esa-sceva/satcom-chunk-collection huggingface dataset:
# Advancements and Prospects of Electronic Nose in Various Applications: A Comprehensive Review
## 3 Application Areas
### Environmental Monitoring
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Source of Malodor** & **Type of Sensor** & **Description and Results** & **Reference** \\ \hline Landfill gas odors & 16 tin oxide sensors (Keeling \& Walker, Stoke-on-Tent, UK) & The research focuses on quantifying landfill gas (LFG) odor in terms of odor units per cubic meter (\(\mathrm{o}\mathrm{u}\mathrm{/}\mathrm{m}^{3}\)) using a sensor array and employs artificial neural networks (ANN) as the analysis method. It strategically identifies the most effective neural models (MLP and RBF networks) for accurately approximating odor concentrations. Additionally, the study assesses the influence of multiple biogas sources on the accuracy of the approximations. Notably, the results highlight a robust correlation between sensors and odor concentration, underscoring the reliability of the approach. The achieved low prediction errors (MSE) of 0.000410 for MLP and 0.000755 for RBF within the 0 to 200 \(\mathrm{o}\mathrm{u}\mathrm{/}\mathrm{m}^{3}\) range further emphasize the effectiveness of the proposed method. & This study develops an electronic-nose-based system for continuous odor monitoring at specific receptors. It focuses on a composting plant in Italy, detailing training procedures and data processing. The optimized electronic nose achieves a qualitative accuracy of 96.4% and a correlation index of R\({}^{2}\) = 0.90172 for odor concentration determination. Results highlight the compost storage area as the main odor source, validated by comparing instrumental responses with meteorological data. & The Odor Vector system based on quartz-microbalance sensors coated with gas chromatography stationary phases, successfully monitored odors at a waste incineration plant. It detected odor breakthroughs in charcoal filter conditions and calculated odor concentrations online. The method demonstrated pattern-based classification and was effective in aligning with industry standards. Strong correlation between specific sensor responses and odor concentrations in the range of 0 to 500 \(\mathrm{o}\mathrm{u}\mathrm{/}\mathrm{m}^{3}\) was observed. \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Applications of electronic noses for environmental odor monitoring. Figure 7: Map of e-nose locations relative to water treatment plants [130]. The realm of environmental monitoring has been significantly transformed by the integration of e-noses, showcasing their adaptability and efficacy in addressing diverse challenges. E-noses have emerged as versatile tools that hold the potential to revolutionize the assessment and management of environmental odors and air quality. These innovative devices find application in various contexts, including air and water quality analysis,
## 2 Optimisation Techniques in Reinforcement Learning
### Reinforcement Learning (RL)
#### 2.1.1 Q-Learning and Deep Q-Learning (DQN)  
Q-learning is an off-policy RL algorithm that iteratively updates Q-values to approximate an optimal policy. The Q-function represents the expected return for a given state-action pair and is updated using the Bellman equation:  
\[Q(S,A)\gets Q(S,A)+\alpha\Big{[}r+\gamma\max_{a}Q(S^{\prime},A^{\prime})- Q(S,A)\Big{]}, \tag{1}\]  
where \(\alpha\) is the learning rate, \(r\) is the reward, and \(\gamma\) is the discount factor [11].  
In Deep Q-Learning (DQN), a neural network approximates the Q-function to handle complex state spaces. The algorithm, as outlined in Algorithm 1, employs a replay buffer to store experiences and a target network to stabilise training. Mini-batches of experiences are sampled from the buffer to compute temporal-difference targets and update the network parameters, reducing overestimation of Q-values [3; 11].  
