esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results  
### Forming Limit Curves  
The forming limit curves determined in the experimental tests were based on the modified Marciniak test. The displacement was determined by image analysis (stochastic network) [17; 18].  
The capture speed for the camera type used in the analysis (PROSILICA CV 1280, Allied Vision Technologies Canada Inc., Burnaby, Canada) was 30 images/s. Based on the comparison between the first captured image and each of the following images, the position of one or more points (in a user-specified area) was determined.  
This data was processed by applying the Ludwik law of plasticity, which is, in fact, the amended Hollomon law. This model is often used to analyse plastic deformations of metallic materials and TWB. The model also characterizes the elastic-plastic behaviour by considering the hardening phenomenon (Equation (1)).  
\[\bar{\sigma}=\sigma_{y}+K\bar{\epsilon}_{p}^{n} \tag{1}\]  
where: \(\bar{\sigma}\) and \(\bar{\epsilon}_{p}\) are the equivalent stress and strain, \(K\) and \(n\) are the strength and hardening coefficients, respectively. The constitutive relation, which additionally includes the strain hardening rate, the Cowper-Symonds parameters [19], is of the well-known form (Equation (2)):  
\[\sigma=\left[1+\left(\frac{\dot{\epsilon}}{\dot{C}}\right)^{\frac{1}{p}} \right]K\Big{(}\epsilon_{e}+\varepsilon_{p}^{\ell}\Big{)}^{n} \tag{2}\]  
where: \(\dot{\epsilon}\) is the strain rate, \(C\) and \(P\) are the Cowper-Symonds parameters of strain rate, \(K\) is the coefficient of resistance, \(\epsilon_{e}\) elastic strain, \(\epsilon_{p}^{\ell}\) is the real plastic strain, and \(n\) is the hardening coefficient.  
In this model, the stress/strain ratio is expressed only in the conditions of a single temperature. Other data needed to calculate and obtain the forming limit curves are material density--\(\rho\), modulus of elasticity--E, and Poisson's ratio--\(\
u\), respectively.  
After the measurement of the displacements, the following results were obtained:  
* forming limit curve for the two materials and the welded assembly (Figure 3a),
* forming limit curve for both welded materials and weld line (Figure 3b).  
As presented in Figure 3, the formability of the TWB structure is reduced compared to homogeneous materials. This is largely due to the presence of the weld line, which does not have the same forming capabilities due to the thermally affected structure. This is, in fact, the biggest disadvantage of TWB, which is counteracted by the fact that materials with different characteristics can be placed in critical areas of the structure where they are needed most. These areas either need stronger or perhaps lighter materials.  
Figure 2: Average stress/strain curves for both steel sheets and TWB.
## 4 Experiment and Discussion
### Worldwide Availability Coverage Test
#### 4.1.1 Results under Baseline Scenario  
Table 3 shows the ARAIM 99.5% availability and relative computational complexity of five groups under the LPV-200 criteria. As mentioned above, the 99.5% availability herein means that the ARAIM is available during 99.5% of the time at the test point. About the relative computational complexity, it is defined as the percentage of the computational time compared with the longest one. Here the longest one is the ARAIM with four constellations. The five groups' tests are executed on the same software-defined receiver (SDR). The SDR runs on a mobile workstation with Intel (R) Core (TM) i7-8750H CPU @2.20 GHz and 16.00 GB RAM.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Mode** & **Group by** \\ \hline
1 & ARAIM with two fixed constellations & GPS + Galileo \\
2 & ARAIM with four constellations & GPS + GLONASS + Galileo + BDS \\
3 & ARAIM with constellation dynamic selection & VDOP of constellation combination \\  & & VDOP of single constellation \\ \hline \hline \end{tabular}
\end{table}
Table 2: ARAIM modes and groups.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Mode** & **Group by** \\ \hline
1 & & GPS + Galileo & 89.01\% & 7.08\% \\
2 & & GPS + BDS & 89.08\% & 7.09\% \\
3 & & GPS + GLONASS + Galileo + BDS & 100\% & 100\% \\
4 & & VDOP of two constellation combination & 99.33\% & 9.69\% \\
5 & & dynamic selection & VDOP of single constellation & 7.78\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Worldwide availability and relative computational complexity of five groups.  
