esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 The Proposed Algorithm
### Ego-Motion Application  
For each candidate movement \(M_{k}\), we apply the ego-motion transformation to the second image \(I_{2}\) to generate a transformed image \(I_{2,k}\):  
\[I_{2,k}=\text{Ego-motion}(I_{2},M_{k}) \tag{8}\]  
The transformation of ego-motion can be expressed as follows: given a movement \(M_{k}\) defined by displacements \((\Delta x,\Delta y)\) and a rotation angle \(\Delta\theta\), the transformation for a pixel coordinate \((x,y)\) in the image \(I_{2}\) can be represented as follows:  
\[\begin{split} x^{\prime}&=x\cdot\cos(\Delta\theta) -y\cdot\sin(\Delta\theta)+\Delta x\\ y^{\prime}&=x\cdot\sin(\Delta\theta)+y\cdot\cos( \Delta\theta)+\Delta y\end{split} \tag{9}\]  
This defines how each pixel of the image \(I_{2}\) is transformed based on the movement parameters. The transformed image is then compared with the first image \(I_{1}\) using a cost function defined in terms of the differences in pixel intensity to evaluate the quality of the candidate movement.  
The main goal of this step is to assess how well a transformed image \(I_{2,k}\) (obtained through a candidate movement \(M_{k}\)) aligns with the reference image \(I_{1}\). This alignment is quantified through a cost function that measures the dissimilarity between the two images. For that purpose, we adopt the Mean Squared Error (MSE), which is a widely used measure that computes the average squared differences between pixel intensities of the two images. It is defined as follows:  
\[\text{MSE}(I_{1},I_{2,k})=\frac{1}{N}\sum_{i=1}^{W}\sum_{j=1}^{H}(I_{1}(i,j)-I _{2,k}(i,j))^{2} \tag{10}\]  
where \(W\) and \(H\) are the width and height of the images, respectively, and \(N=W\cdot H\). For more details please see Algorithm 3.  
Parallel Ego-motion Application: Given the computational demands of evaluating multiple candidate movements, we leverage CUDA to implement the ego-motion application in parallel. This allows for the simultaneous processing of numerous image pairs, significantly accelerating the process.
# Evolutionary System Design with Answer Set Programming
## 6 Experiments
### Experimental Evaluation
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\epsilon\)D & & HD\(\times\epsilon\)D \\
**C** & **AVG-R** & **C** & **AVG-R** \\ \hline XYZ-B-H1-L & 3.9 & BOU-BR-H1-L & 12.1 \\ XYZ-B-H2-L & 3.9 & BOU-BR-H2-L & 13.1 \\ XYZ-BR-H1-L & 4.7 & XYZ-B-H2-L & 13.6 \\ XYZ-BR-H2-F-8 & 6.1 & XYZ-B-H1-L & 13.7 \\ XYZ-BR-H1-F-2 & 6.5 & XYZ-BR-H1-L & 14.4 \\ XYZ-BR-H2-L & 6.6 & BOU-BR-H1-F-8 & 15.9 \\ XYZ-BR-H2-F-4 & 6.9 & XYZ-BR-H2-L & 16.9 \\ XYZ-BR-H1-F-8 & 6.9 & XYZ-BR-H1-F-8 & 17.8 \\ XYZ-BR-H2-F-2 & 7.1 & BOU-BR-H2-F-8 & 18.1 \\ XYZ-BR-H1-F-4 & 7.3 & XYZ-BR-H1-F-2 & 18.8 \\ XYZ-B-H2-F-4 & 8.0 & XYZ-B-H2-F-4 & 19.1 \\ XYZ-B-H1-F-4 & 8.1 & XYZ-BR-H1-F-4 & 19.2 \\ XYZ-BR-H2 & 8.5 & XYZ-B-H1-F-4 & 19.4 \\ XYZ-B-H1-F-2 & 9.3 & XYZ-BR-H2-F-4 & 19.5 \\ XYZ-B-H2-F-2 & 9.3 & XYZ-BR-H2-F-8 & 19.8 \\ XYZ & 9.5 & BOU-BR-H1-F-4 & 20.3 \\ XYZ-B-H1-F-8 & 10.1 & BOU-BR-H1-F-2 & 20.6 \\ XYZ-B-H2-F-8 & 10.1 & XYZ-BR-H2-F-2 & 20.6 \\ XYZ-B-H1 & 10.7 & XYZ-B-H1-F-8 & 20.7 \\ XYZ-B-H2 & 10.7 & XYZ-B-H2-F-8 & 20.7 \\ XYZ-BR-H1 & 11.3 & BOU-BR-H2-F-4 & 20.8 \\ XYZ-B-P2 & 13.0 & XYZ-B-H2-F-2 & 21.8 \\ BOU-BR-H1-L & 14.8 & XYZ-B-H1-F-2 & 21.8 \\ BOU-BR-H2-L & 15.5 & XYZ-BR-H2 & 22.7 \\ BOU-B-H1-F-4 & 19.1 & BOU-BR-H2-F-2 & 23.1 \\ BOU-B-H2-F-4 & 19.1 & XYZ-BR-H1 & 24.3 \\ BOU-BR-H1-F-8 & 19.6 & BOU-BR-H2 & 24.4 \\ BOU-BR-H2-F-8 & 20.7 & BOU-BR-H1 & 24.7 \\ XYZ-B-P1 & 21.1 & BOU-B-H1-F-4 & 26.0 \\ BOU-B-H1-F-2 & 21.6 & BOU-B-H2-F-4 & 26.0 \\ BOU-B-H2-F-2 & 21.6 & XYZ-B-H2 & 26.1 \\ XYZ-BR-P1 & 22.3 & BOU-B-H1-L & 26.2 \\ XYZ-BR-P2 & 22.3 & BOU-B-H2-L & 26.2 \\ BOU-BR-H1 & 22.3 & XYZ-B-H1 & 26.2 \\ BOU & 22.4 & BOU-B-H1-F-2 & 26.9 \\ BOU-BR-H2 & 22.6 & BOU-B-H2-F-2 & 26.9 \\ BOU-B-H1-L & 22.8 & BOU-B-H1-F-8 & 27.0 \\ BOU-B-H2-L & 22.8 & BOU-B-H2-F-8 & 27.0 \\ BOU-BR-H1-F-4 & 22.8 & BOU-B-H1 & 29.0 \\ BOU-BR-H1-F-2 & 23.1 & BOU-B-H2 & 29.1 \\ BOU-B-H1-F-8 & 23.4 & XYZ-B-S2 & 30.9 \\ BOU-B-H2-F-8 & 23.4 & XYZ & 32.0 \\ BOU-B-H1 & 23.5 & ARB-BR-H2-L & 33.4 \\ BOU-B-H2 & 23.5 & ARB-BR-H1-L & 33.5 \\ BOU-BR-H2-F-4 & 24.2 & XYZ-B-P2 & 35.5 \\ BOU-BR-H2-F-2 & 25.7 & BOU-B-S2 & 35.7 \\ BOU-B-P2 & 29.2 & BOU & 37.1 \\ BOU-B-P1 & 29.3 & XYZ-B-P1 & 37.5 \\ BOU-BR-P1 & 29.3 & XYZ-BR-P1 & 38.1 \\ BOU-BR-P2 & 30.4 & ARB-BR-H1-F-8 & 39.2 \\ ARB & 44.3 & ARB & 50.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average rank regarding \(\epsilon\)-dominance and the product with average Hamming distance after cutoff time.
# Computation of Psycho-Acoustic Annoyance Using Deep Neural Networks
## 4 Evaluation and Results
### Training Results and Accuracy Test  
The training process produces an RMSE value of 3.0393 by comparing the directly calculated PA of the validation dataset with the predicted PA using the trained CNN. Taking into account a  
\begin{table}
\begin{tabular}{c c} \hline \hline
**N\({}^{o}\) Conv. Stages** & **PA Prediction RMSE** \\ \hline
2 stages & 12.981 \\
3 stages & 4.512 \\
4 stages & 3.039 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Root mean square error (RMSE) with different number of convolutional stages.  
PA range from 0 to 100, this is the best value achieved after testing several CNN architectures and taking into account that PA values are considerably unbalanced (Figure 1). Similarly, we used the 1000 audio clips of the test dataset obtaining an RMSE equal to 1.7672. The improvement of the RMSE over the test dataset (1000 signals) is probably due to the fact that it is much smaller than the validation dataset (11,830 signals) and contains fewer PA values located at the extremes of the range, where most errors occur.  
