esa-sceva/satcom-chunk-collection huggingface dataset:
# Multi-Objective Message Routing in Electric and Flying Vehicles Using a Genetics Algorithm
## 1 Introduction
The proposed genetics algorithm identifies the Pareto front and subsequently reduces or chooses the best possible solution. The proposed multi-objective routing method in a the proposed paradigm for mobile battery-powered vehicles employs two objective functions, data rate and residual energy. Considering data rate not only means higher data transfer but also confirms UAV's inclusion in most communications routes, which leads to minimal blockage, better propagation, and faster communications. On the other hand, utilization of residual energy not only means sustaining the UAV's power, but is also an ingenious way to avoid numerous routes employing the same communication devices. Moreover, the proposed scheme ensures reliability and identifies that the chosen path stays connected during the complete transaction. Figure 1 The novel optimal multi-objective solution has strong potential and applications in numerous similar problems. To the best of the authors' knowledge, there exists no scheme which innovates with an analytical optimal solution for multi-objective routing in both high mobility networks of EnFVs. The following are the major contributions:  
* An efficient and novel message routing scheme that considers battery-constrained mobile vehicles;
* Mathematical modeling of a multi-objective problem for message routing and a genetics algorithm;
* An efficient and reliable routing scheme for swift data transmission in a high mobility ad hoc environment;
* An exhaustive performance evaluation using real traces of simulation for urban mobility (SUMO) and OpenStreetMap (OSM); and
* 90%+ successful packet delivery as compared to existing solutions. The organization of the remainder of the paper is as follows. Section 2 analytically models the proposed unified E-VANET and FANET environment system. In Section 3, we discuss the proposed algorithms and our solution. The proposed scheme and existing state-of-the-art routing solutions have been comparatively evaluated in Section 4. Section 5 concludes the paper.
## 5 Discussion
### Implications for the Vanuatu Arc Volatile Budget
Our estimated fluxes are thus H\({}_{2}\)O \(\sim\)5758 t d\({}^{-1}\), CO\({}_{2}\)\(\sim\)259 t d\({}^{-1}\), H\({}_{2}\)S \(\sim\)30 t d\({}^{-1}\), and H\({}_{2}\)\(\sim\)0.5 t d\({}^{-1}\), and correspond to a total volatile flux (TVF) of about 6482 t d\({}^{-1}\) for Mount Garet. Our inferred CO\({}_{2}\) fluxes are especially relevant because they contribute new data to recent cataloguing efforts [19; 20; 21; 29] aimed at a more robust quantification of the global volcanic CO\({}_{2}\) output. Such global estimates have remained poorly constrained until recently, because technical challenges in volcanic CO\({}_{2}\) measurements have resulted in sparse and incomplete global CO\({}_{2}\) flux catalogues. With a CO\({}_{2}\) flux of \(\sim\)259 t d\({}^{-1}\), Mount Garet ranks as intermediate-size volcanic CO\({}_{2}\) source (the median volcanic CO\({}_{2}\) flux in catalogues [20; 29] is \(\sim\)320 t d\({}^{-1}\)). Notably, our measured Gaua CO\({}_{2}\) flux is a factor \(\sim\)3 lower than the CO\({}_{2}\) flux (\(\sim\)745 t d\({}^{-1}\)) predicted by [PERSON] et al. [21]. The latter authors circumvented the lack of direct gas measurements at Gaua (unavailable at the time of their study) by predicting the time-averaged volcanic gas CO\({}_{2}\)/S\({}_{\rm T}\) ratio from trace element compositions (Ba/La and Sr/Nd ratio) of Gaua lavas and global gas vs. trace element relationships. The mismatch between the direct (this study) and indirect [21] estimates reflect the difference between measured and predicted CO\({}_{2}\)/S\({}_{\rm T}\) ratio (0.9 vs. 2.5), as discussed above (cfr. 5.1). Our results suggest persistent degassing at Mt Garet (Gaua) contributes an additional \(\sim\)2% to CO\({}_{2}\) emissions along the Vanuatu arc, which during the 2005-2015 period appeared dominated by prodigious lava lake degassing at Ambrym [33; 34] (the inferred 2005-2015 average is \(\sim\)7586 t d\({}^{-1}\)[21]) and, to a lesser extent, by open-vent degassing at Aoba and Yasur (inferred 2005-2015 averages of \(\sim\)4933 and \(\sim\)1549 t d\({}^{-1}\), respectively) [21].
