esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 A General Solution
### Solutions for Series Composed of Terms \(\left(j_{p,k}^{2}-j_{p+r,n}^{2}\right)^{-l}\)
#### 2.2.1 Solutions for \(l=1\)  
The commonly known recursive formula for the Bessel function is as follows:  
\[\frac{2(\
u+1)}{z}J_{\
u+1}(z)=J_{\
u}(z)+J_{\
u+2}(z) \tag{27}\]  
If, in this formula for \(\
u\), coefficient one assumes \(\
u=p-1\), then  
\[\frac{2p}{z}J_{p}(z)=J_{p-1}(z)+J_{p+1}(z) \tag{28}\]  
Rearranging this gives the following:  
\[J_{p+1}(z)=\frac{2p}{z}J_{p}(z)-J_{p-1}(z) \tag{29}\]  
Using Equation (29) in Equation (6) gives the following:  
\[\frac{2p}{z}-\frac{J_{p-1}(z)}{J_{p}(z)}=2z{\sum_{k=1}^{\infty}\frac{1}{j_{p, k}^{2}-z^{2}}} \tag{30}\]  
The above form of Equation (30) and its appropriate derivatives allow all the formulas to be determined from the right columns of the final formulas (some of which are summarized in Appendix A).  
To derive a general formula for selected solutions, when only the first derivatives of the difference in the denominator are taken into account \(\left(j_{p,k}^{2}-z^{2}\right)^{1}\), the following recursive formula for the Lommel polynomials [21], p. 109, needs to be used:  
\[(-1)^{m}J_{\
u-m}(z)=J_{\
u}(z)R_{m,-\
u}(z)+J_{\
u+1}(z)R_{m-1,\;1-\
u}(z) \tag{31}\]  
By making simple transformations to the above formula, the following form can be obtained:  
\[(-1)^{m}\frac{J_{\
u-m}(z)}{J_{\
u+1}(z)}\frac{1}{R_{m,-\
u}(z)}-\frac{R_{m-1,\;1-\
u}(z)}{R_{m,-\
u}(z)}=\frac{J_{\
u}(z)}{J_{\
u+1}(z)} \tag{32}\]  
When substituting for \(\
u=p-1\), one obtains the following:  
\[(-1)^{m}\frac{J_{p-m-1}(z)}{J_{p}(z)}\frac{1}{R_{m,\;1-p}(z)}-\frac{R_{m-1,\;2 -p}(z)}{R_{m,1-p}(z)}=\frac{J_{p-1}(z)}{J_{p}(z)} \tag{33}\]By inserting the formula Equation (33) to Formula (30) one obtains the following:  
\[\frac{2p}{z}-(-1)^{m}\frac{J_{p-m-1}(z)}{J_{p}(z)}\frac{1}{R_{m,\ 1-p}(z)}+\frac{R_{m-1, \ 2-p}(z)}{R_{m,1-p}(z)}=2z{\sum_{k=1}^{\infty}}\frac{1}{j_{p,k}^{2}-z^{2}} \tag{34}\]  
Substituting \(z=j_{p-m-1,r}\), i.e., the roots (zeros) of the function \(J_{p-m-1}\big{(}j_{p-m-1,r}\big{)}\) into Equation (34) results in the following final form:  
\[\boxed{\frac{p}{j_{p-m-1,r}^{2}}+\frac{R_{m-1,\ 2-p}\big{(}j_{p-m-1,r}\big{)}}{2j_ {p-m-1,r}\cdot R_{m,1-p}\big{(}j_{p-m-1,r}\big{)}}={\sum_{k=1}^{\infty}}\frac{ 1}{j_{p,k}^{2}-j_{p-m-1,r}^{2}}} \tag{35}\]  
The derived formula Equation (35) can be used to prove the correctness of some formulas found in Table A1: (A7), (A13), (A19) and (A24). Their detailed derivation can be found in Appendix C.
