esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Discussion  
The study investigated the anatomical position of the mental foramen through a comprehensive analysis of CBCT images. The mental foramen is a crucial landmark in dental and maxillofacial surgeries, and its accurate localization is essential for successful procedures. The literature has widely described the anatomical characteristics of the mental foramen [16]. The study aimed to determine the relationship between various metrical parameters to enhance the precision of MF localization. The results indicate that there were no significant age differences between males and females concerning the position of the mental foramen, suggesting that age may not play a significant role in determining the localization of the mental foramen in the population studied. The lack of age-related differences may be beneficial in clinical practice, as it implies that age might not be a critical factor to consider when planning dental and surgical procedures involving the mental foramen. [PERSON] et al., in fact, observed that the MF position may change during primary dentition, remaining stable during the eruption of the primary and mixed dentitions [17]. As our samples include only subjects aged >18 years of age, we therefore found no significant differences according to age, and this agrees with the results of [PERSON] et al., who observed that the distance from the mental foramen to the midline and inferior border of the mandible was similar between different ages [6]. The study found that all metrical measurements were repeatable, demonstrating the reliability and consistency of the CBCT analysis in determining the dimensions and positions of the mental foramen. The repeatable measurements indicate that the CBCT method is a valid and robust tool for accurately assessing the mental foramen's anatomical position. The analysis revealed differences in certain metrical parameters between males and females. Specifically, the depth of the mental foramen and the distances from the inferior and superior mandibular edges were significantly higher in males compared to females. These findings may have important implications for treatment planning and surgical procedures in different genders. Surgeons should be mindful of these gender-based variations to achieve better outcomes and minimize potential complications related to the mental foramen's position. The study identified significant positive correlations between specific metrical parameters. First, in both males and females, a positive correlation was found between the height and width of the mental foramen, independent of the side. This relationship suggests that, as the height increases, the width also tends to increase proportionally. This finding can be valuable in predicting the mental foramen's dimensions based on one of the other parameters when the first is unknown.
# MS Location Estimation Based on the Artificial Bee Colony Algorithm
## 3 Artificial Bee Colony Algorithm
### Scouts Phase  
In ABC, scouts are in charge of searching the whole range surrounding the nest if the abandoned food source exists. In the scouts' phase, a parameter called limit would be defined. The value of limit, which is used to determine the abandoned case, presents the upper bound of the searching number without any improvement. The memory in the ABC algorithm records the number of times that the food source does not improve. When the frequency exceeds limit, the food source should be abandoned and transformed to a scout. A scout randomly searches for a new food source in the whole solution space. The food source supported by the scout replaces the abandoned food source.  
1. Determine whether the searching number without improvement exceeds the limit value.
2. If the abandon case exists, the food sources are changed to the scouts.
3. Send scouts to randomly find new food sources in the whole searching range by: \[s_{i,j}=s_{\min,j}+rand(0,1)(x_{\max,j}-x_{\min,j}),\] (6) where \(i=1,2,\ldots,N_{p}\) and \(j\) is the dimension.
4. The food sources derived from scouts are substituted for abandoned food sources directly.  
In each cycle, the ABC algorithm creates a new population in the searching range. Then, the employed bee phase, onlookers' phase, and scouts' phase are implemented serially. For the final cycle, the ABC algorithm memorizes the best solution and determines whether the formulated requirements are satisfied. If the convergence condition is satisfied, the loop will be terminated and the best food source will be outputted as the optimal solution. Otherwise, the bees go back to the employed bee phase. The cycles are iterated continuously until the condition is satisfied. Generally, the best solution can be derived from the optimal procedure of the ABC algorithm during the iterations.
