esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Materials and Methods
### Preparation of Geopolymer Specimens  
The initial mixtures were produced by mixing the fly ash (FA) with waste glass (WG). The FA was replaced by the WG with 10%, 20%, and 30% by mass. The mixture of 10-molar NaOH aqueous solutions with sodium silicate, in a ratio of 1:2.5, was prepared separately. The solution was added to the mixtures of FA and WG. The liquid-solid ratio was fixed at 1:2.5. To synthesise geopolymer samples, the mixed solids and liquids underwent mechanical stirring for 1 h. The obtained homogeneous slurry of FA and GP was transferred into silicone forms of 40 \(\times\) 40 \(\times\) 40 mm\({}^{3}\) (in order to test the thermal properties and compressive strength). The beams 40 \(\times\) 40 \(\times\) 160 mm\({}^{3}\) were prepared to determine the flexural strength. The forms with geopolymer were stored in an oven at 60 \({}^{\circ}\)C for 48 h to complete the polycondensation reaction. After curing, the samples were demoulded and stored in air-dry conditions (20 \({}^{\circ}\)C and RH < 50%).  
The samples containing 100% FA and no WG were labelled G0 WG. The sample marked as G10 WG contained 10% WG and 90% FA; the sample G20 WG contained 20% WG and 80% FA; and the sample G30 WG contained 30% WG and 70% FA (by mass).
## 3 Results and Discussion
### Material Properties
#### 3.4.6 Biological Properties  
Figure 9 represents the studies investigating the biological response and briefly describes the only study found. [PERSON] et al. [54] evaluated the response of two gingival cell lines to CAD-CAM RCBs. The study examined the cytotoxicity and effect on the proliferation of two gingival cell lines, Human gingival fibroblasts (HGFs) and Human gingival keratocytes (HGKs), exposed to RCB and PICN CAD-CAM resin blocks. The results showed that all the materials examined had a more significant cytotoxicity effect on HGK proliferation than HGF. The conventional composite, however, exhibited comparable or better proliferation and lower cytotoxicity levels than the CAD-CAM resin blocks. These findings highlight the importance of considering the biocompatibility of dental materials when selecting materials for clinical use, especially in restorations that come into contact with gingival tissues.  
Figure 8: The percentage distribution of investigations involving optical properties and a brief description of the only two studies found.
## 2 Results
### Validation of a Set of DEGs by RT-qPCR  
Among the different categories of DEGs, we selected 11 _M. graminicola_ genes encoding either CWDE (_Mg449_ and _Mg693_), neuropeptides (_Mg1702_ and _Mg2129_), VAP (_Mg707_ and _Mg11937_) or candidate effectors (_Mg757_, _Mg4965_, _Mg12322_, _Mg13532_, and _Mg44061_) to validate their expression in RT-qPCR assays. We successfully cloned the cDNA sequences of _Mg693_, _Mg1702_, _Mg2129_, _Mg707_ and _Mg44061_ in this study, the others had been already cloned in [PERSON] et al. [10]. Specific primers were designed for each gene and used in RT-qPCR assays on RNAs extracted from pre-parasitic J2 and from susceptible or resistant rice plants after a 2-, 4-, or 8-day challenge with _M. graminicola_. Expression profiles were obtained for the 12 genes on 3 independent biological replicates (Figure S2). The ratio of nematode genes expression between resistant and susceptible plants gave values highly similar in qPCR and RNA-Seq data (Table 1).
# A Modified Bio-Inspired Optimizer with Capsule Network for Diagnosis of Alzheimer Disease
## 3 Methodology
### Classification  
The informative features selected by the MGTO algorithm are passed into the CapsNet model for AD classification. The CapsNet is an efficient neural network model, which has recently evolved in the field of medical image classification [44; 45]. Here, the term capsule represents a vector, which contains a group of neurons, and further, the parameters denote several characteristics of an sMRI, such as orientation, size, and position. In the CapsNet model, the lower-level capsule's output \(u_{i}\) is considered for predicting the higher-level capsules \(j\). This statement is mathematically represented in Equation (9), where, \(W_{ij}\) denotes the weighting matrix, and it is learned by back-propagation. In this neural network, every capsule \(l\) predicts the higher-level capsule's output. The coupling coefficient \(C_{ij}\) among the capsules is increased when the prediction yields the actual output. The coupling coefficient \(C_{ij}\) is computed utilizing the softmax function on the basis of the degree of conformation, and it is mathematically stated in Equation (10).  
