esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 A Brief Introduction of the Model Test
Based on the internal Fish language in UDEC, the relevant parameters in the calculation process of the constitutive model were modified through the custom functions and variables to establish the user-defined constitutive model, and the calculation procedure of the established Mohr-Coulomb elasto-plastic constitutive model considering the initial damage is shown in Figure 6.  
Combined with Figure 6, the detailed calculation process was as follows: The initial damage variable \(D_{0}\) was first calculated based on the biaxial static load \(\sigma_{\text{b}}\) of the numerical model using Equation (4), and the physical and mechanical parameters of the rock considering the initial damage such as \(\overline{K}\) and \(\overline{G}\), as well as the total strain increment \(\Delta\varepsilon_{i}\) of the element under the initial static load were derived. Then, based on the Lemaite strain equivalence principle and combined with the initial damage variable \(D_{0}\), the effective principal stress increment \(\Delta\widetilde{\sigma}_{i}\) was derived by Equation (6), and finally the effective principal stress \(\widetilde{\sigma}_{i}\) of the element was obtained by an iterative calculation. When the effective principal stress \(\widetilde{\sigma}_{i}\) of the element reached the yield condition and entered the plastic phase, the updated stress state of the element was obtained by the plastic flow law, and the above process was divided into two cases: The first case was when \(h(\widetilde{\sigma}_{1},\widetilde{\sigma}_{3})\leq 0\), the shear failure occurred in the element, through the shear yield function \(f^{s}\) expressed by the effective principal stress and the shear plastic flow method, the new effective principal stress increment \(\Delta\widetilde{\sigma}_{i}\) was calculated by the total strain increment \(\Delta\varepsilon_{i}\), and finally the effective principal stress \(\widetilde{\sigma}_{i}^{N}\) of the element was obtained. The other was when \(h(\widetilde{\sigma}_{1},\widetilde{\sigma}_{3})\geq 0\), the element underwent tensile damage, and the new effective principal stress \(\widetilde{\sigma}_{i}^{N}\) of the element was calculated by the tensile yield function \(f^{t}\) and the tensile plastic flow law according to the same steps of the first case. It is worth noting that the established rock constitutive model was based on the model test results and the damage mechanics theory, which can take into account the initial damage of intact rock under different biaxial equal static loads. For an underground rock mass with caverns, blast holes, and stress relief holes, numerical modeling can be carried out based on the established model as long as the initial boundary static load condition can be simplified to biaxial equal static loading.
# Efficient Continuous Subgraph Matching Scheme Based on Trie Indexing for Graph Stream Processing
## 4 Performance Evaluation
In contrast, the proposed scheme, which applies a cache replacement strategy, showed a linear increase in the window processing time despite an increase in the size of the window. Figure 12: Average window processing time ratio according to \(\alpha\) (the longest window processing time: \(\alpha=90\)). Figure 13: _Cont._  
Figure 15 shows the average window processing time according to the stream adjustment ratio. In this evaluation, the size of the window was considered as 100, and the window processing performance was compared based on 1000 windows. To measure the window processing performance according to the stream adjustment ratio accurately, the graphs of the initial 500 windows were input and the graph streams of the other 500 windows were adjusted. The window processing time was measured by varying the graph stream adjustment ratio as 10%, 20%, 30%, and 50%. The results of applying the existing and proposed algorithms to each dataset are as follows. The average window processing time of the existing algorithm increased by 206% when the stream adjustment ratio increased from 10% to 50%. The average window processing time of the proposed algorithm increased by 35% to 130% when the stream adjustment ratio increased from 10% to 50%. The existing algorithm requires a longer time to regenerate query results as the stream adjustment ratio increases. In contrast, the proposed algorithm exhibits a comparatively high processing speed owing to its function of managing a duplicated area. In addition, the window processing performance of the proposed algorithm based on the wiki-Talk dataset increased despite an increase in the graph stream adjustment ratio when the size of the cache was 0.5 kB. As indicated above the existing technique shows a delay of processing speed by twice when a stream adjustment ratio increased. In contrast, an increase in the graph stream adjustment ratio did not have a significant effect on the processing