esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Uncertainty Analysis and Wind Farm Modeling
### Wind Turbine Modeling  
The power output of a wind turbine is associated with the wind speed, which is converted to electrical power by different types of wind turbine generators. Our model representing a wind turbine's power is given by  
\[P_{w}(S_{w})=\left\{\begin{array}{ll}0&S_{w}<S_{cut-in}\\ P_{w,rated}\frac{S_{w}^{2}-S_{cut-in}^{2}}{S_{rated}^{2}-S_{cut-in}^{2}}&S_{ cut-in}<S_{w}<S_{rated}\\ P_{w,rated}&S_{rated}<S_{w}<S_{cut-out}\\ 0&S_{w}>S_{cut-out}\end{array}\right. \tag{6}\]  
Figure 1 shows the representative power curve for a wind turbine. The cut-in wind speed \(S_{cut-in}\) is the minimum speed required to generate power. If the wind speed reaches the cut-in value, power is generated by the wind turbine. The generator produces the machine's rated power \(P_{w,rated}\) when the wind speed reaches the rated wind speed \(S_{rated}\). As shown in Figure 1, power production is almost constant between \(S_{rated}\) and \(S_{cut-out}\). At the cut-out wind speed \(S_{cut-out}\), power generation is shut down to protect the wind turbine from damage and defects, and the power output becomes zero.  
Recently, both permanent magnet synchronous generators (PMSGs) and doubly fed induction generators (DFIGs) have begun to be used more widely [24]. PMSG wind turbines have more highly reliable operations, lower maintenance expenses, and smaller weights with simpler structures than DFIG wind turbines do. Accordingly, this paper focuses on PMSG wind turbines. Maximum power point tracking control is usually employed to maximize the turbine energy-conversion efficiency through the regulation of the rotational speeds of variable-speed wind turbines. Depending on the wind's aerodynamic conditions, the power captured by the wind turbine can be maximized versus rotational speed characteristics by adjusting the coefficient \(G_{p}\), which represents the aerodynamic  
Figure 1: Wind turbine power curve.  
efficiency of the wind turbine and is a function of the tip speed ratio (TSR). The maximum mechanical output power of the wind turbine is then defined as  
\[P_{max}=\frac{1}{2}\rho\pi R^{2}S_{w}^{3}G_{p,opt}\left(\beta,\gamma_{w,opt}\right) \tag{7}\]  
The optimal TSR of the mechanical output is given as  
\[\gamma_{w,opt}=\frac{\omega_{m,opt}R}{S_{w}} \tag{8}\]  
For the PMSG wind turbine modeled in this paper [24], the maximum value of the power coefficient (\(G_{p,opt}\) = 0.4412) is obtained according to the optimal value of the TSR (\(\gamma_{w,opt}\) = 6.9) calculated using (8). Because wind farms consist of several PMSG wind turbines, the power coefficient of a wind farm located at bus \(i\) is the sum of the active powers generated by the wind turbines, given by  
\[P_{WF,i}=\sum_{n=1}^{NT_{u}}P_{WT,n} \tag{9}\]
# LSTM-DQN-APF Path Planning Algorithm Empowered by Twins in Complex Scenarios
## 2 Preliminary  
In the dynamic and complex urban low-altitude environment, path planning algorithms need to balance real-time performance, safety, and global optimization. Traditional APF methods are difficult to adapt to dynamic obstacles due to their tendency to get trapped in local minima and unreachable goals. While DQN can optimize global strategies, it lacks the ability to model temporal dynamics, leading to lag in trajectory prediction. To address this, this section proposes the LSTM-DQN-APF fusion framework, which combines three modules: \"temporal prediction, global decision making, and physical constraints\", to provide theoretical support for autonomous obstacle avoidance in urban low-altitude environments.
