esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Related Work and Our Contribution in Context
### Suffix Trees and CSTs
\begin{table}
\begin{tabular}{l l} \hline \hline
**Operation** & **Description** \\ \hline _Root_() & the root of the suffix tree \\ _Locate_(\(v\)) & position \(i\) such that \(\pi(v)\) starts at \(T[i]\), for a leaf \(v\) \\ _Ancestor_(\(v,w\)) & true if \(v\) is an ancestor of \(w\) \\ _SDepth_(\(v\)) & string-depth of \(v\), _i.e._, \(|\pi(v)|\) \\ _TDepth_(\(v\)) & tree-depth of \(v\), _i.e._, depth of node \(v\) in the suffix tree \\ _Count_(\(v\)) & number of leaves in the subtree rooted at \(v\) \\ _Parent_(\(v\)) & parent node of \(v\) \\ _FChild_(\(v\)) & alphabetically first child of \(v\) \\ _N Sibling_(\(v\)) & alphabetically next sibling of \(v\) \\ _SLink_(\(v\)) & suffix-link of \(v\), _i.e._, the node \(w\) s.th. \(\pi(w)=\beta\) if \(\pi(v)=a\beta\) for \(a\in\Sigma\) \\ _SLink\({}^{i}\)_(\(v\)) & iterated suffix-link, _i.e._, the node \(w\) s.th. \(\pi(w)=\beta\) if \(\pi(v)=\alpha\beta\) for \(\alpha\in\Sigma^{i}\) \\ _LCA_(\(v,w\)) & lowest common ancestor of \(v\) and \(w\) \\ _Child_(\(v,a\)) & node \(w\) s.th. the first letter on edge \((v,w)\) is \(a\in\Sigma\) \\ _Letter_(\(v,i\)) & \(ith\) letter of v’s path-label, \(\pi(v)[i]\) \\ _LAQ_S_(\(v,d\)) & the highest ancestor of \(v\) with string-depth \(\geq d\) \\ _LAQ_T_(\(v,d\)) & the ancestor of \(v\) with tree-depth \(d\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main operations over the nodes and leaves of the suffix tree. transforming it as we move back to the original node. The suffix link operation, defined in Table 1, can be computed using \(\Psi\) and the lowest common ancestor operation [11].
## 3 Results
### Functional Changes  
The large-bodied species _Silurus glanis_ exhibited the highest dissimilarity compared to others, while the Xenocyprights and _Escox lucius_ showed similarities (Figure 4). The introduced species _Lepomis gibbosus_, _Pseudorasbora parva_, and _Gambusia holbrook_ clustered together, while the remaining species, including the middle-sized species favoring the lake's open waters, formed another distinct group.  
The functional richness among the assemblages of 1900 and 2020 was increased due to species introductions (Figure A1, Appendix A). The estimated value of FDiv was 0.8021, indicating a moderate to high level of dissimilarity in functional traits between the assemblages from 1900 and 2020, meaning that the functional composition has changed significantly over time. The estimated value of FTur was 0.357, indicating a moderate level of functional turnover and suggesting some change in the species compositions and their functional traits between the two time periods. Last, the value of FNes was 0.446, indicating a moderate level of functional nestedness and suggesting that there is a fair amount of overlap in functional traits between the two assemblages, with a significant portion of one assemblage's traits being a subset of the other's.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Family** & **Species** & **Origin** \\ \hline
**Leucistidae** & _Rutilus rutilus_ ([PERSON], 1758) & N \\  & _Sardinius erythythythallus_ ([PERSON], 1758) & N \\  & _Squalius vardensis_ ([PERSON], 1928) & N \\
**Percidae** & _Perca fivatiils_ ([PERSON], 1758) & T \\
**Poeciliidae** & _Gambusia holbrook_ ([PERSON], 1859) & A \\
**Siluridae** & _Silurus glanis_ ([PERSON], 1758) & N \\
**Tincidae** & _Tinca tinca_ ([PERSON], 1758) & T \\
**Xenocyprididae** & _Ctenopharyngodial declia_ ([PERSON], 1844) & A \\  & _Hypophthalmichthys molitirix_ ([PERSON], 1844) & A \\  & _Hypophthalmichthys molitis_ ([PERSON], 1845) & A \\ \hline
**Total** & & **16** \\ \hline \hline \end{tabular}  
* A: alien, N: native, T: translocated. The nomenclature of species and their classification into families are according to the most recent changes [37].  