Regarding the availability, the worldwide availability of the first two groups, with two fixed constellations, can reach nearly 90% with the least complexity. The availability can be 100% after four GNSS constellation are involved. However, the computation complexity is 14 times than that of ARAIM with two fixed constellations. Focusing on the last two groups based on constellation dynamic selection, availability of both two groups using the proposed constellation dynamic selection is encouraging. The group using the two constellations with the minimum VDOP can cover 100% of the earth. The computational complexity is 7.78% of the time spent by the third group. Even compared with the first two group, the increased complexity is less than 10%. The fourth group, ARAIM using the combination of the minimum VDOP, can cover nearly 100%. However, the computational time is slightly longer than the fifth group as it need to calculate six combinations and the dimensions of matrix are also larger than those of the fifth group. In conclusion, the ARAIM using two constellations of minimum VDOP shows the best performance.
# A Programmable SRv6 Processor for SFC
## 4 Application and Validation
### Application Scenarios for Prototype System  
A programmable SRv6 processor can support a wide range of application scenarios, such as VXLAN, SRoU, INT, and SFC. The comparison and analysis of these four application scenarios is shown in Table 3.  
The VXLAN encapsulates data frames of the virtual network in packets transmitted in the actual physical network. The encapsulation of the VXLAN packet headers can be carried out through the encapsulate instruction in this architecture.  
The SRoU essentially inserts SRH into UDP payloads. The processing in this architecture is similar to that of SRv6 packets, and SRoU packets can be generated and processed by changing the insertion position of SRHs.  
Figure 5: Prototype system test environment.  
The INT is a framework for network data plane collection and reporting network status without the intervention of network control plane. As the telemetry packet passes through the switching device, the telemetry instruction tells the network device with network telemetry capability what network state information should be collected and written. The header information and telemetry information can be inserted by insert instructions in this architecture to realize the generation and processing of INT packets.  
The SFC directs network traffic through business points in a predetermined order required by business logic. The processing idea of SR forwarding technology can also be used in SFC. It is possible to add SFC headers for different network traffic by using the insert instruction. It is also possible to run the delete instruction to delete the SFC header from the packet and submit it to the host for network processing.
## 1 Introduction
### Disc Cutter Sizes and Applications  
Disc cutters are important tools for mechanized tunneling using tunnel-boring machines (TBMs). In general, the size of disc cutters increases with the diameter of the TBM's cutter head. Choosing the right disc size plays an important role in efficient rock removal and excavation. For TBMs with larger cutter head diameters of more than 5 m, disc cutters with diameters of 432 mm (17\({}^{\prime\prime}\)) to 483 mm (19\({}^{\prime\prime}\)) are generally used [8; 22; 23; 24]. These larger disc cutters are suitable for major tunneling projects, especially in hard rock with a high compressive strength, where high cutting forces are required for efficient rock breaking.  
Smaller disc cutters are used for microtunneling projects in which microtunnel-boring machines (MTBMs) are equipped with cutter head diameters of up to about 4 m. Disc cutters with diameters of 203.2 mm (8\({}^{\prime\prime}\)) to 355.6 mm (14\({}^{\prime\prime}\)) are usually used for such projects [25; 26]. These smaller disc cutters are suitable for minor tunneling projects, such as various utility tunnels using trenchless pipe-jacking technology in rock and soil. Regardless of the size of the disc cutter, its function is the same for all tunneling projects, namely breaking the surrounding rock on the tunnel face.  
The breaking of the rock is caused by a high concentration of stresses under the tip of the disc cutter. When the stress locally exceeds the strength of the rock, radial tensile cracks are formed, while rock fragments (or rock chips) are created when the cracks reach the free surface or when they interact with other cracks formed by adjacent cuts [7; 27].
## 4 Calibration and Application Experiments
### Comparison Measurement Experiment  
To verify the measurement accuracy of the proposed precision level, a comparison measurement experiment was designed. The set-up of the comparison experiment is shown in Figure 7a. The precision level was mounted on a linear stage, and the pitch error of the linear stage was simultaneously measured by the proposed precision level and the autocollimator. After the performance of one direction was tested, the proposed precision level was turned to 90\({}^{\circ}\) to compare the other direction. The pitch error of the tested linear stage was adjusted to be close to 100 arc-sec in order to compare the accuracy of the proposed precision level in a large measurement range. The comparison results are shown in Figure 7b. It can be seen that the peak-to-valley value of the residual error is less than 5% of the total pitch error. The experiment results proved that the accuracy of the proposed precision level is acceptable.
