esa-sceva/satcom-chunk-collection huggingface dataset:
# Derivation of New Staggered Compact Schemes with Application to Navier-Stokes Equations
## 4 Application to Incompressible Navier-Stokes Equations  
The motion of an incompressible fluid is governed by the Navier-Stokes equations,  
\[\frac{\partial u_{i}}{\partial t} =-u_{j}\frac{\partial u_{i}}{\partial x_{j}}-\frac{\partial P}{ \partial x_{i}}+\frac{1}{\mathrm{Re}}\frac{\partial^{2}u_{i}}{\partial x_{j} \partial x_{j}}+u_{i}, \tag{35}\] \[\frac{\partial u_{j}}{\partial x_{j}} =0, \tag{36}\]  
where \(P\) is the pressure, \(\mathrm{Re}\) is the Reynolds number, \(u_{i}\) are the nondimensional cartesian components of the velocity field, and \(u_{i}\) the components of any given velocity source/sink field. Discretization of Equations (35) and (36) follows here a standard semi-discrete approach [26; 27; 28], in which the momentum equation is discretized in space and then advanced in time without taking the pressure term into account; subsequently, a Poisson equation is solved for the pressure; finally the divergence-free velocity at the following time level is obtained by correcting with the gradient of pressure.  
In Equation (35) the nonlinear convective term is expressed in the so-called _advective_ form. By employing the continuity Equation (36), it can be equivalently expressed in _divergence_ form (i.e., as the divergence of the dyadic tensor \(u_{i}u_{j}\)), or in _skew-symmetric_ form, in which the arithmetic mean of divergence and advective forms is considered. This distinction has little importance on the continuous level, once all the analytical manipulations of standard calculus are assumed to be valid. However, the direct discretization of each form behave usually differently, since the standard rules of calculus (even the simplest ones, as the product rule) are in general not guaranteed to be valid for discrete operators.  
The choice of the form in which the convective term is discretized is usually dictated by the behaviour of the discrete set of equations with respect to induced balance equations. The preservation of some global quadratic invariants, such as, for instance, kinetic energy integrated over the whole domain (in the inviscid limit and for periodic or homogeneous flux boundary conditions), is an important target for stable and reliable simulations at high Reynolds numbers [29]. Different strategies have been developed in order to fulfill this requirement, some of which are briefly recalled in the following section. A more in-depth discussion on this and related topics can be found in [30].
# Closed-Form Expressions of Upper Bound for Polarization-MDCSK System
## 2 System Model of P-MDCSK
In the polarization modulation part, considering the characteristics of differential modulation and polarization modulation, the maximum energy comparator is represented, where the \(t\)-th polarization state on the sphere is estimated by the following method:  
\[\hat{t}=\operatorname*{arg\,max}_{t\in(t,\varepsilon)}(|ES_{h}|,|ES_{v}|), \tag{4}\]  
where \(ES_{h}\) and \(ES_{v}\) are expressed as  
\[ \begin{split} ES_{h}&=\mathbf{r}_{\mathbf{h}_{ \text{ref}}}\mathbf{r}_{\mathbf{h}_{\text{inf}}}^{\mathbf{T}}+j\cdot\mathrm{H} (\mathbf{r}_{\mathbf{h}_{\text{ref}}})\mathbf{r}_{\mathbf{h}_{\text{inf}}}^{ \mathbf{T}},\\ ES_{v}&=\mathbf{r}_{\mathbf{v}_{\text{ref}}}\mathbf{ r}_{\mathbf{v}_{\text{inf}}}^{\mathbf{T}}+j\cdot\mathrm{H}(\mathbf{r}_{\mathbf{v}_{ \text{ref}}})\mathbf{r}_{\mathbf{v}_{\text{inf}}}^{\mathbf{T}},\end{split}  \tag{5}\]  
where \(|\cdot|\) denotes the absolute value, and \(\mathrm{H}(\cdot)\) is Hilbert transform operator. After \(\hat{t}\) is determined, for the MDCSK part, the decision variables \(z_{a}\) and \(z_{b}\) are obtained as  