\[\hat{u}_{j|i}=W_{ij}u_{i} \tag{9}\]  
\[C_{ij}=\frac{exp\big{(}b_{ij}\big{)}}{\sum_{l}exp\big{(}b_{il}\big{)}} \tag{10}\]  
where the log probability is represented as \(b_{ij}\); here, it is fixed to zero. In this context, the lower-level capsules \(i\) are coupled with the higher level capsules \(j\). Furthermore, the input vectors of the higher-level capsules \(j\) are computed utilizing Equation (11).  
\[s_{j}=\sum_{j}C_{ij}\hat{u}_{j|i} \tag{11}\]In this neural network, a non-linear squash (NLS) activation function is utilized to ensure that the short vectors are reduced to 0 and the long vectors are closer to 1. This NLS activation function ensures that the capsules' output vectors are not beyond the limit of one, and it is mathematically illustrated in Equation (12).  
\[v_{j}=\frac{\left\|s_{j}\right\|^{2}}{1+\left\|s_{j}\right\|^{2}}\frac{s_{j}}{ \left\|s_{j}\right\|} \tag{12}\]  
where the input vectors are represented as \(s_{j}\), and the output vectors are represented as \(v_{j}\). The agreement \(qg_{ij}\) to update the coupling coefficients \(C_{ij}\) and the log probabilities \(b_{ij}\) are determined in Equation (13).  
\[qg_{ij}=\hat{u}_{ij}\vspace{-0.2 cm}\
u_{j} \tag{13}\]  
The parameters of the CapsNet model are a size of kernel of 3, a learning rate of 0.0001, a total iteration of 200, a capsule dimension of 8, a batch size of 140, a number of total nodes in hidden layers of 128, and a number of total nodes in the primary caps layers of 64. The empirical analysis of the fuzzy-based superpixel-clustering algorithm and MGTO-CapsNet model is described in Section 4.
## 2 Chitosan Modifications
### Grafting of Functional Groups  
Grafting of additional functional groups can noticeably increase the number of adsorption sites in a CS molecule and, consequently, its adsorption capacity [35]. Recently, [PERSON] et al. [36] synthesized 2-(4-acetamido-2-sulfanilamide) chitosan (Figure 3a)--water soluble derivatives with molecular weights of 200, 350 and 600 kDa. 2-(4-Acetamido-2-sulfanilamide)-CS was synthesized with high yield (75-83%) through the reaction of CS with 4-acetylsulfanilchloride in DMSO medium. A synthesized CS derivative was used for the successful immobilization of different cysteine proteases: ficin, papain and bromelain.  
The formation of Schiff's bases is widely used in the modification of amines, allowing for better complexation with metal ions. Recently, [PERSON] et al. [37] synthesized [PERSON]'s base of carboxymethyl CS/p-dimethylaminobenzaldehyde (Figure 3b) for complexation with Co, Ni and Zn for further biomedical application. Moreover, the obtained Zn complexes were shown to reveal promising catalytic properties in the oxidation of cyclohexane to cyclohexanol, allowing \(>\)70% of cyclohexanol yield for 12 h.  
In addition to functional groups, other polymers can be grafted to CS as well. For example, [PERSON] et al. [38] grafted cellulose to CS using EDTA (Figure 4). The CS-EDTA-cellulose network contained both acidic and basic sites on the surface and was used as a multifunctional organocatalyst for the synthesis of 2-amino-4_H_-pyran derivatives with high yields (85-96%) at room temperature via a one-pot reaction between ethyl acetoacetate aromatic aldehydes and malononitrile in EtOH as a green solvent. The CS-EDTA-cellulose nanocatalyst was easily recovered from the reaction mixture by using filtration and reused at least five times without any significant decrease in its catalytic activity.  
Figure 2: Functional groups of CS that can be chemically modified (based on Ref. [1]).  
the mucoadhesive properties. In addition, soluble TCS exhibits gel-forming properties at physiological pH values. There is a large variety of TCS, some of which are presented in Figure 5[39; 40; 41; 42; 43].
# A Trust-Based Predictive Model for Mobile Ad Hoc Network in Internet of Things +
## 3 Proposed Protocol
### Trust Generation
#### 3.2.2 Resultant Trust Calculation  
1. **Neighbor Management:** Each member of a cluster (including CH) maintains a list of neighboring nodes. CH broadcasts Hello messages periodically and maintains a list of node-IDs of members in the cluster. Each member also exchanges Hello messages periodically to keep track of its neighbors.
