esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Mathematical Modeling
### Adsorption Isotherm Model of Type I
#### 3.1.4 D-A Model  
The D-A (Dubinin-Ashtakov) model has been developed as a more generalized model of the D-R model and builds on the potential concept of Polanyi [44,45]. Currently, it is one of the most applied models, and it is adopted in many studies due to its high accuracy and simplicity. To further expand the field of application of the D-A model, [PERSON] et al. [21] have recently formulated a method to obtain the isosteric heat of adsorption using the parameters of the D-A model. The following Equations (15) and (16) express the D-A model without the adsorbed volume correction and with the adsorbed volume correction, respectively.  
\[w =w_{0}\exp\left[\left(-\frac{RT\ln(P_{0}/P)}{E}\right)^{n}\right] \tag{15}\] \[w =\frac{C_{0}}{v_{a}}\exp\left[\left(-\frac{RT\ln(P_{0}/P)}{E} \right)^{n}\right] \tag{16}\]  
In Equations (15) and (16), \(w\) is once more the specific uptake at the equilibrium expressed in kg/kg, and \(w_{0}\) and \(C_{0}\) are the maximum uptake and maximum volumetric uptake in kg/kg and m\({}^{3}\)/kg, respectively. Finally, the \(E\) is the adsorption energy and \(n\) is similar to the Toth equation the heterogeneity factor. It is worth noting that once the heterogeneity factor becomes \(n=2\), the D-A isotherm formally becomes the D-R isotherm. Then, both of the models practically share the same adsorption potential \(\varepsilon\) dependent on the natural logarithm of the inversed relative pressure:  
\[\epsilon=RT\ln\left(\frac{P_{0}}{P}\right) \tag{17}\]  
To express the volumetric adsorption, another parameter for the limited compressibility of the liquid phase has to be taken into account, especially when working at high pressures (often known as adsorbed phase volume correction). With this consideration, the density of the adsorbed phase \(v_{a}\) can be written as follows [46]:  
\[v_{a}=\left\{\begin{array}{l}v_{b}\exp(\alpha[T-T_{b}]),\text{ if }P_{Trip}\ <\ P_{Amb}\\ v_{Trip}\ \exp\bigl{(}\alpha\bigl{[}T-T_{Trip}\bigr{]}\bigr{)},\text{ otherwise}\end{array}\right. \tag{18}\]  
The thermal expansion coefficient \(\alpha\) can be expressed using three approaches, which are the constant value of 0.0025, \(1/T\), and a model that was suggested by [PERSON] and [PERSON] [47], which is shown in the following Equation (19):  
\[\alpha=\left\{\begin{array}{l}\frac{\ln\left(\frac{b_{w}}{b}\right)}{T_{Cri -Trip}},\text{ if }P_{Trip}\ <\ P_{Amb}\\ \frac{\ln\left(\frac{b_{w}}{b}\right)}{T_{Cri-Trip}},\text{ otherwise}\end{array}\right. \tag{19}\]  
where \(b_{w}\) is the van der Waals volume of the adsorbate in cm\({}^{3}\)/mol.
# A Dynamic-Routing Algorithm Based on a Virtual Quantum Key Distribution Network
## 1 Introduction
A lower key-blocking probability indicates a higher distribution success rate, while a higher number of remaining keys means sufficient resources are available for subsequent key generation. By optimizing these parameters, a more efficient and reliable QKD can be achieved. In addition, with the dynamic routing algorithm, we can maximize the use of available essential resources and reduce the costs of network deployment and operation. Finally, we performed a theoretical analysis and an experimental comparison of the proposed method with the algorithm, and the results show that the algorithm can significantly improve the quality of the QKD system, save costs, and improve resource utilization relative to other algorithms. The rest of this article is organized as follows: Section 2 first describes the SDN-based QKD network framework and trusted relay QKD network. Then, it introduces the QKP structure, the steps to design a tunable QKP, and the remaining key amount in the QKP. Finally, the probability of link blocking and the threshold of link blocking are calculated. Section 3 proposes a dynamic routing algorithm that combines the remaining key amount, the likelihood of link blocking, and the evaluation metrics for the algorithm. In Section 4, the experimental platform is introduced, and the simulation results of the algorithm comparison are analyzed. Finally, Section 5 summarizes the article.