time except when the size of the cache was small. Figure 13: Ratios of increase in the processing speed according to the complexity of the query. (**a**) Wiki-Talk; (**b**) Cit-Patents; (**c**) YouTube. Figure 14: Cont. Figure 16 shows the memory cost according to the datasets. Performance comparisons between the existing scheme and the memory replacement techniques in the proposed scheme were performed. We measure the amount of memory (the number of bits) per time(ms) based on the simple query. As a result of the performance evaluation, the existing scheme used about four bits per ms, while the proposed cache replacement techniques used less than one bit on average. In terms of memory usage, it was confirmed that the PUSQ technique showed the best performance. In conclusion, the proposed cache replacement techniques have excellent performance over the existing scheme in terms of memory usage and query throughput. Figure 14: Average window processing time according to the size of the window. (**a**) Wiki-Talk; (**b**) Cit-Patents; (**c**) YouTube. Figure 15: _Cont._
## 3 Conditions of the Field Survey
### UAV Data Collection  
Data were all collected on May 12 th, 2016. The survey was performed using DRELIO 10, an UAV based on a multi-rotor platform D56, assembled by DroneSys (Figure 4). This electric hexacopter UAV has a diameter of 0.8 m and is equipped with a collapsible frame allowing the UAV to be folded back for easy transportation. DRELIO 10 weighs less than 4 kg and can handle a payload of 1.6 kg, for a flight autonomy of about 20 min. The camera is mounted on a tilting gyro-stabilized platform. It is equipped with a reflex camera Nikon D700 with a focal length of 35 mm, taking one 6.7 Mpix photo in intervalometer mode every 2 seconds. The images have no geolocation information encoded in their EXIF. The flight control is run by the DII(r) software iOSD. DRELIO 10 is lifted and landed manually and it performs autonomous flights controlled from the ground station software. The mean speed of autonomous flight is programed at 4 m/s.  
A set of three flights (Table 1) has been performed over the studied beach:  
* Flight 1 was performed following a typical flight plan (from S to A, B, C, D and S on Figure 3) with nadir pointing camera and parallel flight lines at a steady altitude of 50 m.  
Figure 4: **(a)** Example of red target used as Ground Control Point. **(b)** Example of blue target used as check point to assess the quality of the reconstructed DEM. **(c)** DRELIO 10, Unmanned Aerial Vehicle (UAV) designed from a hexacopter platform 80 cm in diameter.  
* Flight 2 was performed following the same parallel flight lines at 50 m of altitude with an oblique pointing camera tilted at 40\({}^{\circ}\) forward. The inclination has been set to 40\({}^{\circ}\) because this angle would be compatible with a survey of the cliff front ([PERSON], 1997) or of parts of the upper beach situated under the canopy of coastal trees. The two flight lines were carried out in opposite direction. Large viewing angles induce scale variations within each image (from 1.64 cm/pixel to 2.95 cm/pixel). Increasing the tilting angle makes the manual GCPs tagging more difficult.
* Flight 3 was performed following the two parallel flight lines with a nadir-pointing camera but at different altitudes. The altitude was about 40 m from S to A, then 60 m from B to C and finally 40 m from D to S (Figure 3). The disadvantage is that the footprint and the spatial resolution of the photos vary from one flight line to another and therefore the ground coverage is more difficult to plan.
# Quadrotor Formation Strategies Based on Distributed Consensus and Model Predictive Controls
## 9 Conclusions  
In this study, the formation control strategies for quadrotors considering the leader-follower architecture are proposed in Section 5. The leader is designated to track the predefined waypoints in horizontal motion and the desired altitude/climb rate in vertical motion. Furthermore, the leader generates the followers' desired formation trajectories using the methods in Sections 5.1.1 and 5.1.2 as a guidance for the followers to perform the formation flight. The follower's formation strategy is proposed in Section 5.2. The consensus control and MPC with the QP problem are adopted in the horizontal formation control, and the MPC with the LQT is adopted in the vertical formation control. The formation control strategies are examined based on the 6 DOF nonlinear simulation under the Matlab/Simulink environment and the simulation results are illustrated in Section 7. A discussion of the simulation results as well as the performance of the formation strategies are carried out in Section 8.  
Figure 22: Zoom-in of altitude vs. time during upward circling motion.  
The results of the simulation of comprehensive maneuver in Section 7.2 show that the proposed formation strategies are feasible in straight flight, turning, and upward circling motion.  
