esa-sceva/satcom-chunk-collection huggingface dataset:
# Analysis and Evaluation of Performance Gains and Tradeoffs for Massive MIMO Systems
## 3 Massive MIMO Performance Gains
### Spatial Multiplexing Gain
#### 3.3.1 Multiplexing Gain under Perfect CSI  
With perfect CSI, there is no need to pilot sequences received from users to make a channel estimation because the base station (transceiver) knows the propagation channel matrix \(G\) of massive MIMO system, and the precoding matrix is built on propagation channel matrix \(G\). Users will receive the desirable data transmission from their BS without interfering with other users from other cells. It is assumed that the system is behaving as a single cell.  
Considering the expression (31) for receiving data at downlink phase, and with perfect CSI, the precoding matrix is \(O_{j}=G^{*}\) under MRT precoding method [3], and using the key concept for massive MIMO system on orthogonality when the number of antennas grows to infinity and using expressions (19) and (20), then  
\[Q_{\ell}=M\sqrt{p_{d\ell}}D_{\ell\ell}s_{\ell}+M\sum\limits_{j=1}^{L}\sqrt{p_{dj }}D_{j\ell}s_{j}+n_{d\ell}, \tag{42}\]  
with perfect CSI, the base station knows the propagation channel matrix, so it is assumed that the system behaves as a single cell. There is no interference between cells and the received signal vector for \(k\)th user is expressed as expression (31). The signal to noise ratio SNR for \(k\)th user in \(\ell\)th cell can be obtained as follows:  
\[SNR_{k\ell}=\frac{Mp_{d\ell k}\beta_{k\ell}^{2}}{\sigma^{2}}, \tag{43}\]  
where \(\sigma^{2}\) is the noise variance for the uncorrelated received noise. Then, the achievable rate for \(k\)th user in \(\ell\)th cell and achievable sum rate is given as  
\[R_{\ell k}=\log_{2}(1+SNR_{k\ell})\] \[R_{\ell}=\sum\limits_{k=1}^{K}R_{\ell k} \tag{44}\]  
Multiplexing gain under perfect CSI is defined as the deviation of the achievable sum rate as a function of transmitting power [33],  
\[G_{MUX}^{perf,CSI}=\frac{dR_{\ell}}{d\log_{2}p_{d}}=\frac{d}{d\log_{2}p_{d}} \sum\limits_{k=1}^{K}\log_{2}\left(1+\frac{Mp_{d\ell k}\beta_{k\ell}^{2}}{ \sigma^{2}}\right), \tag{45}\]  
\[G_{MUX}^{perf,CSI}=\sum\limits_{k=1}^{K}\frac{M\beta_{k\ell}^{2}}{\sigma^{2} +Mp_{d\ell k}\beta_{k\ell}^{2}}, \tag{46}\]  
with massive MIMO system, the number of base station antennas increases with unlimited number, then the above expression becomes  
\[G_{MUX}^{perf,CSI}=\sum\limits_{k=1}^{K}\frac{\beta_{k\ell}^{2}}{p_{d\ell k} \beta_{k\ell}^{2}}=\sum\limits_{k=1}^{K}\frac{1}{p_{d\ell k}}=tr(p_{d\ell})^ {-1}. \tag{47}\]
# The Response of NDVI to Climate Change in the Lowest and Hottest Basin in China
## 5 Conclusions  
This study systematically analyzed the spatiotemporal changes of NDVI in the lowest altitude Turpan-Hami Basin in China from 2001 to 2020 and its response to climate change (temperature, precipitation, and PET), addressing the research gap in vegetation dynamics and driving mechanisms in lowest altitude and highest temperature arid regions of China. It revealed the composite response mechanism of vegetation dynamics to climate and human intervention, providing a scientific basis for ecological restoration and water resource management in arid areas. The specific conclusions are as follows:  
1. NDVI in the Turpan-Hami Basin exhibited a significant upward trend from 2001 to 2020, indicating gradual improvements in vegetation coverage and growth conditions. The most substantial increases occurred in winter, while the highest values were observed in summer. Spatially, high-value areas were concentrated in oases and mountainous forest and grassland zones, whereas low-value areas predominated in desert Gobi regions. Notably, 34.2% of the region experienced significant vegetation improvement, yet some areas (particularly the western and central regions) showed marked degradation.
