esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Research Frameworks and Methodologies
### Research Methodologies
#### 2.2.3 XGBoost  
The core idea of the XGBoost [30] algorithm originates from boosting trees. It involves continuously adding boosting trees to form a robust classifier when integrated. The objective function of XGBoost is designed to optimize both the predictive power of the model and its complexity, ensuring a balance between accuracy and overfitting prevention [31; 32; 33]. The objective function is as follows:  
\[L(\phi)=\sum_{i}l\left(y_{i},\overset{\wedge}{y_{i}}\right)+\sum_{k}\Omega(f_ {k}) \tag{1}\]  
In the formula, \(l\left(y_{i},\overset{\wedge}{y_{i}}\right)\) represents the loss function; \(\overset{\wedge}{y_{i}}\) represents the predicted output; \(y_{i}\) represents the actual output; \(\Omega(f_{k})=\gamma T+\frac{1}{2}\lambda\|W\|^{2}\) represents the regularization term; \(f_{k}\) represents the k-th tree model; \(T\) represents the penalty for the number of leaves; \(W\) represents the penalty for the leaf weight values; \(\gamma\) represents the penalized regularization term for the number of leaves; and \(\lambda\) represents the leaf-weighted penalized regularization term.  
The objective function of the XGBoost algorithm incorporates regularization terms, including node weights, mainly to reduce the complexity of the model and prevent overfitting. In addition, the loss function uses a second-order Taylor expansion, as shown in Equation (3). This approach effectively enhances the convergence speed and accuracy of the algorithm.  
The second-order Taylor expansion of the loss function allows XGBoost to optimize the model more efficiently. By considering not only the first derivative (which represents the direction of the steepest descent) but also the second derivative (which gives information about the curvature of the loss function), XGBoost can make more informed steps during the optimization process. This results in faster convergence towards the minimum of the loss function and generally leads to a more accurate model.  
\[L^{(t)}\approx\sum_{i=1}^{n}\left[l\left(y_{i},\overset{\wedge}{y_{i}}^{(i-1) }+g_{i}f_{i}(x_{i})+\frac{1}{2}h_{i}f_{i}^{2}(x_{i})\right)\right]+\Omega(f_ {t}) \tag{2}\]  
where \(g_{i}\) and \(h_{i}\) are the first derivative and the second derivative of the loss function, respectively.
## Numerical Implementation  
### Setup of the Numerical Wave Tank  
The experiments were performed at the Large Wave Channel (GWK) in Hannover, Germany. The dimensions of the wave flume are 309 m long, 7 m high, and 5 m wide with a 1:10 slope at the bottom. A cylinder with the diameter \(D\) = 0.7 m was installed with its central axis at the edge of the slope. More details of the experiments can be seen in [PERSON] et al. [3]. The configuration of the present three-dimensional numerical wave tank (NWT) is based on the experimental setup, as shown in Figure 1. The length and height of the NWT working zone are 70 m and 8 m, respectively. The width of the whole computational domain varies with the transverse inclined angle \(\theta\), ensuring that both ends of the cylinder are at least 4D away from the front and back boundaries. Three numerical wave gauges (WG1, WG2, and WG3) are used to measure the free surface elevations \(\eta\), i.e., WG1 is mounted at 0.01 m in front of the cylinder, WG2 is placed near the wall along the frontline of the cylinder and WG3 is arranged at 0.7 m behind the cylinder. The specific positions of wave gauges can be seen in Figure 1. In this study, six cases with different transverse inclined angles are simulated, as shown in Table 1. The incident wave height \(H\) = 1.3 m, wave period \(T\) = 4.0 s, and water depth \(d\) = 3.8 m are chosen for all the simulations.
## 2 Theoretical Foundation
### Mathematical Morphology  
Mathematical morphology (MM) is a framework for analyzing spatial structures through the application of structural transformations [37].  
Dilation and erosion are the basic morphological operators from which other operators are derived, namely opening, closing, and thinning. A structuring element \(B\), whose size and shape are chosen a priori, determines the points to be added or removed in a shape \(A\) defined in the Euclidean space \(E\). We provide a brief and simple definition of these operations since details of morphological mathematics are beyond the scope of this paper.  