# Lazy Aggregation for Heterogeneous Federated Learning
## 4 Evaluation
### Effects of the Proposed Algorithm
#### 4.2.1 Performance
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & **FedAvg** & **FedProx** & **FedDyn** & **FedLA** & **FedLAM** & **CFL** \\ \hline \multirow{4}{*}{**Mnist**} & IID & 91.5 & 91.5 & 93.7 & 91.4 & **95.3** & 91.6 91.6 \\  & Class 1 & 83.3 & 83.2 & 85.8 & 87.6 & 90.6 & **93.4**/70.8 \\  & Class 3 & 90.0 & 90.0 & 88.9 & 89.8 & **92.4** & 90.0 & 90.0 \\  & Dir 0.1 & 90.0 & 90.0 & 88.7 & 88.8 & **91.5** & 91.2 & 88.8 \\  & Dir 0.3 & 89.8 & 89.8 & 89.1 & 90.3 & **90.4** & 89.8 & 89.8 \\  & IID & 89.4 & 89.7 & **91.4** & 89.9 & 89.4 & 89.9 & 89.9 \\  & Class 3 & 79.1 & 79.6 & 84.9 & 79.3 & **85.3** & 79.2 & 79.2 \\
**Emnist** & Class 9 & 87.6 & 87.4 & **90.0** & 85.7 & 89.1 & 87.6 & 87.6 \\  & Dir 0.1 & 84.3 & 84.9 & **88.5** & 84.2 & 87.8 & 85.1 & 85.1 \\  & Dir 0.3 & 89.1 & 89.3 & 90.7 & 89.1 & 89.7 & 89.1 & 89.1 \\  & IID & 70.8 & 69.6 & 71.5 & 70.4 & **76.3** & 70.9 & 70.9 \\  & Class 1 & 27.0 & 27.0 & **41.8** & 28.0 & 30.0 & 0.07 & 107.1 \\
**Cifar10** & Class 3 & 65.3 & 66.2 & 64.1 & 67.3 & **71.1** & 66.0 & 66.0 \\  & Dir 0.1 & 62.5 & 62.1 & 59.3 & 60.4 & **64.6** & 62.7 & 62.7 \\  & Dir 0.3 & 66.0 & 66.1 & 65.6 & 68.1 & **71.5** & 66.5 & 66.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons of FedAvg, FedProx, FedDyn, CFL, FedLA, and FedLAM on Mnist, Emnist, and Cifar10 (Ir = 0.01) in IID and four kinds of non-IID settings. Local epoch E = 5, batch size B = 32.
# Complex Network Modeling and Analysis of Microfracture Activity in Rock Mechanics
## 4 Results and Discussion
### Limitations and Uncertainties
#### 4.4.2 Uncertainties  
Measurement Errors: Although we utilized state-of-the-art acoustic emission monitoring and precise testing equipment, there is always a margin of error associated with these measurements. These errors could affect the accuracy of the network model parameters derived from the data.  
Figure 17: Evolution of the microfracture network (Green dots represent acoustic emission events, red lines indicate the connections (edges) between these events, and purple circles highlight the clustering phenomena.). (**a**) N = 21, \(\epsilon_{1}\) = 3.43627; (**b**) N = 83, \(\epsilon_{1}\) = 3.44714; (**c**) N = 88, \(\epsilon_{1}\) = 3.92437; (**d**) N = 115, \(\epsilon_{1}\) = 3.94495; (**e**) N = 119, \(\epsilon_{1}\) = 4.04766; (**f**) N = 122, \(\epsilon_{1}\) = 4.06374; (**g**) N = 189, \(\epsilon_{1}\) = 4.24120; (**h**) N = 269, \(\epsilon_{1}\) = 4.37675; (**i**) N = 309, \(\epsilon_{1}\) = 4.42737; (**j**) N = 637, \(\epsilon_{1}\) = 4.55394.  
Data Interpretation and Model Assumptions: The construction of a complex network model relies on certain assumptions regarding the relationships between microfractures and network nodes/edges. The interpretation of these relationships introduces a level of uncertainty that should be considered when evaluating the model's predictions.  
Statistical Variability: Statistical analysis of the network parameters, such as the average degree and clustering coefficient, involves calculations on the basis of the data collected. The variability within the data could lead to different outcomes if the studies were replicated with a different sample set.  
In conclusion, while these limitations and uncertainties present challenges, they also highlight areas for future research. We recommend that subsequent studies address these limitations through expanded sample sizes, diverse geological applications, and further advancements in experimental techniques and modeling approaches. By doing so, the understanding of microfracture behavior in rock formations can be enriched, leading to more accurate predictions of rock failure and instability.