## 4 Computation of the Spring and Damping Constants: Two Opposite Edges Venting
### An Application: Approximation of the Critical Frequency where \(k=\gamma\beta\)  
Our representations allow the approximate computation of the frequency for which \(k=\gamma\beta\), where \(\gamma\) is a given constant with the appropriate dimensions. At this frequency, the ratio \(k/\beta\) of viscous force and spring force is equal to the given value \(\gamma\). According to Equations (12) and (13), this problem is equivalent to the solution of the equation  
\[x^{4}B(x)=CF(x) \tag{15}\]  
with \(x=\alpha b\omega^{1/2}/\pi\) and the dimensionless constant \(C=\gamma\alpha^{2}b^{2}/\pi^{2}\). Equation (15) is equivalent to  
\[cosh(w(x))+cos(w(x))=(2^{1/2}/\pi)[(1/x+C/x^{3})\sinh(w(x))+(1/x-C/x^{3})\sin( w(x))] \tag{16}\]  
If we let \(w=w(x)\) and \(x=(2^{1/2}/\pi)w\), we obtain the equation  
\[cosh(w)+cos(w)-sinh(w)/w-sin(w)/w=(\pi^{2}C/2)\left[sinh(w)-sin(w)\right]/w^{3} \tag{17}\]  
If we replace the functions by the corresponding power series, this yields the equation  
\[w^{4}/15+w^{8}/22680+\ldots= (\pi^{2}C/2)\left[1/3+w^{4}/2520+w^{8}/19958400+\ldots\right] \tag{18}\]  
By considering only the constant term and the terms with \(w^{4}\) we obtain the approximation  
\[w=[\pi^{2}C/(0.4-\pi^{2}C/840)]^{1/4} \tag{19}\]  
For Equation (15) this yields the approximate solution  
\[x=(2^{1/2}/\pi)[\pi^{2}C/(0.4-\pi^{2}C/840)]^{1/4} \tag{20}\]  
If we replace the denominator \((0.4-\pi^{2}C/840)\) by \(0.4\), this yields the critical frequency  
\[\omega=[2\pi/(\alpha^{2}b^{2})][C/0.4]^{1/2} \tag{21}\]  
**Example** With \(C=2\times 10^{-7}\), Equation (17) has the solution \(w=0.0471321702447414\ldots\). The approximation \(w_{0}=[\pi^{2}C/0.4]^{1/4}\) yields the value \(w_{0}=\pi^{1/2}/(2^{1/4}10^{1/2})\)\(=0.0471321702139757\ldots\). Moreover, we have \(w_{1}=[\pi^{2}C/(0.4-\pi^{2}C/840)]^{1/4}=0.04713217028319835\ldots\).
## 3 Results  
During the two-year study period, a total of 124 patients met all the inclusion criteria and were therefore included in the study. The mean patient age at the time of virtual surgery planning was 26.3 years (range 18-49). Fifty patients were male (40.3%) and 74 were female (59.7%).  
All patients underwent upper maxilla advancement (mean 6.79 \(\pm\) 3.53 mm), as is typical in class III patients. However, regarding mandibular sagittal movement at the B point, 112 patients (90.3%) received mandibular advancement (mean 5.22 \(\pm\) 4.82 mm), only nine (7.3%) received mandibular setback (mean \(-\)2.55 \(\pm\) 1.16 mm), and no changes along the sagittal dimension occurred in three patients (2.4%). Therefore, in this series of class III patients, the chi-squared test confirmed mandibular advancement as being a significantly more frequent option than mandibular setback or mandibular sagittal non-movement (\(p\) = 2.7 \(\times\) 10\({}^{-12}\) (\(p\) < 0.001)).  
The mean distance at the bilateral sagittal split osteotomy gaps was 5.86 \(\pm\) 4.64 mm on the right side and 5.87 \(\pm\) 4.60 mm on the left side, which is in concordance with the mandibular advancement amount at the B point.  
Regarding the occlusal plane changes, the CCW rotation of the occlusal plane was performed in 65 patients (52.4%, mean 3.6 \(\pm\) 1.76\({}^{\circ}\)), while CW rotation was not carried out in any patient. A centering movement was performed in 84 of the patients (67.7%, mean 0.8 mm), and 39 (31.5%) received both centering and CCW rotation of the mandible (Table 1). Out of the 112 patients subjected to mandibular advancement, only six received a pure sagittal movement (5.4%), while, in the remaining 106 cases, mandibular advancement was accompanied by centering, CCW rotation, or both (94.6%). Thus, mandibular CCW rotation always involved its advancement (\(p\) < 0.001, MW), as well as the combination of mandibular CCW rotation and centering (\(p\) = 0.012, MW). On the other hand, mandibular setback never needed centering (\(p\) = 0.001, MW).  