The erosion of a shape A is denoted by \(A\ominus B=\left\{x\mid B_{x}\subseteq A\right\}\), where \(B_{x}=\left\{b+x|b\in B\right\}\) is a translation \(b+x\) of the structuring element \(B\). All points where \(B_{x}\) is not completely contained in \(A\) are removed. Dilation is the complement of an erosion, and is defined by \(A\oplus B=\left\{x\mid B_{x}\bigcap A\
eq\emptyset\right\}\). In dilation, points will be added where \(B_{x}\) intersects with \(A\).  
The opening of \(A\) can be obtained by an erosion followed by a dilation. It is denoted by \(A\circ B=(A\odot B)\oplus B\). As a result, points belonging to the smaller structures of \(A\) are eliminated. The closing operation, denoted by \(A\bullet B=(A\oplus B)\odot B\), is the reverse, making the gaps in \(A\) decrease.  
Skeletonization, shrinking, or thinning are operations guided by influence zones [38], using a combination of basic morphological operators. For the sake of simplicity, a skeleton can be viewed as the successive removal of the points on the edge of the shape, on the condition that they do not break the connectivity of the shape area, thus preserving its original topology.  
For better understanding, the skeleton can be defined by the set \(D\) of the centers of maximal disks on the 2D grid \(A\). Given a family of structuring elements \(\{nB\}\) constructed by successive dilations of a disk \(B\),  
\[nB=\underbrace{B\oplus\cdots\oplus B}_{n\text{ times}},n=0,1,\cdots,\]  
exists a disk \(nB_{c}=\{x\in A\mid x-c\in nB\}\) centered in \(c\) and translated by \(x-c\), \(nB_{c}\in D\), under the condition that, for each point \(y\) and an integer \(m\), \(mB_{y}\
ot\subseteq D\) where \(nB_{c}\subseteq mB_{y}\). This procedure is illustrated in Figure 2.
# Sequence-to-Sequence Video Prediction by Learning Hierarchical Representations
## 4 Experiments
### Moving MNIST
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Method** & **MSE** & **PSNR** & **SSIM** \\ \hline DRNet [15] & 207.9 & 13.2 & 0.42 \\ MCnet [16] & 172.2 & 13.9 & 0.66 \\ PredRNN++ [41] & 50.66 & 20.12 & 0.8984 \\ \hline
2-level HRPAE & 66.36 & 18.75 & 0.839 \\
3-level HRPAE & 52.91 & 19.99 & 0.891 \\
4-level HRPAE & 49.67 & 20.47 & 0.8987 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results with the Moving MNIST dataset. The metrics are averaged over 10 predictions. **Resource Efficiency. ** Next we discuss the resource efficiency of models, for which we compare the model sizes. The number of trainable parameters is compared on Table 3. The 2 nd to the 5 th row show the total number of convolutional weights in corresponding LSTMs. The 6 th row shows the total number of convolutional weights. Overall, our models use a smaller number of trainable weights when compared with PredRNN++. For instance, our model only has about 74 K convolutional weights in the LSTM-1. By contrast, PredRNN++ requires 5921 K convolutional weights in its first layer of Causal LSTM unit, as shown in the 1 st row of Table 3. With only 15% of the weights of PredRNN++, 3-level HRPAE is able to achieve comparable performances, which proves the effectiveness of our model. Note that our training settings are identical to the default settings of PredRNN++. The efficiency is attributable to the model's capability of automatically learning hierarchical structures, e.g., low-level features for generating the details of digit shapes, and high-level features for tracking digit positions. Figure 4: Frame-wise performances over the testing MMNIST dataset. (**a**–**c**) represent the averaged MSE, PSNR and SSIM evaluation metrics over the next 10 predicted frames, respectively. Figure 5: Qualitative results on MMNIST. Our model is able to generates sharp frames during all the time steps, and accurately predicts the digit locations. \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **PredRNN++** & **3-Level** & **4-Level** \\ \hline LSTM 1 & 5921 K & 74 K & 74 K \\ LSTM 2 & 3359 K & 295 K & 295 K \\ LSTM 3 & 2261 K & 1180 K & 1180 K \\ LSTM 4 & 2261 K & 0 & 4719 K \\ \hline Total & 15,441 K & 2313 K & 9391 K \\ \hline Ratio & 1 & 0.15 & 0.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the number of convolutional weights of LSTMs at different levels, bias excluded.
