esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Proposed Method for Estimating the Tail Probability of the MMPP/D/1 Queue
### The ISDC (Importance Sampling Dequue Counter)  
In the previous section, we determined the most favorable parameters for simulating the distribution of IS simulation. As a result, the service rate decreased by a factor of \(e^{\theta_{0}}\). The updated service rate \(\mu^{*}\) of the proposed method is as follows:  
\[\mu^{*}=e^{-\theta_{0}^{*}}\mu \tag{15}\]  
where \(\mu\) is the conventional service rate of IS and MC simulations.  
An important concept is called Importance Sampling Dequuee Counter (ISDC). The Algorithm 1 describes the operation of ISDC. The \(ISDC\) counts the number of dequeue events. Denote \(Q^{*}\) as the queue length in IS by using the optimal distribution. Next,the value of \(Q^{*}\) will be computed using ISDC. Figure 4 illustrates the functioning of ISDC. The ISDC algorithm is defined as follows. Initially, the virtual IS queue length, denoted as \(Q^{*}\), and the variable _counter_ are both set to 0. Additionally, the value of _step_ is determined as \(e^{-\theta_{0}^{*}}\). The variable _counter_ will tally the occurrences of dequeue events in the IS virtual queue.  
During the _enqueue_ event, the virtual queue length is incremented by 1, resulting in \(Q^{*}=Q^{*}+1\), which corresponds to the addition of one packet to the virtual IS queue length \(Q^{*}\). In this work, it is specified that the queue length is measured in packets. In this case, we add a single packet to the queue \(Q^{*}\) as there is only one packet that has arrived.  
During the _dequeue_ event, the algorithm operates in the following manner. Initially, the value of _counter_ is incremented by _step_. Next, evaluate the value of _counter_ in relation to 1. If _counter_ is more than or equal to 1, then one packet will be processed, and both \(Q^{*}\) and _counter_ will be reduced by 1.  
By using _counter_ and _step_, the _\"virtual queue\"_ reduces the processing rate \(e^{\theta_{0}^{*}}\) times.
## 4 Analysis Results and Discussion of Coupled Multi-Body Dynamics
### Analysis of Thermo-Solid Coupling Characteristics during Braking
#### 4.1.2 Results of Stress Field Distribution of High-Speed Train Brake Disc  
Temperature gradient action causes the brake disc to expand and deform, but due to boundary condition restrictions, the phenomenon cannot happen naturally, causing the brake disc to produce a substantial amount of thermal stress. At the same time, the rotation of the brake disc is driven by the rigid connection between the rotating pair and the inner ring. The creation of a stress concentration during the deceleration causes mechanical stress in this area. Figure 8a-c are the stress contours of the brake disc at the initial braking time \(t=0.5\) s, \(t=10.0\) s, the maximum stress time \(t=22.8\) s, and the braking end time \(t=56.6\) s, respectively.  
Similar to the temperature change, the overall change in brake disc stress presented a rising and then dropping tendency. During the entire working process of the brake, the maximum stress occurred at 22.8 s, which was earlier than the maximum temperature. This was mainly because at this time, compared with the mechanical stress, the thermal stress of the brake disc played a dominant role, and the temperature had a great influence on the thermal stress distribution.  
When the temperature rises to a certain value, due to the decrease of the heat flux of the friction pair, it begins to enter a slow rising stage. At this time, the temperature of the disc surface reaches approximately the peak value, while the internal temperature of the disc body is relatively low. The temperature difference between the inside and outside of the brake disc reaches the highest, and there is a large temperature gradient. The disc body expands and deforms when heated, and internal constraints limit its unrestricted growth. Therefore, a large stress is generated, reaching a maximum of 198 MPa. Additionally, the stress on the disc surface is mainly concentrated in the friction radius area of the brake disc and distributed in a ring shape. The main reason is that the vibration of the brake disc and  
Figure 7: Temperature field distribution of brake disc at different braking moments. (**a**) \(t=0.05\) s; (**b**) \(t=10\) s; (**c**) \(t=30.0\) s; (**d**) \(t=56.6\) s.  
the brake pad causes the friction pair to form repeated contact and clutch states, which affects the stress distribution on the friction disc surface of the brake disc.