## 4 Time Domain Spectral Finite Element Method (TDSFEM)
### Wave Propagation in 1D Elements  
As in the case of FDSFEM, the process of modelling the phenomenon of elastic wave propagation by the use of TDSFEM is also usually based on the force-displacement method. This approach in connection with well-known rod theories from the area of strength of materials has been analysed by a research group from Gdansk, Poland [130; 131; 132]. The first two papers cover the problem of comparison of different rod theories and the influence of the proper choice of theory on the obtained results reliability, the third paper comprises the experimental verification of proposed numerical models for modelling of longitudinal waves in structural rod elements.  
Apart from the numerical and experimental analysis of the wave propagation in elements of the rod type, the researchers have also been interested in the same process in elements of the beam type. For example, in the case of beam elements modelled with FDSFEM, among the interesting scientific reports, one can find e.g., [133], where the comparison of different beam theories is given in terms of the correlation of the accuracy of the results obtained and the theory applied for different wave propagation parameters. Numerical and experimental analysis of wave propagation in beam and rod structures has also been examined in [132]. This research has been extended to include L-joint structure [134]. It has been shown that the proposed numerical procedure is suitable for damage detection in a frame structure, modelled by the use of TDSFEM.
## 3 Automatic Feature-Based Approach
### Transform Model Estimation and Resampling  
The affine transformation parameters are estimated based on the final positions of the reference contours. It consists of computing a bilinear regression from the initial and final positions for each of the points of the accepted contours. We have assumed that the relationship between the reference and sensed images, obtained from an orbital prediction model, can be expressed by a 2-D affine transformation [1, 15], since the systematic errors have been previously compensated by the Kepplerian model. The affine transformation can model six types of distortions, including translation, scaling and rotation. More complex transformations, as adaptative mapping functions or splines, are used  
Figure 4: Flowchart of the exhaustive search algorithm.  
with non-linear geometric distortions or with local geometric distortions in high resolution images [12].  
For the considered affine transformation model, we can write for each pair of related points,  
\[X_{O}=\begin{bmatrix}1&X_{I}&Y_{I}\end{bmatrix}\begin{bmatrix}a_{0}\\ a_{1}\\ a_{2}\end{bmatrix};\;\;Y_{O}=\begin{bmatrix}1&X_{I}&Y_{I}\end{bmatrix}\begin{bmatrix} b_{0}\\ b_{1}\\ b_{2}\end{bmatrix} \tag{7}\]  
where \((X_{O},Y_{O})\), \((X_{k},Y_{I})\) are, respectively, the initial and final positions of a contour point and \(\{a_{\alpha}\ a_{l}\ a_{2}\}\), \(\{b_{0}\ b_{l}\ b_{2}\}\) are the transformation parameters. This allows to generate initial transformations with respect to rotation, scaling and translation. The six transformation parameters are estimated using all pairs of accepted points (N), through a minimum squares solution,  
\[\hat{X}=\left(W^{T}W\right)^{-1}\left(W^{T}R_{X}\right);\;\;\hat{Y}=\left(W^{T} W\right)^{-1}\left(W^{T}R_{Y}\right) \tag{8}\]  
where,  
\[W=\begin{bmatrix}1&X_{I_{i}}&Y_{I_{i}}\\ \cdots&\cdots&\cdots\\ 1&X_{I_{s}}&Y_{I_{s}}\end{bmatrix};\;R_{X}=\begin{bmatrix}X_{O_{s}}\\ \vdots\\ X_{O_{s}}\end{bmatrix};\;R_{Y}=\begin{bmatrix}Y_{O_{s}}\\ \vdots\\ Y_{O_{s}}\end{bmatrix} \tag{9}\]  