2. **Trust Information Collection:** Here, CH collects the recommendation from common neighbors to compute the resultant trust of a node under review.
3. **Trust Aggregation:** On receiving the recommendation of trust evidences from the members, CH executes ARMA(1, 1)/GARCH(1, 1) to calculate the resultant (or final trust) of a node under review. The resultant trust of a node can be calculated using ARMA(1,1), as shown in Equation (3).  
\[X_{t}=\varepsilon_{t}+\Sigma_{i=1}^{p}\varphi_{i}X_{t-i}+\Sigma_{i=1}^{p} \theta_{i}X_{t-i} \tag{3}\]To estimate \(\epsilon_{t}\), which is independent of \(s\) (where \(s\) is set of independent trust evidences collected from common neighbors and self-evidence also), we adopt normal distribution with zero mean and constant variance \(\sigma_{t}^{2}\). So, the likelihood function for the ARMA (1,1) model [5] is computed by the following equation.  
\[L(\varphi_{1}\theta_{1},\sigma_{\epsilon}^{2})=\prod_{t=2}^{T} \frac{1}{\sqrt{2\Pi}\sigma_{\epsilon}}\] \[\times\exp\{-\frac{(y_{t}-c-\varphi_{1}y_{t-1}-\theta_{1} \epsilon_{t-1}^{*})^{2}}{2\sigma_{\epsilon}^{2}}\} \tag{4}\]  
Therefore, the log likelihood function is  
\[l(\varphi_{1}\theta_{1},\sigma_{\epsilon}^{2})=-(T-1)\log\sigma _{\epsilon}-\frac{1}{2\sigma_{\epsilon}^{2}}\] \[\times\sum_{t=2}^{T}(y_{t}-c-\varphi_{1}y_{t-1}-\theta_{1} \epsilon_{t-1}^{*})^{2} \tag{5}\]  
where \(\epsilon_{t}^{*}=y_{t-1}-c-\varphi_{1}y_{t-2}-\theta_{1}\epsilon_{t-2}^{*}\) for \(t=3,...,T\) are obtained recursively.  
The GARCH (1, 1) model is expressed as  
\[\sigma_{t}^{2}=k+G_{1}\sigma_{t-1}^{2}+A\epsilon_{t-1}^{2} \tag{6}\]  
where \(\sigma_{t}^{2}\epsilon_{t}\) is taken from from the ARMA(1,1) model and it is assumed that it has conditional variance \(\epsilon_{t}^{2}\). In case of Gaussian \(\epsilon_{t}\), the likelihood function is  
\[L(k,G^{1},A_{1})=\prod_{t=2}^{T}\frac{1}{\sqrt{2\Pi}\epsilon_{t}}\exp\{-\frac {\epsilon_{t}^{2}}{2\sigma_{\epsilon_{t}^{2}}^{2}}\} \tag{7}\]  
The log likelihood function, neglecting the constant term, can be written as  
\[l(k,G^{1},A_{1})=\frac{1}{2}\sum_{t=2}^{T}\{\log\sigma_{t}^{2}+\frac{\epsilon _{t}^{2}}{\sigma_{t}^{2}}\} \tag{8}\]  
where \(\sigma_{t}^{2}=k+G_{1}\sigma_{t-1}^{2}+A_{1}\epsilon_{t-1}^{2}\) are obtained recursively.  
CH can predict the multiple-step ahead value of the trust series using ARMA/GARCH model, therefore finding the likelihood of good nodes has been increased significantly and it also reduces the trust revocation largely. For energy constrained environments like IoT-MANET, this scheme provides flexibility in terms of energy. In the following Section we will examine the efficacy of the proposed model.
## 7 Conclusions  
This paper focuses on the capacity credit evaluation of wind energy, whose key points are modeling the uncertainty of the correlated wind speed and load and assessing the power system reliability. The main achievements and conclusions are listed below:  
1. A novel method of fitting the joint PDF is proposed for wind speed and load. Particularly, SNMM is used to fit the marginal PDFs, while the correlation model is established by D-vine copulas.
