esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 The Proposed Algorithm
### Theoretical Justification and Computational Efficiency  
Given that the real-world case analyzed in this study involves a relatively small instance (17 product types) and that the solution obtained is optimal, we assess the effec  
Figure 4: Stage 2 of the algorithm—the minimum number of operators required.  
tiveness of the proposed algorithm through analytical means, focusing on performance and computational complexity.  
The first stage, which determines the minimum number of machines, begins with the heuristic FFD, which runs in \(O(n\log n)\) time and has a well-established performance bound. In our case study, the result obtained by FFD matched the theoretical lower bound, thus proving optimality. In general, if the FFD result does not match the lower bound, an integer linear programming (ILP) model may be used to verify optimality. However, since the BPP is NP-hard, solving its ILP formulation can require exponential time in the worst case and may become computationally impractical for larger instances. In such cases, the FFD solution offers a fast, effective, and practical approximation.  
The second stage, which assigns machines to operators while avoiding overlapping setup intervals, is also NP-hard in the general case. The assignment process involves evaluating, for each of the M machines, whether it can be added to one of the existing operator groups without conflicts. This is done by first checking a simple capacity condition and, when needed, solving a small ILP with cyclic non-overlap constraints. In the worst case, up to M ILP problems of size \(O(K^{2}\cdot G^{2})\) may be solved for each machine (where K is the number of setups per machine and \(G\leq M\) is the size of the operator group), resulting in an overall complexity of \(O(K^{2}\cdot G^{2})\). Nevertheless, since most assignments are rejected early via simple feasibility checks and the ILPs involve small groups (typically three to five machines per operator), the algorithm performs efficiently in practice. Suppose an ILP instance fails to solve or becomes too time-consuming. In that case, the algorithm can fall back to the heuristic assignment by simply allocating the machine to the next operator, ensuring progress and maintaining low computational overhead.  
Combining both stages, the overall computational complexity of this heuristic algorithm is: \(O(n\log n)+O(K^{2}\cdot G^{2})\). This hybrid approach balances optimality, feasibility, and runtime performance. It is particularly well-suited for real-world manufacturing environments and can be extended in future work to incorporate larger instances or alternative solution techniques.  
Although no formal benchmarking has been conducted against metaheuristics in this study, the presented algorithm demonstrates practical efficiency in the real-world case examined. Future research will explore systematic performance comparisons with established heuristics and metaheuristics.
## 1 Introduction
To overcome the above challenges, an optimization mechanism for RPL, introducing context-aware features (_i.e._, remained energy, hardware/software reliability, link quality, _etc._) into the Objective Function (OF), has been taken into account in our proposed Routing Protocol for A-LLNs (RPAL) model. The RPAL routing algorithm is devoted to the application and network infrastructure of PA, experimented and evaluated as a part of IoT protocol stack with 6 LoWPAN and CoAP in both simulation and field tests. In what follows, the routing challenges and design issues in A-LLNs are described in Section 2. In Section 3, the RPL protocol is briefly presented, and then in Section 4 the SCAOF is presented, evaluated and the results are discussed in the simulation scenario (Section 5) and hardware testbeds (Section 6). Finally, the conclusions of this paper are mentioned in Section 7.
## 4 Problem Definition and Modeling
### Problem Definition  
Having formulated the objective function, the problem is then defined as a constrained non-linear integer optimization problem to find the optimal plan \(p^{*}\). The entire model can be described by Equations (27)-(29):  
\[p^{*}=\arg_{p\in p}\max gain(p) \tag{26}\]  
s.t.  
\[\sum_{s\in p}f(s)\leq B \tag{27}\]  
\[\sum_{s\in p}\sigma(v,s)\leq 1,\forall vs.\in V \tag{28}\]  
\[\rho(s)\leq 1,\forall s\in p \tag{29}\]  
Equation (27) denotes that the limitation of the financial cost by a fixed budget B, Equation (28) ensures one node just chooses one charging station, and Equation (29) is used to make the waiting time well-defined. \(f(s)\) is the total cost of installing one new charging station.