## 6 Benchmarks
### Secure Federated \(\chi^{2}\)-Test  
We tested our secure federated \(\chi^{2}\)-test protocol against 3 of the 12 real world datasets used by [PERSON] et al. (2014) listed below in Table 7. The three datasets (Mushroom, Credit, and Adult) were chosen to cover a range of sizes for the contingency table (\(|\mathcal{D}|\)) while keeping the number of divisions practical for the SMPC method. We compare the communication overhead (MB), runtime (s) and relative error (%) of computing the \(\chi^{2}\)-statistic across the three datasets in Tables 8-10, respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**ID**} & \multicolumn{2}{c}{\(t\)} & \multicolumn{2}{c}{**d.f.**} \\ \cline{2-4}  & **MHE** & **SMPC** & **MHE** & **SMPC** \\ \hline
1 & 4.04 & 0.0433 & 0.0897 & 0.0286 \\
2 & 4.23 & 0.0161 & 0.0317 & 1.75 \\
3 & 4.07 & 0.341 & 0.363 & 12.7 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Relative error (%) of calculating \(t\) statistic and degree of freedom (d.f.) in the secure federated \(t\)-test on each pair of classes as indicated by the ID.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**ID** & **MHE** & **SMPC** \\ \hline
1 & 86.0 & 4008 \\
2 & 86.0 & 5661 \\
3 & 86.0 & 11,810 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Communication overhead (MB) of running the secure federated \(t\)-test on each pair of classes as indicated by the ID.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Mushroom** & **Credit** & **Adult** \\ \hline Attr 1 & Cap color & Feature 6 & Occupation \\ \# Attr 1 & 10 & 10 & 14 \\ Attr 2 & Odor & Feature 7 & Native Country \\ \# Attr 2 & 9 & 10 & 41 \\ \(|\mathcal{D}|\) & 90 & 100 & 574 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Details of datasets used in benchmarking the secure federated \(\chi^{2}\)-test on various datasets.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**ID** & **MHE** & **SMPC** \\ \hline
1 & 25.3 & 42.9 \\
2 & 25.5 & 60.9 \\
3 & 29.2 & 129 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Runtime (s) of running the secure federated \(t\)-test on each pair of classes as indicated by the ID.  
For the secure federated \(\chi^{2}\)-test, we can see that our MHE method is clearly much more efficient in terms of the communication overhead and runtime as this is the perfect setting to leverage the amortized cost of our secure batch division protocol. The minimum number of divisions required is 90 for the Mushroom dataset where our MHE method is already \(2\times\) faster than the SMPC method. At the high end, the ADULT dataset required 574 divisions to be performed simultaneously, resulting in a \(10\times\) improvement in runtime and \(300\times\) improvement in communication for our MHE method over the SMPC method.  
The secure batch division protocol remained highly accurate in this setting, with an average relative error of \(1.06\times 10^{-3}\%\) for calculating the \(\chi^{2}\) statistic in our MHE method and \(2.06\times 10^{-4}\%\) in the SMPC method.
# Phase Transition and Controlled Zirconia Implant Patterning Using Laser-Induced Shockwaves
## 2 Materials and Methods  
### Preparation of Zirconia Sample  
Zirconia pellets were prepared using MSE PRO Monoclinic Zirconium Oxide Nanoparticles, MSE Supplies LLC, Tucson, AZ, USA (20-40 nm in size) with a purity of over 99.9%. Zirconia powder was mixed with 5 wt% polyvinyl alcohol (PVA), which served as the binding agent. The mixture was then placed into a 13 mm-diameter hardened steel dry-pressing die set to form pellets at a maximum pressure of 8 MPa. Each zirconia pellet weighed 1 g and had a 13 mm diameter in its pressed form, referred to as a green body. After patterning, the samples were sintered in an MTI KSL-1500x (MTI Corporation, Richmond, CA, USA) furnace at 1450 \({}^{\circ}\)C. During sintering the pellet's diameter shrank to 10 mm due to densification. Phase transition from monoclinic zirconia (\(\rho=5.68\) g/cm\({}^{3}\)) to tetragonal zirconia (\(\rho=6.1\) g/cm\({}^{3}\)) results in increased density and particle diffusion.  
Before patterning the pre-sintered zirconia samples, surface roughness was reduced to 0.05 \(\upmu\)m using a Buehler EcoMet 250 Grinder-Polisher with an AutoMet 250 Powerhead (Buehler, Lake Bluff, IL, USA) [30]. Aluminum foil (Reynolds Wrap, Louisville, KY, USA)and graphite dry lubricant (Blasters, Tampa, FL, USA) were used as the sacrificial layers. Sizes of 100-2000 mesh-sized copper TEM grids were used as templates. A clean glass slide (Sargent Welch, New York, NY, USA) with 84% transmittance at 1064 nm served as a confinement medium [31]. The laser used for patterning was a 1064 nm, 10 Hz Nd-YAG pulsed laser with a pulse width of 5 ns, 225 Q-switch value, and a focused 3 mm-diameter Gaussian beam.  
