esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Methods
### Spatial Discretization
Recall the arbitrariness of \(\left\{\hat{V}_{l}\right\}_{l=1}^{L}\) and adopt the inner-product notation  
\[\left\langle f|g\right\rangle\coloneqq\int_{\Omega}f(\vec{x})\,g(\vec{x}),\]  
we could turn Equation (3) into a system of ordinary differential equations:  
\[\frac{\mathrm{d}\underline{\hat{U}}_{K\times L}}{\mathrm{d}t}=\underline{B}_ {K\times L}\,\underline{A}_{L\times L}^{-1}=:\underline{R}_{K\times L} \tag{4}\]  
in which  
\[\underline{\hat{U}}(t)= \begin{bmatrix}\langle U_{1}|\phi_{1}\rangle&\cdots& \langle U_{1}|\phi_{L}\rangle\\ \vdots&\ddots&\vdots\\ \langle U_{K}|\phi_{1}\rangle&\cdots&\langle U_{K}|\phi_{L}\rangle\end{bmatrix} _ {K\times L}\]  
is the matrix of temporal functions (which will be solved in Section 2.3), and  
\[\underline{A}= \begin{bmatrix}\langle\phi_{1}|\phi_{1}\rangle&\cdots&\langle \phi_{1}|\phi_{L}\rangle\\ \vdots&\ddots&\vdots\\ \langle\phi_{L}|\phi_{1}\rangle&\cdots&\langle\phi_{L}|\phi_{L}\rangle\end{bmatrix}  _{L\times L}\]  
is a constant matrix for a given \(\Omega\), and  
\[\underline{B}=\int_{\Omega}\left[\underline{F}^{x}\quad\underline{F}^{y} \quad\underline{F}^{z}\right]_{K\times 3} \begin{bmatrix}\partial_{x}\phi\\ \partial_{y}\phi\\ \partial_{z}\partial_{y}\phi\\ \partial_{z}\partial_{y}\phi\\ \partial_{z}\partial_{y}\phi\\ \partial_{z}\partial_{y}\phi\\ \partial_{z}\partial_{y}\phi\\ \partial_{z}\partial_{y}\phi\\ \partial_{z}\partial_{z}\partial_{y}\phi\\ \partial_{z}\partial_{z}\partial_{z}\partial_{z}\end{bmatrix} _{3\times L}- \oint_{\partial\Omega}\underline{F}^{\
u}_{K\times 1}\,\underline{\phi}_{1\times L} \tag{5}\]  
is a variable matrix depending on \(\underline{\hat{U}}\), so is the residual matrix \(\underline{R}=\underline{B}\,\underline{A}^{-1}\). By applying the Gram-Schmidt orthonormalization to \(\phi\), the constant matrix \(\underline{A}\) could be an identity matrix, which would lead to \(\underline{R}=\underline{B}\). The integrals in \(\underline{B}\) would be evaluated by Gaussian quadrature rules. For triangular and tetrahedral cells, we used the quadrature rules given in [32].
# An Enhanced Belief Propagation Flipping Decoder for Polar Codes with Stepping Strategy
## 4 Numerical Results
### Analysis of the Average Number of Iterations  
The stepping strategy is used to skip some bits in FS. Thus, the number of flippings is smaller than the original flipping algorithm without the stepping strategy. To verify this point, some simulations are performed. Figures 9 and 10 compare the average number of iterations among the BPF-\(\Omega\), GBPF-\(\Omega\), EBPSF-\(\Omega\) and EGBPSF-\(\Omega\) algorithms. The average number of iterations for the EBPSF-\(\Omega\) algorithm is lower than the BPF-\(\Omega\) algorithm, while the EGBPSF-\(\Omega\) algorithm is lower than that of the GBPF-\(\Omega\) algorithm. That's because the step-flipping strategy applied in the EBPSF-\(\Omega\) and EGBPSF-\(\Omega\) algorithms reduces flipping attempts by skipping the reliable flipping bits.  
It can be observed from Figures 9 and 10 that there is a significant decrease in the average number of iterations when applying the step-flipping strategy. At high \(E_{b}/N_{0}\), the EBPSF-\(\Omega\) (\(T=256\)) algorithm is close to the BPF-\(\Omega\) (\(T=39\)) algorithm in the average number of iterations. For \(T=39\), the EBPSF-\(1\) (\(\beta=1\)) algorithm reduces the average number of iterations by 14.1% and 62.2% at 1.5 dB compared with the GBPF-1 and BPF-1 algorithms, respectively. In comparison with the GBPF-1 algorithms, the EGBPSF-1 (\(\Gamma=116\), \(\beta=0\)) algorithm reduces the average number of iterations by 16.28% at 1.5 dB.  
