle-\sin\theta|1\rangle=\frac{\cos\theta-\sin \theta}{\sqrt{2}}|+\rangle+\frac{\cos\theta+\sin\theta}{\sqrt{2}}|-\rangle, \tag{2}\] \[|1\rangle \rightarrow \sin\theta|0\rangle+\cos\theta|1\rangle=\frac{\cos\theta+\sin \theta}{\sqrt{2}}|+\rangle+\frac{\sin\theta-\cos\theta}{\sqrt{2}}|-\rangle, \tag{3}\]  
\[|+\rangle \rightarrow \frac{\cos\theta+\sin\theta}{\sqrt{2}}|0\rangle+\frac{\cos\theta -\sin\theta}{\sqrt{2}}|1\rangle=\cos\theta|+\rangle+\sin\theta|-\rangle, \tag{4}\] \[|-\rangle \rightarrow \frac{\cos\theta-\sin\theta}{\sqrt{2}}|0\rangle-\frac{\sin\theta +\cos\theta}{\sqrt{2}}|1\rangle=\cos\theta|-\rangle-\sin\theta|+\rangle. \tag{5}\]  
Notably, the collective-rotation noise introduces bit-flip errors in the following bases \(\{|0\rangle,|1\rangle\}\) and \(\{|+\rangle,|-\rangle\}\). Thus, the weighted sum of the bit-flip errors results in the QBER, defined as the probability that a randomly selected qubit sent from [PERSON]'s lab arrives at [PERSON]'s side flipped. This can be represented as \(|0\rangle\) as \(|1\rangle\), \(|+\rangle\) as \(|-\rangle\), and vice versa. Based on Equations (2)-(5), the effect of noise is that it flips the states \(|0\rangle\), \(|1\rangle\), \(|+\rangle\), and \(|-\rangle\) with probability \(\sin^{2}\theta\). Therefore, if [PERSON] selects and transmits each of the four states with a probability of \(p=1/4\), then the collective-rotation noise in the channel will result in a QBER of:  
\[Q_{0}=\frac{1}{4}(4\sin^{2}\theta)=\sin^{2}\theta. \tag{6}\]  
The QBER is one of the essential QKD security parameters [2]. It gives the ratio of the number of bits in error to the total detected bits. Therefore, QBER provides the percentage of signals chosen by [PERSON] and [PERSON] for the same encoding, but where [PERSON] got a measurement outcome that differs from that prepared by [PERSON] [51].
## 3 Dark Solitons
### Gray Solitons under Dissipation  
According to the perturbation theory for dark solitons [33], the gray soliton of Equation (18) evolves as:  
\[\begin{split} A&=\eta_{0}\left\{b\text{tanh}\left[ \eta_{0}b\left(\sqrt{\left|\frac{q}{k_{r}^{\prime\prime}}\right|}\tau_{1}-aq \eta_{0}\chi_{2}\right.\right.\\ &\left.\left.-\sqrt{\left|\frac{q}{k_{r}^{\prime\prime}}\right|}t _{0}\right)\right]+ia\right\}e^{-iq\eta_{0}^{2}\chi_{2}-i\
u_{0}},\end{split} \tag{37}\]  
where  
\[a =a_{0}\exp(-\Lambda\chi_{2}), \tag{38}\] \[b =b_{0}\exp(-\Lambda\chi_{2}). \tag{39}\]  
The background amplitude \(A=\eta_{0}\sqrt{a^{2}+b^{2}}=\eta_{0}\exp(-\Lambda\chi_{2})\) decays exponentially with the same rate as in the black soliton case, Equation (30). The first-order correction term is given by:  
\[t_{0}=\frac{a_{0}}{4b_{0}\eta_{0}}\exp(-\Lambda\chi_{2})+\frac{3a_{0}}{4b_{0} \eta_{0}}\exp(\Lambda\chi_{2})-\frac{a_{0}}{b_{0}\eta_{0}}, \tag{40}\]  
and \(\sigma_{0}\) is an extra phase induced by the perturbation. In the original coordinates, \(x\) and \(t\), the approximate form of the gray soliton reads:  
