esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Control Strategy
### Particle Swarm Optimization (PSO)  
The particle swarm optimization (PSO) method has been widely used for many years. The PSO algorithm, first developed by [PERSON] and [PERSON] in 1995, was inspired by the social behavior of flying flocks [55].  
While the PSO algorithm sets the PID parameters in this study, it starts with a random position of all particles in the search space, and the positions of the particles are updated according to two values at each step. The first is the previous best solution, called \(P_{best}\). The other is the best result from all iterations since the first iteration, and this result is the optimum PID parameter value found. It is called global best or \(g_{best}\). The search continues in the PSO until the specified number of iterations is reached or the optimum error value is reached. The swarms of particles progressively continue until the specified number of iterations is reached, constantly updating speed and position information to be optimal. The position update formula for the particles used in this study is:  
\[\begin{split} V(k+1)=w(k+1)\;V(k)+c_{1}(k+1)\;rand_{1}\;(P^{\rm{ lbest}}(k+1)-P(k))\\ +c_{2}(k+1)\;rand_{2}\;(P^{\rm{gbest}}(k+1)-P(k))\end{split} \tag{17}\]  
\[P(k+1)=P(k)+V(k+1) \tag{18}\]  
where \(V(k)\) denotes particle velocity and \(P(k)\) represents the particle positions. \(w\), \(c_{p}\) (\(p=1\), \(2\)), \(P^{\rm{lbest}}\) and \(P^{\rm{gbest}}\) denote the inertia weight, positive learning coefficients and the local and global best results, respectively. \(rand_{1}\) and \(rand_{2}\) are random numbers between 0 and 1.  
Inertia weight in Equation (17) represents the momentum degree of particles. For early iterations, this value can be set higher, allowing the particles to widely explore and aggressively investigate the solution area. In order to further optimize the algorithm, this setting is gradually converted, making it smaller in later iterations, and better results can be achieved. In this study, the moment of inertia \(w\), starting from the first iterations (\(w_{\rm{max}}\)), was gradually decreased linearly to the last iterations (\(w_{\rm{min}}\)). For this case, the \(w(k+1)\) value was obtained by the following equation.  
\[w(k+1)=w_{\rm{max}}-\frac{w_{\rm{max}}-w_{\rm{min}}}{i_{\rm{max}}}i \tag{19}\]  
where i and \(i_{\rm{max}}\) indicate the iteration's number and its maximum number, respectively. The optimization parameters used for PSO algorithms are shown in Table 4.  
\begin{table}
\begin{tabular}{l l l} \hline  & **Optimizer-1** & **Optimizer-2** \\ \hline Number of variables & 12 & 16 \\ Population & 20 & 20 \\ Max. iteration & 20 & 20 \\ Wmax (inertia momentum) & 20 & 20 \\ Wmin (inertia momentum) & 0.9 & 0.9 \\ \(C_{1}\) (positive learning coefficients) & 0.2 & 0.2 \\ \hline \end{tabular}
\end{table}
Table 4: The parameters of PSO algorithms for both optimizers.
# Time-Varying Preference Bandits for Robot Behavior Personalization
## Appendix B Proof of Theorem 2  
Proof.: We first decompose the regret into two terms. From (4), we have  
\[\left|(X_{t}^{*})^{\intercal}\hat{\theta}_{t}\right|+\alpha_{t}\big{\|}X_{t}^ {*}\big{\|}_{V_{t}^{-1}}\leq\left|X_{t}^{\intercal}\hat{\theta}_{t}\right|+ \alpha_{t}\big{\|}X_{t}\big{\|}_{V_{t}^{-1}} \tag{17}\]  
where \(X_{t}^{*}:=\max_{X\in\mathcal{X}}\left|X^{\intercal}\theta_{t}^{*}\right|\) and \(X_{t}\) is the query selected by the algorithm. From (17), we can bound the difference of logistics. For \(t\in\mathcal{T}(\gamma)\), we have  