```
\(S\leftarrow\) initial state whileThe terminal state is not reached do  Use \(Q(S)\) to select action \(A\) (e.g., using \(\epsilon\)-greedy method)  Take the action and receive \(S^{\prime}\), \(R\), terminal state  Store (\(S\), \(A\), \(R\), \(S^{\prime}\), terminal state) in the replay buffer  LearnFromExperience() \(S=S^{\prime}\) endwhile functionLearFromExperience  Sample (\(S\), \(A\), \(R\), \(S^{\prime}\), terminal _state) from the replay buffer \(TD_{\text{target}}\gets R+\gamma\max(Q(S^{\prime}))\) \(Q_{\text{expected}}\gets Q(S)[A]\)  Loss \(\leftarrow\) MSE(\(Q_{\text{expected}}\), \(TD_{\text{target}}\))  Update the weights of \(Q\) endfunction
```  
**Algorithm 1** Deep Q-Learning with Replay Buffer
# An Energy-Efficient Evolutionary Clustering Technique for Disaster Management in IoT Networks
## 3 Proposed Method
### AWS Method for LP Formula  
One of the most significant challenges in disaster management is decision-making in harsh environments [44]. In these cases, the decision-maker faces different criteria influenced by the internal and external environment. Hence, multi-criteria decision making (MCDM) schemas are considered to be among the best tools to make decisions [36; 39]. In MCDM, instead of using an optimality criterion, several metric criteria may be used. Among the methods to solve these problems is the adaptive weighted sum (AWS) method [38]. As the simplest method of MCDM analysis, the AWS method can be used only when all criteria are stated precisely in terms of the same domain. Moreover, it permits a multi-objective optimization problem (MOP) to be converted into a single objective mathematical optimization problem (SOMP) format. The MOP method is formulated as follows [28; 37; 38]:  
\[\mathrm{MOP:}\min_{x\in\Omega}\mathrm{F}\left(\mathrm{x}\right)=\min_{x\in \Omega}\left(\mathrm{f_{1}}\left(\mathrm{x}\right),\mathrm{f_{2}}\left( \mathrm{x}\right),\ \ldots,\mathrm{f_{n}}\left(\mathrm{x}\right)\right) \tag{11}\]  
subject to \(F(x):\Omega\to R^{n}\). Multiplying the sum of the fitness functions in the weighted coefficients, the AWS method transforms Equation (11) to the SOMP as per Equation (12) [38]:  
\[\min\sum\limits_{j=1}^{N}w_{j}.f_{j}\left(x\right) \tag{12}\]  
subject to \(j\in\Omega\), where \(w_{j}\geq 0\), \(\left(\forall j=1,2,\ldots,N\right)\), and \(\sum\limits_{j=1}^{N}w_{j}=1\).  
In this paper, we use the above equation to determine the fitness functions. Equation (12) is also called Pareto optimization. Typically, this kind of optimization gives a unique solution (if \(w_{j}\ >0,\ \forall j=1,2,\ \ldots,\ N\)) [38]. As the proposed fitness functions are composed of different criteria and values, it is also essential to normalize the criteria with respect to the Pareto optimization and match them with the weighted coefficients [38].
## 3 Governing Equations  
The displacement fields are postulated in accordance with [PERSON]'s beam theory as follow:  
\[\mathbf{u}=\left\{\begin{matrix}u(x,y,z,t)\\ w(x,y,z,t)\end{matrix}\right\}=\left\{\begin{matrix}u_{0}(x,t)\\ w_{0}(x,t)\end{matrix}\right\}+z\left\{\begin{matrix}\psi_{x}(x,t)\\ 0\end{matrix}\right\} \tag{18}\]  
where \(t\) denotes the time, \(u_{0}\) and \(w_{0}\) denote the axial and transverse displacements of the beam mid-plane, respectively, and \(\psi_{x}\) is the rotation of the beam cross section about the positive \(y\)-axis.  
The composite beam in this study has been discretised through the use of a two-nodded superconvergent beam element. Each node of this element has three degrees of freedom. The interpolation of the generalised displacement vector is expressed as follows:  
\[\bar{\mathbf{u}}=\{u_{0},w_{0},\psi_{x}\}^{T}=\mathbf{N}(x)\mathbf{d}^{e}(t)=\{\mathbf{N}_{u}, \mathbf{N}_{w},\mathbf{N}_{\psi}\}^{T}\mathbf{d}^{e} \tag{19}\]  
where \(\mathbf{d}^{e}=\{u_{0}^{1},w_{0}^{1},\psi_{x}^{1},u_{0}^{2},w_{0}^{2},\psi_{x}^{2 }\}^{T}\) and \(\mathbf{N}_{u},\mathbf{N}_{w},\mathbf{N}_{\psi}\) are the super convergence shape functions [12]. Two further degrees of freedom (DOF) per element are incorporated to represent the electrical voltages of two distinct piezoelectric layers. For each additional piezoelectric layer, an extra voltage DOF is required per element.  