Similarly, for the two-bit flipping, the average number of iterations is shown in Figure 10. Under the same \(T\), the average number of iterations for the EBPSF-2 algorithm is significantly lower than that for the BPF-2 and GBPF-2 algorithms. In the case of 0 dB and \(T=12\), the EBPSF-2 algorithm is inferior to BPF-2 and GBPF-2 algorithms by 40.54% and 47.62%, as shown in Figure 10a, respectively. In Figure 10b, with \(T=128\) and \(T=256\), the EBPSF-2 algorithm reduces the average number of iterations by 77.4% and 95.9% at 1.5 dB against the BPF-2 algorithm, respectively. Consequently, the step-flipping strategy that we propose for the BP one-bit flipping and multi-bit flipping algorithms is effective in reducing the average number of iterations.  
Figure 9: The average number of iterations for GBPF-1 [(35); [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] 2020), BPF-1 [(35); (36); (40)], EGBPSF-1 and EGBPSF-1. **(a)** The average number of iterations for different algorithms with \(N=256\). **(b)** The average number of iterations for different algorithms with \(N=1024\).
# Stochastic Modeling of Smartphones GNSS Observations Using LS-VCE and Application to Samsung S20
## 3 PPP Mathematical Model
### Stochastic Model  
This section outlines the stochastic model of the undifferenced and uncombined GNSS observations. When utilizing the GNSS observations from smartphones, it is more favorable to use the C/N0-dependent weighting method instead of the elevation-dependent weighting approach. In this study, we instead use a combination of both the C/N0 and elevation-dependent weighting models. The C/N0/elevation-based variance of GNSS observations (\(\sigma_{type,i}^{2,sys}\)) is given as  
\[\sigma_{type,i}^{2,sys}=\frac{a_{type}^{sys}10^{\frac{-C/N0_{i}}{10}}}{\sin E _{i}} \tag{13}\]in which _sys_ denotes the constellation type (GPS or GLONASS); _type_ defines the observation type (code or phase); and \(\sigma^{2 sys}_{type,i}\) is the variance of observation in m\({}^{2}\) as a function of its signal-to-noise ratio value \(C/N0_{i}\) and its elevation angle \(E_{i}\). In this formula, \(a^{sys}_{type}\) is a constant that has been estimated for each constellation (GPS and GLONASS) and each observation type (code and phase) uses the LS-VCE method explained in the previous section.  
Considering GPS and GLONASS observations, the covariance matrix of the undifferenced observations is of the form:  
\[Q_{y}=\text{blkdiag}(Q_{GPS},Q_{GLO}) \tag{14}\]  
in which \(Q_{GPS}\) and \(Q_{GLO}\) are the two covariance matrices for the GPS and GLONASS systems, respectively. Assuming \(n_{1}\) and \(n_{2}\) visible satellites for GPS and GLONASS, respectively, \(Q_{GPS}\) and \(Q_{GLO}\) can be expressed as follows:  
\[Q_{GPS}=\begin{bmatrix}Q^{GPS}_{code}&Q^{GPS}_{code,phase}\\ sym.&Q^{GPS}_{phase}\end{bmatrix}\text{ and }Q_{GLO}=\begin{bmatrix}Q^{ GLO}_{code}&Q^{ GLO}_{code,phase}\\ sym.&Q^{ GLO}_{phase}\end{bmatrix} \tag{15}\]  
where \(Q^{GPS}_{code}\) and \(Q^{GPS}_{phase}\) are the two \(n_{1}\times n_{1}\) matrices related to the GPS code and carrier phase observations, \(Q^{GLO}_{code}\) and \(Q^{GLO}_{phase}\) are the two \(n_{2}\times n_{2}\) matrices related to the GLONASS code and carrier phase observations and \(sym\) is the notation of a symmetric matrix. \(Q^{sys}_{type}\) for each system and each observation type can also be obtained as follows:  
\[Q^{sys}_{type}=diag\Big{(}\Big{[}\sigma^{2,sys}_{type,1},\sigma^{2,sys}_{type,2},\ldots,\sigma^{2,sys}_{type,n_{i}}\Big{]}\Big{)} \tag{16}\]  
where _diag_ is the diagonal operator, sys could be \"GPS\" or \"GLO\", _type_ could be \"code\" or \"phase\" and \(n_{i}\); \(i=1,2\) is the number of visible satellites for GPS and GLO, respectively. In Equation (15), \(Q^{GPS}_{code,phase}\) is a matrix showing the possible correlation among the code and phase observations of each constellation. It is of the form:  
\[Q^{sys}_{code,phase}=diag\Big{(}\rho^{sys}\Big{[}\sigma^{sys}_{code,1}\sigma^ {sys}_{phase,1},\sigma^{sys}_{code,2}\sigma^{sys}_{phase,2},\ldots,\sigma^{ sys}_{code,n_{i}}\sigma^{sys}_{phase,n_{i}}\Big{]}\Big{)} \tag{17}\]  
where \(\rho^{sys}\) is the possible correlation among the code and phase observations estimated by using the LS-VCE method.
