esa-sceva/satcom-chunk-collection huggingface dataset:
# An Improved NSGA-II Algorithm Based on Adaptive Weighting and Searching Strategy
## 4 Case Studies
### DTIZ Test Functions  
In order to verify the feasibility of the algorithm proposed in this chapter in the high-dimensional multi-objective problem, the DTLZ standard test set function is selected for simulation experiments. The simulation results are shown in Figure 3 and the specific expressions are shown in Table 4. \begin{table}
\begin{tabular}{l l} \hline \hline
**Function Name** & **Mathematical Formula** \\ \hline \(\min f_{1}(x)=\dfrac{1}{2}x_{1}x_{2}\cdots x_{M-1}(1+g(x_{M}))\) \\ \(\min f_{2}(x)=\dfrac{1}{2}x_{1}x_{2}\cdots(1-x_{M-1})(1+g(x_{M}))\) \\ \(\vdots\) \\ DTLZ1 & \(\min f_{M-1}(x)=\dfrac{1}{2}x_{1}(1-x_{2})(1+g(x_{M}))\) \\ \(\min f_{M}(x)=\dfrac{1}{2}(1-x_{1})(1+g(x_{M}))\) \\ \(g(x_{M})=100\bigg{(}|x_{M}|+\sum\limits_{x_{M}}(x_{i}-0.5)^{2}-\cos(20\pi(x_{ i}-0.5))\bigg{)}\) \\ \(\min f_{1}(x)=(1+g(x_{M}))\cos(x_{1}\pi/2)\cdots\cos(x_{M-2}\pi/2)\cos(x_{M-1} \pi/2)\) \\ \(\min f_{2}(x)=(1+g(x_{M}))\cos(x_{1}\pi/2)\cdots\cos(x_{M-2}\pi/2)\sin(x_{M-1} \pi/2)\) \\ \(\vdots\) \\ DTLZ2 & \(\min f_{M-1}(x)=(1+g(x_{M}))\cos(x_{1}\pi/2)\sin(x_{2}\pi/2)\) \\ \(\min f_{M}(x)=(1+g(x_{M}))\sin(x_{1}\pi/2)\) \\ \(g(x_{M})=\sum\limits_{x_{1}\in x_{M}}(x_{i}-0.5)^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: DTLZ Test functions and characteristics. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test Function** & \multicolumn{3}{c}{**Comparison**} & **Algorithm** \\ \hline  & **NSGA-II** & **MOEA/D** & **IBEA** & **SPEA2** & **INSGA-II** \\ \hline ZDT1 & 0.0052 & 0.0271 & 0.0041 & 0.0042 & 0.0015 \\ ZDT2 & 0.0027 & 0.0132 & 0.0025 & 0.0032 & 0.0016 \\ ZDT3 & 0.0143 & 0.0471 & 0.0083 & 0.0091 & 0.0032 \\ ZDT4 & 0.0072 & 0.0147 & 0.0065 & 0.0062 & 0.0023 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: IGD metric results for ZDT function. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test Function** & \multicolumn{3}{c}{**Comparison**} & **Algorithm** \\ \hline  & **NSGA-II** & **MOEA/D** & **IBEA** & **SPEA2** & **INSGA-II** \\ \hline ZDT1 & 0.7124 & 0.6951 & 0.7199 & 0.7191 & 0.9115 \\ ZDT2 & 0.6074 & 0.5865 & 0.6175 & 0.6327 & 0.8592 \\ ZDT3 & 0.7331 & 0.5753 & 0.7486 & 0.7362 & 0.9269 \\ ZDT4 & 0.7083 & 0.6608 & 0.7168 & 0.7240 & 0.8866 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: HV metric results for DTLZ function. To prove the capability of the improved NSGA-II, we conduct experiments on the test function with the original NSGA-II and other methods, such as MOEA/D [19], IBEA [20] and SPEA2 [21], as comparison algorithms. The average values of the experimental algorithms for IGD are presented in Table 5, respectively. (Each result is the average of the two metrics calculated for 10 independent runs of the same algorithm over the same problem.)
