esa-sceva/satcom-chunk-collection huggingface dataset:
# Signal Consensus in TSP of the Same Grid in Road Network
## 3 Consensus Algorithm with Input Constraints  
### Description of Consensus Algorithm with Input Constrains  
We proposed a consensus algorithm with input constraints in this paper, it is described as follows:  
\[\begin{array}{l}\dot{x}_{i}(t)=u_{i}(t),\\ u_{i}(t)=\sum\limits_{j\in N_{i}}a_{ij}\mathrm{arctan}(x_{j}(t)-x_{i}(t)).\end{array} \tag{4}\]  
Obviously, \(act\tan(x)\) is a bounded function, and \(a_{ij}\) is bounded, so \(u_{i}(t)\) is bounded. Consensus Algorithm (4) can realize input constraints in the process of information interaction.  
**Lemma 3**.: _The Laplacian matrix \(D\) has at least one zero eigenvalue. The other non-zero eigenvalues are in the left half of the complex plane. In particular, when the graph \(G\) has a directed spanning tree, the Laplacian matrix \(D\) has only one eigenvalue, which is zero [29]._  
**Lemma 4**: _If the Laplacian matrix \(\mathbf{D}\) has only one zero eigenvalue, when \(t\rightarrow\infty\)\(e^{t\mathbf{L}}\rightarrow\mathbf{1}_{n}\omega^{T}\), where \(\omega=[\omega_{1},\ldots,\omega_{n}]\) and \(\sum\limits_{i=1}^{n}\omega_{i}=1\)[29]._  
**Theorem 2**: _Consensus Algorithm (4) can gradually form consensus, if and only if the corresponding graph \(G\) has a directed spanning tree._  
**Proof.** Sufficiency: When the graph G has a directed spanning tree, from Lemma 3, the Laplacian matrix D has only one eigenvalue, which is zero. From Lemma 4, when \(t\rightarrow\infty\), \(x(t)=\mathbf{1}_{n}\omega^{T}x(0)\), we have \(x_{i}(t)-x_{j}(t)=0,i,j\in\{1,\ldots,n\}\), consensus Algorithm (4) can gradually form consensus.  
Necessity: Suppose consensus Algorithm (4) can gradually form consensus and graph G has no directed spanning tree, then there is no information interaction between at least two agents in this system, they cannot reach consensus, it is the opposite of the hypothesis. Proof finished.
## 2 General Structure of the Methodology
### Multi-Source Data Input Module
#### 2.2.3 Optimized Application of Mixed-Precision Training Strategies  
To further enhance the computational efficiency of the model, this study employs a mixed-precision training strategy, integrating half-precision floating-point (FP16) and single-precision floating-point (FP32) arithmetic. This approach aims to accelerate computation while reducing memory consumption. During training, model weights are initialized using FP32 precision. In the forward propagation phase, most tensor computations are performed with FP16 precision, whereas loss calculations are retained in FP32 to ensure numerical accuracy and gradient stability. To mitigate potential gradient underflow issues associated with FP16 precision, a loss scaling mechanism is introduced. Prior to gradient computation, the loss value is scaled by a fixed scaling factor (Loss Scale) to preserve numerical precision. During backpropagation, the majority of gradient computations are conducted in FP16 precision, facilitating faster training and lower memory overhead. Subsequently, at the end of backpropagation, the computed gradients are rescaled by the Loss Scale factor to restore their original range. Finally, weight updates are applied in FP32 precision using the optimizer. In cases where gradient overflow is detected, the corresponding weight update step is skipped to maintain training stability. The implementation process is illustrated in Figure 5.
# Fatigue Crack Calculation of Steel Structure Based on the Improved McEvily Model
## 3 The Verification of Engineering Feasibility
### Calculation of Fatigue Crack Growth
The crack depth increment predicted by the improved McEvily model is not much different from that predicted by the Paris model in the initial stage. With the growth of time, the gap between the crack growth predicted by the two models gradually widens. The final crack depth increment predicted by the improved McEvily model is \(32.4\%\) larger than that predicted by the Paris model, and the prediction result is more conservative. The study analyzed the small vehicle load without considering the negative factors such as heavy or super heavy vehicle load and corrosion, so the predicted crack depth developed slowly.