## 3 Multi-Objective Optimization Model for WNN-Based PI Construction  
### PI Multi-Objective Optimization Criteria  
PICP or PICAW can evaluate the quality of PIs from different aspects. In order to obtain the high quality of PIs, a large PICP and small PICAW are both required. Obviously, this is a multi-objective optimization problem for maximizing the coverage probability and minimizing the width of PIs simultaneously. The most famous method for this problem is to transform two primary PIs' assessments into a single one by some hyperparameters. A most common index, called the coverage width-based criterion (CWC), is defined as follows:  
\[\text{CWC}=\text{PINAW}(1+\gamma(\text{PICP})e^{-\eta(\text{ PICP}-\mu)}) \tag{5}\]  
where \(\mu\) is an expected coverage probability, \(\eta\) is a control parameter that magnifies the differences between PICP and \(\mu\) when the coverage probability hardly achieves the expected value. \(\gamma(\text{PICP})=0\) when PICP \(\geq\mu\) and \(\gamma(\text{PICP})=1\) when PICP \(<\mu\). In CWC, the most critical parameter is \(\eta\). If \(\eta\) is small, it will be insufficient to obtain the expected coverage probability. In contrast, if \(\eta\) is too large, there will be too much of a penalty to obtain the optimized solution. Thus, for the CWC, how to choose a suitable \(\eta\) becomes a key problem. \(\eta\) is often set empirically in most of the literature. If an unreasonable \(\eta\) is chosen, the multi-objective optimization problem cannot be transformed into a single optimization problem completely and the quality of PIs cannot be guaranteed.  
In this paper, the multi-objective optimization problem is solved directly by an improved MOABC algorithm. A PIs' multi-objective optimization criteria (PIMOC) is proposed as follows:  
\[\left\{\begin{array}{ll}\min&\alpha=1-\text{PICP}\\ \min&\text{PICAW}\\ s.t.&0\leq\alpha\leq 1,\quad 0\leq\text{PICAW}\leq 1\end{array}\right. \tag{6}\]  
where \(\alpha\) is transformed from the confidence level to satisfy the need of multi-objective optimization problem. Taking into account the real requirement of the electrical power system, the range of constraint conditions will be reduced. Thus, the confident level \(\alpha\) is restricted in \([0,20\%]\) and the width of the PIs is restricted in \([0,25\%]\) after normalization.
# Computational Complexity and ILP Models for Pattern Problems in the Logical Analysis of Data
## 6 Computational Experiments
### How to Boost Instances of Pattern Equivalence  
One way to increase the number of gaps in the instances would be to take two set of equivalent patterns \(A\) and \(B\) and suffix each pattern with a list of \(k\) gaps. This, however, yields very particular, uninteresting, instances. In order to obtain more elaborate, hard pattern equivalence instances, we have developed the following scheme.  
Given a set of patterns \(X\), denote by  
- \(n(X)\) the number of columns (i.e., string length),  
- \(m(X)\) be the number of rows (i.e., of patterns),  
- \(G(X)\) the maximum number of gaps in some pattern.  
Furthermore, given sets of patterns \(A\) and \(B\), denote by \(C=A\times B\) the set of patterns  
\[C=\{(a,b):a\in A,b\in B\}\]  
Note that \(n(C)=n(A)+n(B)\), \(m(C)=m(A)\cdot m(B)\) and \(G(C)=G(A)+G(B)\). We have  
**Claim 1**.: _Let \(A_{1},A_{2},B_{1},B_{2}\) be sets of patterns such that \(A_{1}\) is equivalent to \(A_{2}\) and \(B_{1}\) is equivalent to \(B_{2}\). Then \(A_{1}\times B_{1}\) is equivalent to \(A_{2}\times B_{2}\)._  
Proof.: Let \(C_{i}:=A_{i}\times B_{i}\). We want to show that \(S(C_{1})=S(C_{2})\). We show \(S(C_{1})\subset S(C_{2})\) since the other direction is symmetrical. Let \((x,y)\in S(C_{1})\). In particular, \(x\in S(A_{1})\) and  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(n\) & **ILP** & **enum** \\ \hline
18 & 0.03 s & 0.34 s \\
20 & 0.05 s & 1.38 s \\
22 & 0.07 s & 6.43 s \\
24 & 0.08 s & 29.89 s \\
26 & 0.08 s & 138 s \\
28 & 0.05 s & 1005 s \\
30 & 0.08 s & did not finish \\ \hline \hline \end{tabular}
\end{table}
Table 2: Computational results for Pattern Equivalence—Diagonal instances.  
\(y\in S(B_{1})\). Since \(A_{1}\) is equivalent to \(A_{2}\) also \(x\in S(A_{2})\) and similarly \(y\in S(B_{2})\). Hence \((x,y)\in S(A_{1})\times S(B_{2})=S(C_{2})\).  