and,  
\[\hat{X}=\begin{bmatrix}A_{X}\\ B_{X}\\ C_{X}\end{bmatrix};\;\;\hat{Y}=\begin{bmatrix}A_{Y}\\ B_{Y}\\ C_{Y}\end{bmatrix} \tag{10}\]  
Finally, the input image is transformed using the following correction function:  
\[\begin{bmatrix}X_{1}\\ Y_{1}\end{bmatrix}=\begin{pmatrix}A_{X}&B_{X}\\ A_{Y}&B_{Y}\end{pmatrix}\begin{bmatrix}X_{0}\\ Y_{0}\end{bmatrix}+\begin{pmatrix}C_{X}\\ C_{Y}\end{pmatrix} \tag{11}\]
# Timing Performance Testing and Regularity Analysis of eLoran System
## 2 eLoran Timing Error
### Authorization Performance Assessment Metrics  
#### 2.2.1 Maximum Timing Deviation  
The maximum value of the timing deviation monitored during the valid data period indicates the highest deviation in the eLoran timing system.
## 4 Performance Assessment
### Experiment
#### 4.2.2 Channel Response Estimation  
In the turbo equalization using the low-complexity CE-based MMSE algorithm, each subchannel response in Equation (6) must be first estimated. In the experiment, the subchannel responses are estimated using the recursive least square (RLS) algorithm with the forgetting factor 0.999, and the filter for channel estimation has \(N_{1}=5\) noncausal coefficients and \(N_{2}=18\) causal coefficients. The estimated subchannel responses are shown in Figure 9. It can be observed from Figure 9 that the ISI span of each subchannel is about 20 symbol intervals.  
Figure 8: Time domain waveforms and frequency spectrums of linear frequency modulated (LFM) signals with a hamming window and FMT signals at the transmitter and the receiver on the condition of 8 PSK mapping scheme used: (**a–d**) time domain waveforms and frequency spectrums of the LFM signal and the FMT signal at the transmitter; (**e–h**) time domain waveforms and frequency spectrums of the LFM signal and the FMT signal at the receiver.
## 3 Results and Discussion
### Multi-Element Analysis of Investigated Berries Samples  
The results concerning the elemental analysis (Li, Na, Mg, P, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, As, Rb, Sr, Ag, Cd, Ba, Pb, La, Ce, Pr, Nd, Sm, Eu, Gd, and Tb) in different species of berries are summarized in Table S1, presented in the supplementary files. The multi-element analysis of the investigated samples was used to compare firstly, the composition of the berries according to their botanical origin, and secondly, the elemental content of the berries according to their growing conditions (cultivated vs. wild). The concentrations of macro-, micro-, and trace elements in five species of berries (raspberries, seaberries, blackberries, cranberries, and blueberries) were compared. Our results showed that the investigated berries are a rich source of macro-elements, such as Na, Ca, P, and Mg. The highest levels were found for Mg and P in raspberries (with mean values of 601.57 mg/kg, d.w. and 1531.38 mg/kg, d.w., respectively), then in the investigated blackberry samples (with mean values of 593.43 mg/kg, d.w. and 1473.18 mg/kg, d.w.,  