# Ex Vivo Exposure to Soft Biological Tissues by the 2-um All-Fiber Ultrafast Holmium Laser System
## 2 Materials and Methods
### Ultrafast Ho-Doped Fiber Laser System and Experimental Setup
Figure 1: (a) Experimental setup of the all-fiber Holmium MOPA system operating in the ultrashort pulsed mode: WDM—wavelength division multiplexer, Iso—isolator, SWCNTs—single-walled carbon nanotubes, PC 1,2—polarization controllers; the output spectrum of Ho-doped fiber laser is presented on the inset (MO spectrum); (b) Lasing spectrum and (c) autocorrelation trace of the output pulse corresponding to the average output power of 0.4 W.  
Additionally, we carried out a comparison of pulsed and continuous-wave 2-\(\upmu\)m radiation effects on the same soft biological tissues. Ex vivo investigation of CW Ho-doped fiber laser radiation exposure in a wide range of applied energy (1.5-66 J) at a wavelength of 2.1 \(\upmu\)m on longissimus porcine muscle tissues was presented in our previous work [41], which also contains a detailed description of the CW Ho-doped fiber laser scheme, as well as the setup used in the experiment. A flexible single-mode fiber cable with a polished angle connector (FC/APC) was used for the convenient delivery of radiation in both laser systems. During experiments, we controlled the bending radius of the transport fiber to prevent undesirable losses. The experimental setup for delivering laser radiation to the specimens under study was a vertical stand with a focusing system attached to it (Figure 2). Thus, the output radiation was focused through an optical objective with 8 \(\times\) 0.2 NA (LOMO) and positioned perpendicularly to the surface of the biological tissue fixed on the moving platform for the focal distance adjustment. The laser spot diameter on the specimen surface was about 40 \(\upmu\)m.  
The duration of laser radiation exposure on the tissues was chosen as 5, 30 and 60 s, as in previous work, to make the results comparable. Considering the losses in the optical system for the USP laser, the value of power delivered to the tissue was 0.3 W. Thus, we ensured that the applied energy delivered to the specimens was the same for both CW and ultrafast laser systems, in order to accurately compare the results. In the case of the ultrashort pulsed laser, the range of applied energy varied from 1.5 to 18 J. The value of applied energy was calculated by multiplying the average radiation power by the exposure time [44].
# Ground Target Detection and Damage Assessment by Patrol Missiles Based on YOLO-VGGNet
## 3 Target Detection and Damage Level Assessment Based on YOLO-VGGNet  
As shown in Figure 1, YOLO-VGGNet consists of three modules. Firstly, the YOLO v3 detects, classifies, and localizes mobile targets in the images. Then, the VGG-1 series networks assess the damage level of detected targets coarsely. Finally, image blocks for functionally damaged targets are fed into the VGG-2 network for further analysis of the targets' key components.  
Figure 1: The process of mobile ground target detection and damage assessment by patrol missiles.  
We divide our contributions into two parts. In Section 3, we proposed a two-stage learning-based framework for mobile ground targets based on YOLO prior information, which can meet the requirements of real-time detection and timely damage assessment online. In Section 4, a novel convolutional feature clustering method based on CAM and guided backpropagation of deconvolution was proposed for the first time to evaluate the components of damaged targets.
# An Improved NSGA-II-Based Method for Cutting Trajectory Planning of Boom-Type Roadheader
## 3 Simulations and Experiments
### Virtual Simulation of Section Cutting Verification  
To elucidate the impact of the body pose on the motion space of the roadheader, this paper establishes the size parameters for the boom-type roadheader, as detailed in Table 1. The motion ranges of the cutting arm include the rotation angle \(\theta_{2}\in[-45(^{\circ}),45(^{\circ})]\), lifting angle \(\theta_{1}\in[-135(^{\circ}),-45(^{\circ})]\), and telescoping length \(d\in[0,500\ (\mathrm{mm})]\). Additionally, tunnel parameters \(5\times 3\ (\mathrm{m})\), target cross-section parameters: \(R_{h}=20\ (\mathrm{m})\), \(C_{h}=1\ (\mathrm{m})\), and cutting head size parameters (\(R=380\ (\mathrm{mm})\), \(r=266\ (\mathrm{mm})\), \(l_{1}=84\ (\mathrm{mm})\), \(l_{2}=343\ (\mathrm{mm})\), \(l_{3}=122\ (\mathrm{mm})\)) are defined.  