# TSViT: A Time Series Vision Transformer for Fault Diagnosis of Rotating Machinery
## 2 Time Series Vision Transformer  
Currently, employing vibration signals remains a prominent approach for diagnosing faults in rotating machinery [27]. This study takes a fixed number of sampling points that are continuous in a time sequence as a vibration signal sample, which is used as the model input. In the experiment, 2048 consecutive sampling points are taken as a sample. Figure 1 presents the architecture of the proposed TSViT model. The output is the fault type. It employs a one-dimensional CNN (1D-CNN) to extract local features and employs the transformer encoder to fully learn the long-term temporal features of input signals. It addresses the issue of a restricted receptive field in convolutional kernels, enabling the simultaneous capture of long-term dependencies in signals.
# Improved Brain Storm Optimization Algorithm Based on Flock Decision Mutation Strategy
## 4 Results
### Simulation Results and Analysis  
Tables 1-4 display the optimization performance of each algorithm when the dimension \(D\) is set to 30 and 50. For every benchmark function, 30 trials are conducted, yielding two statistical measures: the mean and the best value. The optimal average for each function is emphasized in boldface. By examining the optimization accuracy of the CEC2018, various insights emerge. First, in assessing 30-dimensional challenges against other enhanced BSO variants, the FDIBSO algorithm significantly outperforms the basic BSO algorithm. Furthermore, the performance improvements are still notably substantial compared to the modestly enhanced versions. For the CEC2018 benchmark test suite, which comprises 29 functions, FDIBSO achieves optimization with greater accuracy on 16 of those functions. Second, when juxtaposed with other enhanced BSO variants, the efficacy of the FDIBSO algorithm exhibits a decline in specific benchmark functions tailored for 50-dimensional issues. Table 2 illustrates that the FDIBSO algorithm outperforms in optimization accuracy for just 14 functions, with a slight decline in its lead. Third, in the context of 30-dimensional challenges relative to other competitive intelligent algorithms, the performance of the FDIBSO algorithm is still superior. The FDIBSO and MFO-SFR algorithms exhibit comparable performance, optimizing 12 functions with greater accuracy. Their overall effectiveness significantly surpasses that of the three other algorithms compared, underscoring the principle that no single intelligent algorithm can perfectly solve every optimization challenge. Fourth, under the 50-dimensional scenario, FDIBSO's performance diminishes relative to other intelligent algorithms, yet it still secures the lead in optimizing ten functions. Its overall performance is only outmatched by the MFO-SFR algorithm, but it remains superior to the three other algorithms it was compared with. In a word, these experimental outcomes collectively affirm the superior optimization performance of the FDIBSO algorithm. To more effectively show the FDIBSO algorithm's ability in convergence speed, Figures 3 and 4 depict the convergence trajectories for various enhanced BSO algorithms across four benchmark functions from the CEC2018. The blue curve in the figure represents the FDIBSO algorithm. Although the convergence speed of this algorithm is significantly improved compared to the traditional BSO algorithm, it is not much improved compared to the BSO variant algorithm. This problem is because the FDIBSO algorithm employs the good point set and the flock decision mutation strategy, significantly improving population diversity. As a result, in the early stages, the search is more comprehensive, and convergence is relatively slow. However, with iterations, the FDIBSO algorithm can escape local optima and achieve higher optimization accuracy.