\[ \begin{split} z_{a}&=\mathbf{r}_{\mathbf{t}_{\text{ ref}}}\mathbf{r}_{\mathbf{i}_{\text{inf}}}^{\mathbf{T}},\\ z_{b}&=\mathrm{H}(\mathbf{r}_{\mathbf{t}_{\text{ ref}}})\mathbf{r}_{\mathbf{i}_{\text{inf}}}^{\mathbf{T}},\end{split}  \tag{6}\]  
where \(\hat{t}\) is determined from \(h\) and \(v\), \(\mathbf{r}_{\mathbf{i}_{\text{ref}}}\) is either \(\mathbf{r}_{\mathbf{h}_{\text{ref}}}\) or \(\mathbf{r}_{\mathbf{v}_{\text{ref}}}\), and \(\mathbf{r}_{\mathbf{i}_{\text{inf}}}\) is either \(\mathbf{r}_{\mathbf{h}_{\text{inf}}}\) or \(\mathbf{r}_{\mathbf{v}_{\text{inf}}}\), depending on \(\mathbf{\hat{t}}\). Then, the phase of MDCSK is decided by \(z_{a}\) and \(z_{b}\). The corresponding phase \(\arccot(z_{a}/z_{b})\) and the decision boundaries are used for recovering the corresponding phase parts of information bits. It is important to remark that the MDCSK estimation depends on the estimation of \(\hat{t}\). Note that the use of MDCSK does not affect the Stokes parameter. The P-MDCSK detection algorithm is shown in Algorithm 1. The first step of the algorithm is polarization demodulation. After estimating the polarization state, \(\mathbf{r}_{\mathbf{t}_{\text{ref}}}\) is selected from \(\mathbf{r}_{\mathbf{h}_{\text{ref}}}\) and \(\mathbf{r}_{\mathbf{v}_{\text{ref}}}\) and \(\mathbf{r}_{\mathbf{i}_{\text{int}}}\) is selected from \(\mathbf{r}_{\mathbf{h}_{\text{inf}}}\) and \(\mathbf{r}_{\mathbf{v}_{\text{inf}}}\). Then the corresponding phase \(\arccot(z_{a}/z_{b})\) is estimated by MDCSK demodulation.
## 4 Application to Quantum Computing Devices: Mach-Zehnder Interferometer
### Numerical Results  
To prove the discussions in the previous sections numerically we implemented the Mach-Zehnder like behaviour in the simulations. We were able to attain the Aharonov-Bohm oscillations where the maximum and the minimum value of the current obtained in one of the drains of the MZI oscillates with the change in the magnetic field (see Figure 5a). These oscillations are a signature of the correct working of our simulations. As expected, we observe that the instantaneous current \(I_{T}(t)\) computed in the quantum device with a large number of electrons is much less noisy than the ones with fewer electrons, as plotted in Figure 5b. The noise in the current value due to fewer electrons results in very high fluctuations in the instantaneous value (black line in Figure 5b) which forces the experimenter to record the values in several experiments to finally get an ensemble value which is non-fluctuating. However, with the successful application of our protocol the fluctuation of the instantaneous value of the current almost disappears (cyan line in Figure 5b) as a result one needs to make just one measurement to get the correct value of the current. The final step of this protocol is determining the value of \(N\) which as discussed above can be given by \(N=T/\tau_{in}\).
## 3 Multi-Ship Collision Avoidance Decision Making Based on Full Communication
### Blockchain-Based Decision-Making Algorithm for Ship Collision Avoidance  
This section introduces the algorithm that employs blockchain technology to enhance ship collision avoidance decision-making. As depicted in Figure 8, the process involves four key steps. The algorithm is grounded in blockchain principles. Each vessel possesses a unique cryptographic identity, ensuring data integrity and authenticity.  
Step 1: Detection of Potential Collision.  
Vessel sensors and radar systems continuously monitor the surroundings, identifying potential collision scenarios based on proximity, relative speed, and trajectory data.  