By using this trick repeatedly, we can snowball from small instances, e.g., 4 or 5 patterns with 5 or 6 gaps each, to instances with a few hundred patterns with more than 20 gaps each.
## 3 Results and Discussion
### Load-Sharing Rate of Target Package  
Accurate calculation of the load-sharing rate between the shipping container and cushioning system in packages equipped with the EPS-based cushioning system is important to achieve the proper packaging design of the product. As the stacking load, excluding the load-sharing rate of the shipping container, is transmitted to the product through the cushioning material, the strength independence of the product is used as the basis for designing the shipping container. In other words, if the strength independence of the product is zero, the shipping container shall be responsible for all stacking loads. However, if there is a certain level of strength independence owing to the nature of the product, the stacking load, excluding this strength independence, becomes the basis of the strength design of the shipping container.  
Figure 8 shows the analysis results of the load-sharing rate acting on the shipping container and the EPS cushioning material of the bottom layer package for each stacking situation (Table 1) of the target packages. The SS models for the target shipping containers in Table 5 and the SS models of the EPS previously published by the researchers [17] were applied to this estimation.  
Figure 7: Example of the average creep rate from a nonlinear creep model: Container B, rh = 70%, L\({}_{\text{o}}\) = 0.1652 kN/m, applied load level (% of CS) = 0.1652/2.07 = 7.98%, correction factor = 7.98/(100\(-\)7.98) = 0.0867 (Tables 4 and 6).  
In the target packages used in this study, the ratio of the load-sharing rate between the shipping container and EPS cushioning material was determined to be about 2%:98%, with most of the stacking load applied to the product through the cushioning material. Therefore, because the compression behavior of the target package depends on the compression behavior of the cushioning material in the package as opposed to the shipping container, data on the compression and compressive creep behavior of the EPS-based cushioning system are considered to be more important in CAE prediction technology for determining the compression behavior of multi-stacked target packages.
# Dual-Channel Mapping-Gas Column Concentration Inversion Method Based on Multispectral Imaging
## 4 Error Analysis
### Gas Column Concentration Inversion Error Evaluation
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Mean Inversion Column** & **Theoretical Column** & **Relative Error** \\
**Concentrations (ppm-m)** & **Concentration (ppm-m)** & \\ \hline
1228.4 & 1340 & 9.1\% \\
2834.4 & 2700 & 4.8\% \\
3792.7 & 3600 & 5.1\% \\
4406.2 & 4500 & 2.1\% \\
5080 & 5000 & 1.6\% \\
5234.7 & 5400 & 3.2\% \\
7835.8 & 7200 & 8.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Inversion accuracy under different column concentrations. Figure 18: Experimental diagram of inversion accuracy detection of gas sampling bag inflation. bag. According to a comprehensive analysis of the two methods, the relative error of this method is less than 10%, and the average relative error is 4.8%. [PERSON] et al. (2019) used an infrared Fourier transform spectrometer (IFTS) to measure the content of CO\({}_{2}\) and water vapor in the exhaust gas emitted by a turbo engine, with an average error of less than 5%. [PERSON] et al. (2019) from the University of Bremen in Germany used the infrared DOAS algorithm to invert the spectra measured by the Scanning Imaging Absorption Spectrometer for Atmospheric Chattorography (SCIAMACHY), and the inversion accuracy of the total column concentrations of H\({}_{2}\)O, CO\({}_{2}\) and CH\({}_{4}\) obtained was better than 1% ([PERSON] and [PERSON] et al., 2019). [PERSON] et al. (2019) proposed a spectral measurement method using an infrared thermal imager as a field-of-view aid and a spectrometer as the main measurement device; the test results showed that this method can effectively obtain the infrared spectral radiance of the exhaust plume, and the measurement uncertainty was 19.54%. Compared with existing multispectral infrared imaging techniques, the method proposed in this paper has advantages in accuracy. However, compared to active and hyperspectral imaging systems, the method proposed in this paper has lower accuracy, mainly due to the use of uncooled detectors and higher noise. In order to improve the accuracy of this method, detectors with higher sensitivity or methods such as image processing can be used.
## 2 Materials and Methods
### Characterization of Asphal Emulsions Used in Microsurfacing Mixtures  
This project used two types of polymer-modified asphalt emulsions (C60 BP4 and C65 BP4) produced in Italy with a class 4 breaking value, the first with 60% \(\pm\) 2% and the latter with 65% \(\pm\) 2% residual binder. The Portuguese Specifications [29] consider these emulsions adequate for microsurfacings.  