2. The goodness-of-fit of SNMM, GMM, Weibull model and KDE is quantified by the Chi-square values, among which that of SNMM is the smallest. Similarly, the goodness-of-fit of D-vine, C-vine, Normal and t copulas is quantified by the ECP-CvM values, among which that of D-vine is the smallest. Therefore, SNMM and D-vine copulas are validated.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \(R_{0}\)/10\({}^{-4}\) & \(R_{d}\)/10\({}^{-4}\) & \(R_{u}\)/10\({}^{-4}\) & CC/MW & CCF/\% \\ \hline \(W1\) & 2.5544 & 1.9227 & 5.6365 & 37.361 & 24.91 \\ \(W2\) & 2.5304 & 1.9246 & 5.5950 & 35.477 & 23.65 \\ \(W3\) & 1.9614 & 1.6219 & 4.8975 & 24.116 & 16.07 \\ \(W4\) & 2.4687 & 1.6075 & 4.8615 & 39.925 & 26.62 \\ \hline \end{tabular}
\end{table}
Table 6: Three LOLP values and CC of four wind farms.  
Figure 7: The convergence of the three methods.  
* DROCE-IS is developed to enhance the efficiency of power system reliability assessment by proposing the idea of \"homogeneous units\" The convergence of reliability indices using DRCE-IS is remarkably faster than that using traditional CE-IS and MCS without compromising accuracy.
* Based on the wind speed data obtained in Northwest China, we integrate four wind farms into IEEE-RTS 79 system, whose CC values are evaluated by the combination of SNMM, D-vine copulas, DRCE-IS and the secant method. The CCF values of four wind farms, which means the ratio of their CC to the installed capacity, are all below 30%, which indicates a failure to make full use of wind energy. Hence, how to improve the CC of wind energy is worth further research.  
Conceptualization, J.C. and Y.Y.; methodology, J.C.; software, J.C.; validation, J.C., Y.Y. and M.C.; investigation, Q.X.; resources, Q.X.; data curation, M.C.; writing--original draft preparation, J.C.; writing--review and editing, M.C. and Q.X.; supervision, Y.Y. and Q.X.; project administration, J.C.; funding acquisition, Q.X.  
This research was funded by National Key R&D Program of China (2017 YFA0700300) and State Grid Science and Technology Program of China (SGJSJX00 YJS1800721).  
In this section you can acknowledge any support given which is not covered by the author contribution or funding sections. This may include administrative and technical support, or donations in kind (e.g., materials used for experiments).  
The authors declare no conflict of interest.
## 3 Methodology and Materials  
### Autoencoder Methodology  
Auto-encoders (AEs), as outlined in [PERSON] et al. [30], are a fundamental technique in unsupervised learning, utilizing neural networks to learn data representations. These tools are particularly adept at managing high-dimensional data, focusing on dimensionality reduction to effectively represent datasets. Auto-encoders also have extensive applications in unsupervised learning tasks, including dimensionality reduction, feature extraction, efficient coding, generative modeling, de-noising, and anomaly detection, as discussed by [PERSON] et al. [31]. They are fundamentally similar to Principal Component Analysis (PCA), particularly in terms of reducing the dimensionality of large datasets, a similarity most apparent when comparing PCA to a single-layered auto-encoder with a linear activation function, as noted by [PERSON] et al. [32].  
For our research experiment, the cycling layer is incorporated within an autoencoder, an artificial neural network designed to learn efficient representations of input data. This autoencoder compresses the input data into a compact representation, which is then decoded back to its original form. By integrating the cycling layer and self-attention mechanism into the encoding process, the model is equipped to effectively capture and represent the cyclical patterns present in the time series data.  
Autoencoders play a crucial role in time series data preprocessing by performing noise reduction and dimensionality reduction. They effectively filter out noise while preserving essential signals, enhancing data quality for analysis. Additionally, autoencoders address the challenge of high-dimensional time series data by reducing dimensionality, which improves computational efficiency and mitigates the risk of overfitting. This is particularly valuable in multivariate time series data, where complex variable interactions are present. By encoding these interactions, autoencoders reveal the underlying structure, providing a more refined input for further analysis.  