2. Overall, no significant correlation was found between temperature and NDVI, and precipitation exhibited limited influence, with only localized positive responses. In contrast, PET demonstrated a significant positive correlation with NDVI across 46.8% of the study area, challenging the traditional paradigm that evapotranspiration represents water stress.
3. Human activities, such as irrigation and shelterbelt projects, have significantly driven the restoration of oasis vegetation. However, excessive reliance on groundwater may lead to unsustainable water resource consumption, highlighting the need for careful management.  
Conceptualization, C.L. and Y.Y.; data curation, L.S., J.H., H.Z., Y.L., Z.G., L.Z. and I.M.; formal analysis, C.L.; methodology, C.L., Y.Y. and Y.L.; software, L.S. and J.H.; supervision, Y.Y. and R.Y.; validation, C.L., Y.L. and M.W.; visualization, C.L., H.Z., Z.G. and L.Z.; writing--original draft, C.L.; writing--review and editing, C.L. and Y.Y. All authors have read and agreed to the published version of the manuscript.  
This research has been funded by the National Key Research and Development Program of China (2023 YFR085603) and the Third Xinjiang Comprehensive Scientific Research Project on Comprehensive Evaluation and Sustainable Utilization of Land Resources in the Turpan-Hami Basin (2022 kjkk1102).  
**Institutional Review Board Statement**: Not applicable.  
**Informed Consent Statement**: Not applicable.  
**Data Availability Statement**: The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.  
**Conflicts of Interest**: The authors declare no conflicts of interest.
## 2 Methodologies
### Mathematical Model of Real-Time Single-/Dual-Frequency PPP
#### 2.4.1 Dual-Frequency PPP  
The dual-frequency ionosphere-free combination pseudo-range and carrier-phase are used to form the observations of dual-frequency PPP [31],  
\[P_{IF}=\frac{f_{i}^{2}}{f_{i}^{2}-f_{j}^{2}}P_{i}-\frac{f_{j}^{2}}{f_{i}^{2}- f_{j}^{2}}P_{j}=\rho_{r}^{s}+c(t_{r}-t^{s})+T_{r}^{s}+\varepsilon_{P,IF} \tag{12}\]  
\[L_{IF}=\frac{f_{i}^{2}}{f_{i}^{2}-f_{j}^{2}}L_{i}-\frac{f_{j}^{2}}{f_{i}^{2}- f_{j}^{2}}L_{j}=\rho_{r}^{s}+c(t_{r}-t^{s})-\lambda_{IF}N_{IF}+T_{r}^{s}+ \varepsilon_{P,IF} \tag{13}\]  
where \(f_{i}\) is the frequency number; the other symbols have the same means as above.  
In addition, if the observed frequencies in Equations (12) and (13) are different from that of precise real-time products, a DCB correction should be applied [32]. In this study, both B1I+B3I and B1I+B2B IF combinations are employed for static and kinematic PPP solutions, and the following equations should be employed,  
\[\left\{\begin{aligned} & t_{B1I,B3I}^{s}=t^{s}-\frac{f_{B1I}^{s}}{f_{B1I }^{s}-f_{B3I}^{s}}b_{B1I}^{s}\\ & t_{B1I,B2b}^{s}=t^{s}-(\frac{f_{B1I}^{s}}{f_{B1I}^{s}-f_{B2b}^{ s}}b_{B1I}^{s}-\frac{f_{B2b}^{s}}{f_{B1I}^{s}-f_{B2b}^{s}}b_{B2b}^{s})\end{aligned}\right. \tag{14}\]  
where \(t_{B1I,B3I}^{s}\) and \(t_{B1I,B2b}^{s}\) represent satellite precise clocks using the B1I+B3I and B1I+B2b IF combinations; \(f_{B1I}\), \(f_{B2b}\) and \(f_{B3I}\) represent the frequencies corresponding to the B1I, B2b, and B3I observations, respectively.  
In this case, the corresponding parameters that should be estimated are position vector, receiver clock offset, residual of troposphere delay, and IF ambiguity, which can be written as,  
\[x=\begin{bmatrix}\delta x_{r}&\delta y_{r}&\delta z_{r}&c\cdot\delta t_{r}&d_{wet}&N_{IF}\end{bmatrix}^{T} \tag{15}\]  
where \(\delta x_{r}\), \(\delta y_{r}\) and \(\delta z_{r}\) indicate the corrected value of the receiver coordinates in three directions; \(\delta t_{r}\) and \(d_{wet}\) indicate the receiver clock offset and the zenith wet tropospheric delay; \(N_{IF}\) denotes the IF ambiguity vector.