## 5 Autonomous Navigation Technology
### Path Planning
#### 5.2.2 Local Path Planning  
Local path planning refers to obtaining real-time environmental obstacle information in an unknown or partially known environment according to various sensors and planning correspondingly to ensure that no collision happens between the outer contour of the vehicle body and the roadway wall or obstacles.  
1. Artificial Potential Field Method The artificial potential field (APF) method regards the task area as a charged potential field. The target point will generate a gravitational field for the underground intelligent scraper, while the obstacles will generate a repulsive field adversely; both fields together compose the potential field distribution. In the mission area, the underground intelligent LHD moves in the direction of combined potential field force, to reach the destination without collision with the obstacles [99; 100; 101]. [PERSON] et al. [102] proposed a real-time trajectory planning method based on two-dimensional search, which mainly focused on the difficulties in underground turning for intelligent LHD. It was demonstrated that the scraper could turn steadily in a short time.  
The fuzzy logic algorithm takes the environmental information obtained by the sensor as the input data, carries out the path planning through the fuzzy reasoning and outputs the calculated accurate result. This method can overcome the problems of uncertainty and ambiguity in the data processing process, eliminate noise and errors and can quickly and accurately plan the local path for even unknown or dynamic situations. Thus, it can perform well in real time. However, the rules for fuzzy control are mainly formulated by human experience. Once the rules are determined, it is difficult to adjust them online in real time and they are inadaptable to the changes in the roadway. Moreover, local minimum value would be attained as it responds rapidly to the input local information [70]. The characteristics of the above-mentioned path planning methods are summarized in Table 3.  
In a word, both the global path planning and the local path planning methods have certain defects. How to quickly find a method that can plan a path in the shortest time, be real-time adjustable to the environmental information and can avoid obstacles make up the main research direction in the future.
## 6 Conclusions  
In this paper, we proposed a fast and high-precision method based on a telecentric measurement system to calibrate transit offset and tilt errors for improving laser tracker measurement accuracy. We first analyzed the causes of the laser tracker's transit offset and tilt errors, established an error model for the transit offset and tilt errors, and set the functional relationship between the transit offset and tilt errors and the coordinates measured by laser tracker. Then, we designed and established a calibration setup based on a dual telecentric silhouette-based system to calibrate the transit offset and tilt errors, which provides guaranteed calibration accuracy. And then, we utilized the numerical simulation method to eliminate the installation eccentricity error of the test rods, which does not require a skilled operator to adjust the coaxiality of the test rods so as to save much time and improve calibration efficiency. Finally, we calculated the compensated coordinates of the laser tracker with raw measurement data and the calibration error parameters, thereby improving the coordinate measurement accuracy of the laser tracker. Furthermore, the calibration method we proposed can be not only applied to the 2D rotary stage in laser trackers but also provide potential improvement to many other similar instruments with a 2D rotary stage, such as theodolites, machine tools, etc.  
There are also works that need improvements. First, the positions of the center axis of the test rods were extracted directly from the image obtained by the telecentric measurement system in the proposed method; we are going to improve the accuracy of the position extraction by improving the algorithm of image processing after obtaining the image. On the other hand, a set of software algorithms can be developed to automate the processing and analysis of least squares fits to the data to improve measurement efficiency.  
Figure 16: The measurement error of laser tracker before and after transit tilt and offset compensation. (**a**) The scale bar at a distance 5 m from laser tracker. (**b**) The scale bar at a distance 10 m from laser tracker.  
**Author Contributions:** Conceptualization, S.W. and Z.Z.; methodology, S.W. and Z.Z.; software, S.W. and F.M.; validation, S.W.and D.D.; formal analysis, S.W. and G.W.; investigation, Y.P., R.J., C.C., and T.F.; data curation, S.W., T.G. and Q.Q.; writing--original draft preparation, S.W.; writing--review and editing, S.W., Z.Z., and W.Z.; supervision, D.D. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Key Research and Development Program under Grant 2023 YFB3407901.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** All data that support the findings of this study are included within the article.  
The authors declare no conflicts of interest.