By utilising the extended Hamilton's variational principle, we can deduce the governing equations of motion of the piezoelectric composite beam in relation to the global coordinates by employing the standard procedure of the finite element (FE) method:  
\[M\ddot{\mathbf{d}}+\mathbf{K}\mathbf{d}+\mathbf{\Theta}_{1}v_{1}+\mathbf{\Theta}_{2}v _{2} =\mathbf{F}_{m} \tag{20}\] \[-\mathbf{\Theta}_{1}^{T}\mathbf{d}+C_{p_{1}}v_{1} =\mathcal{Q}_{1}\] (21) \[\mathbf{\Theta}_{2}^{T}\mathbf{d}+C_{p_{2}}v_{1} =\mathcal{Q}_{2} \tag{22}\]  
where \(\mathbf{d}\) is the global vector of mechanical degrees of freedom, \(\mathbf{M}\) is the global mass matrix, \(\mathbf{K}\) is the global stiffness matrix and \(\mathbf{F}_{m}\) is the global vector of mechanical forces. Also, \(\mathbf{\Theta_{1}},\mathbf{\Theta_{2}}\) are the electromechanical coupling matrices, \(C_{p_{i}}\) and \(Q_{i}\) are the capacitance and the electric charge output of the piezoelectric layer \(i\), respectively. Notice that the enforcement of equipotentiality in the electrodes is achieved by assigning a single electrical degree of freedom for each piezoelectric layer. Details regarding the development of this finite element model can be found in previous works from the authors [12].
# Road Obstacle Detection Method Based on Improved YOLOv5
## 4 Results
### Evaluation Indicators  
Currently, algorithm evaluation is based on key metrics such as precision (P), recall (R), and mean average precision (mAP). Precision (P) measures the accuracy of the algorithm in detecting road obstacles, while recall (R) evaluates the algorithm's ability to comprehensively detect road obstacles. The mean average precision (mAP) provides an overall evaluation of the algorithm's performance across multiple road obstacle detection tasks, and FPS (frames per second) indicates the number of frames processed per second. mAP is derived from two metrics: precision (P) and recall (R). The core metrics used to assess precision include True Positive (TP), False Positive (FP), True Negative (TN), and False Negative (FN). The specific formulas for these metrics are provided in (8) to (12).  
\[Precision=\frac{TP}{TP+FP}, \tag{8}\]  
\[Recall=\frac{TP}{TP+FN}, \tag{9}\]  
\[AP=\int_{0}^{1}P(R)dR, \tag{10}\]  
Figure 8: Training and validation loss curves.  
\[mAP=\frac{1}{n}{\sum_{i=1}^{n}{AP_{i}}}, \tag{11}\] \[FPS=\frac{FrameNum}{ElapsedTime}, \tag{12}\]  
where _TP_, _FP_, and _FN_ represent the correct test frames, incorrect test frames, and missed frames, respectively. _mAP_ refers to the mean average precision value of the P-R curve for a given category. \(N\) denotes the total number of detected target categories, _FrameNum_ represents the number of detected images, and _ElapsedTime_ indicates the image processing time.
Finally, we extracted from our experimental data complex conductivity spectra of graphene nanocomposites and successfully fitted them to the Drude-Smith model, demonstrating that our graphene nanoflakes were isolated in their polymer matrix and exhibited highly localized electron backscattering with a femtosecond relaxation time. Our results shed new light on how the incorporation of exfoliated graphene nanoflakes modifies polymer electrical properties in the THz-frequency range. Importantly, they demonstrate that the complex conductivity analysis is a very efficient, macroscopic and non-destructive (contrary to TEM) tool for the characterization of the dispersion of a graphene nanofililer within a copolyester matrix. graphene; graphene nanoflakes; graphene-polymer nanocomposites; multiblock copolymers; terahertz time-domain spectroscopy; Drude-Smith model for complex conductivity
# Calculation of the Relaxation Modulus in the Andrade Model by Using the Laplace Transform
## 2 Laplace Inversion in Terms of Miller-Ross Functions for \(\alpha=1/3\)  
Consider in (7) the following change of variables:  