To improve the quality of section forming, this paper adopts a segmented cutting method and constructs a feasible cutting trajectory space based on different roadheader body poses. The discrete path points are optimized using an improved NSGA-II algorithm to obtain feasible cutting trajectories. Three scenarios are compared and analyzed as follows:  
Scenario 1: The roadheader body pose for left-side section cutting is set to \(P=(15,563.5\ \mathrm{mm},\ -1250\ \mathrm{mm},983\ \mathrm{mm},0^{\circ},0^{\circ},0^{ \circ})\), and for right-side section cutting, it is set to \(P=(15,563.5\ \mathrm{mm},\ 1250\ \mathrm{mm},983\ \mathrm{mm},0^{\circ},0^{ \circ},0^{\circ})\).  
Scenario 2: The roadheader body pose for left-side section cutting is set to \(P=(15,563.5\ \mathrm{mm},\ -1250\ \mathrm{mm},983\ \mathrm{mm},0^{\circ},0^{ \circ},0^{\circ})\), and for right-side section cutting, it is set to \(P=(15,503.5\ \mathrm{mm},\ 1230\ \mathrm{mm},963\ \mathrm{mm},2^{\circ},-2^{\circ},10^{ \circ})\).  
Scenario 3: The roadheader body pose for left-side section cutting is set to \(P=(15,503.5\ \mathrm{mm},\ -1230\ \mathrm{mm},963\ \mathrm{mm},2^{\circ},-2^{ \circ},10^{\circ})\), and for right-side section cutting, it is set to \(P=(15,563.5\ \mathrm{mm},\ 1230\ \mathrm{mm},1003\ \mathrm{mm},2^{\circ},-2^{ \circ},-10^{\circ})\).  
Based on the above poses, an improved NSGA-II is used to plan the cutting trajectories, and the trajectory tracking effect and forming quality are verified on a virtual simulation platform. As shown in Figure 16, a virtual simulation platform for section forming and cutting is built, achieving coordinate mapping and scale unification between physical and virtual spaces. A cutting head with virtual collision detection function is used to simulate the cutting process.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Para.** & \(\mathbf{a_{1}}\) & \(\mathbf{a_{2}}\) & \(\mathbf{a_{3}}\) & \(\mathbf{a_{4}}\) & \(\mathbf{b_{1}}\) & \(\mathbf{b_{2}}\) & \(\mathbf{b_{3}}\) \\ \hline Roadheader (mm) & 1544 & 501.5 & 2011.5 & 962 & 983 & 290 & 13 \\ \hline \end{tabular}
\end{table}
Table 1: Dimensional parameters of roadheader.
## 2 Results
### Regulation of ABA and NAA on the Biosynthesis and Accumulation of Norisoprenoids
#### 2.2.4 Potential Contribution of Differentially Alternative Splicing of VviDXS and VviCRTISO  
The effects of the ABA and NAA treatments on alternative splicing (AS) events of those genes were also investigated. As a posttranscriptional regulation of genes, AS has been shown to be affected by salt stress and high temperature in grape berry [9; 11]. Splice variants are mainly generated by intron retention (IR), exon skipping (ES), mutually exclusive exon (MXE), alternative 3\({}^{\prime}\) splice site (A3 SS) and alternative 5\({}^{\prime}\) splice site (A5 SS). The differential alternative splicing between two RNA-Seq samples was detected by rMATs [27]. In the present study, besides the norisoprenoid-associated genes mentioned above, the upstream genes involved in the plastidal 2-methyl-D-erythritol-4-phosphate phosphate (MEP) and cytoplasmic nevalonic acid (MVA) pathways were also considered [28]. Among these genes, there were 32 differentially splicing ES or IR events were found (Tables S6 and S7). However, only the occurrence of alternative splicing at the genes encoding 1-deoxy-D-xylulose-5-phosphate synthase (DXS; VIT_204s0008g04970) and prolycopene isomerase (CRTISO; VIT_208s0032g00800) was further validated by reverse transcription PCR (Figure 8). The rMATs paired model identified that the two transcripts of the VviDXS with different ES were up-regulated by NAA at the stage of E-L 34 (Table S6), and a transcript of the VviCRTISO with IR was also expressed at relatively high levels in NAA-treated berries compared to the control at E-L 36 stage (Table S7).