# Global Formulation of the Synthetic Storm Technique Oriented to Satellite Link-Budget Design
###### Abstract  
We have updated the global Synthetic Storm Technique (referred to as the global SST) by reformulating it according to a larger database of rain rate time series collected in several sites in different climatic regions. For each site, the average annual probability distribution of rain attenuation obtained with the global SST, \(P_{SST,glo}(A)\), in a slant path, was compared with that given by the full SST, \(P_{SST}(A)\), which we have considered as experimental data. The test was performed for frequency ranging from 10 to 100 GHz, for elevation angle \(\theta\) ranging from 20\({}^{\circ}\) to 60\({}^{\circ}\) and for annual probabilities 10% to 0.01%. The global SST tends to underestimate the attenuation by approximately 10% for elevation angle \(\theta\leq 30^{\circ}\) and about 20% for \(30^{\circ}<\theta<60^{\circ}\) in the probability range 10% to 0.1%, and approximately 15% in the probability range 0.1% to 0.01%. For any probability, the error is zero for \(\theta=90^{\circ}\) because at the zenith, the global SST coincides with the full SST. link budget; global SST; rain attenuation; Synthetic Storm Technique; SST; satellite communication [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][21][29][20][20][21][22][23][24][25][26][27]  
path length \(L\), is built up by partial values \(\Delta A(t)\) in partial precipitation path lengths \(\Delta L\)[38]. The purpose of this paper is to update the global SST according to the results obtained from a larger database of rain rate time series collected at several sites in different climatic regions than those used many years ago. For each site, the average annual probability distribution of rain attenuation obtained with the global SST, \(P_{SST,glo}(A)\), is compared with that given by the full SST, \(P_{SST}(A)\), which we consider as experimental data. The test is conducted for frequencies ranging from 10 to 100 GHz, for elevation angle \(\theta\) ranging from 20\({}^{\circ}\) to 90\({}^{\circ}\), and for all annual probabilities 10% to 0.01%. Finally, we recommend that whenever 1-min rain rate time series \(R(t)\) are available at a site the full SST [1] be used. After this Introduction, Section 2 describes the full SST and the global SST, Section 3 models the fundamental parameter \(m\) of the global SST, Section 4 reports the results of the comparison between the full SST and the global SST, Section 5 reports the overall error and
# Ultrafast and Wideband Microwave Photonic Frequency-Hopping Systems: A Review
## 2 Microwave Photonic Frequency-Hopping Systems
### Frequency-Hopping through Period-One Nonlinear Dynamcis in Semiconductor Lasers
Thanks to the fast P1 dynamic response, \(\sim\)10 ns hopping speed is demonstrated. P1 dynamic-based frequency-hopping signal-generation scheme can generate multi-level frequency-hopping signal. With a four-level hopping code sequence, the resultant frequency-hopping signal can hop between four different frequencies, as shown in Figure 6e,f. Since the resultant frequency greatly depends on the injection light amplitude, it is important to reduce amplitude fluctuation in the injection light to prevent instability in the frequency-hopping signal frequency.
# Automatic Detection of Sensitive Data Using Transformer-Based Classifiers
## 8 Results
The results in Table 8 confirm that the hierarchical model can reach a slightly better \(F_{1}\)-score than the flat multi-label classifier, causing a negligible increase in the average decision time per sentence. In the comparison between the two models on the sensitive sentence detection, the sensitive class selection and the complete classification tasks, we have shown that the hierarchical classifier can reach a slightly higher accuracy than the flat multi-label classifier. In the end, neither model clearly outperforms the other: if one needs to maximize prediction accuracy, the hierarchical model appears to be preferable even if there is not such a big \begin{table}
\begin{tabular}{l l l l l} \hline \hline  & **Precision** & **Recall** & \(\mathbf{F_{1}}\)**-Score** & **Runtime (s)** \\ \hline
**Multi-class model** & 0.94 & 0.94 & 0.94 & 0.11 (\(\pm\)0.01) \\ \hline Health & 0.91 & 0.95 & 0.93 & \\ Politics & 0.96 & 0.92 & 0.94 & \\ Religion & 0.94 & 0.96 & 0.95 & \\ Sexuality & 0.94 & 0.93 & 0.93 & \\ \hline
**Multi-label model** & 0.95 & 0.87 & 0.91 & 0.12 (\(\pm\)0.01) \\ \hline Health & 0.92 & 0.87 & 0.89 & \\ Politics & 1.00 & 0.81 & 0.90 & \\ Religion & 0.94 & 0.93 & 0.93 & \\ Sexuality & 0.94 & 0.89 & 0.91 & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison between the multi-class neural network of the hierarchical model and the flat multi-label model. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Text** & **Actual Class** & **Predicted Labels** \\ \hline I think they allow medical intervention in life and death cases, & & \\ but I know someone who is a Christian Scientist & Health & Health, Religion \\ and is not getting vaccinated. & & \\ \hline [PERSON] literally said on national TV he would not trust a & & \\ vaccine developed under the [PERSON] administration. & Politics & Health, Politics \\ \hline I wish people’s superstitious beliefs were not so often involved & & \\ in politics, and I wish politicians did not feel the need to & & \\ declare or pretend they are religious to gain support. & Religion & Politics, Religion \\ \hline My family is not open to the idea of me being trans, but I & & \\ already take antidepressants, so they aren not against me & Sexuality & Health, Sexuality \\ taking medication. & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Text and prediction of the four sentences associated with more than one label by the flat classifier. difference between the two. In fact, if one is only interested in detecting sensitive topics and not in their categorization, such a difference becomes negligible. On the other hand, considering computation cost, it is important to consider that the hierarchical classifier uses two neural networks to produce a response and, therefore, requires a slightly longer time than the flat multi-label one, which includes just one NN. In a corporate environment where the amount of data can easily become massive and where it is often required to have a quick response time, even this slight difference may become significant in deciding which model to choose.