\[b=\frac{1}{\tau},\quad c=\frac{\Gamma(\alpha+1)}{\tau^{\alpha}}, \tag{9}\]  
to rewrite \(\tilde{G}_{\alpha}(s)\) as  
\[\tilde{G}_{\alpha}(s)=\frac{\mu}{b+s+c\,s^{1-\alpha}}. \tag{10}\]  
In order calculate the inverse Laplace transform of \(\tilde{G}_{\alpha}(s)\) for the case \(\alpha=1/3\), i.e.,  
\[\tilde{G}_{1/3}(s)=\frac{\mu}{b+s+c\,s^{2/3}}, \tag{11}\]  
apply the identity  
\[(x+y)\Big{(}x^{2}-xy+y^{2}\Big{)}=x^{3}+y^{3}, \tag{12}\]  
taking \(x=b+s\), and \(y=c\,s^{2/3}\), to arrive at  
\[\frac{1}{\mu}\tilde{G}_{1/3}(s)=b^{2}\underbrace{\frac{1}{p(s)}}_{\tilde{R}(s )}+2b\underbrace{s\frac{1}{p(s)}}_{\tilde{Q}(s)=s\,\tilde{R}(s)}+\underbrace {\frac{s^{2}}{p(s)}}_{\tilde{s}\,\tilde{Q}(s)}-bc\underbrace{\frac{s^{2/3}}{p (s)}}_{\tilde{Q}_{2/3}(s)}-c\underbrace{s\frac{s^{2/3}}{p(s)}}_{s\,\tilde{Q}_{ 2/3}(s)}+c^{2}\underbrace{\frac{s^{4/3}}{p(s)}}_{\tilde{a}_{4/3}(s)}, \tag{13}\]  
where  
\[p(s)=s^{3}+\Big{(}3b+c^{3}\Big{)}s^{2}+3b^{2}s+b^{3}=\prod_{k=1}^{3}(s-s_{k}), \tag{14}\]  
and \(s_{k}\) are the roots of the cubic equation \(p(s)=0\), i.e.,  
\[\begin{split} s_{1}&=-\frac{1}{3}(M-N-L),\\ s_{2}&=-\frac{1}{3}\Big{(}M+e^{i\,\pi/3}N+e^{-i\, \pi/3}L\Big{)},\\ s_{3}&=-\frac{1}{3}\Big{(}M+e^{-i\,\pi/3}N+e^{i\, \pi/3}L\Big{)},\end{split} \tag{15}\]  
being  
\[\begin{split}& M=3b+c^{3},\\ & L=\sqrt[3]{\frac{3}{2}\sqrt{3b^{3}c^{6}(27b+4c^{3})}-\frac{27}{ 2}b^{2}c^{3}-9\,bc^{6}-c^{9}},\\ & N=\frac{(6b+c^{3})c^{3}}{L}.\end{split} \tag{16}\]  
First, rewrite \(\tilde{R}(s)\) as  
\[\tilde{R}(s)=\frac{1}{p(s)}=\sum_{k=1}^{3}\frac{\alpha_{k}}{s-s_{k}},\quad \alpha_{k}=\prod_{j\
eq k}^{3}\frac{1}{s_{k}-s_{j}}. \tag{17}\]  
Note that a simple algebraic calculation shows that  
\[\begin{split}&\sum_{k=1}^{3}\alpha_{k}=0,\\ &\sum_{k=1}^{3}\alpha_{k}\,s_{k}=0.\end{split} \tag{18}\]Now, define the following functions  
\[R(t)=\mathcal{L}^{-1}\big{[}\check{R}(s);t\big{]}, \tag{19}\]  
thus,  
\[Q(t)=\mathcal{L}^{-1}\big{[}\check{Q}(s);t\big{]}=\mathcal{L}^{-1}\big{[}s\; \check{R}(s);t\big{]}=R^{\prime}(t)+R(0)\,\delta(t), \tag{20}\]  
and  
\[\mathcal{L}^{-1}\big{[}s\;\check{Q}(s);t\big{]}=Q^{\prime}(t)+Q(0)\delta(t)=R^{ \prime\prime}(t)+R^{\prime}(0)\,\delta^{\prime}(t). \tag{21}\]  
Furthermore,  
\[U_{v}(t)=\mathcal{L}^{-1}\big{[}\check{U}_{v}(s);t\big{]}=\mathcal{L}^{-1} \bigg{[}\frac{s^{v}}{p(s)};t\bigg{]}, \tag{22}\]  
thus  
\[\mathcal{L}^{-1}\big{[}s\;\check{U}_{v}(s);t\big{]}=U^{\prime}_{v}(t)+U_{v}(0 )\,\delta(t). \tag{23}\]  
Therefore, the inverse Laplace transform of \(\check{G}_{1/3}(s)\) is given by  
\[G_{1/3}(t) = \mathcal{L}^{-1}\big{[}\check{G}_{1/3}(s);t\big{]}\] \[= \mu\Big{\{}b^{2}\,R(t)+2b\,\big{[}R^{\prime}(t)+R(0)\,\delta(t) \big{]}+R^{\prime\prime}(t)+R^{\prime}(0)\,\delta^{\prime}(t)\] \[+bc\,U_{2/3}(t)-c\big{[}U^{\prime}_{2/3}(t)+U_{2/3}(0)\,\delta(t) \big{]}+c^{2}\,U_{4/3}(t)\Big{\}}.\]
# Enhancement of Conventional Beat Tracking System Using Teager-Kaiser Energy Operator
###### Abstract  
Beat detection systems are widely used in the music information retrieval (MIR) research field for the computation of tempo and beat time positions in audio signals. One of the most important parts of these systems is usually onset detection. There is an understandable tendency to employ the most accurate onset detector. However, there are options to increase the global tempo (GT) accuracy and also the detection accuracy of beat positions at the expense of less accurate onset detection. The aim of this study is to introduce an enhancement of a conventional beat detector. The enhancement is based on the Teager-Kaiser energy operator (TKEO), which pre-processes the input audio signal before the spectral flux calculation. The proposed approach is first evaluated in terms of the ability to