\end{table}
Table 1: Cont.  
Figure 4: Fish species’ dissimilarity based on their functional traits, estimated by using Euclidean distance. The darker the color, the greater the dissimilarity.
## 2 Improved Skewness Decision Tree SVM (ISDTSVM) Algorithm
### Non-Linear Model of the SDTSVM Based on the Kernel Function  
This section will briefly describe a non-linear model of the SDTSVM algorithm, based on kernel function [22; 23]. In most practical data sets, data are often non-linear and separable. The main idea of the non-linear SVM is to create non-linear kernel classifiers which map the data onto a higher-dimensional feature space, expecting that in the higher-dimensional space, the data could become more easily separated. Equation (2) has been obtained by using the kernel function given in Equation (1).  
\[K(x_{i},x_{j})=(\Phi(x_{i}),\Phi(x_{j})) \tag{1}\]  
\[\max_{\alpha}\quad L_{D}(\alpha)=\sum_{i=1}^{m}\alpha_{i}-\frac{1}{2}\sum_{i= 1}^{m}\sum_{j=1}^{m}y_{i}y_{j}\alpha_{i}x_{j}K(x_{i},x_{j}) \tag{2}\]  
\[\text{Subject to}\sum_{i=1}^{m}y_{i}\alpha_{i}=0\]  
\[0\leq\alpha_{i}\leq C,i=1,2,\cdots,m\]  
Some widely used kernel functions include polynomial, radial basis function (RBF) and sigmoid kernel, which are presented by Equations (3)-(5) respectively.  
Polynomial kernel:  
\[K(x_{i},x_{j})=(1+x_{i}\cdot x_{j})^{d} \tag{3}\]Radial basis function kernel:  
\[K(x_{i},x_{j})=\exp\ (-\gamma\|x_{i}-x_{j}\|^{2}) \tag{4}\]  
Sigmoid kernel:  
\[K(x_{i},x_{j})=\tan\ h\ (\mathrm{kx}_{i}\cdot x_{j}-\delta) \tag{5}\]  
The RBF kernel function is usually used for two reasons. First, this kernel maps samples onto a higher-dimensional space; thus, it can handle the case when the relation between class labels and the attributes is nonlinear. The second reason is that the RBF kernel only requires two parameters \(C\) and\(\gamma\), making this an easily-processed method.
## 5 Discussion
### Discussion and Interpretation of Results
Belt strength (CB Strength) manifests as a significant parameter in nonlinear models (random forest, ANN) (in 2 nd/3 rd place), while in the decision tree it has no significant influence. The results of this study build upon and significantly extend systematic knowledge about the influence of key parameters (impact height, weight of impacting material, strength and shape of impactor) on the impact force and overall resistance of rubber-textile conveyor belts in real operating conditions. The results correspond with research findings [56; 57]. The interpretation of the results shows that compared to previously published studies, where ML models were used more for damage detection or classification of belt conditions [32; 38], the study systematically demonstrates that ANN and random forest are significantly more accurate also in quantitative prediction of impact resistance based on physical parameters. The results clearly illustrate not only the higher accuracy of ANN, but also its increased sensitivity to the quality of training data and lower interpretability compared to traditional models (regression, decision tree). Compared to the work [13; 27], where \"drop height\" was designated as a key input, the study not only confirms these conclusions, but also allows for precisely quantifying that the significance of this input is consistently dominant in all considered model approaches. According to [27], models with included \"drop height\" significantly improved the accuracy of conveyor belt lifespan prediction. We also demonstrated that belt strength is significant especially in nonlinear models (random forest, ANN), which was not explicitly highlighted in previous studies. In contrast, the impactor type (shape of the falling load) was identified as negligible in all models, which is consistent with the findings [53; 54; 55]. Through this approach, we simultaneously extend and refine current knowledge:  
* Not only quality, but also model selection significantly influences the significance of input variables (in some models, neglected inputs may turn out to be important and vice versa), which is also emphasized in [5; 23; 24; 57; 25]. * Nonlinear ML models (random forest model, ANN model) are able to uncover significant relationships that linearized methods do not identify. Similarly, studies [68; 69; 70] state that these approaches are especially suitable when modeling complex systems with multiple inputs and unclear dependencies. * Knowing the precise order of significance of individual input variables allows for more effective experiment design or optimization of maintenance strategy in industrial practice. This approach is also supported by other experimental and model works in the field [27; 33; 57], which document that quality analysis of input importance leads to resource savings, better decisions, and more targeted interventions in planning monitoring or predictive maintenance.