## 3 2D Numerical Simulation Results and Discussion
### Comparison of the M-Packets Temperatures in the Middle Plane of the Cabinet  
Figure 12 presents a distribution of the M-packets (for a definition of the M-packets, see subchapter 2.5) temperatures in the middle plane of both refrigerated cabinets. Temperature values were obtained in the time-dependent study. The minimum temperature in the unmodified refrigerator reaches a value of 1.4 \({}^{\circ}\)C at location B1 (Figure 12). The highest value of 5.4 \({}^{\circ}\)C was obtained at location F6. The average food temperature is +3.38 \({}^{\circ}\)C. The air curtain cannot separate the volume of the refrigerator from the environment, so the most unfavorable temperatures are obtained at the front of the refrigerator. Additionally, the unmodified refrigerator meets only the requirements of the 3M2 class and can be used to store food products at temperatures ranging from \(-1\) to +7 \({}^{\circ}\)C. In the case of the modified cabinet, the lowest temperature value of 0.5 \({}^{\circ}\)C was obtained at the same location B1 (Figure 12) and the highest value of 3.8 \({}^{\circ}\)C is observed at location F8. The average food temperature is +2.18 \({}^{\circ}\)C. The proposed cabinet satisfies the requirements of the 3M0 class (from \(-1\)\({}^{\circ}\)C to +4 \({}^{\circ}\)C).
# A Testbed for GNSS-Based Positioning and Navigation Technologies in Smart Cities:
## 6 Test Campaigns and Results
### SNAP Positioning
#### 6.1.2 Position Accuracy  
Results are shown in Figure 9 for the Cumulative Density Function (CDF) of the 2D horizontal errors obtained with each of the three positioning modes of the SNAP service. Vertical errors were not considered in this experiment because the target application was that of positioning a user in a 2D city map, and thus vertical information was disregarded. Position errors were 95% of the time below 100 m for GPS L1 position fixes with a median error of 40 m, while for cellular position fixes they were below 45 m with a median error of 12 m. When hybridising both GPS L1 observables and cellular observables, 2D horizontals errors went down to roughly 25 m 95% of the time, thus highlighting the convenience of combining different technologies in urban scenarios.  
The results in Figure 9 are a good example on how GNSS accuracy can be improved in urban areas by relying on additional positioning technologies. This helps in mitigating situations where GNSS observables are not available, as it happens due to signal blockage by high buildings, and thus it provides an additional degree of robustness. There are two research directions where efforts could be placed for evolving the current SNAP service. The first one would be to process signals from multiple GNSS constellations (e.g., GPS, Galileo, and Beidou, which share the same band) and combine them to obtain a multi-constellation position fix. This would greatly improve the availability in urban areas due the much larger number of available satellites in the sky. The second research direction would be to expand the hybridisation algorithm of the SNAP service to consider additional technologies apart from cellular signals. The use of information coming from inertial sensors, barometers and signals of opportunity such as DVB-T/-S can certainly improve the reliability and accuracy of the user's position [61]. Interestingly, combining several technologies does also contribute to strengthening the level of trust of the obtained position fix, since each technology is independent from one another and thus difficult to hack or to counterfeit at the same time. Securing and authenticating the user's position is definitely an interesting research topic to explore [62].
## 2 Time-Domain Finite Integration Theory (TD-FIT)
### Explicit Updating Equations of TD-FIT  
The semi-discrete Maxwell grid equations (MGE) and constitutive equations are [30]:  
\[\mathbf{C}\widehat{\mathbf{e}}=-\frac{d}{dt}\widehat{\widehat{\mathbf{b}}},\ \ \widehat{\mathbf{C}}\mathbf{h}=\widehat{\widehat{\mathbf{i}}}_{\text{C}}+ \widehat{\widehat{\mathbf{i}}}_{\text{S}}+\frac{d}{dt}\widehat{\widehat{ \mathbf{d}}},\ \widehat{\widehat{\mathbf{S}}}\widehat{\mathbf{b}}=0,\ \widehat{\widehat{\mathbf{S}} \widehat{\mathbf{d}}}=\widehat{\widehat{\mathbf{q}}}, \tag{18}\]  
\[\widehat{\widehat{\mathbf{d}}}=\mathbf{D}_{\text{\tiny{$\ell$}}}\widehat{ \mathbf{e}},\ \widehat{\widehat{\mathbf{b}}}=\mathbf{D}_{\mu}\widehat{\mathbf{h}},\ \widehat{\widehat{\mathbf{i}}}_{\text{C}}=\mathbf{D}_{\sigma}\widehat{ \mathbf{e}}, \tag{19}\]  
where \(\widehat{\widehat{\mathbf{q}}}\) is the electric charge quantity, \(\widehat{\widehat{\mathbf{i}}}_{\text{C}}\) and \(\widehat{\widehat{\mathbf{i}}}_{\text{S}}\) are the loss term and source term of electric current, respectively.  