\[\begin{split}& p(x,t)\approx 2e\eta_{0}P_{0}b_{0}e^{-\frac{- \Lambda x^{2}\omega_{B}}{\zeta_{0}}x}\\ &\times\tanh\left\{e\eta_{0}b_{0}e^{-\frac{\Lambda x^{2}\omega_{ B}}{\zeta_{0}}x}\sqrt{\left|\frac{q}{k_{r}^{\prime\prime}}\right|}\omega_{B} \left[t-\frac{k_{r}^{\prime}}{c_{0}}x\right.\right.\\ &\left.\left.-ea_{0}e^{-\Lambda e^{2}\frac{\omega_{B}}{\zeta_{0} }x}\eta_{0}\frac{\sqrt{\left|qk_{r}^{\prime\prime}\right|}}{c_{0}}x\right.\\ &\left.\left.-\frac{1}{e\omega_{B}}\left(\frac{a_{0}}{4b_{0}\eta _{0}}e^{-\Lambda e^{2}\frac{\omega_{B}}{\zeta_{0}}x}+\frac{3a_{0}}{4b_{0}\eta _{0}}e^{\Lambda e^{2}\frac{\omega_{B}}{\zeta_{0}}x}-\frac{a_{0}}{b_{0}\eta_{0 }}\right)\right]\right\}\\ &\times\cos\left(\omega\omega_{B}t-\frac{k_{r}\omega_{B}}{c_{0}} x-qe^{2}\eta_{0}^{2}\frac{\omega_{B}}{c_{0}}x-e^{2}\frac{\omega_{B}}{c_{0}} \sigma_{0}\right)\\ &-2e\eta_{0}P_{0}a_{0}e^{-\frac{\Lambda e^{2}\omega_{B}}{\zeta_{0 }}x}\\ &\times\sin\left(\omega\omega_{B}t-\frac{k_{r}\omega_{B}}{c_{0}} x-qe^{2}\eta_{0}^{2}\frac{\omega_{B}}{c_{0}}x-e^{2}\frac{\omega_{B}}{c_{0}}\sigma_{0} \right),\end{split} \tag{41}\]  
with the velocity  
\[v_{g}=\left(\frac{k_{r}^{\prime}}{c_{0}}+\epsilon a_{0}e^{-\Lambda e^{2}\frac {\omega_{B}}{\zeta_{0}}x}\eta_{0}\frac{\sqrt{\left|qk_{r}^{\prime\prime}\right| }}{c_{0}}\right)^{-1}. \tag{42}\]  
During gray soliton propagation, both the background amplitude and the minimum intensity decrease exponentially due to losses, while the width increases (see Equation (41)).  
We numerically integrate the lattice model, Equation (3), with a gray soliton driver of the form given by Equation (35) or Equation (41), with \(\epsilon=0.01\) (\(2e\eta P_{0}=4.39\times 10^{7}\) Pa) and \(f=1300\) Hz. The numerical profile found at \(t=0.58\) s, with \(\phi=\pi/8\), is shown in Figure 7a (blue line), is in a good agreement with the analytical prediction (green dashed line), Equation (41). The numerically obtained gray soliton trajectory [blue circles in Figure 7b], and is in good agreement with the analytical expression given in Equation (42).
## 4 Reduction Factor for the Y-Type Perfobond Rib Shear Resistance
### Design Shear Resistance for the Y-Type Perfobond Rib Shear Connector  
Based on the probabilistic models of the shear resistance of the Y-type perfobond rib shear connector (Table 22), the reduction factor (\(\phi\)) is derived to provide the design shear resistance depending on the target reliability level. The design shear resistance (\(Q_{d}\)) can be calculated from the reduction factor and the nominal shear resistance (\(Q_{n}\), Equation (3)) by either Equation (4) or Equation (5):  
\[Q_{d}=\phi Q_{n} \tag{4}\]  
\[Q_{d}=\phi n^{0.67}\left(970d_{r}f_{yr}{}^{0.2}+4,240\sqrt{f_{y}}\left(\frac{t }{10}\right)\left(\frac{w}{80}\right)^{0.95}\left(\frac{h}{100}\right)^{0.45} \right)f_{ck}{}^{0.3} \tag{5}\]  
The reduction factors (\(\phi\)) are provided in the wide range from 0.50 to 0.90, and the safety levels to be achieved are tabulated in Table 23. The worst estimation error by the proposed nominal resistance is 0.90 (experimental result/Equation (3): Test No. 4R-5-1 in Table 17), in which the estimation by Equation (3) overestimates by 10%. This is the lowest value plotted at 0.895 in Figure 7. This overestimation can be overcome by selecting the reduction factor below 0.90. Since the biasness of the nominal shear resistance increases  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Mean** & **COV** & **n** & **Correlation Coefficient** \\ \hline Sample data & 1.129 & 0.127 & 1,000,000 & - \\ Linear regression & 1.129 & 0.127 & 1,000,000 & 0.9998 \\ \hline \hline \end{tabular}
\end{table}
Table 21: Probabilistic characteristics of the shear resistance from Monte-Carlo simulation.  