# Estimation of Optimal Speed Limits for Urban Roads Using Traffic Information Big Data
## 3 Data Collection and Model Equation Development  
### Research Methodology  
#### Basic Concept and Procedure  
This study was based on \"the speed zoning method\" [28]. The function was modified by adding roadside conditions based on the 85 th percentile speed as follows:  
\[\text{RSL}=\text{MSSL}\times\text{f}_{1}\times\text{f}_{2}\times\text{f}_{3} \times,\ldots\times,\text{f}_{i}, \tag{1}\]  
where RSL is recommended speed limit (km/h); MSSL is maximum statutory speed limit (80 km/h); and f\({}_{i}\) is factor for adjusting the effects of roadside conditions (based on the calculation of the adjustment factor).  
To establish the relationships between the 85 th percentile speed and various variables in a \"safe section\", road sections were selected according to the following criteria:  
1. The sections must have a low accident rate;
2. The sections must have a low standard deviation with respect to traffic flow.  
Figure 4: Real-time driving information collection using cell phone data transmission.  
Figure 5: Big data integration and parameter setting.  
The process for the development of the speed limit estimation model equation is illustrated in Figure 6.
## 2 Mathematical Modeling
### Set of Constraints  
The constraints for the problem regarding the optimal location and size of D-STATCOMs in distribution networks are given by their maximum number and size, the voltage limits,and the active and reactive power balance. This set is presented below. It is important to mention that Equations (4)-(7) are defined for \(\forall k\in\mathcal{N}\) and \(\forall h\in\mathcal{H}\):  
\[P_{kh}^{g}-P_{kh}^{d}=\sum_{h\in\mathcal{H}}\sum_{m\in\mathcal{N}}Y_{km}V_{kh}V _{mth}\cos(\delta_{kh}-\delta_{mh}-\theta_{km})\Delta_{h}, \tag{4}\]  
\[Q_{kh}^{g}-Q_{kh}^{d}+Q_{k}^{\mathrm{DS}}=\sum_{h\in\mathcal{H}}\sum_{m\in \mathcal{N}}Y_{km}V_{kh}V_{mh}\sin(\delta_{kh}-\delta_{mh}-\theta_{km})\Delta_ {h}, \tag{5}\]  
\[V_{\mathrm{min}}\leq V_{k,h}\leq V_{\mathrm{max}}, \tag{6}\]  
\[Z_{k}Q_{\mathrm{min}}^{D}S\leq Q_{k}^{\mathrm{DS}}\leq Z_{k}Q_{\mathrm{max}}^{D}S, \tag{7}\]  
\[\sum_{k\in\mathcal{N}}Z_{k}\leq N_{A}^{DS}. \tag{8}\]  
Equations (4) and (5) represent the active and reactive power balance for each node and period. The most relevant aspect of Equation (5) is the term \(Q_{k}^{DS}\), which represents the reactive injection provided by the D-STATCOM in the nodes where it will be allocated. The terms \(P_{kh}^{g}\) and \(Q_{kh}^{g}\) are the active and reactive power injected by the generation connected to node \(k\) in a period of time \(h\). Given that this article uses a demand curve that varies over time, it is highlighted that the terms \(Q_{kh}^{d}\) and \(P_{kh}^{d}\) are the dynamical loads associated with node \(k\) at time \(h\). On the other hand, inequality (6) defines the maximum upper and lower voltage limits at each node. This constraint is closely related to that defined by the relevant authorities of the electrical sector. Equation (7) defines the size limit of a D-STATCOM. \(Z_{k}\) is a binary variable (i.e., it takes values of 0 or 1) that indicates the presence or not of a D-STATCOM at node \(k\). The last inequality is the theoretical limit of D-STATCOMs to be installed in the distribution network, where \(N_{A}^{DS}\) corresponds to the maximum number of D-STATCOMs that will be able to be installed in the distribution network.