## 2 Literature Review
(2018) analyzed the traffic flow data upstream of the work area based on linear regression and logistic regression and confirmed that the merging position of drivers conforms to a normal distribution. The lane change probability is affected by the merging gap of the target lane and the speed of the leader and follower cars in the target lane. [PERSON] et al. [10] developed a road scenario with a working area based on a virtual driving environment and set up six road scenarios based on the position of control signs and traffic volume level. Based on the experimental data in the above scenarios, a parametric survival model is established, which can reasonably explain the influence of various factors on the decision of lane-changing in the working area. The effect of traffic sign location, driver gender, and traffic status on decision distance and lane-changing distance were analyzed. This study also established a model framework to better describe the process of vehicle lane changing in the working area. While previous studies have provided valuable insights into the factors influencing lane-changing behavior in work zones, many of them primarily focus on vehicle-level factors such as speed and gap size, with limited attention paid to the characteristics of the work zone itself, including traffic flow patterns and lane configurations. This oversight can lead to an incomplete understanding of the merging behavior, as it does not fully account for the dynamic interaction between the merging vehicle and the surrounding traffic environment in different work zone layouts. Notably, [PERSON] et al. [11] studied the speed characteristics of vehicles in three- and four-lane work zones but focused mainly on predicting speed based on the distance from the construction site. Their study, however, lacked a detailed investigation of how different work zone layouts and traffic states affect the merging process, particularly in scenarios with complex interactions between heavy and light vehicles. Moreover, existing studies that examine work zone merging behavior do not provide robust and diverse datasets that can capture the variability across different work zone types and traffic conditions. The lack of a reliable and comprehensive dataset focusing specifically on diverse work zone environments has limited the ability to generalize findings and develop effective traffic management solutions. This study fills these gaps by introducing a high-resolution vehicle trajectory dataset collected via UAV technology and conducting a more detailed and comprehensive analysis of both vehicle-level and location-level factors.
## 3 APD Output Models
### Webb and Gaussian-Approximated APD Output Model  
To balance computational efficiency with model fidelity in APD characterization, Webb model [33] provides an optimal framework for approximating the stochastic response of APD output. Given the mean received photons \(\bar{n}\), the conditional PDF of electron multiplication \(f_{W}(m|\bar{n})\) approximated by the Webb distribution is  
\[f_{W}(m|\bar{n})=\frac{\left(1+(m-G\bar{n})\Big{/}c_{f}\bar{n}\right)^{2/3}}{ \sqrt{2\pi\bar{n}G^{2}F_{a}}}\exp\left(-\frac{(m-G\bar{n})^{2}}{2\bar{n}G^{2}F _{a}\Big{(}1+(m-G\bar{n})\Big{/}c_{f}\bar{n}\Big{)}}\right), \tag{20}\]  
where \(F_{a}\) is the APD noise factor, and \(c_{F}=\frac{GF_{a}}{F_{a}-1}\). Through statistical convolution of the Webb-distributed photon response (20) with Gaussian noise component (18), the composite APD output model preserving avalanche multiplication characteristics is formulated as  
\[p_{w}(i)=\sum_{m=0}^{\infty}\frac{\left(1+(m-G\bar{n})\Big{/}c_{f}\bar{n} \right)^{2/3}}{2\pi\sigma_{m}\sqrt{\bar{n}G^{2}F_{a}}}\exp\left(-\frac{(m-G \bar{n})^{2}}{2\bar{n}G^{2}F_{a}\Big{(}1+\frac{m-G\bar{n}}{c_{f}\bar{n}}\Big{)} }-\frac{(i-\mu_{m})^{2}}{2\sigma_{m}^{2}}\right). \tag{21}\]  
To further simplify the Webb modeled APD output, Gaussian approximation is strategically implemented. That is, the conditional PDF of electron multiplication \(f_{W}(m|\bar{n})\) under mean photon flux \(\bar{n}\) transitions to Gaussian statistics. Hence, (20) is rewritten as  
\[f_{G}(m|\bar{n})=\frac{1}{\sqrt{2\pi}\sigma_{sh}^{2}}\exp\left(-\frac{(m-\mu_ {sh})^{2}}{2\sigma_{sh}^{2}}\right), \tag{22}\]  
where \(\sigma_{sh}^{2}=2G^{2}q_{e}^{2}F_{a}\bar{n}B_{e}T_{s}\) and \(\mu_{sh}=Gq_{e}\bar{n}\) are the variance and the mean of this Gaussian distribution, respectively. Incorporating APD noise characteristics, the APD output approximated by Gaussian model is \[p_{g}(i)=\frac{1}{\sqrt{2\pi}\sigma_{g}^{2}}\exp\left(-\frac{\left(i-\mu_{g}\right) ^{2}}{2\sigma_{g}^{2}}\right), \tag{23}\]  
where \(\mu_{g}=\mu_{sh}+\mu_{m}\) and \(\sigma_{g}^{2}=\sigma_{sh}^{2}+\sigma_{m}^{2}\).  