## 4 Numerical Results  
In this section, Monte-Carlo simulations will be provided to verify the correctness of the theoretical expressions we have derived, and the impacts of various parameters on the system's performance will be provided. In all simulation figures, the theoretical results of the OP and asymptotic OP are determined by (20) and (25), respectively. The theoretical results of the ABER and asymptotic ABER are determined by (34) and (37), respectively. To evaluate Meijer's G-function in our theoretical expressions, we use the software MATLAB R2023a. To facilitate the simulation, the optical power transmitted at node S and each relay are assumed to be the same, i.e., \(P_{\rm t}=P_{\rm o}\). The main simulation parameters used in this paper are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbols** & **Values** \\ \hline Wavelength & \(\lambda\) & 1550 nm \\ \hline Detector radius & \(a\) & 0.025 m \\ \hline Refractive index structure coefficient & \(C_{n}^{2}\) & \(5\times 10^{-14}\) m\({}^{-2/3}\) \\ \hline Standard deviation of UAV position deviation & \(\sigma_{\rm p,u}\) & 0.1 m \\ \hline Photoelectric conversion efficiency & \(T\) & 0.9 \\ \hline Standard deviation of ground position & \(\sigma_{\rm p,g}\) & 0.1 m \\ \hline Atmospheric attenuation coefficient & \(\xi\) & 1 km\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The main parameters used in this paper.
## 2 Models and Methods
### Transmissibility Ratios of Multi-DoF Systems  
In the dynamic analysis of a complex system, it is often important to evaluate whether the vibrations transmitted from one point to another are attenuated or amplified. To that purpose, transmissibility, defined as the dimensionless ratio between forces or displacements at different DoFs, gives useful insights into the dynamic behavior of a system. For a multi-DoF system, its definition is not trivial. Here the displacement transmissibility ratio is used:  
\[T_{ij}^{d}=\frac{x_{i}}{x_{j}}; \tag{21}\]  
in particular, the transmissibility from a given wheel (axle) \(j\) to an internal DoF \(i\) of the system is evaluated considering the displacement only on that wheel (DoF \(j\)), with the other wheels being grounded and no other force acting on the internal DoFs.
# An Algorithm to Generate a Weighted Network Voronoi Diagram Based on Improved PCNN
## 3 Improved PCNN  
### Structure of the PCNN  
The standard PCNN, also known as the third artificial neural network, is a laterally connected feedback network of pulse coupled neurons without requiring any training [26; 27]. The standard neuron model is given by Figure 2 and the following equations [28; 29; 30]:  
\[F_{ij}[n]=e^{-\alpha_{F}}F_{ij}[n-1]+V_{F}\underset{kl}{\sum}M_{ijkl}Y_{kl}[n- 1]+I_{ij} \tag{3}\]  
\[L_{ij}[n]=e^{-\alpha_{L}}L_{ij}[n-1]+V_{L}\underset{kl}{\sum}W_{ijkl}Y_{kl}[n-1] \tag{4}\]  
\[U_{ij}[n]=F_{ij}[n]\big{(}1+\beta L_{ij}[n]\big{)} \tag{5}\]  
\[Y_{ij}[n]=\begin{cases}1&U_{ij}[n]>E_{ij}[n]\\ 0&otherwise\end{cases} \tag{6}\]  
\[E_{ij}[n+1]=e^{-\alpha_{L}}E_{ij}[n]+V_{E}Y_{ij}[n] \tag{7}\]  
where the index \((i,j)\) and index \((k,l)\) refer to the current neuron and its neighbors. \(I\) denotes the external stimulus. \(F\) is feeding input, and \(L\) is linking input in iteration \(n\). \(M\) and \(W\) represent linking synapse weights. Internal activity \(U\) is generated by the modulation of \(F\) and \(L\) through linking strength \(\beta\). The neuron will be stimulated when the internal activity \(U\) is greater than the dynamic threshold \(E\). In addition, \(V_{F}\), \(V_{L}\) and \(V_{E}\) are normalizing constants; and the parameters \(\alpha_{F}\), \(\alpha_{L}\) and \(\alpha_{E}\) are the time constants [31].  