In Figure 3 (left) we can see a comparison between the calculated PA values (ground-truth) represented by red circles and the ones predicted by the CNN, represented by black crosses. In the right part of the same Figure 3 we can see the prediction error made by CNN. The same order of the samples is maintained so we have marked the same areas as in the left side of the figure, where the error tends to be greater due to the fact that we had fewer audio signals with PA values higher than 45 to train the CNN.  
A scatter plot of the predicted PA values versus the calculated ground-truth values is shown in Figure 4, where we can observe more clearly the deviations of the predicted values across the PA range going from 0 to 100. In the figure we have marked with circles the values that move more than 10% away from the ideal straight line (in red). We can see that they are only 5 predictions of the 1000 made over the signals of the test dataset and that they are placed in values superior to 50 of PA, due as we have commented previously to the lack of audio samples with values of high PA in our database. As expected, the error tends to be higher for those audio segments with extremely high PA values but, overall, the CNN model provides PA predictions with very good accuracy in most cases.  
Figure 3: PA calculated vs. CNN prediction (**left**), CNN prediction error (**right**) using test dataset. Areas marked with high PA values where the highest prediction errors are located.
## 2 Theoretical Background
### Sound Absorption
#### 2.1.1 Porous Materials  
This kind of materials is characterized by high porosity, low density and, if possible, a high surface area. Porous materials include fibrous, cellular (foams) and granular materials. The absorption properties depend on a number of parameters including flow resistivity and tortuosity. The dissipation of sound energy is due to three phenomena that are the friction between air and material fibers, the compression and decompression of air, and viscous effects [20,21].  
In the literature, several empirical and theoretical models have been proposed for the prediction of porous materials sound absorption. One of the first available models was proposed by [PERSON] [22] and requires only the flow resistivity \(\sigma\) as an input parameter, but since it neglects the thermal conductive effects, it is accurate in the \(0.01<(\rho_{0}f/\sigma)<1\) range only, where \(\rho_{0}\) is the air density and \(f\) is the sound frequency [23]. More accurate but, at the same time, more complex models were defined by several authors [24; 25; 26; 27]. One of the most popular models was proposed by [PERSON] (JCA) and takes into account the flow resistivity \(\sigma\), open porosity \(\phi\), tortuosity \(\alpha_{\infty}\), the viscous characteristic length \(\Lambda\) and the thermal characteristic length \(\Lambda^{\prime}\)[20].  
Figure 3: Representation of (**a**) a double partition made of two rigid leafs with an internal porous layer, (**b**) Helmholtz resonator and (**c**) mixed system—multiple resonator.
# Recommendation Systems: Algorithms, Challenges, Metrics, and Business Opportunities
## 3 Challenges in Recommendation Systems
### Data Sparsity  
Data sparsity results from the fact that the users only intend to rank limited items. Most RSs group the ratings of similar users; however, the reported user-item matrix has empty or unknown ratings (up to 99%) because of the lack of incentives or user knowledge to rate items [27]. Therefore, RSs can provide unreasonable recommendations to those who provide no feedback or ratings. For example, suppose we assume that an online bookstore sells two million different books, with X number of users (active or cold). In that case, each consumer is exemplified by an integer feature matrix, with 2 million elements, and the value of each component corresponds to the rating given by the consumer to a specific book. This matrix is called the consumer-product interaction matrix [28]. In most large-scale applications, both the numbers of consumers and products are enormous. Therefore, the majority (up to 99%, on average) of these matrix elements are 0. Comparing any two users for a specific item, it is very probable that both elements are 0, resulting in a sparse matrix [29]. Many techniques aim to mitigate the data sparsity issue by modeling users' preferences from their behaviors and trusted social connections. Trust has been extensively used to achieve significant benefits to the robustness of RSs [30]. Trust is described as the belief towards others' ability to provide accurate ratings (explicit and implicit). Many argue that it is possible to calculate trustworthiness based on the trust chart encoded by Epinions.com (a website where users can review items). The trust value can be calculated by measuring users' distance in the number of arcs connecting those users [31]. This offers a trust-aware RS that depends on a web of trust for defining how a user can trust another user. A trust network is constructed by aggregating every trust statement. A trust network consists of users and trust statements, represented by nodes and directed edges, respectively. These methods have significantly lowered the mean error of predictive accuracy. Many trust-based approaches have been introduced with significance given to the merge approach [32]. The merge incorporates the active users' trusted neighbors, seeking to enhance the overall predictive accuracy of RSs. Specifically, the ratings of a trusted neighbor of an active user are merged by averaging on frequently rated items as per the similarity between the active user and trusted neighbor.