## 3 Model Formulation
### Model Development
#### 3.4.2 Model Setting  
Based on the analysis of sub-cost in Section 3.4.1, a two-stage distribution location-routing model with the hard time window constrains for city cold-chain logistics is established as follows:  
\[Minz_{1}=C_{1}+C_{1}^{\prime}+C_{2}^{\prime}+C_{3}+C_{3}^{\prime}+C_{4}+C_{5} \tag{7}\]  
Subject to:  
\[\sum_{i\in M_{1}}X_{i}^{k}q_{i}\leq Q_{1}\;\;k\in K \tag{8}\]  
\[\sum_{i\in N_{g}}q_{i}^{\prime}y_{ig}^{l}\leq Q_{2}\;g\in M_{1},l\in L_{g} \tag{9}\]  
\[\sum_{j\in M}X_{ij}^{k}=X_{i}^{k}\;i\in M;k\in K \tag{10}\]  
\[\sum_{i\in M}X_{ij}^{k}=X_{j}^{k}\;j\in M;k\in K \tag{11}\]  
\[\sum_{i\in N_{g}}\sum_{g\in M_{1}}x_{ijg}^{l}=y_{ig}^{l}\;j\in N_{g},l\in L_{g} \tag{12}\]  
\[\sum_{j\in N_{g}}\sum_{g\in M_{1}}x_{ijg}^{l}=y_{ig}^{l}\;i\in N_{g},l\in L_{g} \tag{13}\]  
\[\sum_{g\in M_{1}}\sum_{l\in L_{g}}y_{ig}^{l}=1\;j\in N_{g} \tag{14}\]  
\[\sum_{j\in N_{g}}x_{ijg}^{l}=\sum_{j\in N_{g}}x_{\bar{j}g}^{l}\leq 1\;i=g\in M _{1};l\in L_{g} \tag{15}\]  
\[\sum_{j\in M_{1}}X_{ij}^{k}=\sum_{j\in M_{1}}x_{\bar{j}i}^{k}\leq 1\;i=0;k\in K \tag{16}\]  
\[\sum_{i\in N_{g}}q_{i}^{\prime}y_{ig}\leq Z_{g}q_{g}\;g\in M_{1} \tag{17}\]  
\[ET_{i}\leq t_{i}^{l}\leq LT_{i} \tag{18}\]  
The objective function of the model is shown in (7). Constraint (8) shows that a vehicle cannot exceed its maximum load in the first level distribution. Constraint (9) shows that vehicle can not exceed its maximum load in the second-level distribution. The first stage of distribution flow balance is shown in (10) and (11). The second-stage of distribution flow balance is shown in (12) and (13). Constraint (14) shows that there is only one refrigerated vehicle providing a delivery service for one customer. As per constraints (15) and (16), the refrigerated vehicles starting from a transfer station must return to the same after serving the customer, and the refrigerated vehicles starting from the distribution center must return to the distribution center after serving transfer stations. The total customer requirements assigned to a transfer station must be lower than or equal to the storage capacity of the transfer station, which is imposed by (17). Constraint (18) represents the time window for customer \(i\).
## 4 Hardware Design
### Hardware Implementation and Test of the Element-Based Lattice Reduction  
The main body of the ELR algorithm was implemented using 12 states in hardware. First, T is initialized to the identity matrix and \(\lambda\) is initialized to all ones so that the condition of having \(\lambda\) equal to zeros in step 4 of the algorithm in Table 1 does not break from the loop. Following that entries on each row of C are divided by the equivalent row element from the matrix diagonal, e.g., C (1, 3) is divided by C (1, 1). The value of this operation is stored in \(\lambda\). After traversing the entire C matrix, \(\lambda\) is checked to see of all of its values are zeros. If that condition is true then the ELR algorithm is done, otherwise the largest value in C and \(\lambda\) are found and then they are used to update matrix T and C as shown in steps 9-11 in Table 1. This process keeps repeating until the condition of \(\lambda\) being all zeros is met and then T is delivered as the output of the ELR block. In hardware T is then passed to a matrix transpose and matrix inverse blocks to perform step 13 of Table 1.  
As described in Table 1, the ELR algorithm uses a while (true) loop and breaks out of it when a certain condition is met. This is generally undesirable and through initial testing of the algorithm it was determined that there are inputs for which this algorithm keeps looping forever. To solve this  
Figure 7: The Effect of the word length on the BER Performance of Element-based Lattice Reduction aided K-Best Detector.  
issue, a counter was added which is incremented at the end of each full iteration. If that counter reaches 20, then the algorithm will exit the while loop and use the current value of T as the output. This has shown to work fine as the final estimation is not affected much by this change. One final note on the algorithm is that when it takes up to 20 iterations, it is significantly the most computationally demanding block of the decoder and takes the largest number of clock cycles (up to 12,000 clock cycles). Additionally, two combinational blocks were designed to be used within the ELR block. Those were the max and rounding blocks which as their names suggest find the maximum number between a set of inputs and round a number up or down respectively.  