Figure 8: Plot of the simulated shear resistances on a normal PDF paper.  
slightly with the increasing number of ribs, two sets of inherent safety levels are provided for 4-rib shear connectors and 10-rib shear connectors. The differences in the safety levels achieved in two sets are quite negligible. It is recommended that the proposed design strength equation, Equation (5), should be applied for the design of Y-type shear connectors with more than 4 ribs. The reduction factor between the tabulated values can be selected by a linear interpolation.
# WSN Nodes Placement Optimization Based on a Weighted Centroid Artificial Fish Swarm Algorithm
## 3 Weighted Centroid Fish Swarm Algorithm
### Time Complexity Analysis  
The effectiveness of the algorithm can be measured by time complexity. The basic operation count is regarded as the time complexity of the algorithm. We analyze the time complexity according to the implementation procedure of WCA-AFSA.  
* Initialization of \(N\) artificial fish needs \(N\) times. Time complexity is \(O(N)\).
* Initialization of other parameters assigns once and compares \(N-1\) times. Time complexity is \(O(N)\).
* Swarm behavior computes crowding factor \(N\) times, judges once, moves once, and swarms \(N\) times. Time complexity is \(O(N^{2}+2\times N)\).
* Follow behavior searches the optimal value \(N\) times, computes crowding factor \(N\) times, judges once, moves once, and follows \(N\) times. Time complexity is \(O(2\times N^{2}+2\times N)\).
* The frequency of prey behavior is, at most, _try_number_ times, at least once. \(N\) artificial fishes prey \(N\) times. Time complexity is \(O(N\times\textit{try\_number})\).  
After \(l\) iterations, time complexity is \(O(l\times(3\times N^{2}+N\times\textit{try\_number}+4\times N))\).
# Enhanced Intrusion Detection Systems Performance with UNSW-NB15 Data Analysis
## 3 Proposed Research Methodology
### Logistic Regression  
For binary classification issues, supervised machine learning methods are typically employed [22]. With the use of one or more predictor variables, it is frequently employed to predict a binary result (True/False). The logistic function, sometimes referred to as the sigmoid function, is used by the algorithm to define the relationship between the predictor variables and the binary output variable. Any input value is translated by the sigmoid function to a number between 0 and 1, which is the likelihood that the binary result will be 1. Within the regression family, a logistic regression has specifically been applied to perform classification, specifically binary classification. Therefore, it is relatively common to use this method when constructing machine learning for binary classification tasks.  
By employing optimization strategies like gradient descent to minimize a cost function, such as the cross-entropy loss, the logistic regression model gains knowledge from the training set [23]. Based on the values of the predictor variables, the model can be trained to predict the binary outcome for new occurrences. The following is the main characteristic of logistic regression:  
* Logit function: The logistic regression model determines the likelihood that the dependent variable will take a particular value using the logit function. \[p=\frac{1}{1+e^{-z}}\] (1) where \(p\) is the predicted binary probability. The predictor variables are combined linearly into \(z\) and \(e\) is the natural logarithm's base. \[z=\beta_{0}+B_{1}x_{1}+\beta_{2}x_{2}\dots B_{k}x_{k}\] (2)
* S-shaped curve: The logistic regression model generates an S-shaped curve that shows the likelihood that, for a given value of the independent variables, the dependent variable will take the value of 1.
* Maximum Likelihood Estimation: The logistic regression model estimates the model parameters using maximum likelihood estimation.  
We included logistic regression because it is a well-established and widely used algorithm for binary classification tasks, making it a standard classifier in the field. Moreover, it is a simple and efficient classifier, making logistic regression a good benchmark for evaluating binary classification problems.