###### Abstract  
Estimating molar solubility from the Hildebrand-Scott relation employing Hansen solubility parameters (HSP) is widely presumed a valid semi-quantitative approach. To test this presumption and to determine quantitatively the inherent accuracy of such a solubility prognosis, L-ascorbic acid (LAA) was treated as an example of a commercially important solute. Analytical calculus and Monte Carlo (MC) simulation were performed for 20 common solvents with total HSP ranging from 14.5 to 33.0 (MPa)\({}^{0.5}\) utilizing validated material data. It was found that, due to the uncertainty of the material data used in the calculations, the solubility prediction had a large scattering and, thus, a low precision. Prediction power is most adversely affected by the uncertainty of the HSP estimates (solvent and solute), followed by the solute heat of fusion. The solute melting temperature and molar volume have minor effects. Computed and experimental solubilities show the same qualitative behavior, while quantitative discrepancies reach one to three orders of magnitude. Solubility estimates were found to provide, at best, rough guiding information but, with the quality of material data on LAA available, they cannot be rated semi-quantitative. It is assumed that these results generally apply at least to solute-solvent systems with a material data quality and solubility similar to LAA.  
molar solubility estimation; ascorbic acid solubility; ascorbic acid Hansen parameter +
Footnote †: journal: Applied Soft. 2020, 10, 4266; doi:10.3390/app10124266
## 3 Clustering Methods
### Gaussian Mixture Model (GMM)
Unlike hard clustering methods, which assign each cell to exactly one cluster, a GMM outputs membership probabilities that indicate how strongly each cell belongs to each cluster. In our case, we leverage these soft memberships  
Figure 6: GMM Clustering results. to form equal-sized modules, by sorting the cells of each cluster in descending order of membership probability and assigning them until the desired module size is reached. If any clusters become over- or underfilled, cells near the boundary of cluster membership are reassigned to maintain the overall equal distribution. This probabilistic approach ensures that each 15-cell module remains compositionally uniform while still respecting the practical requirement of equal-sized modules.
## 5 Results and Discussion
### Limitations  
A limitation of our method is that the tuned models sometimes produced utterances that were poor in terms of fluency. Figure 6 shows an example of the translation of a science fiction, _Snow Crash_[50]. Note that some of the translated utterances (e.g., \"Oh, where do you be?\") are grammatically incorrect. The fluency problem is probably related to the size of the language models [51], and this limitation will be resolved as we tune larger models with larger datasets.  
\begin{table}
\begin{tabular}{c|c c c|c c c} \hline \hline \multirow{2}{*}{**TopK**} & \multicolumn{3}{c|}{**\#Win of \(m_{t}\)**} & \multicolumn{3}{c}{**\#Win of \(m_{b}\)**} \\ \cline{2-7}  & \multicolumn{2}{c}{**Total**} & \multicolumn{2}{c}{**[PERSON]**} & \multicolumn{2}{c|}{**[PERSON]**} & \multicolumn{2}{c}{**Total**} & \multicolumn{2}{c}{**[PERSON]**} & \multicolumn{2}{c}{**[PERSON]**} \\ \hline
10 & 49 & 20 & 29 & 51 & 30 & 21 \\
30 & 52 & 24 & 28 & 48 & 26 & 22 \\
50 & 53 & 24 & 29 & 47 & 26 & 21 \\
73 & 47 & 25 & 22 & 53 & 25 & 28 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Evaluation results of Gemma2-9B, showing win counts for the tuned model (\(m_{t}\)) and base model (\(m_{b}\)) across different TopK values.  