Finally, in order to test and validate the design, simulations were run with different sets of inputs. These inputs were then compared to MATLAB simulations for verification. The test results showed correct functionality of the implemented hardware.
## 3 Designed MGA for Parameter Determination for Multi-Crystalline Silicon Solar Cells
### Mathematical Model
#### 3.2.1 Initialization  
Each material (\(MT_{k}\)) is a combination of elements (\(X_{k,1}\ X_{k,2}\ X_{k,3}.\ldots\ldots\ldots\ldots\ X_{k,Dim}\)) as displayed in Equation (7) where each element symbolized by (\(X\)) refers to one decision variable of the whole set of decision variables with number (\(D\)). Also, the number of materials represents the population size of (\(N_{MT}\)).  
\[MT_{k}=[X_{k,1}\ X_{k,2}\ X_{k,3}.\ldots\ldots\ldots\ \ \ X_{k,D}],\ \ \ \ \ \ \ \ \ k=1:N_{MT} \tag{7}\]  
In order to initial their values, Equation (8) can be utilized to randomly determine each value within defined bounds.  
\[MT_{k}(It=0)=Low_{k}+R1_{k}\times(Up_{k}-Low_{k}),\ \ \ \ \ \ \ \ \ \ k=1:N_{MT} \tag{8}\]where, \(It\) refers to the iteration value and the number (0) refers to the initial population, \(Up_{k}\) and \(Low_{k}\) indicate the upper and lower limits of each decision variable (\(k\)). \(R1\) is a randomized generated number regarding each decision variable (\(k\)).
## 3 Results and Discussion
### Bibliometric Analysis of Research on Pavement Management (2000-2013)
#### Publication Distribution of Countries, Institutes and Authors
The nine most prolific authors in this research topic, who have published at least 10 documents, are shown in Table 4. The total number of papers with author name was 716. Only the top two authors published more than 20 documents each about pavement management, [PERSON] and [PERSON], leading researchers of the most productive institutions, University of Waterloo and Universidad de Coimbra, respectively. The author in the 3 rd position, [PERSON], was also affiliated to University of Waterloo. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Country** & **TP 1** & **(\%) 1** & **SPR 1** & **(\%) 1** & **CPR 1** & **(\%) 1** & **FR 1** & **(\%) 1** & **RPR 1** & **(\%) 1** \\ \hline USA & 348 & (48.9) & 1 & (47.6) & 1 & (59.0) & 1 & (45.4) & 1 & (46.3) \\ Canada & 85 & (12.0) & 2 & (11.5) & 2 & (15.7) & 2 & (11.5) & 2 & (11.1) \\ China & 69 & (9.7) & 3 & (8.9) & 2 & (15.7) & 3 & (8.4) & 3 & (8.6) \\ Taiwan & 24 & (3.4) & 4 & (3.7) & 22 & (1.2) & 4 & (3.2) & 4 & (3.4) \\ Portugal & 23 & (3.2) & 5 & (2.9) & 8 & (6.0) & 5 & (2.8) & 5 & (2.8) \\ South Korea & 19 & (2.7) & 13 & (1.0) & 2 & (15.7) & 9 & (1.7) & 11 & (1.4) \\ Iran & 17 & (2.4) & 7 & (1.8) & 6 & (7.2) & 6 & (2.1) & 9 & (1.7) \\ New Zealand & 17 & (2.4) & 7 & (1.8) & 6 & (7.2) & 8 & (1.8) & 6 & (1.8) \\ Italy & 15 & (2.1) & 7 & (1.8) & 12 & (4.8) & 9 & (1.7) & 6 & (1.8) \\ India & 13 & (1.8) & 6 & (2.1) & 37 & (0.0) & 7 & (2.0) & 6 & (1.8) \\ Japan & 12 & (1.7) & 16 & (0.8) & 5 & (8.4) & 12 & (1.3) & 12 & (1.3) \\ Australia & 12 & (1.7) & 10 & (1.6) & 18 & (2.4) & 11 & (1.4) & 10 & (1.5) \\ Egypt & 10 & (1.4) & 13 & (1.0) & 12 & (4.8) & 14 & (1.1) & 16 & (1.0) \\ Greece & 9 & (1.3) & 11 & (1.3) & 22 & (1.2) & 14 & (1.1) & 14 & (1.1) \\ Singapore & 9 & (1.3) & 11 & (1.3) & 22 & (1.2) & 12 & (1.3) & 12 & (1.3) \\ UK & 9 & (1.3) & 19 & (0.6) & 8 & (6.0) & 17 & (0.8) & 16 & (1.0) \\ Palestine & 8 & (1.1) & 19 & (0.6) & 12 & (4.8) & 16 & (1.0) & 14 & (1.1) \\ Chile & 6 & (0.8) & 31 & (0.2) & 8 & (6.0) & 19 & (0.7) & 23 & (0.6) \\ Hungary & 6 & (0.8) & 13 & (1.0) & 37 & (0.0) & 17 & (0.8) & 18 & (0.8) \\ Saudi Arabia & 6 & (0.8) & 16 & (0.8) & 22 & (1.2) & 19 & (0.7) & 18 & (0.8) \\ \hline \end{tabular}  
* 1 TP: total publications; SPR: single country publication rank; CPR: international collaboration publication rank; FPR: first author publication rank; RPR: corresponding author publication rank; (%): percentage contribution to the total.  