Once the grid patterns were imprinted, the sample was subjected to a sintering process. The sintering process was carefully managed to avoid pattern degradation or melting. To achieve this, a two-stage sintering procedure was implemented. The patterned green body will go through a two-step sintering, while the pre-sintered zirconia will go through a second step of sintering at 1450 \({}^{\circ}\)C [32]. The processes of pre-sintering at 1200 \({}^{\circ}\)C and complete sintering at 1450 \({}^{\circ}\)C are detailed in Table 1. The sintering process was developed after numerous trials to find the one with the best pattern retention. This controlled approach ensured that the patterns remained intact and consistent throughout sintering. The pre-sintering phase is especially important for preventing the patterns from deforming. Based on these findings, zirconia patterning requires careful attention to the material phase and the methods used. Zirconia is functional in the tetragonal phase and malleable only in the monoclinic phase. This change in the zirconia properties makes it a challenging task to find the form with the perfect mix of phases for the best pattern imprinting and retention. The success of the green body form of zirconia demonstrates that patterning at this stage is the most effective strategy.
## 4 Numerical Simulation
### Rayleigh Fading Channel  
The simulation of a Rayleigh fading channel is used to examine the channel structure's influence on the equalization performance. Assume that the channel comprises seven paths, the average delay is 0.5 ms, and the average power of each path decreases exponentially with increasing delay. In the simulation, we measure the performance under channels with different RMS multipath delay.  
\[\kappa=\sqrt{E[(\tau-\overline{\tau})^{2}]}=\sqrt{\overline{\tau^{2}}- \overline{\tau}^{2}} \tag{27}\]  
where the channel average delays \(\overline{\tau}\) and \(\overline{\tau^{2}}\) are given by  
\[\overline{\tau}=E[\tau]=\sum_{i}\frac{p_{i}}{\sum_{k}p_{k}}\tau_{i} \tag{28}\]  
\[\overline{\tau^{2}}=E[\tau^{2}]=\sum_{i}\frac{p_{i}}{\sum_{k}p_{k}}\tau_{i}^{2} \tag{29}\]  
with \(p_{i}\) as the power of each channel path.  
A statistical analysis of the effect of \(\kappa\) on the performance of the two algorithms was performed. Figures 4 and 5 illustrate the BER cumulative distribution function (CDF) of MSK and GMSK with a different SNR, respectively. PF-SCFDE is represented by the solid line, whereas SCFDE is represented by the dashed line. The performance of both equalization methods declines when \(\kappa\) increases.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Equalizer Type** & **Complex Multiplication** & **Complex Addition** \\ \hline SCFDE & \(2\)\(N\) log\({}_{2}\)(\(N\))+\(10\)\(N\) & \(2\)\(N\) log\({}_{2}\)(\(N\))+\(N\) \\ PF-SCFDE & \(2\)\(N\) log\({}_{2}\)(\(N\))+\(11\)\(N\)+\(M\) & \(2\)\(N\) log\({}_{2}\)(\(N\))+\(2\)\(N\)+\(M\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Computational complexity comparison between SCFDE and PF-SCFDE.  
From the simulation results, PF-SCFDE had better BER performance than SCFDE when \(\kappa\) was low. PF-SCFDE was superior to SCFDE for MSK transmission when \(\kappa<0.9\), and SCFDE had certain advantages when \(\kappa>0.9\). For GMSK, PF-SCFDE had better performance when \(\kappa<0.5\). Compared with MSK, owing to the longer pulse memory length (\(L=3\)), the forward information contained other information except for time \(n-1\), so PF-SCFDE performance decreased.
# BDS-3 Integrity Risk Modeling and Probability Evaluation
## 2 BDS-3 Integrity Monitoring Architecture
### BDS-3 Integrity Monitoring Method
#### 2.2.2 Satellite Autonomous Integrity Monitoring  
The BDS-3 GEO/IGSO/MEO satellites all have the SAIM function. BD3-3 SAIM could transmit an alarm message through SIF parameter to users or change the signal modulation mode such that it is immediately unusable once a failure is detected in the satellite. There two independent onboard SAIM receivers and the measurements from different receivers are cross verified to monitor the possible failure modes such as the pseudorange step, carrier phase step, abnormal signal power, code/carrier divergence, distortion of pseudorandom code correlation peaks, the possible satellite clock phase jump and frequency jump. The detail monitoring methods for BDS-3 SAIM are described in [10].  