# Multi-Body Dynamics Modeling and Simulation of Maglev Satellites
## 3 Design of Three Body Multi Closed Loop Control Law
### MM Driving Control Law  
Convert the driving equation of the frame cabin into error form:  
\[\begin{split}\ddot{\theta}_{re}&=-\ddot{\theta}_{rd }-J_{rx}^{-1}\dot{\omega}_{b}^{\mathrm{T}}\mathbf{R}_{r}\mathbf{D}_{r}-J_{rx}^{-1} \omega_{b}^{\mathrm{T}}\dot{\mathbf{R}}_{r}\mathbf{D}_{r}\\ &-J_{rx}^{-1}\mathbf{D}_{r}^{\mathrm{T}}(\tilde{r}_{ru}\tilde{F}_{ur}+ \tilde{r}_{ra}\mathbf{F}_{ar}+\tilde{r}_{rl}\tilde{F}_{tr})+J_{rx}^{-1}\tau_{ra} \end{split} \tag{59}\]  
In the formula, \(\tilde{\mathbf{r}}_{ru}\tilde{F}_{ur}\), \(\tilde{\mathbf{r}}_{ra}\mathbf{F}_{ar}\), and \(\tilde{\mathbf{r}}_{rl}\tilde{F}_{rl}\) are the interference effects of the position follow-up control force of the platform subsystem and the attitude control force of the payload subsystem on the drive control of the MM. Design control torque \(\tau_{ra}\) so that the error states \(\theta_{re}\) and \(\dot{\theta}_{re}\) are zero, that is, states \(\theta_{r}\) and \(\dot{\theta}_{r}\) track the expected states \(\theta_{rd}\) and \(\dot{\theta}_{rd}\). The design control law is as follows:  
\[\begin{split}&\tau_{ra}=J_{rx}\ddot{\theta}_{rd}+\dot{\omega}_{b}^{ \mathrm{T}}\mathbf{R}_{r}\mathbf{D}_{r}+\dot{\omega}_{b}^{\mathrm{T}}\dot{\mathbf{R}}_{r} \mathbf{D}_{r}\\ &+D_{r}^{\mathrm{T}}(\tilde{\mathbf{r}}_{ra}\tilde{F}_{ur}+\tilde{\mathbf{ r}}_{ra}\mathbf{F}_{ar}+\tilde{\mathbf{r}}_{rl}\tilde{F}_{rr})-K_{k}\theta_{re}-D_{k}\dot{ \theta}_{re}\end{split} \tag{60}\]  
where \(K_{k}\) and \(D_{k}\) are the proportional control parameters and differential control parameters for the frame cabin attitude, respectively.
## 2 Data and Methods  
### The SWOT Simulator  
With a view to characterizing the potential of SWOT-derived SSH data, we consider a simulation-based framework using the SWOT Simulator for Ocean Science (version 1). This simulator accounts for both SWOT space-time sampling patterns and noise processes. Using as input the SSH fields from an Oceanic General Circulation Model (OGCM), the SWOT simulator generates SWOT-like outputs along a ground swath and the nadir following the orbit ground tracks [29]. Hereinafter, we refer to these outputs as SSH outputs. Note that these simulated fields correspond to Absolute Dynamic Topography (ADT) values in altimetric terminology.  
A flowchart of the simulator workflow is provided in Figure 1. Two features should be pointed out. Grid files, generated in the first step of the flowchart, account for the planned orbit of the satellite and the specified domain. Instrument noise and geophysical errors are added during the last step of the flowchart, following recent technical characteristics established by the SWOT project team [29]. Instrument noise is composed of Ka-band Radar Interferometer (KaRIN) noise, roll, phase, baseline dilation and timing errors (see [30]). In this version of the simulator, the only geophysical error is associated with the wet troposphere. Therefore, it is important to keep in mind that additional noise patterns, such as sea state bias [29] or the effects of internal waves [2] are not accounted for in the generated pseudo-SWOT data.  
For more details on the instrument noise and geophysical errors added by the SWOT simulator, see Appendix B.
# Low-Resolution Precoding for Multi-Antenna Downlink Channels and OFDM +
### Contributions and Organization  
The contributions of this paper are as follows.  