estimate the GT and beat positions accuracy of given audio tracks compared to the same conventional system without the proposed enhancement. The accuracy of the GT and average beat differences (ABD) estimation is tested on the manually labelled reference database. Finally, this system is used for analysis of a string quartet music database. Results suggest that the presence of the TKEO lowers onset detection accuracy but also increases the GT and ABD estimation. The average deviation from the reference GT in the reference database is 9.99 BPM (11.28%), which improves the conventional methodology, where the average deviation is 18.19 BPM (17.74%). This study has a pilot character and provides some suggestions for improving the beat tracking system for music analysis.  
beat tracking system; music analysis; music information retrieval; onset detection; spectral flux; string quartet music; Teager-Kaiser energy operator +
Footnote †: journal: Applied Sciences
# Overview of Predictive Control Technology for Permanent Magnet Synchronous Motor Systems
## 3 An Overview of the Recent Development for Predictive Control Methods of PMSM
### CCS-Model Predictive Control of PMSM
#### 3.3.2 Explicit Model Predictive Control  
Compared with generalized predictive control, explicit model predictive control can obtain the offline optimal resolution of constrained optimization problems directly, the high bandwidth model predictive control block diagram is shown in Figure 11, so it has significant advantages in the field of multivariable control [161,162]. High-bandwidth  
Figure 10: From [146]. (**a**) The block diagram of the controller with inductance disturbance; (**b**) The experimental diagram with the sudden increase of 100% inductance.  
predictive control converts the optimization problem in predictive control into a multi-parameter quadratic programming problem. The state space is decomposed into multiple convex partitions. The quadratic programming problem in each convex partition can determine the optimal control law offline [163]. At present, the explicit model predictive control based on a cascaded double closed-loop has been successfully applied to the motor drive system [158].  
In addition, many scholars are also trying to use explicit model prediction to directly obtain an AC motor multi-input-multi-output speed controller, in order to eliminate the traditional cascade control mode and achieve direct control of motor speed [164]. Other scholars have considered replacing the precise explicit model predictive control method with the approximate explicit model predictive control method [165]. The accuracy of the control quantity is sacrificed in exchange for lower complexity, thus simplifying the offline and online calculation process [166; 167].
# Roto-Translational Control of Spacecraft in Low Earth Orbit Using Environmental Forces and Torques
## 2 Spacecraft Dynamics  
### The Drag Maneuvering Device (DMD)  
The DMD [21] is self-contained and can be mounted on standard CubeSats [22]. This device provides the host satellite with the capability of independently modulating four surfaces so that the experienced environmental forces and torques can be altered. Each surface is offset 90 degrees and has a fixed inclination of 20 degrees with respect to the anti-ram face of the spacecraft, see Figure 1. The DMD surfaces are rolled from 0.0762 mm tick austenitic 316 stainless steel shim stock, each surface is attached to a drum that is driven by a brushless DC motor. The width and length of the DMD surfaces are 4 cm and 3.7 m, respectively. The DMD is capable of increasing the spacecraft cross sectional area by up to 0.5 \(\,\mathrm{m}^{2}\) as well as modifying the inertia matrix, resulting in modulation of the experienced aerodynamic forces/torques and gravity gradient torque.