## 3 Results
### Setting of Buffer Input Parameters Using Authors' Own Methodology
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Experiment**} & \multicolumn{4}{c}{**Service Level (\%)**} & \multicolumn{4}{c}{**Average Inventory (pcs)**} & \multicolumn{4}{c}{**Total Inventory Cost (EUR)**} \\ \cline{2-10}  & **Min.** & **Average** & **Max.** & **Min.** & **Average** & **Max.** & **Min.** & **Average** & **Max.** \\ \hline Default buffer setting & 97.13 & 99.55 & 100.00 & 213.77 & 222.42 & 234.46 & 138,926.0 & 144,973.6 & 151,498.0 \\ \hline Buffer setting objectification & 98.51 & 99.42 & 100.00 & 197.83 & 201.52 & 209.43 & 142,076.0 & 144,009.6 & 146,684.0 \\ \hline Buffer setting optimisation & 99.75 & 99.94 & 100.00 & 193.78 & 202.60 & 210.31 & 138,932.0 & 142,690.4 & 146,156.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Comparison of the results of the simulation experiments. Figure 17: Comparison of output parameter values. carry out simulation experiments from the process of sizing the strategic stack, while guaranteeing optimal inventory management parameters. The benefits of the proposed methodology of sizing strategic storage in the DDMRP system are summarised in the following points:  
1. Objectification of settings of individual stack zones: Unlike the classical approach [1], the methodology excludes the subjective assignment of parameter values (lead time factor and variability factor) based on the definition of the buffer profile and expert judgement from the process of stack dimensioning. These are replaced by an objective determination of inventory parameters based on statistical analysis of consumption and supply data for a material item. 2. Comprehensive security stock assessment: The methodology uses the evaluation of the variability of all key parameters at input and output when sizing the insurance stock: variability of consumption, variability of the lead time, and variability of delivery quantities. The statistical evaluation of these three components forms the basis for the dimensioning of the insurance stock and the calculation of the red zone of the storage tank. 3. Setting optimal stack parameters: The methodology uses optimisation approaches known from inventory theory to optimise individual inventory parameters (optimum service level, optimum reorder level, and optimum order cycle) and applies them to the dimensioning of individual storage zones. 4. Simplicity of methodology: The methodology uses a simple mathematical and analytical-statistical apparatus that can be easily implemented into software solutions to support DDMRP. The presented methodology is used for the initial setting of buffer zones. From the point of view of the functioning of the DDMRP system in dynamic supply chains, it is necessary that the parameters of the buffer change dynamically and adapt to new conditions of consumption and delivery of individual material items [46]. The subject of further research by the authors will be the search for possibilities to extend and incorporate this methodology into the area of \"buffer adjustment\".
# Phase Space Insights: Wigner Functions for Qubits and Beyond
## 1 Introduction
This is possible because the Wigner function can be expressed as the expectation value of a specific observable: the displaced parity operator [58]. Measuring this value samples the Wigner function directly [59; 60], transforming an abstract concept into a measurable reality. In this work, we revisit the foundations of Wigner functions for quantum systems governed by SU(2) dynamical symmetry--a framework of particular relevance to spin-like systems [61; 62; 63], where the full Hilbert space is effectively constrained to symmetric subspaces. More generally, SU(2) symmetry, as realized through the Jordan-Schwinger construction [64; 65; 66] (which expresses the \(\mathfrak{su}(2)\) algebra in terms of two harmonic oscillator modes), provides a powerful and unifying approach to a wide range of two-mode quantum systems. This includes strongly correlated systems [67], polarization of quantum fields [68; 69; 70; 71; 72], and partially coherent classical Gaussian Schell-model beams [73; 74; 75], among others, and has applications in quantum computing [76], and provides insights into the spin-statistics connection [77; 78]. Within this context, we offer conceptual and methodological tools that may guide a broad range of experiments in modern quantum science and technology. This paper is organized as follows. In Section 2, we briefly review the essential ingredients needed to understand the phase space of the Wigner function for SU(2) dynamical symmetry. In Section 3, we apply this formalism to a menagerie of quantum states that have been proposed for quantum optimal sensing. The exceptional properties of these states are rendered with striking clarity through their Wigner functions. This formalism is fully applicable in scenarios where the number of excitations in the system is fixed; in other words, when working within a single Fock layer [79]. The case of an indefinite number of excitations is addressed in Section 4, where we introduce a generalized SU(2)-based phase-space framework capable of faithfully capturing the quantum correlations inherent in superpositions across multiple SU(2)-invariant subspaces. Section 5 is devoted to illustrate this approach with simple examples that offer insight into the rich and sometimes counter-intuitive structure of these correlations. Finally, our conclusions are summarized in Section 6.