The Webb model [33] establishes a rigorous framework for APD avalanche gain dynamics through the statistical convolution of photon absorption statistics and nonlinear multiplication processes. This approach effectively captures multiplicative shot noise mechanisms (i.e., avalanche fluctuations) that dominate in gain-saturated operational regimes, as quantified in Section 5. In contrast, the Gaussian approximation model employs an additive Gaussian noise assumption to simplify APD output analysis, sacrificing fidelity in modeling nonlinear gain dynamics. While this abstraction disregards the inherent nonlinear gain dynamics captured by the Webb model, it offers significant computational advantages for noise-limited scenarios. Specifically, under high background radiation conditions as discussed in Section 5, where system performance becomes dominated by external noise sources rather than intrinsic APD gain characteristics, the Gaussian model achieves acceptable accuracy.
# Parameters Sensitivity Analysis of Position-Based Impedance Control for Bionic Legged Robots' [PERSON]
## 4 Methods of Sensitivity Analysis
### Deduction of First-Order Matrix Sensitivity Analysis Theory  
Combined with the position-based impedance control method, the equation of the HDU system can be expressed as follows:  
\[\mathbf{g}(\mathbf{x},\mathbf{u},\mathbf{\alpha},t)=0 \tag{11}\]  
where \(\mathbf{x}\) is m\(-\)dimensional state vector, \(\mathbf{u}\) is r\(-\)dimensional vector unrelated to \(\mathbf{\alpha}\), \(\mathbf{\alpha}\) is p\(-\)dimensional vector, and \(t\) is time.  
The  
In Equation (17), supposing:  
\[\mathbf{S}_{u}=\mathbf{g}_{x}{}^{-1}\cdot\mathbf{g}_{u} \tag{17}\]  
where \(\mathbf{S}_{u}\) is \(m\times r\) order matrix, and the \(n\)-th line indicates the relation among the \(n\)-th state variable \(x_{n}\).  
In Equation (17), supposing:  
\[\mathbf{S}_{\alpha}=\mathbf{g}_{x}{}^{-1}\cdot\mathbf{g}_{\alpha} \tag{18}\]  
where, \(\mathbf{S}_{\alpha}\) is the \(m\times p\) order matrix, the \(n\)-th line indicates the relation among the \(n\)-th state variable and \(p\) parameter vectors. Bring Equations (17) and (18) into Equation (16), then:  
\[\Delta\mathbf{x}=-\mathbf{S}_{u}\cdot\Delta\mathbf{u}-\mathbf{S}_{\alpha} \cdot\Delta\boldsymbol{\alpha} \tag{19}\]  
Equation (19) is an approximate expression of \(\Delta\mathbf{x}\) resulted from the change of parameter vector \(\Delta\boldsymbol{\alpha}\) and input vector \(\Delta\mathbf{u}\), in which \(\mathbf{S}_{\alpha}\) indicates an \(m\times p\) order parameter sensitivity matrix of parameter vector \(\alpha\) with time-varying factors. \(\mathbf{S}_{u}\) indicates an \(m\times r\) order input sensitivity matrix of input vector \(u\) with time-varying factors.  