Step 2: Secure Information Sharing via Blockchain.  
Relevant collision data (vessel IDs, positions, speeds, and intended courses) are encrypted and broadcasted through the blockchain network.  
Step 3: Consensus Mechanism.  
Smart contracts validate collision data, ensuring their accuracy and reliability.  
Step 4: Autonomous Collision Avoidance Strategy Generation.  
Vessels autonomously generate collision avoidance strategies based on verified data, considering safe passing distances and maneuvering capabilities.  
It should be noted that the collision avoidance process with blockchain-based decision-making closely resembles the conventional approach, with the addition of blockchain mechanisms in the communication phase. This integration significantly enhances the trustworthiness and security of communication channels. To facilitate more intuitive and effective communication, this paper introduces the concept of propagating collision avoidance path points. These serve as clear indicators of vessels' intended courses, reducing the risk of misinterpretation.  
Figure 7: The message structure of collision avoidance broadcast (CAB) block.
## 4 Results and Discussion
### Evaluation of the ANN-Based LP Model  
#### 4.3.1 Comparison with the Pseudo-Static Test  
The boundary conditions of the RC column during pseudo-static tests are generally close to its real situation. Therefore, it is reasonable to validate the ANN-based bi-linear and tri-linear LP model through a quasi-stable test on a frame. This test was conducted by [42], and the simulation is carried out using the Open System for Earthquake Engineering Simulation (OpenSEES, [28]) platform, as shown in Figure 13a. Each column was simulated by one elastic element and two zero-length elements at the two ends, as shown in Table 5. As illustrated in Figure 13b, the ANN-based LP model can provide an acceptable prediction result, especially for the envelope curve. It also shows that the ANN-based tri-linear model performs better than the bi-linear one during the whole hysteresis curve prediction process, especially after the capping point.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **Parameters** \\ \hline ANN model & \(F_{\max}=27.50\) kN, \(\delta_{u}=4.53\%\), \(\delta_{c}=1.85\%\), \(\delta_{y}=1.17\%\) \\ \hline Bi-linear model & \(K_{e}=1119\) kN-m/rad, \(M_{y}=13.09\) kN-m, \(b=0.061\) \\ \hline Tri-linear model & \(K_{e}=1119\) kN-m/rad, \(M_{y}=13.09\) kN-m, \(\beta_{l}=0.18\), \(\beta_{c}=-0.128\), \(M_{c}/M_{y}=1.17\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: ANN-based method for the LP model of the RC column sample [42].  
Figure 12: Comparison results of the yield drift between the experimental, ANN model and Fardis’ method [40].
## 3 Methodology
### Performance Assessment  
Performance of the proposed algorithm is evaluated on a testing dataset containing 800 nuclei. Six measures namely sensitivity, specificity, precision, F1 score, accuracy, and geometric mean (G-mean) are considered as performance metrics [37,38]. These measures are computed using Equations (10) through (15). It is worth noting that sensitivity is also referred as recall.  
\[Sensitivity=\frac{TruePositive}{TruePositive+FalseNegative}\times 100\% \tag{10}\]  
\[Specificity=\frac{TrueNegative}{TrueNegative+FalsePositive}\times\,100\% \tag{11}\]  
\[Precision=\frac{TruePositive}{TruePositive+FalsePositive}\times\,100\% \tag{12}\]  
\[Accuracy=\frac{TruePositive+TrueNegative}{TruePositive+FalsePositive+TrueNegative+FalseNegative}\times\,100\% \tag{13}\]  
\[F1\ Score=\left(2\times\frac{Precision\times Sensitivity}{Precision+ Sensitivity}\right)\times\,100\% \tag{14}\]  
\[G\ Mean=\left(\sqrt{Sensitivity\,\times Specificity}\right)\times\,100\% \tag{15}\]  
* _TruePositive_ denotes the number of overlapping nuclei correctly detected as overlapping nuclei.
* _TrueNegative_ represents the number of single nuclei correctly classified as a single nucleus.