Figure 3: \(\delta^{2}\)H versus \(\delta^{18}\)O for the studied berries. respectively), and the lowest content in blueberries samples (332.35 mg/kg, d.w. for Mg and 730.34 mg/kg, d.w. for P, respectively). The results of Na analysis, expressed as the mean value, showed that the highest mean concentration of this element was in seaberries samples (187.77 mg/kg, d.w.), followed by blueberries (39.55 mg/kg, d.w.), blackberries (28.22 mg/kg, d.w.), cranberries (27.50 mg/kg, d.w.), and raspberries (26.11 mg/kg, d.w.). In the present study, the Ca concentration in blackberries was higher than the other investigated berries. The general pattern of accumulation of this macro-mineral in the berries studies was in the order of blackberries (866.07 mg/kg, d.w.) \(>\) cranberries (623.01 mg/kg, d.w.) \(>\) raspberries (606.47 mg/kg, d.w.) \(>\) blueberries (559.58 mg/kg, d.w.) \(>\) seaberries (245.15 mg/kg, d.w.). From the micro- and trace elements profile analysis, the mean concentration decreased in the following order: Mn, Fe, Cu, Zn, Ba, Ti, Cr, Ni, Pb, As, Li, Co, V, and Cd (for cranberries); Mn, Fe, Cu, Zn, Ba, Cr, Ti, Ni, Pb, Li, Co, As, V, and Cd (for blueberries); Fe, M, Zn, Cu, Cr, Ti, Ni, Ba, As, Co, Cd, Pb, Li, and V (for raspberries); Fe, Cu, Zn, Mn, Ti, Ni, Cr, Ba, Li, As, Pb, V, Co, and Cd (for seaberries); and Fe, Mn, Cu, Zn, Cr, Ti, Ba, Ni, As, Co, Li, Pb, V, and Cd (for blackberries). The study of [PERSON] et al. (2021) [3] reported the elemental concentrations (mg/kg d.w.) in different varieties of blueberries, as variation ranges: Ca (239-432), Mg (38-361), Na (57-208), P (658-865), Ba (0.64-1.46), Cu (1.65-4.28), Fe (16.1-21.7), Mn (10.4-19.1), Sr (0.49-1.37), Zn (3.7-4.8), As (0.12-0.31), Cd (\(<\)LOD-0.059), Co (0.02-0.07), Cr (\(<\)LOD-0.08), Ni (0.03-0.18), Pb (0.03-0.15), and V (\(<\)LOD-0.067).
## 2 Materials and Methods  
### Configuration of TB-MES  
The trickling-bed bioachode microbial electrochemical system (TB-MES), constructed from Plexiglas, was comprised of two chambers separating by a cation exchange membrane (Ultrex CMI-7000, Membranes International, Inc., Ringwood, NJ, USA) (Figure 1) The cylindrical anode chamber with a total empty bed volume of 0.76 L (11 cm in inner diameter, 8 cm in height) was located at the bottom. The cathode chamber with a total empty bed volume of 2.4 L was located on the top, consisting of a thinner cylinder (8 cm in inner diameter, 25 cm in height) and a thicker cylinder (11 cm in inner diameter, 8 cm in height) connected by a cone frustum (8 cm in upper inner diameter, 11 cm in lower inner diameter, 5 cm in height). The cathode chamber was designed to be an irregular-shape, in order to facilitate the proton transfer, and to increase the differences in dissolved oxygen (DO) concentration between the upper and lower portion of the cathode chamber. Five carbon fiber brushes (4 cm in diameter and 8 cm in length; 3 K carbon fiber, Toray, Tokyo, Japan) were used as anodes [26], leaving the liquid volume of anode chamber to 0.72 L. Column activated carbon (CAC, Beijing Sanye Carbon Co. Ltd., Beijing, China), with a diameter of 2-4 mm and a length of 4-6 mm, was used as the packing material to support cathodic microbial attachment and biofilm formation. A porous Plexiglas plates with a diameter of 8 cm was used to support the CAC. The CAC was only placed in the thinner cylinder section of the cathode chamber, in order to slow down the membrane biofouling of the CEM. The CAC also functioned as auxiliary bioachode, by collecting and transporting electrons from the microorganisms to the main biocathodes, which were composed of four carbon fiber brushes (3 cm in diameter, 35 cm in length). The main biocathodes connected by titanium wires were inserted vertically into the packing material. The anode and biocathode electrodes were connected with titanium wires through an external resistance of 10 \(\Omega\) during a stable operation period. The liquid volume of cathode chamber was reduced to approximate 2.1 L due to the use of main biocathode and auxiliary bioachode.  