The breaking value of the emulsion was determined following the EN 13075-1 standard. A reference filler was added to a specified amount of cationic asphalt emulsion at a uniform rate with constant agitation in a specific apparatus. When the emulsion broke down  
Figure 1: Flowchart of the microsurfacing mix design procedure proposed in this work.  
completely, the amount of filler added was determined by weighing, and the break index value corresponds to the filler mass (in grams) multiplied by 100 and divided by the amount of emulsion (in grams).  
The emulsion adhesion test was based on the European Standard EN 13614. Initially, 200 g of aggregate was weighed, washed, and left in an oven at 110 \({}^{\circ}\)C for 2 h. Subsequently, the aggregates were added to the emulsion, which contained 10 g of residual binder, and mixed with a spatula. The mixture was then spread on a tray lined with parchment paper and put in an oven at 60 \({}^{\circ}\)C for 24 h. Then, the mixture was transferred to a 300 mL water glass beaker at 60 \({}^{\circ}\)C and returned to the oven at 60 \({}^{\circ}\)C for 24 h. Finally, the surface of the emulsion-coated aggregate was evaluated.  
The procedure specified in the EN 13074-1 standard was used to recover the binder of each emulsion. According to this standard, recovery involves evaporating all the water in the emulsion, leaving only the binder. The procedure consisted of spreading a known mass of emulsion on a tray lined with parchment paper and exposing the tray with the emulsion at room temperature under standard laboratory conditions for 24 h. After this, the tray was placed in an oven at 50 \({}^{\circ}\)C for another 24 h. At the end of this period, the tray was removed from the oven and allowed to cool until it reached room temperature, and then all residual binder was collected from the tray.  
After the binder recovery, to evaluate which properties could influence the micro-surfacing mixtures, wide-ranging binder characterization tests were carried out, such as penetration at 25 \({}^{\circ}\)C (EN 1426), softening point temperature determined by the ring and ball method (T\({}_{\text{Rgb}}\)) (EN 1427), dynamic viscosity (EN 13302), cohesion energy by force ductility at 5 \({}^{\circ}\)C (EN 13589), elastic recovery at 25 \({}^{\circ}\)C (EN 13398), and determination of the complex shear modulus on the dynamic shear rheometer (EN 14770). The rheology tests were performed in the linear viscoelastic regime using an 8 mm plate with a 2 mm gap at temperatures below 30 \({}^{\circ}\)C and a 25 mm plate with a 1 mm gap at higher temperatures.
# GNSS Multipath Detection Using Continuous Time-Series C/N0
## 4 Testing and Results
### Test Results in the First Location
The horizontal errors of the DGNSS using our new method are presented in Figure 15. Note that the vertical scale is different from that of Figure 14. The absolute horizontal error was reduced substantially from the beginning to the end, indicating that the selection of multipath-contaminated satellites was quite effective when using our new method and the unfavorable satellites could quickly be removed in order. The maximum horizontal error was 7.85 m, and a 90 th percentile value of only 4.31 m was obtained. The standard deviations in the horizontal direction for E and N were 2.02 and 1.06 m, respectively. The average errors in the horizontal direction for E and N were 1.24 and \(-\)0.67 m, respectively. The accuracy was improved dramatically using the new satellite selection method. Regarding the RTK-GNSS, the fix rate was 47.2% and all solutions were correctly fixed. The standard deviations of the RTK-GNSS in the horizontal direction for E and N were 0.015 and 0.017 m, respectively.
## 2 Model
### Corrugation Model  
In this paper, corrugation with a sinusoidal profile is used as a test case. This choice is based on field observations, such as those shown in Figure 1a. Moreover, our work is a continuation of previous research in which corrugation was assumed to have a sinusoidal profile [3; 9; 43; 44; 45; 46]. A sinusoidal corrugation with a constant wavelength is applied to the rail surface expressed by the equation:  
\[z(x)=\mathrm{A}\cos\left(\frac{2\pi x}{\lambda}+\theta\right)-\mathrm{A} \tag{2}\]  
where A is the amplitude of the corrugation, \(\lambda\) is the wavelength and \(\theta\) is the phase. The second term \(-\mathrm{A}\) guarantees that the peak of the corrugation is not higher than the initial profile of the rail surface.  