However, they exhibit several limitations when applied to time series data. Single autoencoders only compress all input data points into a fixed-size latent representation, which often leads to the loss of crucial long-term dependencies. Moreover, they are not designed to handle cyclical patterns effectively, treating sequences as linear inputs without regard to periodicity. This limitation makes them less suitable for datasets where capturing cycles, such as daily or seasonal variations, is essential. Additionally, autoencoders do not distinguish between important and less relevant data points within a sequence, leading to a loss of focus on critical time steps. These drawbacks motivate the need for additional mechanisms to enhance their capabilities in time series analysis
# Online Static Security Assessment of Power Systems Based on Lasso Algorithm
## 5 Case Studies
### IEEE 14-Bus System
#### 5.1.3 Light and Heavy Load Conditions  
For testing the accuracy of the prediction of the MSA-Lasso, ANN, and SVM algorithms in the light and heavy load conditions of the IEEE 14-bus system, 80% and 110% of the base load situations are employed for representing light and heavy conditions, respectively. The tested controlled variables are still applied to the variables in Table 6. The ranking results of each condition, with the descending order of the NRLF method, are shown in Tables 10 and 11.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{13}{c}{**Method**} & \multicolumn{13}{c}{**Ranking**} \\ \hline NRLF & L13 & L20 & L11 & L15 & L18 & L17 & L7 & L1 & L9 & L12 & L4 & L16 & L3 & L2 & L19 & L5 & L8 & L10 & L6 \\ MSA-Lasso & L13 & L20 & L11 & L15 & L18 & L17 & L7 & L1 & L9 & L12  
With the analysis of the light, normal, and heavy load conditions, it can be seen that the rankings of the security indices are basically the same. In addition, with the aggravating of loads, the insecure states will gradually increase.  
From the results in this section, the conclusion can be drawn that the MSA-Lasso algorithm is also suitable for the light and heavy load conditions of the IEEE 14-bus system. With the utilization of MSA-Lasso, the severities of the \(N{-}1\) contingencies can be ranked, and the contingencies can be screened.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Outage Line** & **NRLF** & **MSA-Lasso Prediction** & **ANN Prediction** & **SVM Prediction** \\ \hline L 20(13–14) & 1.9557 & 1.9500 & 1.9677 & 1.9786 \\ L 13(6–13) & 1.8806 & 1.8829 & 1.8790 & 1.8698 \\ L 1
# Dimensional Reduction-Based Moment Model for Probabilistic Slope Stability Analysis
## 3 Dimensional Reduction Method and Moment
### Evaluate the Statistics Moment Based on MDRM  
Based on the MDRM model, a \(k\)th statistics moment of response can be approximated as  
\[E[y^{k}]\approx E[(g_{0}^{(1-n)}\times\prod_{i=1}^{n}g_{i}(x_{i}))^{k}] \tag{10}\]  
where the mathematical exception operation is denoted as \(E[\;]\) and for \(k=1\), \(E[y^{k}]=E[y]\) is the mean value of \(y\). Assuming that all input random variables are independent, the above equation can be written as  
\[E[y^{k}]\approx g_{0}^{k(1-n)}\prod_{i=1}^{n}E[(g_{i}(x_{i}))^{k}] \tag{11}\]  
Based on the Equation (10), the first and second moment of response can be approximated as  
\[\mu_{y}=E[y]\approx g_{0}^{(1-n)}\prod_{i=1}^{n}E[g_{i}(x_{i})] \tag{12}\]  
\[\mu_{2y}=E[y^{2}]\approx g_{0}^{2(1-n)}\prod_{i=1}^{n}E[(g_{i}(x_{i}))^{2}] \tag{13}\]  
Then, the standard deviation of response can be obtained as  
\[\sigma_{y}=\sqrt{\mu_{2y}-{\mu_{y}}^{2}} \tag{14}\]  
where \(\sigma_{y}\) is the standard deviation of the response such as the safety factor of slope. The computation of the mean and any other \(k\)th moment of response requires the calculation of a \(k\)th moment of all the cut functions through one-dimensional integration. The numerical integration can be significantly optimized using the Gauss quadrature formulas. A \(k\)th moment of an \(i\)th cut function can be approximated as a weighted sum.  
\[E\Big{[}(g_{i}(x_{i}))^{k}\Big{]}=\int_{X_{i}}[g_{i}(x_{i})]^{k}f_{i}(x_{i}) dx_{i}\approx\sum_{j=1}^{L}w_{j}[g_{i}(x_{j})]^{k} \tag{15}\]  
where \(L\) is the number of the Gauss quadrature points, \(x_{j}\) and \(w_{j}\) are the coordinates and weights, respectively, of the Gauss quadrature points (\(j=1,\,\ldots,\,L\)) and \(h_{i}\) (\(i=1,\,2,\,\ldots,\,n\)) is the response when \(i\)th cut function is set at \(j\)th Gauss quadrature point.  