* The analysis of MAGIQ in the workshop paper [39] is extended to larger systems and more realistic channel conditions;
* Replacing the greedy antenna selection rule of MAGIQ with a fixed (round-robin) schedule is shown to cause negligible rate loss. The new algorithm is named quantized coordinate minimization (QCM);
* The performance of QLP-ZF, SQUID, MSM, MAGIQ, and QCM are compared in terms of complexity (number of multiplications and iterations) and achievable rates;
* We develop an auxiliary channel model to compute achievable rates for pilot-aided and data-aided channel estimation. The models let one compare modulations, precoders, channels, and receivers;
* Simulations with a 5G NR low-density parity-check (LDPC) code [44] show that the computed rate and power gains accurately predict the gains of standard channel codes;
* Simulations with imperfect channel knowledge at the base station show that the achievable rates of SQUID and QCM degrade as gracefully as those of LP-ZF.  
We remark that our focus is on algorithms that approximate ZF based on channel inversion, i.e., there is no attempt to optimize transmit powers across subcarriers. This approach simplifies OFDM channel estimation at the receivers because the precoder makes all subcarriers have approximately the same channel magnitude and phase. For instance, a rapid and accurate channel estimate is obtained for each OFDM symbol by averaging the channel estimates of the subcarriers, see Section 4.1. Of course, it is interesting to develop algorithms for other precoders and for subcarrier power allocation.  
This paper is organized as follows. Section 2 introduces the baseband model and OFDM signaling. Section 3 describes the MAGIQ and QCM precoders. Section 4 develops theory for achievable rates, presents complexity comparisons, and reviews a model for imperfect channel state information (CSI). Section 5 compares achievable rates and BERs with 5G NR LDPC codes. Section 6 concludes the paper.
# Performance Analysis of D2D Communication with Retransmission Mechanism in Cellular Networks
## 4 Queuing Model and Feedback Strategy
### Stochastic Geometry Analysis for Service Probability
\begin{array}{l}\mathcal{L}_{I_{D}}\left(s\right){=}E_{\rho}\Phi_{D,\delta m }\left[\exp\left(-s\sum\limits_{n\in\rho\Phi_{D}\backslash\left\{m\right\}}P_{ D}g_{m,n}d_{m,n}^{-\alpha_{D}}\right)\right]\\ \stackrel{{(*)}}{{=}}E_{\rho}\Phi_{D}\left[\prod\limits_{n\in \rho\Phi_{D}\backslash\left\{m\right\}}E_{\delta m,n}\left[\exp\left(-sP_{D}g _{m,n}d_{m,n}^{-\alpha_{D}}\right)\right]\right]\\ \stackrel{{(**)}}{{=}}\exp\ \left(-2\pi\rho\lambda_{d}\int\limits_{0}^{ \infty}\left(1-E_{S_{m,n}}\left[\frac{1}{1{+}sP_{D}v^{-\alpha_{D}}}\right] \right)vdv\right)\end{array}  \tag{8}\]  
where \(\left(*\right)\) is true based on the i.i.d. distribution of \(g_{m,n}\) and \(\left(**\right)\) is from the probability generating functional (PGFL) of the PPP. By the same way, the derivation of \(\mathcal{L}_{I_{C}}\left(s\right)\):\[ \begin{split}\mathcal{L}_{I_{C}}\left(s\right)=& \mathbb{E}_{\Phi_{C}\subset\mathcal{B}_{l,m}}\left[\exp\left(-s\sum\limits_{l \in\Phi_{C}}P_{CU}\mathcal{B}_{l,m}d_{l,m}^{-\kappa_{C}}\right)\right]\\ =&\exp\left(-2\pi\lambda_{B}\int\limits_{R}^{\infty} \left(1-E_{S_{l,m}}\left[\frac{1}{1+\mathcal{B}_{C}\cup\mathcal{B}_{l,m}d_{l,m }^{-\kappa_{C}}}\right]\right)\,\
u d\
u\right)\end{split} \quad. \tag{9}\]  
By substituting (7)-(9) into (6), the closed-form expression of successful transmission probability is obtained, which shows that establishing a D2D link needs to meet the lower bound of SINR.