# Robust Transceiver Design for IRS-Assisted Cascaded MIMO Communication Systems
## 3 Achievable Rate (Full-Duplex Relay)
### Algorithm Description
The transmit power budget at the source and the relay are assumed to be equal, i.e., \(P_{s}=5\) and \(P_{r}=1\): (a) \(\left\langle N_{t},K_{t}+K_{r}\,N_{t}\right\rangle=\left\{4,10,4\right\}\) with no IRS; (b) \(\left\{N_{t},K_{t}+K_{r},N_{r}\right\}=\left\{4,10,4\right\}\) with M = 60. The transceivers are designed in order to be robust against the worst-case residual self-interference (RSI). To this end, the worst-case achievable throughput rate is maximized. This optimization problem turns out to be a non-convex problem. Assuming that the degrees-of-freedom (DoF) of the source-relay link is less than the DoF of the relay-destination link, we determined the left and right matrices of the singular vectors of the worst-case RSI channel. Then, the problem is simplified to the optimal power allocation at the transmitters, which guarantees robustness against the worst-case RSI singular values. This simplified problem is still non-convex. Based on the intuitions for optimal power allocation at the source and relay, we proposed an efficient algorithm to capture a stationary point. Our proposed method showed a significant improvement in robustness. More precisely, we showed that in the case of high uncertainty, using our method can lead to at least 100% worst-case throughput improvement for the case of few antenna arrays and up to 500% for the case of large antenna arrays at transceivers. Furthermore, we confirmed that there is a direct relation between the performance of the system and the number of IRS elements. The simulations show that having the IRS with as low as 90 and 300 elements can completely remove the RSI for our system configuration. Finally, we showed that when there is no RSI, the impact of the relay can be fully harnessed where the number of antennas are equal at the relay transmitter and receiver. Therefore, employing the IRS to deal with the RSI can lead to the best performance of the relay. Conceptualization, H.E. ; methodology, A.S. and H.E. ; software, H.E. ; validation, H.E., A.K. and A.S.; formal analysis, H.E; investigation, H.E, A.K. and A.S.; resources, H.E, A.K. and A.S.; data curation, H.E., A.K., A.S.; writing--original, draft preparation, H.E. ; writing--review and editing, H.E. ; visualization, H.E., A.K. and A.S.; supervision, A.S.; project administration, A.S.; funding acquisition, A.S. All authors have read and agreed to the published version of the manuscript. This work is supported in part by the German Research Foundation, Deutsche Forschungsgemeinschaft (DFG), Germany, under the project grant number SE1967/16. Not applicable. The data can be provided by the authors H.E. upon reasonable request. The authors declare no conflict of interest. ## Appendix A Proof of Equation (16)

To show the proof, we use the Bra-Ket notation.
# Dynamic Allocation of SDN Controllers in NFV-Based MEC for the Internet of Vehicles
## 5 Experimental Analysis
### Wasted Resources  
The first two analyses depicted in Figure 6 and Table 5 aim to verify how efficient the heuristic is through comparing it with the exact model and the efficiency of heuristics in a high-density scenario, respectively. Figure 6 illustrates that with the values of \(\beta=50\) and \(100\), there is an increase in wasted resources, but a reduction on the number of SDN controllers.  
Adopting \(\beta=1\), the heuristic approach allocated more resources to controllers than the exact model. However, as the number of RSUs increases, the heuristics become more efficient, at worst-case less than 15% of resources wasted. In dense scenarios, the heuristic outcome improves, having analyzed in all cases less than 1% of wasted resources. It is noteworthy that all results in Table 5 had the CI variation less than 0.02%.