There were no significant differences in mandibular sagittal movement according to sex (\(p\) = 0.564, MW) or whether maxillary segmentation was performed (\(p\) = 0.582, MW).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **N** & **\%** \\ \hline \multirow{4}{*}{Mandibular sagittal movement} & Total & 124 & 100 \\ \cline{2-4}  & Setback & 9 & 7.3 \\ \cline{2-4}  & Advancement & 112 & 90.3 \\ \cline{2-4}  & No sagittal movement & 3 & 2.4 \\ \hline \multirow{4}{*}{Mandibular centering movement} & Total & 124 & 100 \\ \cline{2-4}  & Yes & 84 & 67.7 \\ \cline{2-4}  & No & 40 & 32.3 \\ \cline{2-4}  & Total & 124 & 100 \\ \cline{2-4}  & Yes & 65 & 52.4 \\ \cline{2-4}  & No & 59 & 47.6 \\ \hline \multirow{4}{*}{Mandibular centering and counter-clockwise rotation} & Total & 124 & 100 \\ \cline{2-4}  & Yes & 85 & 68.5 \\ \cline{2-4}  & No & 39 & 31.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Percentage of patients treated by mandibular advancement, mandibular centering, mandibular counter-clockwise rotation, or combined centering and counter-clockwise rotation.
## 4 Results and Discussions
### Impact of Operational Parameters on the Performance of the Air Compressor
#### 4.3.2 Multi-Objective Optimization Results  
The multi-objective optimization results considering both high isentropic efficiency and low power dissipation (Optimization A) are illustrated in Figure 11 based on the GRA theory formulas. The maximum GRG of 0.7937 is achieved for the initial sample No. 4. At this point, the isentropic efficiency is 58.97%, the total power consumption is 3.56 kW, and the mass flow rate is 0.066 kg/s.  
When considering both high mass flow rate and low energy consumption simultaneously (Optimization B), the solution for the GRG in the multi-objective optimization is shown in Figure 12. The maximum GRG of 0.6873 is discovered for the initial sample No. 8. At the maximum GRG, the mass flow rate is 0.1389 kg/s, the total power consumption is 15.32 kW, and the isentropic efficiency is 41.30%.  
However, the optimized results considering high flow rate, high efficiency, and low energy consumption simultaneously (Optimization C) are illustrated in Figure 13. The results indicate that the maximum GRG of 0.734 is achieved for the initial sample No. 7.  
Figure 11: Multi-objective optimization results in high efficiency and low energy consumption.  
Figure 12: Multi-objective optimization results in high mass flow rate and low energy consumption.  
At the optimal operating parameters, the isentropic efficiency is 61.48%, the total power consumption is 16.12 kW, and the mass flow rate is 0.1274 kg/s.
# An Improved Cuckoo Search Algorithm and Its Application in Robot Path Planning
## 3 The Proposed Bascs
### Strategies
#### 3.1.1 Population Initialization Strategy with Chaotic Mapping and Random Migration  
In the initialization phase, the CS algorithm can suffer from uneven population distribution due to random initialization, increasing the risk of getting trapped in local optima. To tackle this issue, BASCS employs a population initialization strategy that combines chaotic mapping with random migration.  
Chaotic mapping, a class of nonlinear mappings that exhibit chaotic behavior, is adept at efficiently navigating state spaces [35]. Tent mapping, renowned for its computational efficiency, controllable parameters, and straightforward implementation, is a prime example of such chaotic mapping. Random migration, a stochastic mathematical model, depicts the movement of an object or system in arbitrary directions at discrete time intervals. Within this model, each step's direction and distance are randomly determined, facilitating random population displacement.  
During the initial population generation in CS, a strategy that combines tent chaotic mapping with random migration is utilized. On one hand, reference tent mapping ensures a uniform initial distribution across the search space, improving optimization accuracy. On the other hand, the random migration strategy introduces variability by allowing each individual to move within a small range, preserving the initial randomness inherent in CS.  
The tent chaotic mapping is calculated as Equation (14):  
\[X_{tent}=\begin{cases}\frac{rand(0,1)}{a},rand(0,1)\in[0,\alpha)\\ \frac{1-rand(0,1)}{1-\alpha},rand(0,1)\in[\alpha,1]\end{cases}, \tag{14}\]  
where \(\alpha\) lies within (0, 1), typically taking a value of 0.5.  
The improved equation for population position initialization is shown by Equation (15):  
\[X_{0}=X_{tent}+rand(step,dim), \tag{15}\]  
where \(X_{tent}\) is a randomly generated population position by the tent mapping, and \(rand(step,dim)\) represents dim random step size within \([-step,step]\).