Figure 1: Schematic diagram of the trickling-bed bioachode microbial electrochemical system (TB-MES)(CAC; columnar activated carbon; CFB; carbon fiber brush).
## 1 Introduction
The cladding mode envelope was also used to determine the cross-correlation function and calculate its statistical parameters [9]. One of the recently proposed methods is to determine the most sensitive mode and then use it to determine the SRI value [10]; another method is to calculate the length of the optical spectrum [11]. To avoid selecting the single most sensitive resonance, a method of tracking 27 cladding mode resonances to distinguish two slightly different SRI values was proposed [12]. Differences in the shift of four resonances allowed distinguishing the simultaneous influence of temperature, stress and SRI on the TFBG spectrum [13]. The structure of the cladding mode comb of the optical spectrum of the TFBG depends on the tilt angle. For larger angles, the cladding mode comb shifts towards shorter wavelengths [14]. The most common approach to determining SRI from TFBG spectra is to look for changes related to the disappearance of cladding modes. Therefore, gratings with a tilt angle of 6-8 are typically used. Gratings with smaller angles have not been presented in the literature for SRI measurements so far. The method of analysing optical spectra proposed in this article uses a TGBG with a smaller tilt angle than those commonly used for measurement. The developed algorithm allows the use of a specific spectrum range containing a group of cladding modes. The proposed idea is relatively simple and involves determining the shift of the group of cladding modes in the wavelength domain.
## 5 Evaluation of the Models
### Model 2  
Figures 9 and 10 give the overall results and the precision of Model 2. In this model, the 95% interval contains all of the SMIs, but at the expense of very wide confidence intervals, which grow exponentially with increasing number of flight hours. It is also at the expense of poor precision for high values of number of flight hours, as can be seen in the right-hand margin of Figure 9.  
The precision and fit of this model are worse than the previous one. Some values shown in Figure 8 have very high residuals (greater than 600). The plot of residuals versus predicted values shows an increase in error and spread as the predicted values increase. This same effect can be seen at the edges of the Q-Q plot. These effects are especially due to the inability of the model to reproduce the seven data points at the far right of the diagram. This data corresponds entirely to a single ANSP, number 9. For the remaining data and ANSPs the model fits well. Furthermore, there are eight measurements with errors greater than 50, which correspond to ANSPs 9, 22, 28, 20, and 12.  
Figure 11 comprises caterpillar plots giving the distributions of each hyperparameter \(K_{j\mathrm{s}}\) of the model. The numbers show that the mean values of \(K_{j\mathrm{s}}\) are generally high. The graphs show that in the case of parameters K and K4 there is no dispersion, and that for parameters K1, K2, and K3, dispersion is limited to a few service providers, notably ANSPs 13, 8, 22, 19, 6, 10, and 29. This coincides with the analysis of Figure 10.  
Figure 10: Model 2: Residuals, predicted values vs. residuals, and Q-Q plot for Model 2.  
Figure 9: Model 2: predicted values (red) vs. actual values (black), and 2.5% and 97.5% confidence intervals for Model 2.  
Finally, the values of \(\vartheta_{j}\ (\vartheta,\ \vartheta_{1},\ \vartheta_{2},\ \vartheta_{3},\ \text{and}\ \vartheta_{4})\) for this model are summarized in Table 2.