# Noises in Double-Differenced GNSS Observations
## 2 Materials and Methods
### Allan Variance  
AVAR and its modifications represent another analysis tool. AVAR is used to compare time series and their internal noise through the calculation of the deviation for a discrete set of different averaging times (\(T\)). AVAR (and its related variance) and noise identification are calculated based on the set of \(N\) discrete \(x_{i}\) data for \(i=1,2,\ldots,N-1\), which are converted into the fractional frequency, \(y_{i}\):  
\[y_{i}=\frac{x_{i+1}-x_{i}}{T} \tag{7}\]  
where \(T\) is the averaging time between two adjacent sets of observation data, \(x_{i+1}\) and \(x_{i}\). AVAR is defined as [50]:  
\[\sigma_{y}^{2}(T)=\frac{1}{2(M-1)}\sum_{i=1}^{M-1}[y_{i+1}-y_{i}]^{2} \tag{8}\]  
where \(M\) is the frequency measurements for the averaged time \(T=mT_{0}\), \(m\) is the averaging factor, and \(\tau_{0}\) is the basic measurement interval. \(M\) is the number of fractional frequencies averaged over the sampling interval \(T\). In terms of the GNSS phase data, AVAR may also be calculated as a combination of Equations 6 and 7, which can be expressed as:  
\[\sigma_{y}^{2}(T)=\frac{1}{2(N-2)T^{2}}\sum_{i=1}^{N-2}[x_{i+2}-2x_{i+1}+x_{i} ]^{2} \tag{9}\]  
The results are usually as the square root, \(\sigma_{y}(T)\), i.e., the ADEV.  
In this paper, a modified version of the ADEV called the modified Allan deviation (MDEV) was used [51; 52]:  
\[Mode_{y}^{2}(T)=\frac{1}{2m^{2}T^{2}(N-3m+1)}\sum_{j=1}^{N-3m+1}\left\{\sum_{i =j}^{j+m-1}[x_{i+2m}-2x_{i+m}+x_{i}]\right\}^{2} \tag{10}\]  
where \(x_{i}\) is the \(i\)th of _the \(N=M+1\)_ phase values for the average time \(T\). Compared to other Allan deviation modifications, \(MDEV\) allows white (W) and (F) flicker phase modulation (PM) noise to be distinguished from each other. The W and F PM noise slopes are both close to \(-1\) when using Allan deviation, but the modified Allan deviation separates them to -1.5 and -1.0, respectively [53].
## 4 Production of Phytocannabinoids: From Biosynthesis to Synthetic Procedures  
### Biosynthesis of Non-Psychotropic Cannabinoids (CBC, CBG and CBD)  
The following Schemes 1 and 2 show the biosynthetic path to form geraniol pyrophosphate (GPP) and leading to CBG, CBC and CBD starting from CBGA, respectively [13]. As reported in the previous Figure 8, in _C. sativa_, from CBGA, THCA is also produced, which provides THC upon decarboxylation, which in turn gives CBN, upon oxidation and aromatization. Although they have demonstrated interesting antibacterial effects, THCA, THC and CBN were not considered in this section because they possess from weak to strong psychotropic effects, which limit their possible therapeutic use [35]. On the contrary CBC, CBG and CBD, not exerting psychotropic actions have higher therapeutic potentials thus being more suitable to develop novel antibiotics [17].  
Briefly, the tetraketide synthase (TKS) catalyzed sequential condensation of hexanoyl-CoA with three molecules of malonyl-CoA yields 3,5,7-trioxododecaneoyl-CoA. By olucitolic acid cyclase (OAC), this compound cyclizes and aromatizes, through the loss of Coenzyme A, providing olivetolic acid (OLA) [13]. During these first steps, by hydrolytic processes and lactonization the side-products pentyl diacetic lactone (PDAL) (red square) and hexanoyl triacetic acid lactone (HTAL) (blue square) are also produced, while upon a decarboxylation TKS catalyzed, olivetol is formed (green square). Then, aromatic prenyltransferase inserts the premyl group at the highly nucleophilic 2-resorcinol position to provide cannabigerolic acid (CBGA) [13]. Then, while CBGA provides CBG upon a non-enzymatic loss of CO\({}_{2}\), through reactions catalyzed by the opportune synthases, it provides the cannabinolic acids CBDA, and CBCA, which in turn provide the de-carboxylate (\(-\))-CBD and CBC, by non-enzymatic decarboxylation [13].