\[\left|(X_{t}^{*})^{\intercal}\theta_{t}^{*}\right|-\left|X_{t}^{ \intercal}\theta_{t}^{*}\right|\leq\left|(X_{t}^{*})^{\intercal}\hat{\theta}_{t }\right|-\left|X_{t}^{\intercal}\hat{\theta}_{t}\right|+\left|(X_{t}^{*})^{ \intercal}\theta_{t}^{*}\right|\] \[-\left|(X_{t}^{*})^{\intercal}\hat{\theta}_{t}\right|+\left|X_{t}^ {\intercal}\hat{\theta}_{t}\right|-\left|X_{t}^{\intercal}\theta_{t}^{*}\right| \leq 2\pi_{T}\big{\|}X_{t}\big{\|}_{V_{t}^{-1}} \tag{18}\]  
where the inequalities hold due to Theorem 2 for \(t\in\mathcal{T}(\gamma)\). By using this fact, we can decompose and bound the cumulative regret as follows  
\[\mathcal{R}_{\mathcal{T}}\overset{\text{(a)}}{\leq}\sum_{t=1}^{ \mathcal{T}}\left|(X_{t}^{*})^{\intercal}\theta_{t}^{*}\right|-\left|X_{t}^{ \intercal}\theta_{t}^{*}\right| \tag{19}\] \[\overset{\text{(b)}}{\leq}B_{\mathcal{T}}N(\gamma)+2\pi_{T}\sum_{ t\in\mathcal{T}(\gamma)}\left\|X_{t}\right\|_{V_{t}^{-1}} \tag{20}\]where (**a**) holds due to the 1-Lipschitz continuity of \(\mu\), and (**b**) holds by (A9) and the definition of \(\mathcal{T}(\gamma)\). Now, we will bound the second term as follows  
\[2\pi_{T}\sum_{t=1}^{T}\left\|X_{t}\right\|_{V_{t}^{-1}}\leq 2\pi_{T} \sqrt{T\sum_{t=1}^{T}\left\|X_{t}\right\|_{V_{t}^{-1}}^{2}}\] (A13) \[\leq 2\pi_{T}\bigg{[}(1+D\lambda^{-1})T\sum_{t=1}^{T}\left\|X_{t} \right\|_{V_{t+1}^{-1}}^{2}\bigg{]}^{1/2}\] (A14) \[\leq 2\pi_{T}\sqrt{(1+D\lambda^{-1})T\bigg{[}\ln\bigg{(}\frac{ \det(V_{T+1})}{\det(\lambda I_{d})}\bigg{)}+dT\ln\bigg{(}\frac{1}{\gamma} \bigg{)}\bigg{]}}\] (A15) \[\leq 2\pi_{T}\bigg{[}(\lambda^{-1}D+1)Td\ln\bigg{(}\frac{d \lambda(1-\gamma)+D^{2}}{d\lambda(1-\gamma)}\bigg{)}\bigg{]}^{1/2}\] (A16) \[\leq O\Big{(}\pi_{T}\sqrt{dT}\Big{)}\] (A17)  
where inequalities can be derived using lemmas in [12]. Then, by setting \(\gamma=1-(dT)^{-1/2}\), we have that \(N(\gamma)\leq O(d^{1/2}T^{1/2}\ln(dT))\) and \(\gamma^{N(\gamma)}\leq O(d^{-1/2}T^{-1/2})\). Then, \(\pi_{T}\) can be bounded as  
\[\pi_{T}\leq O\bigg{(}\sqrt{d\ln(T^{1/2}/d^{1/2})+2\ln(1/\delta)} \bigg{)}.\] (A18)  
By plugging all bounds into (A12), the cumulative regret bound is computed as \(O(B_{T}d^{1/2}T^{1/2})\).
# Performance of Satellite-Based Evapotranspiration
## 2 Study Area and Datasets
### Global Evapotranspirationiration Products  
The Global Land Evapotranspiration model from Amsterdam (GLEAM 3.3b) and Penman-Monteith-Leuning global ET\({}_{\text{a}}\) products were used to evaluate our implementation of the four-remote sensing SEB ET models. The GLEAM model estimates daily terrestrial evapotranspiration components and root-zone soil moisture from satellite data at 0.25\({}^{\circ}\) spatial resolution [33]. Potential evaporation (ET\({}_{0}\)) is estimated using the Pristley-Taylor equation for the land fractions of bare soil, tall canopy and short canopy. Then, ET\({}_{\text{a}}\) is obtained by multiplying ET\({}_{0}\) with an evaporative stress factor based on microwave Vegetation Optical Depth (VOD) and satellite-based estimates of root-zone soil moisture. The Penman-Monteith-Leuning (PML\({}_{\text{-}}\)V2) product uses estimates of surface conductance (G\({}_{\text{s}}\)) to describe the canopy-soil conductance to water flux at a moderate resolution of 500 m [37]. Actual evapotranspiration in PML\({}_{\text{-}}\)V2 relies mainly on the G\({}_{\text{s}}\) retrieval from remotely sensed land cover, Leaf Area Index (LAI) and Gross Primary Productivity (GPP).