Figure 6: An example of utterance translation. The conversation between [PERSON] and [PERSON] in the novel _Snow Crash_[50] (**left**) is translated into a conversation between two different characters (**right**). The bottom table describes the personality of the four characters by their per-trait keywords (all keywords can be found in Table 1).  
A further limitation is related to the clustering method used to represent character personality. While clustering based on personality trait annotations for each character would be ideal, it requires costly manual annotation. As a practical alternative, we adopted a word-based clustering approach. Notably, the resulting two clusters may reflect an implicit binary structure underlying character styles in the dataset. In future work, we plan to expand the dataset, explore a broader range of cluster numbers, and apply more sophisticated methods such as hierarchical clustering.
# A Novel Protocol Using Captive Portals for FIDO2 Network Authentication +
## 5 Prototype Development and Validation
### Captive Portal Integration with OpenNDS
#### 5.2.1 OpenNDS Authmon: API Server and Enforcement Device  
OpenNDS has a module named Authmon that implements an API Server and an Enforcement Device. As implemented in OpenNDS, the Authmon module sends periodic requests to the FAS server. In this prototype, the FAS server is our WAWA server, which we have made compatible by extending the WAWA API, accepting the requests from Authmon.  
The Authmon module of OpenNDS sends periodic requests to the FAS server to poll for new authenticated clients. Figure 5 shows a flow diagram that represents the final integration of the Authmon operation to authorise clients with the developed FAS server. It is worth mentioning that this integration was possible after the reverse engineering process due to the lack of detailed documentation.  
Following Figure 5, (1-3) the captive portal run by OpenNDS redirects unauthorised clients to the WAWA server URL, together with a hashed id (hid), encoded and encrypted as explained in Section 5.2.3; (4-5) when handling User Equipment requests, the WAWA server must decrypt these details and calculate the authorisation token rhid as explained in Section 5.2.3; (6-9) when the FIDO2 authentication is successful, the WAWA server marks the client as authenticated; (11) all authorisation codes (the rhid) are requested periodically to the WAWA (FAS) server, who returns a list of authorisation tokens is sent to the OpenNDS router; and (12-14) using this token, OpenNDS can authorise the corresponding client for their access to network resources, notifying WAWA about this.
# Vibration Fatigue Analysis of a Simply Supported Cracked Beam Subjected to a Typical Load
## 4 Results and Discussions
### Natural Frequency  
For the simply supported cracked beam, the geometric parameters of the crack are as follows: \(x_{c}\in[0,L]\) and \(a_{0}/h\in[0,0.5]\). As the relative position and depth of the crack change, the first order natural frequency variation is shown in Figure 4.  
As shown in Figure 4, the crack is the important factor affecting natural frequencies of the beam, which cannot be ignored. As the crack's relative depth increases, the first order natural frequency of the beam gradually decreases, and the amplitude of the decrease gradually increases. From the perspective of the crack's relative position, the first order natural frequency variation is symmetrical in the middle section of the simply supported beam. When the crack is in the middle part of the simply supported beam (\(x_{c}/L\in[0.3,0.7]\)), the first order natural frequency decreases faster as the crack's relative depth increases.
# Interactions between Two Deformable Droplets in Tandem Fixed in a Gas Flow Field of a Gas Well
## 4 Conclusions  
The interactions between two droplets with high Reynolds numbers in a tandem arrangement, fixed in a gas flow field of a gas well, was numerically investigated.  
The interactions between the two droplets were analyzed by comparing them with the simulation results of a single isolated droplet at four initial Weber numbers of 1, 4, 6.8, and 12.1. It was demonstrated that the droplet became an ellipsoid, whose aspect ratio decreased as the Weber number rose, and that the critical Weber number for the breakup of the droplet was 12, which was consistent with that of the single isolated droplet. In addition, the drag coefficient of the upstream droplet was slightly smaller than that of the isolated droplet at the beginning of the droplet deformation, but the difference decreased and gradually disappeared.  