* _FalsePositive_ is the number of single nuclei wrongly classified as overlapping nuclei
* _FalseNegative_ is the number of overlapping nuclei missed by our method.  
Moreover, the proposed method is also evaluated graphically using a receiver operating characteristics (ROC) curve and area under ROC (AUROC) [39]. The ROC curve is plotted as sensitivity against (1-specificity).  
Figure 12: Data utilization in constructing a RF classifier.  
\begin{table}
\begin{tabular}{l} \hline \hline
**Double-Strategy RF Algorithm Steps** \\ \hline
1. Prepare training and testing datasets (80–20\% ratio) \\
2. Train an RF classifier using all features on the training dataset. \\
3. Select the most important features. \\
4. Create a new ‘selected featured’ dataset containing only those features. \\
5. Train a second classifier on this new dataset. \\
6. Test the new data using the trained RF classifier. \\
7. Compare the accuracy of the ‘full featured’ classifier to the accuracy of the ‘selected featured’ classifier. \\ \hline \hline \end{tabular}
\end{table}
Table 3: Processing steps of double-strategy RF algorithm used in the study.
# Extracting Sentence Embeddings from Pretrained Transformer Models
## 5 Conclusions
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Model** & **T0** & **T4** & **BERT** & **BERT + Avg.** & **Avg.** & **B2S** & **B2S-100** & **RE** \\ \cline{2-9}
**Layer** & \multicolumn{3}{c}{**Last**} & \multicolumn{3}{c}{**First + Last**} & \multicolumn{3}{c}{**-**} \\ \hline avg. & 62.6 & 64.7 & 64.3 & 63.4 & 56.6 & 61.4 & 66.2 & 48.8 \\ + normalize & 62.6 & 64.7 & 64.3 & 63.4 & 56.6 & 61.4 & 66.2 & 48.8 \\ + quantile-u & 68.4 & 70.9 & 68.3 & 69.0 & 65.5 & 60.4 & 68.9 & 54.8 \\ + quantile-u & 64.0 & 66.5 & 65.7 & 66.8 & 64.0 & 59.2 & 67.2 & 53.3 \\ + whiten & 76.0 & 76.6 & 77.6 & 78.3 & 78.0 & 76.4 & 76.1 & **75.1** \\ + whiten & 62.2 & 66.5 & 64.8 & 65.8 & 66.2 & 60.6 & 60.8 & 63.7 \\ + zscore & 70.7 & 72.5 & 70.4 & 70.7 & 67.1 & 62.8 & 68.9 & 55.9 \\ \hline \hline \(\text{id}^{W}_{t}\) & 75.4 & 74.7 & 77.2 & 79.1 & 77.8 & **77.5** & 77.3 & 72.5 \\ + normalize & 75.4 & 74.7 & 77.2 & 79.1 & 77.8 & 77.5 & 77.3 & 72.5 \\ + quantile-u & 76.7 & 76.0 & 77.7 & 79.3 & 78.7 & 77.1 & 76.3 & 73.4 \\ + quantile-u & 75.6 & 74.7 & 77.1 & 79.3 & 79.1 & 77.2 & 76.7 & 74.2 \\ + whiten & 76.8 & 76.0 & **78.3** & 78.6 & 77.6 & 77.1 & 76.7 & 74.6 \\ + whiten & 68.1 & 68.1 & 74.1 & 75.2 & 75.4 & 73.1 & 73.9 & 72.7 \\ + zscore & 76.7 & 76.4 & 78.2 & **79.7** & **79.3** & 77.5 & **78.0** & 73.0 \\ \hline \hline \(\text{id}^{T}_{t}\) & 70.8 & 73.7 & 74.8 & 76.5 & 76.0 & 61.4 & 66.2 & 68.3 \\ + normalize & 70.8 & 73.7 & 74.8 & 76.5 & 76.0 & 61.4 & 66.2 & 68.3 \\ + quantile-u & 74.7 & 77.0 & 76.0 & 77.2 & 76.7 & 60.4 & 68.9 & 71.9 \\ + quantile-u & 72.0 & 74.6 & 74.8 & 76.4 & 76.0 & 59.2 & 67.2 & 71.5 \\ + whiten & **77.1** & **78.0** & 78.1 & 78.3 & 77.3 & 76.4 & 76.1 & 74.0 \\ + whiten & 67.2 & 71.0 & 70.3 & 70.4 & 70.1 & 60.6 & 60.8 & 68.1 \\ + zscore & 75.9 & 77.7 & 76.2 & 76.9 & 75.8 & 62.8 & 68.9 & 69.8 \\ \hline \hline -biases & 66.5 & 68.7 & 68.4 & 69.9 & 68.1 & 56.3 & 60.5 & 61.3 \\ + normalize & 66.5 & 68.7 & 68.4 & 69.9 & 68.1 & 56.3 & 60.5 & 61.3 \\ + quantile-u & 70.9 & 73.5 & 70.8 & 71.9 & 70.3 & 55.0 & 63.2 & 66.2 \\ + quantile-u & 67.4 & 70.3 & 68.6 & 69.9 & 68.2 & 53.9 & 61.3 & 64.4 \\ + whiten & 63.1 & 67.1 & 65.2 & 65.7 & 65.9 & 56.6 & 56.7 & 63.0 \\ + whiten & 76.2 & 76.8 & 77.9 & 78.5 & 78.1 & 73.3 & 73.1 & 74.7 \\ + zscore & 73.0 & 74.9 & 72.5 & 72.9 & 70.6 & 58.5 & 64.0 & 64.6 \\ \hline \hline \(\text{[MASK]}\) & 63.4 & 76.2 & & & & & & \\ + normalize & 63.4 & 76.2 & & & & & & \\ + quantile-u & 68.1 & 77.3 & & & & & & \\ + quantile-u & 65.2 & 76.0 & & & & & & \\ + whiten & 73.1 & 77.6 & & & & & & \\ + whiten & 61.7 & 70.9 & & & & & & \\ + szscore & 69.4 & 76.9 & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Spearman correlation dependence on token aggregation and post-processing techniques for semantic textual similarity STS13 task. The best result for each model is bolded, while underlined result is the best across all the models.
## 3 Materials and Methods
### Sensors Deployment
#### 3.2.2 On-Site Installation Process  
Successful sensor installation for extended monitoring must fulfill four critical criteria:  
* Operational viability of sensors.
* Effective strain transfer mechanisms.
* Accessible transmission line routing.
* Seamless system integration.  
As depicted in Figure 4, the sensor deployment process was specifically adapted to the experimental road conditions. To ensure measurement accuracy, survival rate, and long-term durability, field implementation followed the following key steps:  
1. [label=(0)]
2. Pavement Preparation  
Firstly, a 5 m \(\times\) 2 m rectangular area was milled at sensor installation locations to expose the base layer. Then, an adjacent transverse milling zone spanning at least 0.4 m in width was created perpendicular to the traffic direction within the fourth lane, specifically designed to enable organized cable convergence and routing. Notably, a deliberate buffer distance was maintained between the sensor installation zones and nearby construction joints, thereby ensuring structural discontinuities remained isolated from critical measurement areas.
3. Sensor Positioning and Installation  
The installation process commenced with the precise marking of pre-embedded sensor locations using measuring tapes and spray paint, followed by trench excavation and the removal of oversized aggregates. Subsequently, total stations and straightedges were employed to achieve millimeter-level positioning accuracy, after which cold asphalt patching material was applied to level the trench base, manually compacted with iron hammers. Upon sensor placement, miniature spirit levels and bullseye levels were utilized to align earth pressure sensors and vertical strain sensors, respectively, ensuring pure vertical force transmission without parasitic horizontal components during loading.
4. Cables Management  
Sensor cables were systematically organized and securely bundled to prevent accidental tension-induced damage, while exit points were reinforced with corrugated protective sleeves to mitigate mechanical abrasion risks.
5. Backfilling and Compaction  
Following sensor installation, trenches were backfilled with cold asphalt patching material and subjected to initial manual compaction. Upper structural layers were subsequently paved and rolled across the full pavement section, with vibratory compaction strictly prohibited near sensor arrays to prevent damage or positional displacement.