# Impact of Groundtrack Pattern of a Single Pair Mission on the Gravity Recovery Quality
## 2 Simulation Environment
### Geophysical Input Models  
For the simulation environment of this study, we employ the dominant mass variations of hydrology, ice and solid Earth of the Earth system by use of the time-variable gravity field models generated within the ESA-project \"ESA Earth System Model for Gravity Mission Simulation Studies\" [23] as an update to previous ESA models by [24], provided as spherical harmonic coefficients up to degree and order 180 at 6 h intervals. The time-span applied in our study starts from 1 January 1996 for 3-days to 9-days gravity recovery. The difference between two ocean tide modelsEOT08a [25] and [26], is assumed as the ocean tide error in simulation, where the error is an important source for aliasing of the high frequency signals to the low frequency signals [27]. Moreover, the atmosphere-ocean error (AO error) product from IAPG (TU Munich) is employed for the forward modeling [15]. The AO error model is defined as two atmosphere models difference (ECMWF-NCEP) plus 10% of the ocean signal of the model OMCT. Furthermore, all geophysical forward models are smoothed by Gaussian filter of radius \(4000/2L_{max}\) km to avoid ringing effects (Gibbs phenomenon) caused by the truncation error.
# Advances in Ionospheric Space Weather by Using FORMOSAT-7/COSMIC-2 GNSS Radio Occultations
###### Abstract  
This paper provides an overview of the contributions of the space-based global navigation satellite system (GNSS) radio occultation (RO) measurements from the FORMOSAT-7/COSMIC2 (F7/C2) mission in advancing our understanding of ionospheric plasma physics in the purview of space weather. The global positioning system (GPS) occultation experiment (GCOX) onboard FORMOSAT-3/COSMIC (F3/C), with more than four and half million ionospheric RO soundings during April 2006-May 2020, offered a unique three-dimensional (3D) perspective to examine the global electron density distribution and unravel the underlying physical processes. The current F7/C2 carries TGRS (Tri-GNSS radio occultation system) has tracked more than 4000 RO profiles within \(\pm\)35\({}^{\circ}\) latitudes per day since 25 June 2019. Taking advantage of the larger number of low-latitude soundings, the F7/C2 TGRS observations were used here to examine the 3D electron density structures and electrodynamics of the equatorial ionization anomaly, plasma depletion bays, and four-peaked patterns, as well as the S4 index of GNSS signal scintillations in the equatorial and low-latitude ionosphere, which have been previously investigated by using F3/C measurements. The results demonstrated that the denser low-latitude soundings enable the construction of monthly global electron density maps as well the altitude-latitude profiles with higher spatial and temporal resolution windows, and revealed longitudinal and seasonal characteristics in greater detail. The enhanced F7/C2 RO observations were further applied by the Central Weather Bureau/Space Weather Operation Office (CWB/SWOO) in Taiwan and the National Oceanic and Atmospheric Administration/Space Weather Prediction Center (NOAA/SWPC) in the United States to specify the ionospheric conditions for issuing alerts and warnings for positioning, navigation, and communication customers. A brief description of the two models is also provided.  
Keywords:FORMOSAT-7/COSMIC-2; GNSS RO; radio occultation; low-latitude ionosphere +
Footnote †: journal: _arxiv  
0000-0002-0001-9993-3880][PERSON]  
0000-0002-0002-3880][PERSON]  
0000-0002-3880-0002-3880][PERSON]  
1 Center for Astronautical Physics and Engineering, National Central University, Taoyuan City 320317, Taiwan; [EMAIL_ADDRESS] (C.-X.L.): [EMAIL_ADDRESS] (F.-Y.C.)  
2 Department of Space Science and Engineer, National Central University, Taoyuan City 320317, Taiwan  
3 Center for Space and Remote Sensing Research, National Central University, Taoyuan City 320317, Taiwan  
4 Department of Earth Sciences, National Cheng Kung University, Taiwan City 70101, Taiwan; [EMAIL_ADDRESS] (P.K.R.): [EMAIL_ADDRESS] (S.-C.)  