Drawn by its characteristics of auto-wave and concurrency, we planned to incorporate the PCNN into the construction process, but in the standard PCNN model, the iteration process is complex and the transmission method of auto-wave is hard to control. In order to make the PCNN more suitable for the construction of the network Voronoi diagram, an improved PCNN is proposed.  
Figure 2: Structure of the PCNN model.
## 3 Materials and Methods
### Monitoring with the Sigfox Network  
The diagram in Figure 5 shows the flow of the collection and monitoring of the location data of patients and objects in a hospital using the Sigfox network. The device transmits a Bluetooth Low Energy (BLE) signal every two seconds. The transmitted BLE signal is sent to the Sigfox Cloud through the base station according to the cycle set in the receiver. The Internet platform, which is an IoT platform, receives data from the Sigfox Cloud through API linkage with Sigfox, converts non-standard data into a standard message set, and stores the converted data in a dashboard server for location monitoring. Figure 6 illustrates the setting of the Sigfox network setting with the location of the sensor, the device attached to the patients, and the Sigfox base transceiver station receiving the Sigfox network data that would be used to monitor the location of patient. In this study, a total of 31 infusion pumps installed among 11 hospital rooms were monitored using the Sigfox network for 5 days for their locations instead of actual patients and the collected data was compared to the actual location of the infusion pumps recorded by the nurses.
# COVID-19 CXR Classification: Applying Domain Extension Transfer Learning and Deep Learning
## 4 Results
### Evaluation Results
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & **Accuracy** & **Precision** & **Sensitivity** & **Specificity** & **F1-Score** & **MCC** & **Balanced Accuracy** \\  & **(\(\pm\)_std_)** & **(\(\pm\)_std_)** & **(\(\pm\)_std_)** & **(\(\pm\)_std_)** & **(\(\pm\)_std_)** & **(\(\pm\)_std_)** & **(\(\pm\)_std_)** \\ \hline Baseline & 86.8\% & 83.1\% & 86.5\% & 87.0\% & 84.2\% & 73.4\% & 86.7\% \\ Model & (\(\pm\)0.005) & (\(\pm\)0.058) & (\(\pm\)0.085) & (\(\pm\)0.059) & (\(\pm\)0.047) & (\(\pm\)0.004) & (\(\pm\)0.001) \\ \hline Proposed & 96.7\% & 96.2\% & 96.1\% & 97.2\% & 96.1\% & 93.2\% & 96.6\% \\ Model & (\(\pm\)0.025) & (\(\pm\)0.016) & (\(\pm\)0.018) & (\(\pm\)0.092) & (\(\pm\)0.097) & (\(\pm\)0.003) & (\(\pm\)0.008) \\ \hline Improvement & 9.9\% & 13.1\% & 9.6\% & 10.2\% & 11.9\% & 20\% & 9.9\% \\ Ratio & 9.9\% & 13.1\% & 9.6\% & 10.2\% & 11.9\% & 20\% & 9.9\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance of the baseline and proposed models. Figure 7: Confusion matrix for the COVID-19 CXR classification. (**a**) (Baseline) non-pretrained ResNet-50. (**b**) (Proposed) pretrained ResNet-50. Figure 8 shows the training and validation accuracies and losses during the training. Table 9 shows the performance comparison of the proposed methodology with other studies. Compared to previous studies, our study showed significant performance improvements in sensitivity and specificity indicators when classifying COVID-19 and non-COVID-19 images. Compared to Elpeltagy at el. [19] who conducted experiments on the same dataset as ours, the model proposed in this study showed significant performance differences in precision and specificity before the five-fold test. After a five-fold test measuring the stability of the model within a small data set, the models showed significant performance differences in accuracy, precision, specificity, and the F1-score. The results of applying the proposed methodology to COVID-19 and non-COVID-19 X-ray imaging classification studies were effectively confirmed. Figure 8: Accuracy and loss curves as a result of applying the proposed model on the Mendeley dataset. (**a**) Train and validation loss (20 epochs) (early stopping applied). (**b**) Train and validation accuracy (20 epochs). (**c**) Training and validation loss. (**d**) Training and validation accuracy.