6. Documentation and Protection  
Finally, the precise locations and identification numbers of the sensors were recorded. The cables were protected and routed into junction boxes, with warning signs installed nearby. Simultaneously, waterproof and anti-corrosion treatments were applied to the sensor cables, and excess cables were properly managed for future connection to the main fiber optic trunk.
## 6 Discussion
### Limitation 1: Limited Pilot Study  
Due to the unprecedented pandemic situation, in-person and lab-based typical human-subjects experiments were out of option until now. Thus, we collected our data through the online video-based survey for this study. One might raise the question of the validity of the online video-based data collection for user studies conducted in this paper. In addition, compared to the existing researches that collected data via online surveys, the number of participants in our survey seemed a bit small ([PERSON] et al., 2016; [PERSON] et al., 2017; [PERSON] et al., 2018).  
Thus, we plan to extend our present study to a face-to-face experiment, where participants actually experience the AR contents in person instead of observing pre-recorded video clips. We will compare the results of the online-based survey presented in this paper with the data collected through the face-to-face experiment to confirm the validity of the video-based survey and/or to see how user's perception differs. This further allows us to objectively measure the engagement levels of participants during the AR experience by, for example, collecting (1) usage time, (2) number of interactions (voice or touch), (3) number of errors, and (4) task load, etc.
## 3 Methodology
### Detection of Water Bodies  
RS is a very efficient tool for monitoring spatio-temporal variations of the extent of surface water at a large scale [32; 33]. Accordingly, optical sensors such as the Moderate Resolution Imaging Spectroradiometer (MODIS), Landsat, HuanJing satellite constellation-1 (HJ-1), GaoFen-1 (GF-1), Synthetic Aperture Radar (SAR), Phased Array type L-band SAR (PALSAR), and Sentinel-1A have been used for water body change detection [34; 35; 36; 37]. Compared to images produced by other satellites, Landsat images have proven to be more  
Figure 2: Average monthly variation of rainfall, temperature, and streamflow in the Maharlou Lake watershed from 1987 to 2016.  
efficient for distinguishing water pixels from non-water pixels, primarily due to their long history of data acquisition and their resolution [38; 39]. So, Landsat imagery has been used in this research. It should be noted that the images from the said dataset were free of clouds, and as such, no additional image pre-processing was required.  
Water bodies absorb in the near-infrared (NIR) and shortwave-infrared (SWIR) and reflect in the green and blue portions of the visible spectrum, so water and vegetation-covered surfaces can be distinguished from each other. Accordingly, various indices based on these main spectra for water-body extraction from imagery have been proposed. These indices include the normalized difference water index (NDWI) [40], the modified normalized difference water index (MNDWI) [41], the high-resolution water index [42], and the automatic water extraction index [43]. The MNDWI segregates and detects water bodies and can be mathematically expressed as follows [44]:  
\[\text{MNDWI}=(\Gamma-M)/(\Gamma+M) \tag{1}\]  
where \(\Gamma\) is the green band and \(M\) is the middle infrared band. To minimize the effects of vegetation on water-body mapping, vegetation indices can be applied. Pixels with water signals greater than vegetation signals would be classified as water, while the rest would be classified as non-water.
# Formal Modeling and Improvement in the Random Path Routing Network Scheme Using Colored Petri Nets
## 4 Experimental Results
### Verification and Validation
#### 4.1.4 Fairness Property  
This type of property tells us whether there exists infiniteness in the model or not. In our proposal, there is exists no infiniteness. In short, there is no loop in the whole model.  
In Figure 5, the state graph shows the state-space graph of the model. In the state-space graph, all the nodes are linked, which means that all the nodes are traversed. This graph shows the authenticity and validation of our proposed model. CRPR has shown the best results in token passing, and it traversed all the nodes present in the network. It calculated all the distances from source note to sink node, irrespective of their location, and then traversed the token along any of the top three shortest paths.