## 3 Execution Section
### Relevance and Pertinence Evaluation  
Table 9 presents the results of the evaluation of the studies according to the relevance and pertinence criteria established. Based on the six quality criteria defined in Table 4, each article can receive a negative (minimum) score of \(-6\) points or a positive (maximum) score of \(6\) points. The total score for each article is obtained by summing the individual values for each of the criteria evaluated. Figure 4 shows the grouping of primary articles according to their total individual relevance and pertinence scores, where it can be observed that 4% of the studies (S24) have the highest score of 5 points, 14% of the studies (S6, S16, S25, and S27) have 4 points, 21% of the studies (S2, S13, S17, S19, S23, and S26) have 3 points, 7% of the studies (S7 and S11) have 2 points, 14% of the studies (S3, S5, S10, and S21) have 1 point (plus 1 point), 29% of the studies (S1, S9, S12, S15, S18, S20, S22, and S28) have 0 points, and 11% of the studies (S4, S8, and S14) have \(-1\) point (minus 1 point). Table 9 presents the results of the evaluation of the studies based on the relevance and pertinence criteria outlined. According to the six quality criteria in Table 4, each article could receive a score ranging from \(-6\) (minimum) to \(6\) (maximum). The total score for each article is the sum of individual scores across all criteria. Figure 4 groups the primary articles based on their overall relevance and pertinence score, where 4% of the studies (S24) achieved the highest score of 5 points, while 11% (S4, S8, and S14) scored \(-1\) point (minus 1 point). Based on the analysis conducted, Figure 5 presents the scores obtained for the relevance and pertinence criterion, it is observed that criterion 4 achieved the highest score with 25 points, followed by criterion 3, which obtained 18 points, this allows us to conclude that, in the evaluated articles, the results and validation of the proposals are presented clearly and well-documented. On the other hand, criterion 2 scored \(-8\), while criterion 5 reached \(-10\) points. These findings highlight the need to publish and share the results in scientific events or conferences, as well as to deepen strategies for mitigating SD.
## 4 Results and Discussion
### Sum of Distances to the Nearest Neighbour  
Figures 5 and 6 and Table 3 show the quantification of diversity using the sum of distance to the nearest neighbour measure (SDNN) and its proposed variants, i.e., modified SDNN (mSDNN) and niche SDNN (nSDNN).  
Figure 5: Quantification of diversity using the sum of distances to the nearest neighbour.  
Figure 6: Quantification of diversity using the sum of distances to the nearest neighbour (_Cont._).  
The standard SDNN obtains diversity as the sum of all the nearest neighbours for the particles in the swarm. As such, it is expected that, as the particles converge towards the optima, SDNN will obtain low diversity scores because a nearest neighbour of a particle will be another particle in the same niche. The results showed in Figures 5 and 6 do not seem to correlate with the expected behaviour. The figures show that diversity starts to decrease monotonically and then rises either at the 100 th iteration (\(f_{2},f_{6},f_{7},f_{8}\)) or around the 400 th iteration (\(f_{1},f_{5}\)) iteration. A trace of the particle positions at various iterations (refer to Appendices A-C) shows that, whereas the particles start to converge, there is a high presence of outliers (the assumption is that since these problems have 3, 1, and 1 global peaks, respectively, the presence of multiple unique solutions means that these are outliers or unknown local optima). For these outliers, the nearest neighbours are likely to be particles in already converged niches. As such, the consideration of these outliers in the calculation raises the diversity.  
The mSDNN considers the nearest neighbours at the niche level, and is therefore not affected by the presence of outliers. In the discussed work, a niche could be formed using one particle and therefore the diversity at that niche is zero. As such, the results obtained mirror what is expected. This means that, although the mSDNN seems to be a good measure, the decrease of diversity does not indicate the true picture of the search space. More investigations into this are required.  
For the nSDNN, the calculation is based on the unique solutions found. Since the outliers will be considered as unique solutions, this has the effect of raising the niche diversity. As such, although the expectation is for the nSDNN to show high diversity in both the exploration and exploitation phases, outliers do play a role in the value obtained.  
In summary, the SDNN as a measure has shown to be highly affected by the presence of outliers. As such, although the results obtained by the nSDNN is as expected, if this measure is used for quantifying dispersion for candidate solutions of niching algorithms, care has to be taken and a technique devised to remove the outliers.