5 Space Weather Operation Office, Central Weather Bureau, Taipei City 100006, Taiwan; [EMAIL_ADDRESS]  
6 NOAA Space Weather Prediction Center, Boulder, CO 80305, USA; [EMAIL_ADDRESS] (T.-W.F.); [EMAIL_ADDRESS] (D.F.-R.)  
7 CIRES, University of Colorado Boulder, Boulder, CO 80309, USA  
8
# Data-Driven Model-Free Adaptive Sliding Mode Control Based on FFDL for Electric Multiple Units
## 3 Model-Free Adaptive Sliding Mode Controller for EMUs
### Discrete Sliding Mode Controller  
When there is no external disturbance and parameter estimation error in the system, the conventional MFAC scheme converges the system output error to zero. On the contrary, when the system is subject to disturbances and parameter estimation errors, the error will converge to a non-zero constant [29]. Therefore, a discrete SMC is incorporated into the controller design to improve the robustness of the system in this paper.  
The output error is defined as:  
\[\mathbf{e}(t)=\mathbf{v}_{d}-\mathbf{v}(t). \tag{15}\]  
Let \(\mathbf{s}(t)=\mathbf{e}(t)\), so \(\mathbf{s}(t+1)\) can be set as:  
\[\mathbf{s}(t+1)=\mathbf{e}(t+1)=\mathbf{v}_{d}(t+1)-\mathbf{v}(t)-(\mathbf{\Phi}(t)-\mathbf{\delta}(t ))\Delta\mathbf{\bar{H}}(t). \tag{16}\]  
The SMC law is designed as:  
\[\mathbf{s}(t+1)=(1-qT)\mathbf{s}(t)-\varepsilon T\text{sgn}(\mathbf{s}(t)), \tag{17}\]  
where \(\text{sgn}(\cdot)\) is a symbolic function. \(\varepsilon>0\), \(q>0\), and satisfies \(1-qT>0\).  
Substituting (16) into (17) yields the following sliding mode control law:  
\[\begin{split}\Delta\mathbf{u}(t)=&\frac{\mathbf{v}_{d}(t+1)- \mathbf{v}(t)}{\mathbf{\[PERSON]}_{L_{\varphi}+1}(t)-\delta_{L_{\varphi}+1}(t)}-\frac{(1-qT )\mathbf{s}(t)-\varepsilon T\text{sgn}(\mathbf{s}(t))}{\mathbf{\[PERSON]}_{L_{\varphi}+1}(t)- \delta_{L_{\varphi}+1}(t)}\\ -&\frac{\sum\limits_{i=1}^{L_{\varphi}}\left(\mathbf{\[PERSON] }_{i}(t)-\delta_{i}(t)\right)^{\mathrm{T}}\Delta\mathbf{v}(t-i+1)+\sum\limits_{i=L_ {\varphi}+2}^{L_{\varphi}+L_{\varphi}}\left(\mathbf{\Phi}_{i}(t)-\delta_{i}(t) \right)^{\mathrm{T}}\Delta\mathbf{u}(t-i+1)}{\mathbf{\Phi}_{L_{\varphi}+1}(t)-\delta_ {L_{\varphi}+1}(t)}.\end{split} \tag{18}\]  
Let \(\Delta\mathbf{u}(t)=\mathbf{u}_{SM}(t)\). Then, the MFASMC algorithm is as follows:  
\[\mathbf{u}(t)=\mathbf{u}_{MFA}(t)+\mathbf{P}\mathbf{u}_{SM}(t). \tag{19}\]  
where \(\mathbf{P}=diag\{p_{1},p_{2},p_{3}\}\in\mathbf{R}^{3\times 3}\), \(p_{1}\), \(p_{2}\), \(p_{3}>0\) are weighting factors.  
The control block diagram is shown in Figure 3. From (18), it is possible \(\mathbf{u}_{SM}\) to become large or even unbounded when \(\mathbf{\hat{\Phi}}(t)\) is small. To avoid this situation, \(\delta(t)\) is introduced as an additional correction term for \(\mathbf{\hat{\Phi}}(t)\).  
From (14) and (18), it can be seen that the design of the controller process requires only the output data generated by each power unit model without any information from the model. Therefore, the MFASMC algorithm is data-driven.