BDS-3 satellites have multifrequency signals, as among them the new generation signals such as B1C and B2a signals are monitored by SAIM. If a certain frequency abnormal signal is detected by SAIM, the SIF parameter corresponding to the frequency signal is updated from 0 to 1. SAIM can provide high real-time integrity monitoring without considering the complex observation environment on the ground. Considering that the broadcast periods of different frequency signals are different, to achieve the shortest alarm time and meet the requirement of 10 s, BDS-3 is clear in ICAO SARPs that the SIF parameters broadcasted by B2a signal have the priority for B1C and B2a dual-frequency users, since that B2a signal can broadcast both B1C and B2a signal SIF parameters and has the shortest broadcast period of 3 s.
## 3 Discussion
### Future Directions  
The findings of this study provide valuable insights for developing stress-tolerant crops. The overexpression of _RrCAX1a_ in tobacco demonstrates the potential of leveraging _RrCaCA_ genes for enhancing calcium tolerance. Further studies are needed to elucidate the interactions between _RrCaCA_ genes and other signaling pathways, such as those involving hormones and reactive oxygen species. The functional validation of additional _RrCaCA_ members and their roles in other abiotic stress conditions will deepen our understanding of the molecular mechanisms underlying stress tolerance in _R. roxburghii_. Moreover, exploring the evolutionary dynamics of the _CaCA_ gene family in other _Rosa_ species can provide insights into the adaptive strategies of calcium tolerance across different environmental contexts.
# A New Online Service for the Validation of Multi-GNSS Orbits Using SLR
## 2 Materials and Methods
### Tools for Identification of GNSS Satellites in GOVUS  
Currently, there is no standardized and official numbering system for the satellites. Depending on the scientific community or the satellite system characteristics, other numbering systems are preferred. Those mostly used include SVN, PRN, COSPAR designation, and NORAD/Satellite Catalog. In the case of the GOVUS system, SVN numbers are preferred, however, being aware of the problem of the diversity of the common nomenclature, helpful tools have been developed:  
* PRN2 SVN allows for checking which satellites (SVN) were related with the particular broadcast channel (PRN) in the selected range of time.
* SVN2 PRN informs to which channel (PRN) from the satellite system a particular satellite (SVN) was assigned.
* CONSTELLATION shows the complete list of the satellites (SVN) which constituted the constellation of the particular satellite system in the specified date.
# A Comparative Analysis of Wi-Fi Offloading and Cooperation in Small-Cell Network
## 4 Comparison between Cooperation and Wi-Fi Offloading in Small-Cell Network
### Switching between SCRE and SORE  
Figure 2 shows the switching strategy employed by the network. The network performs switching between Wi-Fi offloading and cooperative communication depending on the network conditions. In this network the data rate of each user can be enhanced by either serving it with more than one SC base stations simultaneously, i.e., cooperative communication or by offloading the traffic to the unlicensed band which is also used by the Wi-Fi. In this network, switching mainly depends on the data rate requirement and user's density. As shown in Figure 2, SCs bounded with dashed lines are present in a MC. Based on data rate demand of users and user's density, central BS (Macro BS) switches to the scheme that performs better under different conditions. As shown in figure, UE \(j\) is served cooperatively by connecting to its own SBS using LTE link and then additionally connecting to two neighboring SBS using cooperative communication. Similarly, UE \(j+1\) is served using unlicensed Wi-Fi band in addition to its own LTE link. Next we present a switching algorithm that tries to maximize the user data rates while switching between the SCRE and SORE while considering the network conditions. Switching between Cooperation and Offloading (SCO) Algorithm  
Similar to SCRE and SORE, SCO is also a centralized algorithm and is assumed to be aware of the channel state information between each BS \(i\) to UE \(j\), switching criteria, user density and their data rate demand. Algorithm 3 shows the switching logic of SCO. The inputs to this algorithm are rate thresholds \(R_{j}^{th}\), maximum power \(P_{i}^{max}\) of each SBS \(i\), total number of RBs \(RB_{total}\), leftover rate \(L_{i}\) of each SBS \(i\), total number of UEs \(N\), switching parameter for data rate threshold \(\alpha\) and switching parameter for user density \(\beta\). Similar to SCRE and SORE, in the SCO algorithm the user is associated with the SBS with the highest channel gain. Then its data rate is calculated according to (3) or (8). If the data rate requirement is not fulfilled through connection with a single SBS and more resources need to be allocated, then the SCO algorithm switches to either SCRE or SORE to fulfill the additional data rate requirement. Figure 2: Switching Model Between Cooperation Communication and Wi-Fi Offloading.