## 2 Study Area, Dataset, and Methodology  
### Study Area  
The research area of this paper includes Aksu region and the scope of Alar City, which are referred to as Aksu. Aksu is situated in southern Xinjiang of China, between the Tianshan Mountains to the north and the Tarim Basin to the south, in the mid-southern part of Xinjiang. It is geographically located between 78\({}^{\circ}\)03\({}^{\prime}\) E and 84\({}^{\circ}\)07\({}^{\prime}\) E and 39\({}^{\circ}\)30\({}^{\prime}\) N and 42\({}^{\circ}\)41\({}^{\prime}\) N, as shown in Figure 1a. The area is bounded by the Ili Kazakh Autonomous Prefecture of Xinjiang, China, and to the north and borders Hotan, Kashgar, and Kezhou to the south of Xinjiang, China. Covering approximately 132,500 km\({}^{2}\), the terrain includes mountains (29.4%), plains (39.8%), and deserts (32.58%). Major rivers in Aksu include the Tarim River, the Aksu River, and the Dolang River. The region is characterized by abundant solar energy and heat, with an average annual temperature of 11.6 \({}^{\circ}\)C and annual precipitation of about 112 mm (Figure 1b,c). The primary oases are the Aksu Oasis and the Weiku Oasis.
## 2 Materials and Methods
### The Sampling Grid  
On the basis of previous studies on the distribution of radionuclides in the fluvial and marine-coastal area under examination [9; 24], a fluvial sampling grid was created, upstream and downstream of the NPP, and marine-coastal from Massico (about 12 km south of the mouth of the Garigliano) upstream of the promontory of Gaeta, north-west of the mouth itself. In total, 9 sampling points were chosen on the coastline, equally spaced about 2.5 km apart; a sediment sample (SC) and a water sample (AC) were collected from each point. The base point (T0) of this line of points was set on the north side of the mouth of the Garigliano (Figure 1).  
The marine grid was chosen by identifying six transects (Figure 1), originating from six of the coastal points mentioned above (T0, T1, T2, T5, T6, and T7), and fanning out towards the open sea to better cover the gulf in front of the mouth. For each transect, 7 points with fixed bathymetry of 5, 10, 15, 20, 40, 70, and 100 m have been identified. Surface water (AS), depth water (AP), immediately above the sea floor, and sediment (SM), taken directly from the sea floor, were sampled at each of these points.  
Finally, eight sampling points were identified along the Garigliano River: two upstream of the power plant, representing an undisturbed reference area, and six downstream, along the river course. The points were chosen considering the sediment accumulation areas, so they were identified near the banks of the meanders where sediments accumulate. Near the mouth, there are two points that complete, with T0, the transect transverse to the outflow of the river, where the current slows down and helps sedimentation. One sediment sample and one water sample were collected at each point.  
The study area with the location of all sampling points in the river and the sea is shown in Figure 1.  
Figure 2 shows the bathymetric profile of a typical transect in the area under study (T0). After a slight descent in the first 5-6 km, there is a steeper slope. A similar behavior can be seen in the other transects.  
Figure 1: Map with the location of the sampling points. In blue are the sediment and coastal water sampling points; in orange: the points for deep and superficial marine waters and marine sediments; in dark red: the points of fluvial waters and sediments. The GNPP is indicated in green; its distance from the sea is 7 km. The bathymetric lines at 5, 10, 15, 20, 40, 70, and 100 m are also shown.  
Figure 2: Bathymetric profile of the transect T0.
# Sphere Fitting with Applications to Machine Tracking
## 2 Methods
### Algorithms
#### 2.3.3 Overview of Algorithm 2  
The input for Algorithm 2 is a set \(P\) of \(n\) points in \(\mathbb{R}^{d}\), a weight function \(u:P\to[0,\infty)\), and an error parameter \(\varepsilon\in(0,1]\). The output of the algorithm is an \(\varepsilon\)-coreset for median-sphere. In Line 3, we compute (iteratively) a coreset \(Q\) for thinnest-sphere of \(P\), see Algorithm 3. In Line 5, we assign a sensitivity \(s(p)\) for every point \(p\) in \(Q\). The sensitivity of each point depends on the iteration number in which it was selected. In Line 7, we update the set \(P\) by removing the coreset \(Q\) from \(P\). In Lines 8-11, we sample points to obtain coreset.  