## 3 Results and Discussion
### Corrosion Resistance Evaluation
#### 3.2.5 The Equivalent Circuit R(Q(R(Q(RW))))  
The circuit shown in Figure 7 was used to describe the superficial properties of the OPS samples immersed in water from the Black Sea and fire extinguishing solution for one hour (the OPS/RW and OPS/FES systems). As in the case of the circuit described prior, this system consists of a double-layer structure in which the reaction rate is controlled by kinetics and diffusion. The main difference, compared to the previous system, is that the capacity of the surface layer is represented by a non-ideal capacitor emphasized by the constant phase element CPE1. The experimental values obtained for the parameters of this circuit are presented in Table 6.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**System**} & \(\rm R_{s}\), & \(\rm C_{ext}\) & \(\rm R_{ext}\) & & \(\rm CPE\) & & \(\rm R_{ct}\) & \(\rm W\) & \\  & \(\rm\Omega\ cm^{2}\) & \(\rm\mu F/cm^{2}\) & \(\rm\Omega\ cm^{2}\) & \(\rm Q\) & & \(\rm\Omega\ cm^{2}\) & \(\rm\Omega\ cm^{2}\) & \(\rm\bf S\ s^{\frac{1}{2}}/c\) & \(\rm\Omega^{3}\chi^{2}\) & \(\rm\epsilon_{Z}\) \\  & & & & & \(\rm S.s^{9}/cm^{2}\) & & & & \\ \hline C45/FES & 4.64 & 1.71 & 6.42 & \(1.43\times 10^{-3}\) & 0.65 & 1544 & 0.277 & 0.55 & 2.3 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The values of the equivalent circuit elements for C45 immersed for one hour in fire extinguishing solution.  
Figure 6: The equivalent circuit R(C(R(Q(RW)))) for a corrosive alloy under mixed kinetic and diffusion control.  
The polarization resistance value (RP = R\({}_{\text{ext}}\) + R\({}_{\text{ct}}\)) for the OPS/BSW system (8.65 k\(\Omega\) cm\({}^{2}\)) is double than the value for the OPS/fire extinguishing solution system (4.51 k\(\Omega\)\(\cdot\)cm\({}^{2}\)). Also, the effect of the diffusion on the decrease of the corrosion rate favors the OPS/RW system (the diffusion impedance ZW is inversely proportional to W). The sum of these components (kinetic and diffusion) leads to a significant reduction in the corrosion rate, which is incomparably lower than that obtained for the C45 sample and the phosphate samples in the same solutions (2 to 5 times in the case of seawater and 2 to 6 times in the case of the fire extinguishing solution); furthermore, the instantaneous diffusion rate is 114 \(\upmu\)m/year in seawater, while in fire extinguishing solution the rate is of 243 \(\upmu\)m/year.
# An Adaptive Contextual Relation Model for Improving Response Generation
## 4 Dialogue Generation Model
### Bidirectional Relevance Learning  
This component learns the relevance of history-response and response-future through the representations \(H\), \({R_{h}}^{*}\), and \({F_{h}}^{*}\). In order to simulate the strength of different contextual correlations in different relations, we use the annotated \(0/1\) relevance \(w_{hr}\) and \(w_{rf}\) as the gold labels to constrain the model to learn the bidirectional relevance hidden representations \(c_{1}\) and \(c_{2}\) and then obtain the history-response relevance score \(w_{1}\) and response-future relevance score \(w_{2}\) from \(c_{1}\) and \(c_{2}\) through soft learning.  
Forward relevance learning. The quality of \({R_{h}}^{*}\) generated from the gold history is better than \({R_{f}}^{*}\) generated from the simulated future in Section 4.2, so we use \({R_{h}}^{*}\) to represent the response in relevance learning. We first concatenate the history and response as the input of the BART-encoder (Enc in Figure 1) to obtain the hidden representation \(h_{1}\):  
\[h_{1}=Enc([H,{R_{h}}^{*}]) \tag{5}\]  
Then, \(h_{1}\) is fed into multiple MLPs to obtain the 1-dimensional relevance hidden vector \(c_{1}\) of history and response. The specific relevance value \(p_{1}\) is obtained with sigmoid activation:  
\[c_{1}=MLP_{c_{1}}(h_{1}) \tag{6}\]  
\[p_{1}=sigmoid(c_{1}) \tag{7}\]  
We constrain \(p_{1}\) by the Mean Square Error (MSE) loss with the binary \(0/1\) annotated relevance label \(w_{hr}\), where N is the number of training examples:  
\[Loss_{MSE}=\frac{\sum_{1}^{N}(w_{hr}-p_{1})^{2}}{N} \tag{8}\]  
To reduce the impact of noise in the annotation and error in the model learning, instead of using \(p_{1}\) directly, the model learns the history-response relevance \(w_{1}\) from the hidden vector \(c_{1}\) with the soft learning method. We feed \(c_{1}\) into MLPs and sigmoid to learn a soft relevance value \(w_{1}\) of the history and response, then pass it to the next component of the model:  
\[w_{1}=sigmoid(MLP_{w_{1}}(c_{1})) \tag{9}\]  
Note that to guarantee the effect of relevance labels, the hidden vector \(c_{1}\) is only constrained by MSE loss. The NLL loss in Section 4.4 is not back-propagated to \(c_{1}\).  