[PERSON] organized and supervised the main research of the study. [PERSON] completed the design and simulation of the study under [PERSON]'s supervision.  
This research was supported by the Ministry of Science and Technology (MOST), Taiwan, under Grant MOST 107-2221-E-032-028.  
The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; and in the decision to publish the results.
## 2 Materials and Methods
### Outcomes
#### 2.3.3 Accuracy of Implant Placement  
Superimposition of the Virtually Planned Implant and the Actually Placed Implant  
The superimposition and measurement process of placement accuracy using the VARO guide are summarized in Figure 3.  
The pre-surgical plan data comprising the CBCT imaging and the guide design were extracted from the VG planning software (VARO Plan, Neobiotech, Seoul, Korea) and uploaded to a dental CAD software (exoCAD, exocad GmbH, Darmstadt, Germany). The STL files from the postsurgical optical impression were also uploaded to the same software, and the scan body was transformed into a virtual abutment. This data set containing the pre and postsurgical information was transferred to a 3D analysis software (Geomagic Verify, SculptCAD, Dallas, TX, USA), and by using teeth as the reference, the pre and postsurgical data were superimposed. The pre-planned fixture position was extrapolated from the position of the drilling hole and the postsurgical fixture position from the virtual abutment. This process of extrapolating the fixture position is known as \"reverse engineering\" and has been described in a previous study [11].  
Parameters for Accuracy of Implant Placement  
The measurements were taken by one examiner ([PERSON]). Each parameter was measured twice, and then the mean of the two measurements was used.  
* Vertical deviation (mm): the vertical distance between the planned and placed fixture apices.
* Angular deviation (\({}^{\circ}\)): the angle between the axes of planned and placed fixtures.
* Horizontal platform deviation (mm): the horizontal distance between the planned and placed fixtures at the base of the transmucosal component of the tissue level implants.  
Figure 3: Measurement of the positional accuracy of the VARO guide surgery. (**A**) The pre-surgical plan data was uploaded to a dental CAD software. (**B**) The STL files from the postsurgical optical impression were also uploaded to the same software. (**C**) The data set was transferred to a 3D analysis software and superimposed using teeth as references. (**D**) The drilling hole from the pre-surgical data and the virtual abutment from the postsurgical data were used to “reverse engineer” the fixture positions. (**E**) The angular, vertical, and horizontal deviations were measured at implant apex and platform levels.  
Horizontal apex deviation (mm): the horizontal distance between the planned and placed fixture apices.
## 5 Numerical Simulations
### Modeling Matrix
where only the first \(N_{f}\) singular values are taken into account, the other ones being discarded because they are equal to zero from the numerical point of view, as illustrated in Figure 5. As a consequence of this rank deficiency [36] of \(\mathbf{G}\), the pseudo inverse of the regularized matrix \(\widetilde{\mathbf{G}}\) is given by the decomposition:  
\[\widetilde{\mathbf{G}}^{+}=\sum_{\ell=1}^{Nf}\frac{1}{\sigma_{\ell}}\mathbf{V} _{\ell}\mathbf{U}_{\ell}^{T}. \tag{8}\]  
This decomposition does not give rise to any problem because the smallest singular values (and in particular those equal to zero) no longer play any role in the inversion. In such a situation, the propagation of random errors from the complex visibilities \(V\) to the retrieved brightness temperature distribution  
\[\widetilde{T}=\widetilde{\mathbf{G}}^{+}V \tag{9}\]  
is governed by the so-called condition number [39] of the regularized modeling matrix \(\widetilde{\mathbf{G}}\), which is defined by the ratio:  
\[\kappa(\widetilde{\mathbf{G}})=\frac{\sigma_{1}}{\sigma_{N_{f}}}. \tag{10}\]  
By definition, as the singular values are ordered in descending order, this ratio is larger than \(1\). However, it should be kept in mind that this value is an upper bound for this propagation. For example, referring back to Figure 5, \(\kappa(\widetilde{\mathbf{G}})\simeq 320\) with \(d=0.71\lambda\), whereas \(\kappa(\widetilde{\mathbf{G}})\simeq 32,000\) with \(d=0.69\lambda\). Shown in Figure 6 are the variations of \(\kappa(\widetilde{\mathbf{G}})\) with the shortest spacing \(d\). As noted in Figure 3a, here again two regions are well-separated: in the first one the value of \(\kappa(\widetilde{\mathbf{G}})\) is almost constant, whereas in the second one it is a growing function of the inverse of the shortest spacing. The frontier between these regions is estimated anew between \(0.704\lambda\) and \(0.705\lambda\).