## 1 Introduction
[PERSON] described a mechanism for improving the measurement resolution of measuring straightness and angular errors [24]. [PERSON] established a unified measurement model by using the ray-tracing method, to compensate for the measurement errors introduced by the error crosstalk, element fabrication error, laser beam drift, and nonparallelism of two measurement beams [25]. [PERSON] et al. proposed using a single-mode and fiber-coupled laser as the light source to improve the spatial stability and energy distribution of the measured laser beam [26; 27]. This type of measurement method has a simple structure, few optical devices, and low cost. This paper provides a compact five-degree-of-freedom simultaneous measurement system based on the laser collimation method. Four industrial cameras are used to detect the position of each collimated light spot, to solve all five-degree-of-freedom changes of the measured object. The optical path structure of the measurement system is provided in Section 2, and the measurement methods of straightness and angle error are introduced in detail. We use optical components to make each beam pass through two corner cube retroreflectors, which magnify the lateral movement and roll of the retroreflector twice. This method improves the measurement resolution of roll and horizontal straightness compared to other laser collimation measurement methods. Moreover, a common optical path compensation method is proposed to eliminate the influence of laser beam drift. Finally, an experimental setup is constructed and a series of experiments are performed to verify the feasibility and stability of the system in Section 3.
## 4 Conclusions  
A new and simple numerical method was developed to analyze the effects of concentrated masses, axial loading, and elastic supports on the eigenpairs of single- and double-tapered beams. The shear force and bending moment were determined by considering the equilibrium equation, in which the sum of the forces at the joint of the elastic support and beam as well as at arbitrary positions becomes zero. Based on this assumption,  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{
\begin{tabular}{c} **Beam** \\ **Type** \\ \end{tabular} } & \multirow{3}{*}{\(c\)} & \multirow{3}{*}{\(\omega_{i}\)} & \multicolumn{6}{c}{**Natural Frequencies [rad/s]**} \\ \cline{3-9}  & & & & & \multicolumn{3}{c}{\(K_{\Phi}\)**[Nm/rad], \(K_{w}\) [N/m]**} \\ \cline{3-9}  & & & **exp(10)** & **exp(11)** & **exp(12)** & **exp(13)** & **exp(14)** & \(\dots\) & **exp(23)** \\ \hline uniform & 0 & 1 & 65.088 & 73.831 & 77.664 & 79.158 & 79.718 & \(\dots\) & 80.050 \\  & & 2 & 196.66 & 276.06 & 375.73 & 449.31 & 482.21 & \(\dots\) & 501.55 \\  & & 3 & 690.90 & 734.44 & 831.66 & 1032.3 & 1245.3 & \(\dots\) & 1403.9 \\ \(n=1\) & 0.5 & 1 & 73.738 & 81.827 & 85.100 & 86.332 & 86.788 & \(\dots\) & 87.055 \\  & & 2 & 194.91 & 270.67 & 349.02 & 391.83 & 407.95 & \(\dots\) & 416.99 \\  & & 3 & 548.78 & 593.63 & 701.92 & 880.65 & 1005.4 & \(\dots\) & 1075.8 \\ \(n=2\) & 0.5 & 1 & 88.825 & 99.002 & 102.979 & 104.4 & 105.0 & \(\dots\) & 105.3 \\  & & 2 & 209.18 & 290.00 & 374.71 & 419.67 & 436.01 & \(\dots\) & 445.00 \\  & & 3 & 567.63 & 611.77 & 722.14 & 908.61 & 1036.3 & \(\dots\) & 1105.7 \\ \hline \hline \end{tabular}
\end{table}
Table 13: First three natural frequencies of elastically restrained beams relative to the increase in spring values.  
Figure 17: Effects of the elastic supports on the first three mode shapes of uniform beams and single and double tapered beams having \(c=0.5\).  
a free-free condition was established at both ends, and the displacements and forces of the tapered beam were determined using a simple procedure. The displacements and forces of the tapered-beam model were determined. The effectiveness of the proposed method was demonstrated by computing the results, considering diverse examples that can be experienced in practical problems.  
Moreover, the relationship between the elastic supports and compressive loading was analyzed in detail for the values of compressive loading at which the first natural frequency vanished. The compressive loading decreased depending on the taper ratio and was significantly influenced by the taper ratio. The concentrated mass significantly affects the mode shape and natural frequency, and the results analyzed through parametric studies can be used as a benchmark solution for other approaches.  
This research was funded by the National Research Foundation of Korea (Grant number NRF-2021R1F1A1064233).  
Not applicable.  
The author gratefully acknowledges the financial support for this research from the National Research Foundation of Korea (Grant number NRF-2021R1F1A1064233).  
The author declares no conflict of interest.