###### Abstract  
Network-security situation prediction is a crucial aspect in the field of network security. It is primarily achieved through monitoring network behavior and identifying potential threats to prevent and respond to network attacks. In order to enhance the accuracy of situation prediction, this paper proposes a method that combines a convolutional neural network (CNN) and a gated recurrent unit (GRU), while also incorporating an attention mechanism. The model can simultaneously handle the spatial and temporal features of network behavior and optimize the weight allocation of features through the attention mechanism. Firstly, the CNN's powerful feature extraction ability is utilized to extract the spatial features of the network behavior. Secondly, time-series features of network behavior are processed through the GRU layer. Finally, to enhance the model's performance further, we introduce attention mechanisms, which can dynamically adjust the importance of different features based on the current context information; this enables the model to focus more on critical information for accurate predictions. The experimental results show that the network-security situation prediction method, which combines a CNN and a GRU and introduces an attention mechanism, performs well in terms of the fitting effect and can effectively enhance the accuracy of situation prediction.  
network security; situation prediction; attention mechanism; 1D CNN; GRU +
Footnote †: journal: Applied sciences
## 4 Proposed mmWave Assisted CR-IoV
### Dual Step Security Provisioning
#### 4.3.2 PUE Attack Detection  
To detect a PUE attack, we proposed the FA-TDoA algorithm, which estimates the position of the signal source (can be PU or attacker) accurately. Then, the position information is compared with the original position of PUs to detect the attackers accurately. In this work, PUs are the TV receivers, and most PUs are static, i.e., the location of PUs is known priorly. During spectrum sensing, the PUE attacker emulates the PU signal so that the SU generates a report as the PU presence. Before sending the sensing reports to the CBS, each SU detects whether the signal is received from the attacker. In this work, spectrum sensing is performed by using the Enriched Energy Detection (E2D) method, which is capable of working in low Signal-to-Noise Ratio (SNR) scenarios. We have improved the conventional energy detection method by incorporating a dynamic threshold value based on the current SNR level. The reason behind the enriching spectrum sensing method is that the spectrum sensing report may also be falsified due to the presence of noise. In a noisy environment, the energy detection method may provide an incorrect report which may lead to considering the SU as malicious. To assure high-level accuracy, we have enriched the energy detection method. The presence of PU is detected by the E2D method based on the following hypotheses,  
\[RS(l)\ =\ \left\{\begin  
The noise uncertainty factor computed is the function of noise frequency (\(\mu\)) of each signal sample from the total \(M\) number of signal samples. It can be expressed as,  
\[\rho_{F}=\frac{\underset{1\leq m\leq M}{\max}\mu_{I}^{2}(m)}{\frac{1}{M}\underset {m=1}{\sum}\mu_{I}^{2}(m)} \tag{7}\]  
The above factor is dynamic upon the noise frequency which varies with the noise level present in the environment. The reason for using dynamic threshold value is that the presence of high-level noise results in incorrect sensing results. In the proposed E2D, the sensing report is accurate. Based on this report, PUE attack detection is performed. It is worth mentioning that presenting a new dynamic threshold value also increases the sensing accuracy. In general, the PU presence decision is made in two scenarios as (i) truly PU is presented on the particular channel or (ii) the PUE attacker emulates the PU signal. In the first case, SUs are unable to use the available spectrum, but in the second case, SUs can use the spectrum. For that, it is necessary to detect whether the signal comes from the PU or PUE attacker. For accurate detection, we presented the FA-TDoA algorithm. TDoA shows versatile performance in localization problems [52]. However, in TDoA, ambiguous positioning occurs due to misalignment between the reference receivers. Thus, we have combined FA with TDoA to achieve accurate positioning of the signal source.
## 1 Introduction
Considering the 8-year database of COMS data, it is anticipated that a COMS/MI-derived SST database could contribute to the production of continuous time series of SST in this particular region. Therefore, in order to understand ocean phenomena using COMS/MI SST data and to improve predictions of SSTs in the western Pacific Ocean, it is necessary to derive SST retrieval coefficients. In response to this necessity, the main objective of this study is to provide SST coefficients for COMS data. The more detailed objectives are (1) to produce a matchup database between COMS satellite data and in situ measurements, (2) to remove cloudy and cloud-contaminated pixels from the regression procedure, (3) to compare the estimated SSTs in this study with the SST retrievals using previously-known algorithms, (4) to present the coefficients of MCSST and NLSST for COMS data,  
Figure 1: (a) Bathymetry and the sea surface temperature climatology in the COMS/MI full-disk area in (b) February and (c) August. (5) to understand and discuss the characteristics of SST errors, especially in the seas around Korea, and (6) to validate the satellite SST retrievals using the drifting buoy measurements.