The wavelength is 30 mm, which is approximately equal to one of the recorded corrugation wavelengths on the Dutch railway network shown in Figure 1a,c (see the measurement in Figure 3a). For the analysis, 10 waves are considered; thus, \(L_{2}\) equals 300 mm. The corrugation considered is located above a sleeper support (as shown in Figure 1b), which has been reported as a position where corrugation is more likely to develop [22]. To examine the wheel-rail contact during the growth process of the corrugation, the amplitudes of A = 0 \(\upmu\)m for smooth rail and A = 2.5 \(\upmu\)m, 5 \(\upmu\)m, 10 \(\upmu\)m and 20 \(\upmu\)m for corrugated rail are modeled (the peak-to-trough distance is twice the amplitude). By maintaining \(\theta\) between \(-\pi/2\) and \(\pi\), contact solutions can be studied at different locations within one complete corrugation wavelength, i.e., the falling edge (P1), the trough (P2), the rising edge (P3) and the peak (P4), as shown in Figure 3b. Figure 3c shows a magnified 3D configuration of the corrugation in the rail surface.  
Figure 3: \(Cont\).
## 4 Simulation Experiments: Security Analysis and Comparison
### Entropy Analysis  
The degree of randomness in data is commonly measured by a fundamental criterion called information entropy. To calculate the entropy \(H\) of a message source \(M\), [PERSON] [46] proposed the following equation:  
\[H(M)=-\sum_{m\in M}\mathrm{Prob}(m)\mathrm{log}_{2}\mathrm{Prob}(m), \tag{9}\]  
where Prob denotes the probability of the symbol \(m\) in \(M\). If there are \(2^{N}\) possible symbols for encrypting a message \(M\), then the optimal amount of entropy \(H(M)=N\).  
By examining texts of various sizes, we calculated the entropy and displayed the results in Table 1. The results demonstrate that the entropy of the ciphertext is higher than that of the plaintext. Furthermore, Table 2 presents a comparison of entropy between the proposed scheme and some state-of-the-art schemes [10; 11; 12; 13; 14; 15; 16; 17; 18]. Our evaluation reveals that the entropy of the ciphertext is lower than that of the plaintext in the schemes [10; 11; 12; 13; 14; 15; 16; 17; 18], whereas in [14; 15], the entropy of the ciphertext is higher than that of the plaintext but not as high as in the proposed scheme. Therefore, the proposed scheme outperforms [10; 11; 12; 13; 14; 15; 16; 17; 18] in terms of entropy.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline \multirow{2}{*}{**Scheme**} & \multirow{2}{*}{**Number of Characters in \(P\)**} & \multicolumn{2}{c}{**Time (Seconds)**} \\ \cline{3-4}  & & **Encryption** & **Decryption** \\ \hline Proposed & 1126 & 0.0272 & 0.0926 \\ Ref. [14] & 999 & 0.2650 & 0.3590 \\ Ref. [41] & 409 & 0.0930 & 0.1400 \\ Ref. [42] & 1126 & 0.1400 & 0.1090 \\ Ref. [43] & 409 & 1.9500 & 0.8300 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Computation time comparison of the proposed scheme with the state-of-the-art text encryption schemes.
###### Abstract  
Satellite precipitation products provide alternative precipitation data in mountain areas. This study aimed to assess the performance of the latest Global Precipitation Measurement (GPM) Integrated Multi-satellite Retrievals for GPM (IMERG) version 5 (IMERG V5) and Global Satellite Mapping of Precipitation version 7 (GSMaP V7) products and their hydrological utilities over the Tibetan Plateau (TP). Here, two IMERG Final Run products (uncalibrated IMERG (IMERG-UC) and gauge-calibrated IMERG (IMEEG-C)) and two GSMaP products (GSMaP Moving Vector with Kalman Filter (GSMaP-MVK) and gauge-adjusted GSMaP (GSMaP-Gauge)) were evaluated from April 2014 to March 2017. Results show that all four satellite precipitation products could generally capture the spatial patterns of precipitation over the TP. The two gauge-adjusted products were more consistent with the ground measurements than the satellite-only products in terms of statistical assessment. For hydrological simulation, IMERG-UC and GSMaP-MVK showed unsatisfactory performance for hydrological utility, while GSMaP-Gauge demonstrated comparable performance with gauge reference data, suggesting that GSMaP-Gauge can be selected for hydrological application in the TP. Our study also indicates that accurately measuring light rainfall and winter snow is still a challenging task for the current satellite precipitation retrievals.  
satellite precipitation; Tibetan Plateau; GPM; IMERG; GSMaP Article