To achieve second order accuracy for the two curl equations in MGE, temporal discretization is carried out with central difference. Then, explicit time-marching is performed by the staggered leap-frog (SLF) algorithm:  
\[\widehat{\mathbf{e}}^{n+1}=\underline{C}\underline{A}\underline{E}\cdot \widehat{\mathbf{e}}^{n}+\underline{C}\underline{A}H\cdot\bigg{(}\widehat{ \mathbf{C}}\widehat{\mathbf{h}}^{n+1/2}-\widehat{\widehat{\mathbf{i}}}_{\text{ S}}^{n+1/2}\bigg{)}, \tag{20}\]  
\[\widehat{\mathbf{h}}^{n+1/2}=\widehat{\mathbf{h}}^{n-1/2}-\Delta t\mathbf{D}_ {\
u}\mathbf{C}\widehat{\mathbf{e}}^{n}, \tag{21}\]  
where \(\mathbf{D}_{\
u}\) denotes diagonal matrices of magnetic reluctivity and it is the inverse matrix of \(\mathbf{D}_{\mu}\), \(\Delta t\) denotes the time step and it should meet the Courant-Friedrichs-Lewy (CFL) stability constraint for stable time integration. Coefficients \(\underline{C}\underline{A}\underline{E}\) and \(\underline{C}\underline{A}H\) in Equation (20) are expressed as:  
\[\underline{C}\underline{A}\underline{E}=\bigg{(}\frac{\mathbf{D}_{\text{ \tiny{$\ell$}}}}{\Delta t}-\frac{\mathbf{D}_{\sigma}}{2}\bigg{)}\bigg{/} \bigg{(}\frac{\mathbf{D}_{\text{\tiny{$\ell$}}}}{\Delta t}+\frac{\mathbf{D}_{ \sigma}}{2}\bigg{)}, \tag{22}\]  
\[\underline{C}\underline{A}\underline{H}=\,1/\bigg{(}\frac{\mathbf{D}_{\text{ \tiny{$\ell$}}}}{\Delta t}+\frac{\mathbf{D}_{\sigma}}{2}\bigg{)}. \tag{23}\]
## 5 Conclusions  
Beginning with micro-level tests on bacteria co-cultured with CG and FA, and ending with macro-tests on mortars made with CG, FA and bacteria, the conclusions of this paper are as follows:  
* Both CG and FA environments are favorable for the growth of _B. pasteurii_.
* CG and FA environments can significantly shorten the initiation time for urea hydrolysis and mineralization. The time for the occurrence of _B. pasteurii_ mineralization is reduced by 72% when using CG and by 28% in the presence of FA.
* A reason why _B. pasteurii_ performs better in the CG environment than in FA may be ascribed to the substrate surface roughness, which offers more attachment sites.
* SEM and FTIR analyses confirmed that the mineralization precipitate, generated by the co-culture of _B. pasteurii_ with CG or FA, is bio-CaCO\({}_{3}\).
* Mortars with CG, 30% FA and _B. pasteurii_ with mineralized solutions showed a better pumping performance than in the absence of FA.
* The compressive strength of biomineralized materials at 28 days is 5.34 times higher than that obtained without biomineralizing.
* Finally, our findings support the viability of using microbial mineralized coal gangue and fly ash for eco-friendly backfilling materials, demonstrating potential benefits for sustainable practices in coal mining operations.  
As this is the first study on the effect of CG and FA on the mineralizing capacity of _B. pasteurii_, future research will be devoted to accelerating _B. pasteurii_ mineralization and improving the strength of the backfilling material. Moreover, the use of other solid wastes, with a rougher surface, will also be investigated.  
S.G.: Conceptualization, Methodology, Writing--Original Draft. A.F.F.: Supervision, Writing--Review and Editing. H.Y.: Writing--Review and Editing. K.S.: Validation. L.D.: Validation. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the China Scholarship Council (CSC, No.202106420067), the future scientists Program of China University of Mining and Technology (2021 WLAKJ018) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX21_2336).  
Figure 11: Results of the compression test on (**a**) B-strength: microbially mineralized solid waste CG and FA materials; and (**b**) C-strength: microbial-free original solid CG and FA.