## 3 System Model
### Optimization Model Mathematical Formulation  
Let the set of sensor nodes be denoted by \(N=\{1,2,\ldots,N\}\), and let the set of available channels be denoted by \(C=\{ch_{1},ch_{2},\ldots,ch_{K}\}\). The network's objective is to optimize channel allocation and power control while minimizing collisions and energy consumption.  
The optimization problem is formulated as follows:  
\[\max\sum_{k\in C}\sum_{i\in N}P_{k,i,t}\cdot I_{i,t,k},\]  
where \(P_{k,i,t}\) is the probability of successful transmission on channel \(k\) for node \(i\) at time \(t\); \(I_{i,t,k}\) is the indicator function that equals 1 if node \(i\) is assigned to channel \(k\) at time \(t\); and 0 otherwise.  
The reward function for the Actor-Critic RL is given by the following:  
\[R_{i,t}=\alpha\cdot P_{k,i,t}-\beta\cdot E_{i,t},\]  
where \(\alpha\) and \(\beta\) are constants, and \(E_{i,t}\) represents the energy consumption of node \(i\) at time \(t\).
# Adaptive Hierarchical Sliding Mode Control for Double-Pendulum Gantry Crane Based on Neural Network
## 3 Controller Design
### Crane Trolley Trajectory Planning  
In order to minimize the swing angle within the constraint range during the crane transportation process, and ensure that the load swings as little as possible when the trolley reaches the ideal position, a smooth S-curve is selected as the reference trajectory for the trolley positioning [23].  
\[x_{d}=\frac{p_{d}}{2}+\frac{{k_{\mathit{v}}}^{2}}{4{k_{a}}}In[\frac{\cosh(2{ k_{a}}t/{k_{\mathit{v}}}-\varepsilon)}{\cosh(2{k_{a}}t/{k_{\mathit{v}}}- \varepsilon-2{p_{d}}{k_{a}}/{{k_{\mathit{v}}}^{2}})}] \tag{6}\]  
Here, \(p_{d}\) is the target position of the crane trolley, and \(k_{a}\) and \(k_{\mathit{v}}\) represent the maximum velocity and maximum acceleration of the trolley, respectively. The parameter \(\varepsilon\) is introduced to adjust the initial acceleration of the crane trolley.  
Based on the ideal trajectory, the expressions for the trolley's velocity and acceleration can be obtained:  
\[\dot{x}_{d}(t)=k_{\mathit{v}}\frac{\tanh\left(\frac{2{k_{a}}t}{{k_{\mathit{v} }}}-e\right)-\tanh(\frac{2{k_{a}}t}{{k_{\mathit{v}}}}-e-\frac{2{p_{d}}{k_{a} }}{{k_{\mathit{v}}}^{2}})}{2} \tag{7}\]  
\[\ddot{x}_{d}(t)=k_{a}[\frac{1}{cosh^{2}(2{k_{a}}t-e)}-\frac{1}{cosh^{2}\left( 2{k_{a}}t-e-\frac{2{p_{d}}{k_{a}}}{{k_{\mathit{v}}}^{2}}\right)}] \tag{8}\]  
In this study, the parameters for the target trajectory are selected as follows: the target position of the trolley \(P_{d}\) is 20 m, the maximum speed of the trolley \(k_{\mathit{v}}\) is 3, the maximum acceleration is 0.5, and \(\varepsilon\) is set to 5 [24].
## 4 Technical Stack
### JSON Web Token (JWT)  
The JSON web token is the most popular standard for validating users' identities without revealing personal or sensitive information in the exchange.  
Figure 3: Metamask interaction.  
Conventionally, sessions were used to store the authentication state of users. For example, sessions would be stored server-side and accessed via cookies in the browser.  
Since modern architectures rely on data and information decoupling, using sessions creates a single point of failure on the memory storage layer.  
JWTs are generated after the user identity has been validated by the server, and usually contain information such as username, claims, and expiration time. JWT [13] signatures cannot be manipulated since they are generated by encrypting the data with a specific key. Thus, any alteration or manipulation would render the key invalid.  
JWTs can be validated by multiple systems and are usually short-lived to avoid potential hacker access to the key, thus gaining access to the users' systems.