## 4 DPS: Grid-Based Dual Phantom Node Source Location Privacy Protection Scheme
### The Routing Phase  
In the routing phase, the SoN sends the data packets to the SN periodically through the selected two PNs. The data packets need to go through three transmission steps: The SoN sends the data packets to the SPN, the SPN sends the data packets to the RPN, and the RPN sends the data packets to the SN.  
(1) Step 1: The source node sends data packets to the sending phantom node:  
The process that the SoN sends data packets to the SPN is the same as described in Section 3.3.1;  
(2) Step 2: The sending phantom node sends data packets to the receiving phantom node:  
Since the SPN and the RPN are randomly selected by the SoN, according to whether the SPN and the RPN are on the same side of the SN, there are two possibilities: The same side (as shown in Figure 7, the SPN and RPN are on the same side of the SN) and the opposite side (as shown in Figure 8, the SPN and RPN are on different sides of the SN). When it is the same side case, the transmission path is determined using the operations described in Section 3.3.1. When it is the opposite side case, the data packets may pass through the SN when they are transmitted from the SPN to the RPN, and the DPS scheme will degenerate to the SPS scheme. In order to avoid the above situation and ensure the privacy of the source location, we propose that the SPN first transmits the data packets to a transition node whose row (or column) is the same as that of the RPN, and then the transition node transmits the data packets to the RPN;  
(3) Step 3: The receiving phantom node sends data packets to the sink node:  
The RPN transmits the data packets to the SN using the single-path routing method described in Section 3.3.2.  
Figure 9 shows the flowchart of our proposed DPS scheme.
## 4 Discussion  
By analyzing the obtained results and graphs, it can be concluded that the dependence of the recoiling assembly velocity on the factors is not linear. However, the calculated and  
Figure 5: Diagram of the maximum recoiling assembly velocity as a function of the normalized (coded) value of the initial volume of the gas chamber.  
Figure 6: Diagram of the maximum recoiling assembly velocity as a function of the normalized (coded) value of the recoil spring stiffness.  
presented quadratic function approximation gives a very close estimation of the simulation results. The function obtained from plan Bi allows us to state that the strongest influences on the results are (in decreasing order): the recoiling assembly mass, the gas port location and the gas port diameter. Theoretically, increasing the recoiling assembly mass is the easiest way to reduce the recoiling assembly velocity (such a solution is characteristic of simple blowback weapons). The consequence of this is to primarily increase the weight of the entire firearm. Therefore, it was very significant to verify the influence of the other factors.  
It is significant that the expected result was that the most advantageous solution--from the point of view of recoiling assembly braking--and is the shortest distance (for the starting position of the bullet--when the cartridge is in the chamber) of the bullet to the gas port. The minimum value of this distance is forced by the cartridge case length. Then, the largest coefficient in the quadratic function has this factor. This is justified by the fact that the location of the gas port, in close proximity to the front edge of the cartridge case, causes the propellant gases to have energy, which results in a significant decrease in recoiling assembly velocity. As the port is moved toward the muzzle of the barrel, much less gas flows into the gas chamber, and so the deceleration is increasingly negligible. This is largely due to the characteristics of pistol ammunition, in which a propellant charge is burned very dynamically.  
As can be seen, the recoil spring stiffness has the least influence; it is practically insignificant in the assumed range (even though the maximum value is twice the minimum). The research reported in study [24] also found negligibly small effects of this factor on recoiling assembly velocity; these results were for gas-operated small arms. Therefore, it was concluded that its impact would not be further investigated. This is very important when considering the cost and time-consuming nature of research.