\end{table} 
Table 2: The top 20 most productive countries.
# Analysing Land Cover Change in the Valencian Community through Landsat Imagery: From 1984 to 2022
## 2 Materials and Methods
### Algorithm
#### 2.3.2 Classification and Regression Trees  
To facilitate a comparison between algorithms and subsequently determine the most efficient one, land cover was also computed using the Classification and Regression Trees (CART) algorithm developed by [PERSON] [48].  
The CART algorithm adopts a conventional classification approach, which remains prominent despite the development of various classification algorithms [49]. This methodology addresses a range of performance, precision, and operational issues encountered by  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Satellite** & **Year** & **Images** & **Built-Up Area** & **Water Bodies** & **Dense Vegetation** & **Sparse Vegetation** & **Other** \\ \hline
**Landsat 5** & 1984 & 35 & 239 & 121 & 983 & 1023 & 59 \\  & 1985 & 38 & 126 & 60 & 614 & 535 & 38 \\  & 1990 & 60 & 214 & 37 & 750 & 490 & 43 \\  & 1995 & 48 & 273 & 74 & 1063 & 1051 & 110 \\  & 2000 & 42 & 247 & 31 & 1052 & 723 & 32 \\  & 2005 & 45 & 212 & 34 & 760 & 754 & 42 \\  & 2010 & 45 & 270 & 86 & 1137 & 862 & 37 \\
**Landsat 8** & 2015 & 58 & 321 & 71 & 1196 & 850 & 24 \\  & 2020 & 57 & 440 & 77 & 1013 & 641 & 65 \\
**Landsat 9** & 2022 & 57 & 395 & 50 & 1345 & 930 & 34 \\  & 2023 & 28 & 236 & 44 & 761 & 497 & 45 \\ \hline \end{tabular}
\end{table}
Table 1: Summary of the total training points used to classify each year, employing both Random Forest and Classification and Regression Trees algorithms. The data points are categorised by land cover classes, and details regarding the satellite used, along with the total number of images for each year, are specified.  
many decision tree methods [50], including challenges like determining the appropriate tree size and handling missing values. Employing a strictly binary subdivision, CART maximises the homogeneity of subsets until the node achieves the maximum possible homogeneity. When no further split enhances homogeneity, the process stops, and the node becomes terminal. The prediction is made based on these terminal nodes, determining the class [48].  
The algorithm was applied using the same procedure and training points as the RF algorithm (Table 1) to ensure comparability between the classifiers. Another GEE function, named smileCart and part of the same Classifier package, was utilised for this purpose.
# Study of Gravelly Soil Core Material Using a Large-Scale Triaxial Wetting Test
## 3 Results
### Deformation Characteristics of the Specim  
Determining the direction of the wetting strain increase is one of the core requirements of establishing the wetting calculation model of the gravelly soil core material. Assuming that no elastic deformation occurs during the wetting process, all strain is assumed to be plastic. Figure 4 shows the relationship between the volumetric strain, \(\varepsilon_{v}\) and the axial strain, \(\varepsilon_{1}\), in the dry-state loading stage and wetting state under different confining pressures and stress levels. The direction of the wetting strain increase refers to the increase relationship between the wetting volumetric strain and the wetting axial strain; thus, it can be directly determined using the experimental data obtained from the wetting test. In Figure 4, arrow a represents the direction of the dry-state loading strain increase; arrow c represents the direction of the wetting deformation increase.  