# Design of Chaotic Interleaver Based on Duffing Map for Turbo Code
## 3 Interleaver
### Chaotic Interleaver Based on the Lozi Map  
The chaotic interleaver based on the Lozi map has been presented in [34]. The Lozi map is a two-dimensional map introduced by [PERSON] via a direct modification of the Henon map. Simply speaking, a quadratic term in the latter is replaced with a piecewise linear version in the former. The same procedure is conducted for the quadratic map to derive the skew tent map. The state or system equations \(x_{n}=f(x(n-1))\) for the Lozi map, expressed component-wise, are the following:  
\[x(n)=1-a\cdot|x(n-1)|+y(n-1); \tag{16}\]  
\[y(n)=b\cdot x(n-1) \tag{17}\]  
where \(n\) is the iteration number, and \((x_{0},y_{0})\) are the initial conditions. The system exhibits a chaotic behavior for the typical values \(a=1.7\) and \(b=0.5\).  
The chaotic interleaver based on the Lozi map is performed as follows:  
Step 1: the integer sequence \(\{n\}_{n=1}^{N}\in\mathbb{Z}\) is mapped to a real number sequence \(\{x_{n}\}_{n=1}^{N}\in\mathbb{R}\) using Equations (16) and (17).  
Step 2: \(\{x(n)\}_{n=1}^{N}\) is mapped to another integer sequence \(\{s(n)\}_{n=1}^{N}\in\mathbb{Z}\) by designing \(s(n)\) as the position of index of \(x(n)\) in the sort ascending of \(\{x(n)\}_{n=1}^{N}\).  
Step 3: the chaotic interleaver indexes are given by: \(\pi(\{s(n)\}_{n=1}^{N})=\{n\}_{n=1}^{N}\).
# Performance Comparison of Machine Learning Disruption Predictors at JET
## 2 Materials and Methods
### Machine Learning Methods
#### 2.3.2 Generative Topographic Mapping (GTM)  
GTM [40] is a probabilistic manifold learning method, which allows us to embed a high-dimensional (n-D) space into a low-dimensional (typically 2-D), possibly nonlinear, latent space. The latter is a grid of \(K\) prototype nodes that have coordinates in both the embedded and input space. During the training, the algorithm performs mapping \(f\left(\mathbf{z},\mathbf{W},\ \beta\right)\) from the set of training feature vectors \(\mathbf{X}=\{\mathbf{x}_{1},\mathbf{x}_{2},\cdots,\mathbf{x}_{1}\ \}\in\Re^{n}\) into the prototypes \(\mathbf{Z}=\{\mathbf{z}_{1},\mathbf{z}_{2},\cdots,\mathbf{z}_{K}\ \}\in\Re^{2}\) by linearly combining a radially symmetric Gaussian's basis function (RBF) \(\Phi\), where \(\mathbf{W}\) and \(\beta\) are the adaptive parameters of the model. The model parameters are optimized with the expectation maximization (EM) algorithm:  
\[\max_{\mathbf{W},\beta}\mathcal{L}=\sum_{i=1}^{I}ln\left(\frac{1}{K}\sum_{k=1}^{K} p(\mathbf{x}_{i}|\mathbf{z}_{k},\mathbf{W},\beta)\right) \tag{2}\]  
where  
\[p(\mathbf{x}_{i}|\mathbf{W},\beta)=\frac{1}{K}\sum_{k=1}^{K}\left(\frac{\beta}{2\pi} \right)^{-\frac{n}{2}}\cdot\exp\left\{-\frac{\beta}{2}f\left(\mathbf{z}_{k},\mathbf{W} \right)-\mathbf{x}_{i}{}^{2}\right\}\]  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Sets** & **Disrupted** & **Non-Disrupted** & **JET Campaigns** \\ \hline Training set & 63 & 54 & 2011–2013 \\ Validation set & 22 & 16 & 2011–2013 \\ Test set & 108 & 149 & 2011–2020 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Datasets for developing the models.  
Once the model has been optimized, the corresponding posterior distribution over the latent space can be computed through the [PERSON] theorem referring to the prior distribution of the latent variable, where the asterisks indicate the optimal parameter values.  
\[p(\mathbf{Z}_{k}|\mathbf{x}_{i})=\frac{p(\mathbf{x}_{i}|\mathbf{Z}_{k},\mathbf{W}^{*},\beta^{*})\cdot p (\mathbf{z}_{k})}{\sum_{k^{\prime}=1}^{K}p(\mathbf{x}_{i}|\mathbf{Z}_{k},\mathbf{W}^{*},\beta^{* })\cdot p(\mathbf{Z}_{k^{\prime}})} \tag{3}\]  
To visualize the input space on the 2D map, statistic measures such as the mean or the mode, can be used to visualize the posterior probability distribution over the latent space. Note that the overfitting can be managed by setting the latent space properties, as suggested in [40].