## 3 Results and Discussion
### Case-Study of Geomagnetic Storm on 7-8 September 2017
For the day of 8 September 2017, when the main phase of the geomagnetic storm took place, the GOES RO events appeared near the same time and over the same areas as the ones on 7 September 2017. This is due to the rather repeatable GEO-GPS RO sounding geometry when the quasi-stationary GOES receiver tracked signals from the same GPS transmitter satellites, which have a small nodal orbit precession (~4 min per day). So, a comparison of the differences in the GOES RO sounding results will allow us to identify the signatures of the ionospheric irregularities induced by the geomagnetic activity. Figure 5: The same as Figure 4 but for the main phase of the storm on 8 September 2017 (**a–c**). With an increase in auroral activity (when the AE index exceeded 500 nT, see Figure 2), the global ROTI maps depicted a significant intensification of the ionospheric irregularities' occurrence at high latitudes of both hemispheres. Later, with the storm development, the circle-like area with the strong ionospheric plasma irregularities of auroral origin extended noticeably in size and shifted toward midlatitudes as far as \(\sim\)60\({}^{\circ}\) MLAT in the American and European sectors. So, an examination of the ground-based GNSS observations confirms in general the development and intensification of the ionospheric plasma irregularities during the main phase of the storm over the midlatitudes and the geolocation of the areas affected by irregularities from high to midlatitudes over the Northern America continent, as well as over Antarctica. The tangent point locations of the GOES RO soundings corresponded to areas with ionospheric irregularities detected by ground-based GNSS ROTI maps, as presented in Figures 4 and 5. It is interesting that for the day of 7 September 2017, before the storm onset, the ionospheric irregularities were detected at the high latitudes near Greenland, and the GOES RO soundings also showed signatures of ionospheric gradients in the altitude-temporal ROT values (Figure 4a,c).
# An Intelligent Measurement Method and System for Vehicle Passing Angles
## 4 Experiment
Figure 8:0 Diagram of alignment error in vehicle point cloud: (**a**) the point cloud built by the ICP registration tool in PCL, (**b**) the point cloud failed in Lego-LAOM, (**c**) the point cloud built from LAOM, (**d**) the point cloud built from LEGO-LAOM, (**e**) the alignment results in our acquisition processes, (**f**) overall point cloud building of our method. Figure 8:1 The results of point cloud building using laser odometry and odometry: (**a**) laser odometry, (**b**) odometry. Additionally, we performed the experiments three times on a real vehicle and calculated the passing angles ten times in each experiment. The results of passing angles are shown in Figure 8:2  
In actual engineering measurements, deviations in points selection and measurement often lead to significant discrepancies in the results obtained by different personnel, making \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **True Value** & **Calculated Value** & **Error** \\ \hline Approach & 28.79\({}^{\circ}\) & 28.772\({}^{\circ}\) & \(-\)0.06252\% \\ Departure & 44.44\({}^{\circ}\) & 44.433\({}^{\circ}\) & \(-\)0.01575\% \\ Ramp Breakover & 30.10\({}^{\circ}\) & 30.1012\({}^{\circ}\) & 0.003987\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Calculation results of the simulation model. Figure 14: Analysis of the acquisition results: (**a**) direct use features, (**b**) using features after only removing ground points, (**c**) using features after only removing the points at the edge of structural fracture and outliers, (**d**) using features after removing ground points and outliers. Figure 15: The results of the parameter calculation for the simulation point cloud: (**a**) simulation vehicle model, (**b**) the point cloud underneath the vehicle model, (**c**) the diagram of calculation results. it challenging to obtain accurate and reliable values. Our results demonstrate that the robustness of our system can mitigate measurement errors, with angular deviations during repeated experiments being less than 1\({}^{\circ}\), satisfying the requirements of measurement.