When taking no account of the variation of input vector, Equation (19) can be simplified as follows:  
\[\Delta\mathbf{x}=-\mathbf{S}_{\alpha}\cdot\Delta\boldsymbol{\alpha} \tag{20}\]  
The output equation of the system can be expressed as follows:  
\[\Delta\mathbf{Y}=\mathbf{C}\cdot\Delta\mathbf{x}+\mathbf{D}=-\mathbf{C}\cdot \mathbf{S}_{\alpha}\cdot\Delta\boldsymbol{\alpha}+\mathbf{D} \tag{21}\]  
where \(\mathbf{C}\) and \(\mathbf{D}\) are matrices of output equation factors. The change of output variable \(\Delta\mathbf{Y}\) resulting from the parameter variation can be reached after solving parameter sensitivity matrix \(\mathbf{S}_{\alpha}\).
###### Abstract  
Human mesenchymal stem cells can differentiate into various cell types and are useful for applications in regenerative medicine. Previous studies indicated that dental pulp exfoliated from deciduous teeth is a valuable alternative for dental tissue engineering because it contains stem cells with a relatively high proliferation rate. For clinical application, it is necessary to rapidly obtain a sufficient number of cells in vitro and maintain their undifferentiated state; however, the abundance of stem cells in the dental pulp tissue is limited. Non-thermal atmospheric pressure plasma (NTAPP) has been applied in regenerative medicine because it activates cell proliferation. Here, we examined the effects of NTAPP to activate the proliferation of human deciduous dental pulp fibroblast-like cells (hDDPFs) in vitro. Compared with untreated cells, NTAPP increased cell proliferation by 1.3-fold, significantly upregulated well-known pluripotent genes for stemness (e.g., _Oct4_, _Sox2_, and _Nanog_), and activated the expression of stem cell-specific surface markers (e.g., CD105). Overall, NTAPP activated the proliferation of various mesodermal-derived human adult stem cells while maintaining their pluripotency and stemness. In conclusion, NTAPP is a potential tool to expand the population of various adult stem cells in vitro for medical applications.  
non-thermal atmospheric pressure plasma (NTAPP); human deciduous dental pulp fibroblast-like cells; regenerative medicine +
Footnote †: journal:  
Various stimuli, such as drugs and incubation under hypoxia, have been used to activate pulp undifferentiation potential [12]; however, their use is currently limited because of safety and cost issues. Therefore, a safer and simpler alternative method is needed.  
Recently, \"plasma medicine\", which involves the application of non-thermal atmospheric pressure plasma (NTAPP) for medical treatment, is a novel tool being applied in regenerative medicine. Plasma medicine aims at irradiating inorganic materials for surface modification or sterilization, whereas NTAPP combines irradiation at low temperatures and under atmospheric pressure, allowing the direct treatment of biological tissues for wound healing [13], selective apoptosis of cancer cells [14], and proliferation of pluripotent stem cells [15]. In the field of medical science, NTAPP has been studied worldwide for clinical applications. Although the information on the effects of direct plasma irradiation on the dental pulp and periapical soft tissues is limited, NTAPP is a simple, safe, and inexpensive tool that could be used in clinical dentistry.  
In this study, we aimed to evaluate the effectiveness of NTAPP in activating the proliferation of undifferentiated human deciduous dental pulp fibroblast-like cells (hDDPFs). To this end, we examined the rate of cell multiplication in vitro, the expression of genes related to cell proliferation, and changes in mesenchymal stem cell (MSC) markers.
## 2 Materials and Methods
### Perfusion Culture Setup for 3-D Scaffold  
Human hepatoma HepG2 (Japanese cancer research bank, JCRB) cells were maintained in low-glucose Dulbecco's modified minimum essential medium (DMEM) supplemented with 10% fetal bovine serum (FBS), 1% non-essential amino acids (NEAA), 4 mM hydroxyethyl piperazine-N' -2-ethanesulfonic acid (HEPES), and 1% antibiotic-antimycotic. Confluent cells were washed with PBS and retrieved using Trypin/EDTA. The cells were resuspended in DMEM culture medium for subsequent use in the experiment.  
Human umbilical vein endothelial cell HUVEC (Catalog #: C2517A, Lonza) cells were maintained in Endothelial cell basal medium supplemented with endothelial growth factors (EBMTM-2 Basal medium and EGMTM-2 SingleQuotesTM supplements, Lonza, Switzerland) and 1% antibiotic-antimycotic. Prior to seeding the cells into the scaffold, confluent cells were washed with PBS, followed by Trypin/EDTA treatment, and the retrieved cells were resuspended in EBM-2 medium.  