## 3 Results
### Morphological Analysis of the \"PCI/MSC Constructs  
The morphological analysis of the cell/scaffold constructs performed by CLSM is shown in Figure 3.  
Figure 3: Confocal laser scanning microscopy (CLSM) analysis on hMSC/*PCL constructs how cell nuclei imaged in green and \(f\)-actin in red: (**a,d**) differentiated in static conditions; (**b,e**) differentiated in dynamic conditions; (**c,f**) undifferentiated. (**a–c**) Scale bar = 100 \(\upmu\)m, original Magnification 200\(\times\); (**d–f**) Scale bar = 30 \(\upmu\)m, original magnification 600\(\times\).  
Figure 2: Collagen gene expression analysis performed on hMSC/*PCL constructs for the following genes: (**a**) Col1-\(\alpha\)1; (**b**) Col2-\(\alpha\); (**c**) Col4-\(\alpha\)1; and (**d**) Col4-\(\alpha\)2: (**a–d**) Statistical significance: * = \(p<0.05\); **\(=p<0.01\) vs undifferentiated; $ = \(p<0.05\); $$ = \(p<0.01\) vs differentiated statically cultured hMSC/*PCL constructs.  
HMSCs were quite uniformly distributed over the entire surface of the scaffolds, cell nuclei were well visible and \(f\)-actin bundles in the cytoplasm were well extended. In particular, \(f\)-actin was more expressed in both differentiated construct types (Figure 3a,b), and less expressed in the undifferentiated controls (Figure 3c,f). Dynamically differentiated constructs showed the most intense \(f\)-actin expression (Figure 3b,e), whereas statically differentiated ones showed a regular distribution of cytoskeletal filaments (Figure 3a,d).
# Characterization of Shallow Sedimentary Layers in the Oran Region Using Ambient Vibration Data
## 4 Results and Discussion  
### The Soil Fundamental Frequencies  
For each site, the HVSR curves of all the stations forming the array (07 stations) have been calculated. The obtained curves, which are relatively similar, have then been averaged to obtain the resonance frequency \(f_{0}\) and the corresponding amplitude \(A_{0}\) of each site with their respective standard deviation (Table 2).  
In our study area, the obtained results (Figure 4) show that most HVSR curves have two peaks: the fundamental peak \(f_{0}\) and a secondary peak \(f_{1}\) of lower amplitude.  
The fundamental frequency peak varies between 0.3 and 1.6 Hz. This frequency range is in agreement with the fundamental frequency variation maps obtained in a previous measurement campaign [27]. The sites P12 and P14 show the highest values with 1.6 and 0.8 Hz, respectively. These two points are located at the Murdjado massif toe in the west of our study area, where a thinning of the sedimentary layers and the Cretaceous of the Murdjado mountain are observed [27].  
The higher mode frequency peak, \(f_{1}\), represents a lower velocity contrast between the Plio-Quaternary and the Miocene sedimentary layers. It has higher values than \(f_{0}\) and varies between 6.25 and 9 Hz (see Table 2). Higher mode frequency peaks have already been observed before in the Lower-Chelif Basin [26,27].  
According to our results (Figure 4), two distinctive groups can be observed: one group with an amplitude \(A_{0}<\)3 (sites P1, P8, P10, P11, P12, P13, P14) and another group (P02, P03, P04, P05, P06, P07, P09, P15) with an \(A_{0}\) value varying between 3 and 4.  
\begin{table}
\begin{tabular}{c c c c c  
Figure 4: The average HVSR curves obtained for each of the arrays analyzed (P1 to P15), whose position is indicated in Figure 2. For each curve, the thick black line corresponds to the averaged HVSR curve; meanwhile, the vertical gray bars reflect the standard deviation values at each frequency.