Figure 4: Characteristics of wetting deformation: (**a**) \(\sigma_{3}=400\) kPa; (**b**) \(\sigma_{3}=800\) kPa; (**c**) \(\sigma_{3}=1200\) kPa; (**d**) \(\sigma_{3}=2000\) kPa.  
It is generally believed that the direction of the wetting strain increase remains unchanged throughout the wetting process [13; 20], but the experimental results show the converse. According to Figure 4, the direction of the wetting deformation increase exhibits different behaviors under different stress levels. At low stress levels, compared with direction arrow a, the direction of the strain increase changes significantly when wetting begins. This suggests that the direction features of the wetting strain appear to differ from those displayed during dry-state loading. At high stress levels, the initial wetting strain increase direction is essentially consistent with that of the dry-state loading strain under the same conditions, and the strain increase direction significantly changes at a later stage of wetting deformation. [PERSON] et al. compared rheological and wetting features and suggested that the characteristics in the later stage of wetting at high stress levels are similar to those displayed by the rheological behavior [22].  
Figures 5 and 6 illustrate the relationship between the volumetric strain and shear strain during the dry-state loading stage and in the wetting state under two typical confining pressures and three different stress levels. According to Figures 5 and 6, the direction of the wetting plastic flow is typically linear at low stress levels, but, at high stress levels, in the early and late stages of plastic flow, this may occur in
## 5 Interpretation and Discussion
### Source Area (Provenance)  
Using major oxides as variables, [PERSON] [30] established major element discriminant functions to differentiate four major provenance fields, namely mafic, intermediate, felsic and quartzose recycled. Likewise, the binary plots of TiO\({}_{2}\) vs Zr, and La/Sr vs Th/Co have been successfully used to infer provenance of clastic sedimentary rocks [5; 6; 7; 14; 31]. The bivariate plot of discriminant 1 against discriminant 2 on the background diagram of [30] shows that the samples are of quartzose sedimentary provenance (Figure 12). This deduction is in agreement with a probable deposition in the realm of a passive margin (as highlighted in the previous section), with a significant influence of the sedimentary processes (transport from source areas far away from the sedimentary basins) over the mineralogical and geochemical features observed in these rocks, resulting in mature sedimentary rocks with an enrichment of the quartzose fraction. The binary diagrams of the TiO\({}_{2}\) versus Zr (Figure 13) and La/Sr against Th/Co (Figure 14) show that the studied rocks are from silicic or felsic igneous rocks. The XRF result also shows the enrichment in Sr and Ba and depletion of transitional elements like Cr, Co, Ni and V, suggesting the trivial or minor influence of mafic provenance as indicated by [32]. The high ratio of Ba to Co (Ba/Co) (Supplementary data;Supplementary Materials Data; Table S2) perhaps point to the fact that the sediments were derived from weathered felsic-granitic sources [33]. In general, the findings of this study agree with the work of [10; 16; 19] in that the Madzaringwe Formation is of quartzose sedimentary provenance derived from felsic igneous rocks.  
Figure 12: Major element Discriminant Function diagram for sedimentary provenance (shale, and coal samples (Background field after [30]). The discriminant functions are: Discriminant Function 1 = (\(-\)1.773 TiO\({}_{2}\)) + (0.607 Al\({}_{2}\)O\({}_{3}\)) + (0.760 Fe\({}_{2}\)O\({}_{3}\)) + (\(-\)1.500 MgO) + (0.616 CaO) + (0.509 Na\({}_{2}\)O) + (\(-\)1.224 K\({}_{2}\)O) +(\(-\)9.090); Discriminant Function 2 = (0.445 TiO\({}_{2}\)) + (0.070 Al\({}_{2}\)O\({}_{3}\)) + (\(-\)0.250 Fe\({}_{2}\)O\({}_{3}\)) + (\(-\)1.142 MgO) + (0.438 CaO) + (1.475 Na\({}_{2}\)O) + (\(-\)1.426 K\({}_{2}\)O) + (6.861).  
Figure 14: Binary plot of La/Sr versus Th/Co for the studied samples showing provenance (Background field after [28]).  
Figure 13: Binary plot of TiO\({}_{2}\) against Zr for the studied samples showing provenance (Background after [34]).