The scaffolds were rinsed carefully to remove remnants of NaOH and PGA particles, followed by collagen surface treatment on PCL. Collagen (0.01% collagen type I, Nitta Gelatin, Japan) was adsorbed onto the surface overnight at 4 \({}^{\circ}\)C. After collagen treatment, the scaffold was rinsed thoroughly with 1X PBS and allowed to soak in culture medium for 2 h prior to cell seeding.  
Hep G2 cell suspension of 1 \(\times\) 10\({}^{7}\) in 10 mL culture medium was injected into the scaffold by two 10 mL syringes inserted in the inlet and outlet, which were depressed and released at a slow speed within 3 min. To ensure the homogeneous distribution of cells inside the scaffold, the scaffold was kept in 3 different directions (0\({}^{\circ}\), 180\({}^{\circ}\), and 240\({}^{\circ}\)) and held each time for 5 min. The perfusion was gently started at 1 mL/min. After 2 h, the flow rate of the culture medium was gradually increased to 5 mL/min. The culture medium was replaced on day 1, and thereafter, every 2 days until day 10. The total volume of the culture medium was kept constant to 100 mL in the medium reservoir. The configuration of perfusion culture system is illustrated in Figure 1b. The perfusion culture system comprised of a peristaltic pump, bubble trap, PCL-based scaffold, and medium reservoir.  
For the co-culture system, the human umbilical endothelial cells (HUVECs) were introduced into the scaffold in a similar manner as mentioned above, with a cell suspension of 0.5 \(\times\) 10\({}^{7}\) in a 10 mL culture medium after Hep G2 were grown at day 2 in the scaffold to allow the coverage of endothelial cell layer growing on the grown Hep G2 on the scaffold. The co-culture medium consisted of DMEM and EBM-2 and was supplemented with EGM-2 mixture (1 DMEM: 1 EBM-2+EGM-2), 10% fetal bovine serum (FBS), 1% non-essential amino acids (NEAA), 4 mM hydroxyethyl piperazine-N' -2-ethanesulfonic acid (HEPES), and 1% antibiotic-antimycotic. Scaffold without cells were considered as a control group. All the cultures were performed at 37 \({}^{\circ}\)C in a CO\({}_{2}\) incubator.
## 3 Data and Methods
### Estimation of the SUHI
This fitting technique works well for urban areas with regular shapes. The method is suitable for large-area analysis by satellite data of spatial resolution like MODIS. Since the fitting provides a smoothed surface, the greater variability of higher spatial resolution images (e.g., Landsat maps) reduces the correlation coefficient and the representativeness of the Gaussian footprints [35].
## 3 Artificial Intelligence Prediction
### Algorithm Results and Discussion
#### 3.3.1 Normalized Ultimate Load Prediction
Figure 28a reveals the train and test phase of the model with a single input for which the performance parameters are shown in Table 11 (R2 test = 0.8848, R2 train = 0.9914). Figure 28b shows the testing and training phase of the model with two inputs (R2 test = 0.9707, R2 train = 0.997). According to this procedure, it is obvious that the MLP-PSO-FS model shows acceptable performance where the number of inputs is increased to five inputs. Nevertheless, the MLP-PSO-FS model with six inputs does not perform well enough in comparison with other models. Figure 28d,e represents the best-achieved predictions amongst other models, although there is a little difference between these two models in the prediction capability which is shown in Table 11. As can be seen, some improvements in the performance of the MLP is captured by utilizing the PSO algorithm in such a way that the r and R2 values are increased and the RMSE value is decreased. The testing phase is also improved with respect to the MLP-PSO-FS model. Figure 29 indicates the capability of the models in the testing phase to predict each of the measured values of the test samples. As can be observed, both of the MLP-PSO-FS with four input models are capable of predicting most of the test samples closely. As shown in Table 9 and Figure 30, the best performance parameters for the PSO-FS neural network are RMSE = 0.001, r = 1.000, R2 = 1.000, NSE = 1.000, MAE = 0, and WI = 1.000. Considering that the best result for RMSE is the lowest result and for r, the best positive correlation coefficient is 1, then numbers closer to 1 are considered better results. Additionally, for NSE and MAE, smaller results and for WI, larger results, indicate better performance.