# Unmanned Surface Vehicle Using a Leader-Follower Swarm Control Algorithm
## 4 System Structure of the USV
### Communication System of the USV  
Communication between the land operation console and each USV is performed through the access point (AP) bridge. Commands transmitted from the land operation console are transmitted to the receiving antennas of each USV through the AP bridge and are classified by the switch hub installed inside and delivered to each required place. In addition, the communication system was designed so that information such as position, direction angle, and operation speed could be shared between the leader and the follower. Figure 12 is a block diagram showing the communication system between the land operation console and the leader and follower USVs.
# IoT-Based Small Scale Anomaly Detection Using [PERSON]'s Q Test for e-Health Data
## 3 System Design
### IoTDixon Algorithm  
We present the IoTDixon algorithm for detection of single anomaly from a packet of samples taken from an small test data stream \(X=\{x_{1},x_{2},x_{3},\cdots,x_{n}\}\). The IoTDixon technique works as follows: We assume that IoT-based health sensor data are being streamed on a regular interval to an edge device. We assume that small test data stream is divided into \(m=\lceil\frac{len(X)}{\eta}\rceil\) number of packets, where \(\eta\) is a given as the amount of samples in each data packet. We select the appropriate \(r\) statistic based on the sample size \(\eta\). By default, we use \(r_{10}\) as the Dixon statistic where a sample of data packet must lie within the range of \([3,7]\). However, one can change the range and \(r\) statistic according to the need to adjust with the packet size. The partitioning task required \(\mathcal{O}(m)\) that depends on the \(\eta\). We then perform the insertion sort on the \(j^{th}\) generated data packet \(x_{\eta j}\). In this study, we select \(\eta=7\); however, as mentioned earlier, it can be changed to other values, though keeping  
Figure 1: IoTDixon flow chart.  
the minimum limit to three samples. We select insertion sort due to its faster response time for small datasets typically less than 10. Thus, we expect the sorting time to be around \(\mathcal{O}(1)\), i.e., negligible. Then, we perform the normality checking procedure by using the Kolmogorov-Smirnov test in \(\mathcal{O}(\eta)\) time. Once the given data packet is statistically proven to be normally distributed, then the data packet is forwarded for the two-sided Dixon's Q test. Finally, the outlier \(o_{\eta j}\) from the sample data packet is returned. Thus, we can find the maximum \(m\) number of outliers as the total number of data packets is \(m\). It is the duty of the data analyst to further investigate the obtained outliers to find the most effective anomaly. The overall time complexity of the proposed algorithm can be obtained in a linear time \(\mathcal{O}(m+\eta)\). The IoTDixon Algorithm is shown in Algorithm 1.  
```
1 Input: IoT-based small test data stream \(X\) where \(1\leq i\leq n\) and select appropriate \(r_{j,i-1}\) statistic for [PERSON]'s Q test depending on sample packet size \(\eta\)
2 Output: Possible anomalies
3 Make packet \(x_{\eta j}\) of each \(\eta\) amount of small test data samples
4 while(\(m\)=\(\lceil\frac{\lceil\epsilon max\rangle}{\eta}\rceil>0\))do
5 Perform insertion sort on the \(j^{th}\) data packet \(x_{\eta j}\)
6 Evaluate for normality by the Kolmogorov-Smirnov test where \(\alpha=0.05\)
7 if(\((x_{\eta j})\)==Normally Distributed)then
8 Perform two-sided [PERSON]'s Q test on \(x_{\eta j}\)
9 Return an outlier \(o_{\eta j}\) from the sample data packet
```  
**Algorithm 1**IoTDixon Algorithm
## Appendix A  
For the coefficients, \(C_{1}\) and \(C_{2}\) in Equation (16), by substituting the boundary condition in Equation (21) into Equation (16), the following equation can be derived:  
\[\left\{\begin{array}{l}C_{1}(K_{0}(a*r_{c})-b*I_{1}(a*r_{c}))+C_{2}(I_{0}(a*r _{c})+b*K_{1}(a*r_{c}))=\frac{\sigma_{i}h}{M_{C}}-\frac{\sigma_{B}}{K}\\ -a*C_{1}*K_{1}(a*\frac{d}{2})+a*C_{2}*I_{1}(a*\frac{d}{2})=0\\ b=\frac{2 aGh^{2}}{r_{c}\gamma M_{C}}*(\cot(\eta)-\frac{1}{\eta})\end{array}\right. \tag{17}\]  
At the same time, the functions \(w(r)\) and \(\phi(z)\) are coupled together. To decouple these two functions, the initial value of \(\eta\) can be assumed, then the shape function \(\phi(z)\) can be obtained using Equation (14). The next step is to substitute the shape function into Equation (9), then the \(m\) and \(n\) can be represented by \(\eta\).  