# An Efficient Probe-Based Routing for Content-Centric Networking
## 3 Design and Description of Our Proposal
### Data Structure  
#### 3.1.1 Routing Tables  
* _FIB_: In our design, FIB is modified to keep track of the potential content providers. In the FIB of a basic CCN, the outgoing interface is replaced to hold potential content providers by router ID. Figure 1 demonstrates our FIB table.  
* _PIT_: It has the same definition as basic CCN.
* _Shortest Path Table_ was designed to optimize routing to decrease network delay. As shown in Figure 2, the fields of Shortest Path Table (SPT) include _Destination_, _Cost_, and _Outgoing Interface_. _Destination_ is the router ID. _Cost_ obtaining content from the designated router might be measured by response time, hop count, or other metrics. _Outgoing Interface_ is the outgoing interface to a certain destination. In this paper, the path is calculated using a dynamic routing algorithm (OSPF), which is described in Section 3.2.
## 4 Experiment and Results  
### Experimental Details  
The generalization ability of the model is the most important engineering application ability. The model trained on the high-precision camera parameter _DTU_ dataset [21] was directly used to test the UAV image data of Jinniu Village in Yangbi, Yunnan. The experiment was carried out on a computer with an Intel Xeon (R) W-2295 3.00 GHz * 36 processor and a 24 GB GeForce RTX3090/PCIe/SSE2 graphics processor.  
The network was trained for 16 epochs, with an initial learning rate of 0.001, which was reduced by a factor of 2 after 10, 14, and 16 epochs. The pixel resolution of the input image in the network was fine-tuned according to the original public test parameters. The _stage_ of CasMVSNet was set to 3, _numdepth_ was set to 192, _ndepths_ was set to corresponded to [48; 32; 8] and _interval_scale_ was set to 1.06.
## 3 Charrelation Matrix Based Blind Detector for DS-CDMA System
### Estimation Charrelation Matrix \(\Psi_{{}_{\mathbf{i}}}\left(\mathbf{u}\right)\)  
In practical applications the exact charrelation matrix \(\Psi_{{}_{\mathbf{i}}}\left(\mathbf{u}\right)\) of observations is estimated by sampling of a random variable. The generalized characteristic function of observation vector is estimated as:  
\[\phi_{{}_{\mathbf{i}}}\left(\mathbf{u}\right)=\frac{1}{M}\sum_{m=1}^{M}\exp \left(\mathbf{u}^{{}_{\mathbf{i}}}\mathbf{\tilde{r}}\left(m\right)\right) \tag{17}\]  
Similarly, the first and second derivatives of the generalized characteristic function is as follows:\[\Gamma_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{ }}}}}}}}}}}}}}}\left({\bf{u}}\right)\triangleq\frac{{{\partial{\phi_{{}_{\rm{{}_{\rm{{}_{\rm{{ }_{\rm{{{}_{\rm{{{}}}}}}}}}}}}}}}\left({\bf{u}}\right)}}{{\partial{\bf{u}}}}= \frac{1}{M}{\sum\limits_{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{{}_{\rm{{{}}}}}}}}}}}}}^{ \rm{{}^{\rm{{}^{\rm{M}}}}}}}{\rm{exp}}\left({{\bf{u}}^{{}^{\rm{{}^{\rm{T}}}}}{ }}{\bf{\tilde{r}}}\left({\it{m}}\right)\right){\bf{\tilde{r}}}\left({\it{m}} \right)} \tag{18}\]  
\[\Xi_{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}}}}}}}}}}}}\left({\bf{u}} \right)\triangleq\frac{{{\partial^{2}{\phi_{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{ }}}}}}}}}}}}\left({\bf{u}}\right)}}{{\partial{\bf{u}}}{\partial{\bf{u}}^{{} ^{\rm{{}^{\rm{T}}}}}}}=\frac{1}{M}{\sum\limits_{{}_{\rm{{}_{\rm{{}_{\rm{{}_{ \rm{{}_{\rm{{}}}}}}}}}}}^{\rm{{}^{\rm{M}}}}}}{\rm{exp}}\left({{\bf{u}}^{{}^{ \rm{{}^{\rm{T}}}}}{\bf{\tilde{r}}}\left({\it{m}}\right)}\right){\bf{\tilde{r} }}\left({\it{m}}\right){\bf{\tilde{r}}}\left({\it{m}}\right)^{{}^{\rm{{}^{\rm{T}}}}} \tag{19}\]  
Based on the previous analysis, the charrelation matrix \(\Psi_{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}}}}}}}}}}}}}\left({\bf{u}}\right)\) of the second generalized characteristic function \(\varphi_{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}}}}}}}}}}}}\left({\bf{u}}\right)\) can be easily given by:  