# Life Cycle Assessment of Bridges Using Bayesian Networks and Fuzzy Mathematics
## 5 Discussion
### Case Environmental Impact
#### 5.1.1 BNFC Comprehensive Assessment
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Environmental** & **Bridge** & **Range** & **GWP (kg)** & **AP (kg)** & **FEP (kg)** & **PMFP (kg)** & **WP (kg)** & **Transportation** & **The** \\
**Stage** & **Name** & & & & & & **(kg)** & **Proportion** \\ \hline \multirow{2}{*}{Survey and design} & SQ & 322,603.10 & 0.29 & 1444.66 & 14.12 & 5609.22 & 4525.62 & 1.37\% \\  & EH & 6,075,65.23 & 0.52 & 2781.15 & 27.12 & 10,798.15 & 12,504.05 & 2.01\% \\ \hline \multirow{2}{*}{Material manufacturing} & SQ & 35,783,970.10 & 338,386.32 & 218,677.39 & 1,027,034.48 & 1,911,752.52 & 551,965.85 & 1.41\% \\  & EH & 36,070,70.35 & 297,990.71 & 193,603.27 & 915,282.34 & 1,679,511.52 & 554,608.67 & 1.55\% \\ \hline \multirow{2}{*}{Construction and installation} & SQ & 21,604,311.50 & 334.85 & 22,516.66 & 1212.05 & 86,335.68 & 98,670.19 & 0.45\% \\  & EH & 23,954,72.44 & 337.00 & 29,475.12 & 1389.47 & 113,471.60 & 89,074.70 & 0.37\% \\ \hline \multirow{2}{*}{Maintenance and operation} & SQ & 79,173,042.18 & 155,891.23 & 514,843.27 & 702,336.77 & 1,390,668.18 & 1,057,111.78 & 1.29\% \\  & EH & 69,602,711.16 & 238,252.02 & 466,229.79 & 850,705.27 & 1,325,559.61 & 1,345,777.99 & 1.86\% \\ \hline \multirow{2}{*}{Dissassembly and recycling} & SQ & 4,184,764.66 & 43.94 & 234.27 & 31.98 & 891.24 & 1,985,014.96 & 47.42\% \\ \cline{1-1}  & EH & 2,412,687.90 & 12.23 & 316.02 & 11.24 & 1222.36 & 194,206.26 & 8.04\% \\ \hline \end{tabular}  
* Note (Table 5): The percentage value (%) = transportation contribution (kg)/total value of environmental contribution at each stage (kg).\(\sum\)EC\({}_{\text{SQ}}=\sum\)EC\({}_{\text{GWP}}+\sum\)EC\({}_{\text{AP}}+\sum\)EC\({}_{\text{EP}}+\sum\)EC\({}_{\text{FEP}}+\sum\)EC\({}_{\text{PMFP}}+\sum\)EC\({}_{\text{WP}}=\) 1474,46.95 tonnes; \(\sum\)EC\({}_{\text{EH}}=\) 135,311.42 tonnes.  
\end{table} 
Table 5: Summary table of bridge environmental impact contributions (Table 4 formula calculation). The assessment result can be obtained as follows by the compound operation \(\mathrm{E}(\Lambda,\mathrm{V})=\mathrm{K}_{\mathrm{j}}^{\prime}\mathrm{R}_{ \mathrm{SQ}}\):  
\[\mathrm{E}_{\mathrm{SQ}} =\left(0.9567\ 0.0034\ 0.0051\ 0.0117\ 0.0230\ \right)\times\left[ \begin{array}{ c c c c c}0.23&25.37&15.31&56.12&2.97\\ 0.00&68.41&0.07&31.52&0.01\\ 0.19&28.86&2.97&67.95&0.03\\ 0.00&59.34&0.07&40.58&0.00\\ 0.17&51.75&0.08&48.17&0.00\\ \end{array} \right]\] \[=\left(0.2249\ 26.5358\ 15.0851\ 55.7264\ 2.8416\right)\]  
\[\mathrm{(E}_{\mathrm{EH}}) =\left(0.9547\ 0.0040\ 0.0051\ 0.0131\ 0.0231\ \right)\times\left[ \begin{array}{ c c c c c}0.47&25.24&18.54&53.88&1.87\\ 0.00&55.50&0.06&44.43&0.00\\ 0.40&27.94&4.25&67.36&0.05\\ 0.00&51.75&0.08&48.17&0.00\\ 0.34&53.61&3.62&42.38&0.04\\ \end{array} \right]\] \[=\left(0.4586\ 26.4560\ 17.8067\ 53.5705\ 1.7865\right)\]