However, the dynamics of the downstream droplet were influenced significantly by the upstream droplet for a separating space between the droplets of L \(<\) 4D, but the influence could be ignored for a separating space of L \(>\) 4D. Such critical separating spaces was smaller than the value found in previous studies with Reynolds numbers smaller than 200. The downstream droplet was deformed into a gyroscopic downward as the Weber number grew under the suction force from the low-pressure region behind the upstream droplet. The critical Weber number for the breakup of the downstream droplet was much greater than 12 if sheltering from the upstream droplet still existed. The drag coefficient of the downstream droplet decreased with the increase in the Weber number and the decrease in the separating space, reducing to zero or below zero.  
Based on the results of the numerical simulation, a formula for predicting the final drag coefficient of the downstream droplet was devised.  
Conceptualization, Z.W. and T.S.; methodology, Z.W.; software, Z.W., Z.Y., and G.Z.; writing--review and editing, Z.W. and H.S.; investigation, T.S. and Z.Y. All authors have read and agreed to the published version of the manuscript.  
This study is financially supported by the National Natural Science Foundation (No. 51974263).  
The authors declare no conflict of interest.  
Figure 8: The deviation of the final drag coefficient between the downstream droplet and the single isolated droplet.
## 5 Discussion
### Spectral Parameters and Their Implications for Redox Conditions  
In alteration wall rocks of Gongchangling high-grade iron ore, the changes of wavelength position and absorption depth at ca. 1200 nm wavelength position represent the content Fe\({}^{2+}\) in octahedron lattice position for chlorite and dodecahedron lattice position for garnet. With the gradual increase content of Fe\({}^{2+}\), the wavelength position moves towards the short wavelength direction and the absorption depth increases dependently [11; 54; 55; 56].  
The chlorite and garnet in alteration rocks of Gongchangling iron deposit were analyzed emphatically. Fe\({}^{2+}\) could result in a crystal field effect, due to the spin-allowed transition between the E\({}_{\text{g}}\) and T\({}_{\text{2g}}\) levels into which the D ground state splits in an octahedral field, which is the most important factor for the spectroscopy [57]. In previous research, the absorption band, caused by the crystal field effect and electron transition of Fe\({}^{2+}\) at 1000-1200 nm, resulted from to the large amount of Fe\({}^{2+}\) in chlorite and other phyllosilicates [57]. The absorption peak wavelength position moves towards the long wavelength direction with decreased content of Fe\({}^{2+}\)[52; 56]. The absorption characteristic of Fe\({}^{2+}\) at 1200 nm generally is sixth coordination divalent iron for chlorite, and eighth coordination iron divalent for garnet [11]. If iron ion is located in a complete octahedral lattice site, and only one spin allows transition, it will produce a characteristic band in the visible and near-infrared region. However, when the octahedral position is distorted and the iron ion is in the non-equivalent position, another characteristic transition will occur [57]. Therefore, the spectral features of Fe\({}^{2+}\) have been used to obtain information on the changes of mineral texture and implications for mineralization environment.  
From proximal ore bodies to the outer zones of wall rocks, the movement of wavelength position towards the long wavelength direction and the decreases of absorption depth for chlorite and garnet indicated a gradual decrease in the content of Fe\({}^{2+}\), a change of water-rock interaction and a relatively reductive environment of the formation for the whole altered rock. Additionally, it is implied that the garnet's formation environment is more reductive and higher in water-rock interactions in proximal than distal ore bodies. That is consistent with the previous research; therefore, the content of Fe\({}^{2+}\) revealed by HySpex spectrum can be vector of deposit exploration.
## 2 Method  
### Overview of the Dual-Domain Joint Deep Learning Framework  
In this study, we proposed a joint deep learning framework based on dual-domain (projection and image domains) for the correction of metal artifacts in industrial CT images. As illustrated in Figure 1, our framework incorporates two main components: initially employing a UNet architecture in the projection domain to perform a pre-correction on the projection data, followed by generating images using a reconstruction algorithm, and then applying a ResNet architecture in the image domain to further refine the reconstructed images. The joint training process allows the two network modules to learn interactively, enabling a collective optimization of the overall correction performance.