## 3 Experimental Study
### Experimental Results
The experimental results show that the prior of the Gaussian mixture distribution used in this paper has certain advantages in probability RUL prediction and can be extended to other RUL predictions. \begin{table}
\begin{tabular}{l l l l l} \hline
**Window Size** & **RMSE** & **MAE** & **Score** & **SMAPE (\%)** \\ \hline
20 & 16.00 & 12.46 & 4.39 & 22.02 \\
30 & 9.91 & 7.60 & 1.84 & 11.96 \\
40 & 10.16 & 8.47 & 1.96 & 14.37 \\
50 & 14.06 & 10.05 & 2.19 & 15.97 \\ \hline \end{tabular}
\end{table} 
Table 4: RUL prediction comparison with different time window size. Figure 11: Comparative experimental results of different window size. \begin{table}
\begin{tabular}{l l l l l} \hline
**Model** & **RMSE** & **MAE** & **Score** & **SMAPE (\%)** \\ \hline \(\rho=0\) & 13.85 & 11.67 & 4.16 & 16.25 \\ \(\rho=0.25\) & 9.91 & 7.60 & 1.84 & 11.96 \\ \(\rho=0.50\) & 11.85 & 9.44 & 2.67 & 12.76 \\ \(\rho=0.75\) & 13.88 & 11.19 & 4.05 & 15.34 \\ \(\rho=1.00\) & 14.43 & 11.27 & 4.34 & 16.87 \\ \hline \end{tabular}
\end{table} 
Table 5: Experimental comparison results of different \(\rho\):
## 1 Introduction
The effect factors of the orbit accuracy of LEO satellites include not only the quality of GNSS observations, but also the quality of the above-mentioned GNSS products and the processing methods of GNSS data. That is why we cannot directly use the precise kinematic orbit of GRACE-FO and Swarm satellites for the joint multi-satellite inversion of time-varying gravity fields, even the published orbits from the Deutsche GeoForschungsZentrum (GFZ) and the European Space Agency (ESA) with centimeter-level accuracy. Thus, the research on KPOD and the assessment of the orbit accuracy for multi-LEO satellites should be carried out. This paper performs and presents a KPOD solution based on an undifferenced ionosphere-free (IF) combination for Swarm and GRACE-FO satellites simultaneously over 14 days from 1 June to 14 June 2021. The most precise GNSS precise orbit and clock products from International GNSS Service (IGS) are used for Swarm and GRACE-FO satellites as well as the same processing strategy and least squares batch processing method. To minimize the effects of abrupt position offsets that occurred in the kinematic orbit, a Reduced Dynamic POD (RDPOD) was performed along with the KPOD to facilitate subsequent quality control of the solved kinematic orbit. Finally, we demonstrated the reliability of the quality control method and the accuracy of the solved orbits by evaluating the carrier phase residual, Satellite Laser Ranging (SLR) validation and comparison with a precise ephemeris.
## Problem Formulation
### Wind Output Characteristics
#### 2.1.2 Uncertainty  
Plenty of statistical analyses of the wind forecast error show that the hourly forecast error of wind output tends to be normal distribution and different wind speed segments appear in different deviation normal distributions [16]. Assuming that the hourly maximum deviation from the mean value is three times to the standard deviation, the prediction interval of wind power can be illustrated in Figure 2 based on the probability density function (PDF) of wind forecast error in literature [17].  
Figure 2 shows that the forecast error interval of wind power corrected by the deviation normal distribution is not symmetric with the forecast value, which provides a more accurate spinning reserve information for the wind power participation in the scheduling plan. Unlike the highly repetitive of load demand [18], the wind output has a great range of uncertainty. In order to cope with the uncertainty of wind power, conventional units need to reserve additional climbing ability as the spinning reserve, which is also the main limitation reason for \"wind power difficult integration\".  
Figure 1: Load demand/wind output under four seasons; (**a**) net load fluctuation with and without wind power integration; and, (**b**) ramping demand of systems with and without wind power.  
The spinning reserve constraint of conventional units with wind power integration can be expressed as Equation (3).  
\[\left\{\begin{array}{l}\sum\limits_{i=1}^{N_{g}}u_{i,t}P_{gi}^{\max}-\sum \limits_{i=1}^{N_{g}}u_{i,t}P_{gi,t}\geq\Delta P_{load,t}+\Delta P_{wind,t}^{up} \\ \sum\limits_{i=1}^{N_{g}}u_{i,t}P_{gi,t}-\sum\limits_{i=1}^{N_{g}}u_{i,t}P_{gi}^ {\min}\geq\Delta P_{load,t}+\Delta P_{wind,t}^{dn}\end{array}\right. \tag{3}\]