## 2 Model Derivation
### Momentum Equation  
The momentum equation expresses the equilibrium of forces that originate from inertia, pressure and viscosity. It is possible to write it as follows:  
\[\rho\cdot\frac{\partial\mathbf{v}}{\partial t}+\rho\cdot\mathbf{v}\cdot( \
abla\mathbf{v})-\
abla\cdot\mathbf{\Pi}+\
abla p=0, \tag{16}\]  
where the stress tensor is a function of shear viscosity and second viscosity:  
\[\mathbf{\Pi}=\eta\cdot\left(\
abla\mathbf{v}+\
abla\mathbf{v}^{T}\right)+\eta _{2}\cdot\mathbf{I}\cdot(\
abla\cdot\mathbf{v}). \tag{17}\]  
Substituting Equation (17) into Equation (16) yields:  
\[\frac{\partial\mathbf{v}}{\partial t}-\frac{\eta}{\rho}\cdot\
abla\cdot( \
abla\mathbf{v})-\frac{\eta+\eta_{2}}{\rho}\cdot\
abla\left(\
abla\cdot \mathbf{v}\right)+\frac{1}{\rho}\cdot\
abla p=0, \tag{18}\]  
where the convective acceleration is neglected because the liquid velocity is much lower than the speed of sound. When Equation (18) is integrated over the volume defined in Figure 1, the momentum equation for the axial direction is obtained:  
\[\frac{\partial Q}{\partial t}-\frac{2\cdot\eta+\eta_{2}}{\rho}\cdot\frac{ \partial^{2}Q}{\partial x^{2}}-\left(\frac{4\cdot\eta}{\rho\cdot D^{2}} \right)^{2}\cdot\int\limits_{0}^{t}W\left(t-\tau\right)\cdot Q\left(\tau\right) \cdot\mathrm{d}\tau+\frac{S}{\rho}\cdot\frac{\partial p}{\partial x}=0. \tag{19}\]Here, the function \(W\) represents energy loss due to an unsteady velocity profile. The function is well described in [22; 23]. The unsteady velocity profile has a significant impact on energy loss in the case of viscous liquids (e.g., oil).  
Applying the Laplace transform to Equation (19) and using Equation (15) yields the final shape of the momentum equation:  
\[s\cdot\bar{Q}-\left(\frac{4\cdot\eta}{\rho\cdot D^{2}}\right)^{2}\cdot\bar{W} \cdot\bar{Q}+\left(\frac{S}{\rho}+\frac{2\cdot\eta+\eta_{2}}{\rho^{2}}\cdot \frac{S\cdot s}{a_{c}^{2}}\right)\cdot\frac{\partial\bar{p}}{\partial x}=0. \tag{20}\]
## 5 Conclusions and Outlook  
The present fertilization trials evaluated various systems and their variations, demonstrating the high performance of both GFO and sensor-based fertilization strategies This was evident in the high yields achieved (yields > 10 t ha\({}^{-1}\)), the excellent NUE (up to 88%), and the low N surpluses (mostly balanced) observed under the controlled conditions of the trials. In contrast, N surpluses in agricultural practice in Germany remain significantly higher, ranging between 70 and 100 kg ha\({}^{-1}\) over the past decade. The consistent implementation of GFO and sensor-based fertilization in practice could lead to a substantial reduction in N surpluses without compromising yields. However, challenges remain, particularly in regions with intensive organic fertilization, where the highest N surpluses are observed. The trials conducted at the Roggenstein research station benefited from excellent soil and climatic conditions, achieving very high yields and NUE. It is essential to investigate how these systems perform under less favorable conditions, such as sandy soils in arid regions with pronounced early-summer droughts, which are becoming more common due to climate change. Further studies should also explore the long-term impact of integrating sensor-based systems with organic fertilization to address N surpluses in mixed farming systems. Additionally, scaling these systems for larger heterogeneous fields could offer new insights into their practical applications across diverse agricultural landscapes. M.M. : Writing--review and editing, Writing--original draft, Visualization, Validation, Software, Methodology, Investigation, and Formal analysis. F.-X.M. : Methodology, Conceptualization, Investigation, Funding acquisition, and Review. J.D. : Methodology, Writing--review and editing, Writing--original draft, Visualization, Validation, and Software. S.K. : Investigation. J.L. : Formal analysis and Validation; K.-J.H. : Writing--review and editing, Writing--original draft, Supervision, Project administration, Funding acquisition, and Conceptualization. All authors have read and agreed to the published version of the manuscript. This study was funded by the Bavarian State Ministry of Food, Agriculture, and Forestry. Not applicable. The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. Figure 11: Design of the plot trial. The trials were consistent in each study year (2021–2023). Figure 12: Relationships between N fertilization, yield, and nitrogen surplus for the year 2022 (Sandra). Yield is given in fresh matter with a dry matter content of 86%. The lines above describe the relationship between N fertilization and yield, while the lines below illustrate the relationship between N fertilization and N surplus.