## 2 Theoretical Background
The dashed red line in Figure 1b shows the optimized Schottky barrier \(\Phi_{B}^{*}\) as a function of the wavelength. This behavior can be explained by considering that when the wavelength is reduced the photon energy \(h\upsilon\) increases by diminishing the responsivity \(R\), as shown in Equation (3), requiring a reduction of the \(NEP\) to maintain the maximized \(R/NEP\) ratio. In turn, the \(NEP\) reduction can be achieved by an increase of the optimized \(\Phi_{B}^{*}\), which decreases the amount of charge carriers able to overcome the Schottky barrier due to thermal effects. Even if the \(\Phi_{B}^{*}\) increment also produces a decrease in responsivity, it is important to recall that while the \(NEP\) is characterized by an exponential decay as a function of \(\Phi_{B}^{*}\) (\(NEP\sim e^{-\frac{\Phi_{B}^{*}}{2\mathcal{H}_{I}}}\)), the responsivity is characterized by a simple quadratic behaviour (\(R\sim\Phi_{B}^{*2}\)). The substitution of Equation (14) in Equation (3) provides the responsivity when the ratio \(R/NEP\) is maximized (here we refer to it as the optimized responsivity), as shown by the blue solid line in Figure 1b. Note that this optimized responsivity depends only on the SBH of the junction. Figure 1b shows how the optimized responsivity is increased by increasing the wavelength owing to a drop in the optimized SBH \(\Phi_{B}^{*}\), providing values at room temperature of 0.10 A/W, 0.14 A/W, and 0.23 A/W at 1.3 \(\upmu\)m, 1.55 \(\upmu\)m, and 2 \(\upmu\)m, respectively, as reported in \[\eta_{\rm int}^{\rm SLG}=\frac{1}{2}\cdot\frac{(h\
u)^{2}-(q\Phi_{B})^{2}}{(h \
u)^{2}}. \tag{2}\]4 If higher responsivities are required, they can be achieved by lowering the SBH but at the expense of the \(SNR\). \[\eta_{\rm int}^{\rm SLG}=\frac{1}{2}\cdot\frac{(h\
u)^{2}-(q\Phi_{B})^{2}}{(h \
u)^{2}}. \tag{2}\]5 (**a**) Behavior of \(g(\Phi_{B})\) at 300 K for three wavelengths: 1.3 \(\upmu\)m, 1.55 \(\upmu\)m, and 2 \(\upmu\)m; (**b**) optimized responsivity \(R\) (blue solid line) and optimized Schottky barrier height (SBH) \(\Phi_{B}^{*}\) (red dashed line) as a function of the wavelengths.
# GNSS Signal Quality in Forest Stands for Off-Road Vehicle Navigation
## 3 Results
### GNSS Signal Quality Evaluation
It follows from the figures that the \(\sigma_{Hz}\) data, obtained from GNSS measurement files, always included the projected route of the vehicle directed terrestrially (using tachymetry). One of the prerequisites for GNSS signal quality analysis is the signal-to-noise ratio (SNR) evaluation as the important factor of influence of signal quality on off-road vehicle navigation in a wooded area. SNR is a measure comparing the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to noise power (SNR = P\({}_{signal}\)/P\({}_{noise}\)), often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. The following summary characteristics were chosen for the individual locations (1 and 2):  
1. Square mean of radial (horizontal) deviations: \[\vec{\sigma}_{Hz}=\sqrt{\frac{1}{n}{\sum}\sigma_{Hz}^{2}}\] (1) \[\vec{t}_{Hz}=\sqrt{\frac{1}{m}{\sum}t_{Hz}^{2}}\] (2) where \(n\), \((m)\) represent the number of values obtained from GNSS measurement records, respectively, from terrestrial measurements. The calculated values of radial (horizontal) deviations are shown in Table 1. In area 1, two groups of accuracy characteristics are presented, which correspond to two measurement sections--see Figures 6 and 7 (Figures 12 and 13). 2. Percentiles of values \(\sigma_{Hz}\) and \(t_{Hz}\). Two percentile levels were chosen: 63%, which theoretically corresponded to the value \(\vec{\sigma}_{Hz}\), and 95%, theoretically corresponding to the value \(\vec{t}_{Hz}\). The calculated percentile values are shown in Table 2.