```
Input: A set \(P=\{p_{1},p_{2},\ldots,p_{n}\}\subseteq\mathbb{R}^{d}\) of points,  a weight function \(u:P\to[0,\infty)\), and  a constant \(m\geq 0\) that can be determined from  Theorem 1. Output: A pair \((C,w)\) which is an \(\varepsilon\)-coreset of \(P\) for the median-sphere, see Definition 2.
1 Set \(i:=1\); \(C:=\emptyset\) // Initialization. while\(P\
eq\emptyset\)do // Computes sensitivity for each point in \(P\).  Set \(Q:=\)ThinnestSPHERECOREST(\(P\)) // Compute thinnest-sphere for \(P\), see Algorithm 3. forevery\(p\in Q\)do // Compute sensitivity for each point in \(Q\) with respect to the  iteration number \(i\).  Set \(s(p):=\frac{u(p)}{i}\)  Set \(i:=i+1\) // Update iteration number \(i\).  Set \(P:=P\setminus Q\) // Remove the surface of the thinnest-sphere from \(P\). while\(|C|<m\)do  Randomly sample a point \(p\) from \(P\) into the coreset (for a total of \(m=\frac{d^{2}\log_{2}^{2}(n)\log(1/\delta)}{\varepsilon^{2}}\) points), where the probability of sampling \(p\in P\) is \(\Pr(p):=\frac{s(p)}{\sum_{q\in P}s(q)}\)  Set \(C:=C\cup\{p\}\)  Set \(w(p):=\frac{u(p)}{\Pr(p)}\) Return\((C,w)\)
```  
**Algorithm 2**MedianSphereCoreset(\(P,u,m\))
## 2 Materials and Methods
### Lumbosacral Angle (LSA) Measurements  
Prior to data collection, four adhesive reflective markers were attached to participants' specific joints (i.e., acromial shelf, greater trochanter, lateral epicondyle and lateral malleolus) and two stick  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **Mean** & **Standard Deviation** & **Range** \\ \hline Age (years) & 20.0 & 0.4 & 19.0–21.0 \\ Height (cm) & 172.2 & 3.9 & 166.0–179.0 \\ Weight (kg) & 63.5 & 4.5 & 55.0–73.0 \\ Acromial height (cm) & 139.5 & 3.7 & 134.0–146.5 \\ Knuckle height (cm) & 71.7 & 3.0 & 66.0–78.0 \\ Hip height (cm) & 88.9 & 2.7 & 84.0–93.8 \\ Knee height (cm) & 44.0 & 2.1 & 40.5–47.5 \\ Toe-touch test, TTT (cm) & 0.1 & 11.4 & \(-\)26.0–30.0 \\ Sit-reach test, SRT (cm) & 0.9 & 9.9 & \(-\)24.0–21.6 \\ Modified Schober’s test, MST (cm) & 6.8 & 1.1 & 4.5–9.2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Anthropometric data and the flexibility values of participants in the study.  
Figure 1: The three flexibility measurements employed in this study: (**a**) toe-touch test; (**b**) sit-and-reach test; (**c**) modified Schober’s test.  
markers we applied to specific skin areas (i.e., first lumbar (L1) and first sacral spinous processes (S1); Figure 2). In this study, lumbosacral angle (LSA) was measured when participants stood upright and flexed their trunk to 90\({}^{\circ}\) in increments of 15\({}^{\circ}\); the trunk angle was formed by the line linking the acromial shelf and the hip (points S and H, respectively; Figure 2) to the vertical. Each participant's external LSA (formed by stick markers S1 and L1) at a specific trunk position was subsequently used to calculate the internal LSA according to the prediction equations developed by [PERSON] and [PERSON] [29]. The equations are as follows:  
\[\text{IL}_{1}=0.9882\times\text{EL}_{1}+3.6274,\qquad R^{2}=0.968\]  
\[\text{IS}_{1}=0.7339\times\text{ES}_{1}+29.6776,\qquad R^{2}=0.916\]  
where EL1 and ES1 indicate the respective angles of the external stick markers L1 and S1, respectively. IL1 and IS1 indicate the internal angles. The LSA can be obtained by calculating the angle between IL1 and IS1 [29].  
A motion analysis system (Qualisys MacReflex, Goteborg, Sweden) was used and positioned approximately 5 m to the participant's dominant side and perpendicular to the participant's sagittal plane to record the 2D marker positions during the test. To ensure that the trunk flexion angle of each participant was in the desired position, the participants were requested to adjust until their trunk line (i.e., line SH, Figure 2) matched with a preset line in the feedback monitor [3].