Backward relevance learning. Similar to the calculation process of \(w_{1}\), we use \([{R_{h}}^{*},{F_{h}}^{*}]\) as input to learn the relevance value \(w_{2}\) of the response and future by the constraint of label \(w_{rf}\).
# Solution of Bin Packing Instances in Falkenauer T Class: Not So Hard
## 3 Algorithm Description
### Local Search Phase  
If the local search mode is used, the solution is usually not complete, but also cannot be naturally continued. The purpose of the local search phase is to improve the current solution by adding and removing triplets.  
This phase corresponds to the local improvements in the rainbow matching problem where a good matching has been already found, and we seek to improve it by removing and adding cells.  
However, to systematically explore all possible options, the representation of possible steps is different here.  
From this point, the A-set and the distinction of a-groups and bc-groups are ignored. Instead, simply item groups are considered, which contain all items of the same weight. This effectively allows the change of the A-set during the search--note that in the illustration, there were no such operations.  
The algorithm is also allowed to over-deplete an item group \(g\) by adding more triplets into the solution than a group \(g\) allows. Such collections can be fixed later by removing other triplets.  
We define a priority between collections as follows.  
* Collections with lower total over-depletion are prioritized. The total over-depletion is defined as follows: \[\left|\sum_{g:L(g)<0}L(g)\right|.\] A solution with zero over-depletion is called feasible.
* If there is tie, collections with more triplets are prioritized.
* If there is still a tie, the larger \(L(g)\) is prioritized, where \(g\) is the largest item group that differs.  
The main, outer loop of the local search consists of replacing a single, feasible collection with a new one with more triplets. At the beginning of the local search phase, this feasible collection is the one returned by the branching phase. This outer loop is repeated until a solution is found.  
Within the outer loop, a set of collections and its subset of visited collections is maintained. At the beginning of the outer loop iteration, the set has a single element, called starting collection, and it is not visited. Then, an inner loop is performed which expands the set of collections as follows.  
* Pick the non-visited collection with the highest priority, and mark it as visited. This will be the current collection, and it is now investigated.
* If the current collection is feasible and has more triplets than the starting collection, the inside loop stops.
* If the current collection is feasible but does not have more triplets than the starting collection, then additional collections are generated by adding any single triplet to the current collection.  
If the current collection is infeasible, then additional collections are generated by removing any single triplet from the current collection, where only triplets using an over-depleted group are considered.  
Note that the set of collections is reset each time the inner loop stops and an improved, feasible collection is found. Theoretically, this local search could explore all collections, so finding a solution is guaranteed if one exists.
## 3 Results  
### Temporal Variation Trends of NDVI  
Figure 2 and Table 2 illustrate the interannual and seasonal variations of NDVI from 2000 to 2018, alongside results from Sen's trend analysis and Mann-Kendall tests. Overall, NDVI exhibited a fluctuating upward trend, with a Sen slope of 0.00179/year, insignificant at \(p<0.05\), ranging between 0.26 and 0.33, peaking in 2018, and bottoming in 2000. Seasonally, spring, summer, and autumn NDVI showed fluctuating increases, with Sen slopes of 0.00998, 0.00420, and 0.00208 per year, respectively, all significant except for winter (Figure 2a-d). Winter NDVI remained stable, with a slope of 0.00022/year. Specific ranges and peak years varied by season, highlighting distinct seasonal vegetation responses.  
Figure 2: Annual and seasonal variations of NDVI values and MK values. Note: (**a**) spring variations of NDVI values; (**a**) spring variations of MK values; (**b**) summer variations of NDVI values; (**b**) summer variations of MK values; (**c**) autumn variations of NDVI values; (**c**) autumn variations of MK values; (**d**) winter variations of NDVI values; (**d**) winter variations of MK values; (**e**) annual variations of NDVI values; (**e**) annual variations of NDVI values; (**e**) annual variations of NDVI values; (**e**) annual variations of MK values.  