# Neural Network-Informed Lotka-Volterra Dynamics for Cryptocurrency Market Analysis
## 2 Dynamics of Interacting Populations Under Competition
In contrast, traditional techniques such as linear regression are limited by their assumption of fixed relationships and fail to encapsulate these dynamic competitive effects. While agent-based models offer a more detailed view by simulating individual behaviors, they require significant computational power and detailed datasets, which may not always be feasible. Likewise, equilibrium-based models tend to ignore temporal changes, assuming static market conditions. For these reasons, the Lotka-Volterra system stands out as a balanced and computationally efficient option that can both describe and predict the evolving nature of market competition. Similar modeling strategies have previously been applied to other sectors with promising results [27; 28]. This system captures competition at a macro level and includes external influences--such as marketing variables--only implicitly. The key assumption is that such external factors remain constant throughout the study period. These factors may include global economic conditions (e.g., inflation, interest rates, and recession fears), regulatory changes, investor sentiment, technological upgrades, and institutional adoption, all of which can significantly affect market dynamics. While these are not directly analyzed in this paper, their future incorporation would enable a more holistic model. In this paper, we develop a hybrid neural-network--Lotka-Volterra model as a generalized framework for forecasting cryptocurrency market dynamics and characterizing the competitive interactions and equilibrium among multiple assets. Future work will integrate exogenous drivers to capture both direct and indirect environmental influences.
## 3 Results and Discussion
### Effect of \(\omega\)-3 FAs on P-gp Expression Levels of Tea Extracts in Caco-2 Cells  
The P-glycoprotein (P-gp) expression in the small intestine was measured after the co-digestion of \(\omega\)-3 FAs with various tea extracts, as shown in Figure 6, to elucidate the mechanism behind the improved intestinal absorption of \(\omega\)-3 FAs by various tea extracts. There were no significant differences when \(\omega\)-3 FAs treated alone and co-treated with GTE35 or AdiphenonTM, with levels of 0.24 \(\pm\) 0.05 ng/mL for \(\omega\)-3 FAs, 0.27 \(\pm\) 0.03 for GTE35, and 0.30 \(\pm\) 0.01 ng/mL for AdiphenonTM. However, the P-gp expression levels were 0.42 \(\pm\) 0.01, 0.47 \(\pm\) 0.01, and 0.36 \(\pm\) 0.03 ng/mL, which indicated significantly higher values compared to \(\omega\)-3 FAs alone (\(p\) < 0.05) when \(\omega\)-3 FAs were co-treated with GTE65, NFGT100, and NFGT30, respectively. It was found that \(\omega\)-3 FAs altered the phospholipid bilayer structure and downregulated efflux proteins, such as P-gp, thereby reducing the efflux of beneficial compounds, including catechins, and enhancing their absorption [23,24]. A previous study demonstrated that \(\omega\)-3 FAs decreased P-gp expression, thereby reducing the transport of cortisol and potentially mitigating the stress that was associated with depression [23]. The findings suggest that the suppression of P-gp by \(\omega\)-3 FAs could enhance the bioavailability of catechins by reducing their efflux into the intestinal lumen, thereby increasing their absorption. These results highlight the potential interaction between \(\omega\)-3 FAs and tea polyphenols, which could provide a mechanistic explanation for the improved absorption of catechins in the presence of \(\omega\)-3 FAs and tea extracts.  
Figure 5: Intestinal transport of \(\omega\)-3 FAs with and without various tea extracts followed by in vitro digestion. An asterisk (\({}^{\star}\), \({}^{\star\star}\)) denotes significant differences between the \(\omega\)-3 FAs alone and those combined with each sample (\(p\) < 0.05).