\[\left\{\begin{array}{l}k=\frac{(1-v_{s})E_{s}\eta*(\sinh(\eta)*\cosh(\eta)+ \eta)}{2(1+v_{s})(1-2v_{s})H\sinh(\eta)^{2}}\\ G=\frac{E_{s}H(\sinh(\eta)*\cosh(\eta)-\eta)}{4(1+v_{s})\sinh(\eta)^{2}\eta} \end{array}\right. \tag{18}\]  
The coefficient, \(a\), will then be obtained. By substituting the \(a\) and \(\eta\) into Equation (17), the coefficients, \(C_{1}\) and \(C_{2}\) will be obtained.  
The above procedure needs just one iteration. If a more precise result is to be obtained, the updated function \(w(r)\) may be substituted into Equation (11). By using Equation (12) to update \(\eta\), the error between the updated \(\eta\) and previous \(\eta\) can be calculated. The iteration will be terminated when the error meets the threshold.
## 5 Experiments
### Ablation Experiments  
We conducted ablation experiments to validate the effectiveness of each component in the proposed DSTGFCN model. All ablation experiments were performed on the METR-LA dataset. We named the variants of DSTGFCN as follows:  
* w/o Dg: We replaced the dynamic adjacency matrix in DSTGFCN with a predefined adjacency matrix. That is, dynamic graph fusion was also removed. The predefined adjacency matrix was constructed in reference to the way defined by [PERSON] et al. [14]. The calculation formula is as follows: \[A_{v_{i}v_{j}}=\begin{cases}\exp\left(-\frac{d_{v_{i}v_{j}}^{2}}{\rho^{2}} \right),&if\ d_{v_{i}v_{j}}\leq k\\ 0&otherwise\end{cases}\] (15) where \(d_{v_{i}v_{j}}\) represents the road network distance from sensor node \(v_{i}\) to \(v_{j}\). \(\sigma\) is the standard deviation of the distance and \(k\) is the threshold value, which was assigned a value of 0.1.  
Figure 5: Prediction errors for each time step on PEMS04 and PEMSD8.  
* w/o Fus: We removed dynamic graph fusion when building the dynamic graphs.
* w/o Res: We removed the residual connections in the graph convolution gated recurrent layer.
* w/o Fus & Res: We removed both dynamic graph fusion and the residual connections.
* Dg2 Sg: DSTGFCN replaced the dynamic adjacency matrix with a predefined adjacency matrix while removing dynamic graph fusion and the residual connections.
* Dg w/o X: Traffic states are not considered as input when constructing the dynamic graph.
* Dg w/o T: Time embedding was not considered as input when constructing the dynamic graph.
* Dg w/o E: Node embedding was not considered as input when constructing the dynamic graph.  
As shown in Table 4, we can observe that DSTGFCN outperformed other variants in terms of prediction accuracy for 15 min, 30 min, and 60 min. Analysis of the results indicates a significant decline in predictive performance when the dynamic adjacency matrix was removed (w/o Dg, Dg2 Sg). Therefore, it is necessary to construct a dynamic adjacency matrix to capture dynamic spatio-temporal features effectively. Additionally, dynamic graph fusion further enhanced the prediction performance (w/o Fus), validating that the adjacency relationships of road nodes exhibit certain similarities in adjacent time steps. The residual connections improved the model's ability to capture long-term dependencies. Specifically, in 60 min predictions, DSTGFCN achieved an MAE reduction from 3.45 to 3.28 compared to DSTGFCN w/o Res, resulting in a 4.92% improvement in prediction accuracy. Meanwhile, DSTGFCN w/o Fus & Res validated that only considering the dynamic adjacency matrix is inadequate for accurate prediction. Ablation experiments on the input of dynamic feature extraction indicate that the deficiencies in the current traffic state (Dg w/o X), time embedding (Dg w/o T), and node embedding (Dg w/o E) will lower the prediction performance. In summary, these components are all crucial for the prediction performance of DSTGFCN.