Mann-Kendall tests revealed multiple intersection points within confidence intervals, indicating significant trend shifts across seasons and years. Notably, spring NDVI shifted positively in 2004 (Figure 2a'), summer trends showed significant changes around 2005 and 2010 (Figure 2b'), autumn experienced shifts in multiple years (Figure 2c'), and winter transitioned from a declining to an increasing trend post-2009 (Figure 2d'). Annual NDVI trends also demonstrated significant upward shifts in several years (Figure 2e').  
In summary, the West Liao River Basin's NDVI displayed an overall upward trend from 2000 to 2018 with distinct seasonal vegetation dynamics, underscoring the complex interplay between vegetation and climatic changes.
# Comparative Analysis of LiDAR and Photogrammetry for 3D Crime Scene Reconstruction
## 3 Methodology
### Hardware and Software Technology Utilized  
The scanning method involves creating three models, by utilizing an iPhone equipped with LiDAR technology and the Recon 3D app (Model 1), a photogrammetry model using iPhone with PiX4 Dcatch [22], for data collection, and Pix4 Dmapper [22] for the processing (Model 2); a second-generation Leica scanner BLK360 model (Model 3) was used as the ground truth. This is summarized in Table 4 with more details. The first model uses iPhone's built-in LiDAR sensor to scan the scene with four different scanning settings at a 5.0 mm resolution specified in the Recon-3D application settings. The second model uses Pix4 Dcatch with the Pix4 Dmapper or photogrammetry using the same four scanning settings. However, Pix4 Dcatch does not have resolution settings. When comparing resolutions between LiDAR and photogrammetry models, it is essential to understand that these  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Marker Pair** & **Markers** & **Actual Measures (M)** \\ \hline
1 & 1–2 & 2.519 \\ \hline
2 & 1–3 & 1.893 \\ \hline
3 & 1–4 & 2.288 \\ \hline
4 & 1–5 & 2.505 \\ \hline
5 & 4–5 & 0.753 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Actual measurements between the five markers.  
Figure 2: A laser ruler and tape measure are used to measure between markers.  
technologies use different methodologies to capture and process data, leading to differences in the type and detail of their results. Photogrammetry could offer minute details, as low as 0.097 mm per pixel at 1 m away from the target and as high as 0.486 mm per pixel at 5 m away using the iPhone 15 Pro Max. Thus, various factors should be considered, such as the distance to the subject, the camera's specifications, and environmental conditions like lighting and texture. The third model is the Leica BLK 360 G2 reference model. It compares the efficiency of the best scan from the first and second models using the ICP (Iterative Closest Points) algorithm to align the 3D models, and CloudCompare was utilized for point-wise evaluation.
# Robust Sales forecasting Using Deep Learning with Static and Dynamic Covariates
## 4 Results and Discussion
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Model** & **RMSSE** & **MASE** \\ \hline DeepAR & 0.78245 & 0.5718 \\ \hline DeepAR + Prices & 0.78493 & 0.5829 \\ DeepAR + Events & 0.78247 & 0.5692 \\ DeepAR + Time & 0.78190 & 0.5742 \\ DeepAR + IDs & 0.77356 & 0.5404 \\ \hline DeepAR + Prices + Events & 0.78402 & 0.5776 \\ DeepAR + Prices + Time & 0.78330 & 0.5740 \\ DeepAR + Prices + IDs & 0.77461 & 0.5466 \\ DeepAR + Events + Time & 0.78511 & 0.5766 \\ DeepAR + Events + IDs & 0.77221 & 0.5393 \\ DeepAR + Time + IDs & 0.76990 & 0.5359 \\ \hline DeepAR + Prices + Events + Time & 0.78471 & 0.5777 \\ DeepAR + Prices + Events + IDs & 0.77231 & 0.5438 \\ DeepAR + Prices + Time + IDs & 0.76971 & 0.5360 \\ DeepAR + Events + Time + IDs & 0.76866 & **0.5344** \\ \hline DeepAR + Prices + Events + Time + IDs & **0.76864** & 0.5354 \\ \hline Seasonal Naive & 1.03543 & 0.5889 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance of DeepAR global models and benchmark evaluated with respect to RMSSE and MASE. It is worth emphasizing that the importance of each feature type hinges on the specific application domain. It is expected that the significance of these specific features may vary in other application domains, and different features may assume a more prominent role.