Obviously, MDRM could determine the moment of the response function and avoid determining the response function and its partial derivatives, which is a challenging task for the traditional response surface method using FOSM.
## 4 Benchmarking
### Test on Max-Cut Problems
\begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline
**Graph** & **Problem** & \(n\) & \begin{tabular}{c} **Best** \\ **Known** \\ \end{tabular} & \begin{tabular}{c} **VNS** \\ **BestDiff** \\ \end{tabular} & \begin{tabular}{c} **VNS** \\ **AvgDiff** \\ \end{tabular} & \begin{tabular}{c} **B-VNS** \\ **Time** **\end{tabular} & \
\begin{tabular}{c} **Test (\(p\)-Value)** \({}^{*}\) \\ **BestDiff** \\ \end{tabular} &
\begin{tabular}{c} **Test (\(p\)-Value)** \({}^{*}\) \\ **Time** **\end{tabular} \\ \hline Random & G1 & 800 & 11624 & 0 & 0.033 & 180.13 & 0 & 2.533 & 158.702 & *** & *** \\  & G2 & 800 & 11620 & 0 & 7.133 & 185.804 & 0 & 6.8 & 162.854 & 0.830 & *** \\  & G3 & 800 & 11622 & 0 & 1.733 & 195.169 & 0 & 2.833 & 172.003 & 0.222 & *** \\  & G4 & 800 & 11646 & 0 & 0.567 & 193.595 & 0 & 0.633 & 175.664 & 0.507 & *** \\  & G5 & 800 & 11631 & 0 & 5.133 & 191.32 & 0 & 4.433 & 169.104 & 0.654 & *** \\ \hline Random (\(\pm 1\)) & G6 & 800 & 2178 & 0 & 1.867 & 203.065 & 0 & 2.2 & 136.156 & 0.299 & *** \\  & G7 & 800 & 2006 & 0 & 4.533 & 195.770 & 0 & 5.2 & 169.933 & 0.286 & *** \\  & G8 & 800 & 2005 & 0 & 3.4 & 154.650 & 0 & 2.733 & 164.133 & 0.845 & *** \\  & G9 & 800 & 2054 & 0 & 4.3 & 195.341 & 1 & 4.6 & 169.740 & 0.622 & *** \\  & G10 & 800 & 2000 & 0 & 3.2 & 160.173 & 0 & 2.333 & 141.589 & 0.191 & *** \\ \hline Toroidal & G11 & 800 & 564 & 14 & 25.267 & 66.274 & 20 & 27.733 & 44.726 & 0.001 & *** \\  & G12 & 800 & 556 & 18 & 24.4 & 66.716 & 16 & 24.133 & 57.920 & 0.916 & *** \\  & G13 & 800 & 582 & 16 & 22.8 & 68.079 & 18 & 24.067 & 62.023 & 0.127 & *** \\ \hline Planar & G14 & 800 & 3064 & 29 & 37.733 & 78.656 & 32 & 39.6 & 69.983 & 0.087 & *** \\  & G15 & 800 & 3050 & 31 & 38.633 & 77.195 & 32 & 39.867 & 67.350 & 0.179 & *** \\ \hline Random & G43 & 1000 & 6660 & 1 & 8.967 & 431.314 & 1 & 9.733 & 381.073 & 0.323 & *** \\  & G44 & 1000 & 6650 & 3 & 8.467 & 428.178 & 2 & 9.533 & 375.822 & 0.114 & *** \\  & G45 & 1000 & 6654 & 0 & 12.067 & 425.304 & 1 & 11.033 & 374.124 & 0.445 & *** \\  & G46 & 1000 & 6654 & 9 & 16.1 & 410.047 & 5 & 16.633 & 373.864 & 0.494 & *** \\  & G47 & 1000 & 6654 & 9 & 20.433 & 415.607 & 13 & 20.267 & 370.332 & 0.472 & *** \\ \hline Planar & G51 & 1000 & 3846 & 39 & 47.433 & 194.891 & 39 & 49.533 & 192.633 & 0.070 & 0.007 \\  & G52 & 1000 & 3849 & 41 & 49.1 & 126.208 & 42 & 50.033 & 110.035 & 0.265 & *** \\ \hline \hline \end{tabular}  
*: Mann–Whitney test; the difference is significant if \(p\)-value \(<\alpha\), (\(\alpha=0.05\)). **: average computation time (second). ***: \(<\)0.001.  
\end{table} 
Table 3: Results for Helmberg–Rendl [39] problems.