\[\Psi_{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}}}}}}}}}}}}}}}\left({ \bf{u}}\right)=\frac{{\Xi_{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{} }}}}}}}}}}}}}\left({\bf{u}}\right)}}{{\phi_{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{} \rm{{}_{\rm{{{}_{\rm{{}}}}}}}}}}}}}}}}}-\frac{{\Gamma_{{}_{\rm{{}_{\rm{{}_{\rm{{ }_{\rm{{}_{\rm{{}_{\rm{{}}}}}}}}}}}}}}\left({\bf{u}}\right)\Gamma_{{}_{\rm{{}_{ \rm{{}_{\rm{{}_{\rm{{}_{\rm{{{}}}}}}}}}}}}^{\rm{{}^{\rm{T}}}}}\left({\bf{u}} \right)}}{{\phi_{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}_{\rm{{}}}}}}}}}}}}^{\rm{{}^{ \rm{{}^{\rm{T}}}}}}}\left({\bf{u}}\right)}} \tag{20}\]
## 2 Materials and Methods
### Earthquake Catalogue
The schematic illustration of the time intervals for the analysis of the aftershock sequences is shown in Figure 2.  
Earthquakes occur due to sudden energy release associated with the slippage of faults and are characterized by finite rupture areas. However, for statistical analysis of seismicity, the point assumption is utilized to characterize each earthquake. On time scales larger than the propagation of rupture along the fault, earthquakes can be treated as points in time and space. This idealization helps to describe the earthquake process by point process models. The point process becomes a marked point process by assigning magnitudes to each event. Therefore, each earthquake can be characterized by the magnitude, \(m_{i}\), and the occurrence time, \(t_{i}\), in order to generate a stochastic marked point process during a specific time interval, \(S=\{(t_{i},\,m_{i})\}:i=1,\,2,\ldots,\,n\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Mainshock Name**} & \multirow{3}{*}{**Start Date and Time**} & \multicolumn{6}{c}{**Elliptical Aftershock Zone**} \\ \cline{3-8}  & & **Center** & & & **Radii** & **Magnitude Cut-Off, \(m_{0}\)** \\ \cline{3-8}  & & **Latitude** & **Longitude** & **\(R_{1}\)** & \(R_{2}\)** & \\ \hline Denali & 3 November 2002 (22:12:41) & 63.1 & \(-145.40\) & 117.5 & 1.85 & 0.55 & 3.0 \\ Kodiak & 23 January 2018 (09:31:40) & 56.2 & \(-149\) & 40 & 0.85 & 0.65 & 3.2 \\ Anchorage & 30 November 2018 (17:29:29) & 61.425 & \(-149.91\) & 35 & 0.22 & 0.16 & 2.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters of the elliptical regions used for the identification of the aftershock sequence and the corresponding lower magnitude cutoffs \(m_{0}\). Figure 2: An illustration of the time intervals used in the analysis.
## 2 Materials and Methods
### Methodology
#### 2.4.10. Validation for Real-World Feasibility  
Although the optimization of robot trajectories is performed on a two-dimensional plane (\(X\), \(Y\)) to reduce computational complexity, the resulting solutions are subsequently validated in a three-dimensional environment using Mitsubishi RT TOOLBOX3 PRO. This industrial-grade software enables full simulation of robot motion, including vertical displacements (\(Z\)-axis), forward and inverse kinematics, collision detection, and reachability constraints.  
Incorporating this 3D validation stage ensures that the optimized paths are not only theoretically efficient but also physically executable under real-world operational conditions. This methodological decision addresses the need to balance the computational efficiency of the model with its practical feasibility in industrial environments.  
The use of RT TOOLBOX3 PRO acts as a bridge between algorithmic optimization and actual implementation, allowing for the detection of inconsistencies not visible in a planar model, such as vertical interferences or errors in end-effector orientation. This hybrid strategy, 2D optimization followed by 3D validation, reinforces the applicability of the proposed framework in manufacturing scenarios, where both performance and operational precision are critical.