## 3 Results and Discussion
### Comparison of Leaf Segmentation Performance
#### 3.2.3 Comparison of Segmentation Algorithms
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Segmentation**} & \multicolumn{4}{c}{**Average Precision**} & \multicolumn{4}{c}{**Maximum Precision**} \\ \cline{2-7}  & **Daytime** & **Nighttime** & **Whole Day** & **Daytime** & **Nighttime** & **Whole Day** \\ \hline Isodata & 0.575 & 0.279 & 0.403 & 0.650 & 0.454 & 0.472 \\ \hline Li & 0.593 & 0.506 & 0.522 & 0.702 & 0.545 & 0.571 \\ \hline Local & 0.479 & 0.168 & 0.319 & 0.597 & 0.324 & 0.347 \\ \hline Mean & 0.592 & 0.520 & 0.532 & 0.689 & 0.546 & 0.570 \\ \hline Min & 0.538 & 0.277 & 0.366 & 0.699 & 0.545 & 0.571 \\ \hline Otsu & 0.575 & 0.276 & 0.401 & 0.649 & 0.454 & 0.471 \\ \hline Multi-Otsu & 0.598 & 0.496 & 0.513 & 0.731 & 0.503 & 0.538 \\ \hline Triangle & 0.411 & 0.299 & 0.290 & 0.655 & 0.480 & 0.332 \\ \hline Yen & 0.514 & 0.367 & 0.400 & 0.669 & 0.457 & 0.474 \\ \hline K-Means (K = 2) & 0.570 & 0.379 & 0.456 & 0.630 & 0.462 & 0.477 \\ \hline K-Means (K = 3) & 0.603 & 0.539 & 0.534 & 0.751 & 0.572 & 0.575 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Average and maximum Recall for each segmentation method. Table 13 shows that K-Means (K = 3) performed best on the F1 score for most conditions. The average F1 score values for daytime, nighttime, and whole day images are 0.585, 0.509, and 0.496, respectively. The maximum Precision values for nighttime and whole day images are 0.636 and 0.599, respectively. The maximum Precision of 0.794 for daytime images was achieved by Multi-Otsu. From Tables 11-13, we can conclude that K-Means (K = 3) is the best choice when considering F1 score and Precision. In the case of Recall, there is no single algorithm that outperforms under all conditions.
# Data Fusion of Multivariate Time Series: Application to Noisy 12-Lead ECG Signals
## 2 The Local Weighted Linear Prediction Algorithm
### Fuzzy Inference System Design for NDFA
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & \multicolumn{3}{c}{\(D\)} \\ \cline{3-6}  & & \(S_{D}\) & \(M_{D}\) & \(B_{D}\) \\ \cline{2-6}  & \(S_{D_{r}}\) & \(S_{O_{d}}\) & \(SR_{O_{d}}\) & \(M_{O_{d}}\) \\ \cline{2-6} \(D_{r}\) & \(M_{D_{r}}\) & \(SR_{O_{d}}\) & \(M_{O_{d}}\) & \(BR_{O_{d}}\) \\ \cline{2-6}  & \(B_{D_{r}}\) & \(M_{O_{d}}\) & \(BR_{O_{d}}\) & \(B_{O_{d}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Inference rules of fuzzy inference system (\(\text{FIS}_{d}\)) on the evolutionary trend of reconstruction trajectory. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & \multicolumn{3}{c}{\(\alpha\)} \\ \cline{3-6}  & & \(NB_{\alpha}\) & \(NM_{\alpha}\) & \(Z_{\alpha}\) & \(PM_{\alpha}\) & \(PB_{\alpha}\) \\ \cline{2-6}  & \(S_{\alpha_{r}}\) & \(VB_{\alpha_{s}}\) & \(B_{\alpha_{s}}\) & \(\text{BR}_{\alpha_{s}}\) & \(\text{MR}_{\alpha_{s}}\) & \(M_{\alpha_{s}}\) \\ \cline{2-6} \(\alpha_{r}\) & \(M_{\alpha_{r}}\) & \(B_{\alpha_{s}}\) & \(BR_{\alpha_{s}}\) & \(\text{MR}_{\alpha_{s}}\) & \(M_{\alpha_{s}}\) & \(SR_{\alpha_{s}}\) \\ \cline{2-6}  & \(B_{\alpha_{r}}\) & \(BR_{\alpha_{s}}\) & \(MR_{\alpha_{s}}\) & \(M_{\alpha_{s}}\) & \(SR_{\alpha_{s}}\) & \(S_{\alpha_{s}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Inference rules of fuzzy inference system (\(\text{FIS}_{\alpha}\)) on the angle of adjacent vectors. Figure 2: Partitioning results of variables with triangular membership function. (**a–f**) are partitioning results of \(D\), \(D_{r}\), \(O_{d}\), \(\alpha\), \(\alpha_{r}\) and \(O_{\alpha}\) respectively. The two parameters \(\omega_{d}\) and \(\omega_{\alpha}\) can describe the change of the reconstruction trajectory from the modulus of the vector and the angle between neighboring vectors perspectives, respectively. Thus, the parameters \(\omega_{d}\) and \(\omega_{\alpha}\) should be comprehensively calculated as:  
\[\widetilde{\omega}(p)=\omega_{d}(p)+\omega_{\alpha}(p) \tag{9}\]  
where \(\omega_{d}(p)\) and \(\omega_{\alpha}(p)\) are the values of the data point at \(p\)-step. For the \(l\)th evolutionary trajectory \(L_{l}\), the weighted coefficient \(\omega_{l}\) in the Equation (1) can be computed as:  
\[\omega_{l}(p)=\frac{\exp\{\gamma[\widetilde{\omega}_{l}(p)-\omega_{\text{min} }(p)]\}}{\sum_{s=1}^{L_{n}}\exp\{\gamma[\widetilde{\omega}_{s}(p)-\omega_{\text {min}}(p)]\}} \tag{10}\]  
where the \(L_{n}\) is the number of the phase trajectories and the parameter \(\gamma\) is set to 1 [26]. Here, the minimum value \(\omega_{\text{min}}(p)=\text{min}\{\widetilde{\omega}_{s}(p),s=1,2,\cdots,L_{ n}\}\) needs to be selected.
# Design Procedure for Motion Profiles with Sinusoidal Jerk for Vibration Reduction
## 2 General Formulation of Motion Profiles
### Mathematical Expressions of Sinusoidal Jerk Profile
\tag{7}\]  
The expression of the displacement profile is then found as follows:\[ \begin{array}{l}d(t)=\\ \begin{cases}\frac{A_{\text{peak}}}{4}(t-t_{0})^{2}+\frac{A_{\text{peak}}T_{1}^{2} }{2\pi^{2}}\cos\frac{\pi}{T_{1}}(t-t_{0})-\frac{A_{\text{peak}}T_{1}^{2}}{2\pi ^{2}},&t_{0}\leq t<t_{1}\\ \left(\frac{1}{4}-\frac{1}{\pi^{2}}\right)A_{\text{peak}}T_{1}^{2}+\frac{A_{ \text{peak}}T_{1}}{2}(t-t_{1})+\frac{A_{\text{peak}}}{2}(t-t_{1})^{2},&t_{1} \leq t<t_{2}\\ \left(\frac{1}{4}-\frac{1}{2\pi^{2}}\right)A_{\text{peak}}T_{1}^{2}+\frac{A_{ \text{peak}}T_{1}T_{2}}{2}+\frac{A_{\text{peak}}T_{1}^{2}}{2}+A_{\text{peak}} \left(\frac{T_{1}}{2}+T_{2}\right)\left(t-t_{2}\right)+\frac{A_{\text{peak}}}{ 4}(t-t_{2})^{2}-\frac{A_{\text{peak}}T_{1}^{2}}{2\pi^{2}}\cos\frac{\pi}{T_{1 }}(t-t_{2}),&t_{2}\leq t<t_{3}\\ V_{\text{peak}}\left(T_{1}+\frac{T_{2}}{2}\right)+V_{\text{peak}}(t-t_{3}),&t_{3 }\leq t<t_{4}\\ V_{\text{peak}}\left(T_{1}+\frac{T_{2}}{2}+T_{3}\right)+V_{\text{peak}}(t-t_{4})- \frac{A_{\text{peak}}}{4}(t-t_{4})^{2}-\frac{A_{\text{peak}}T_{1}^{2}}{2\pi^{ 2}}\cos\frac{\pi}{T_{1}}(t-t_{4})+\frac{A_{\text{peak}}T_{1}^{2}}{2\pi^{2}},& t_{4}\leq t<t_{5}\\ V_{\text{peak}}\left(2T_{1}+\frac{T_{2}}{2}+T_{3}\right)-\left(\frac{1}{4}-\frac{1}{ \pi^{2}}\right)A_{\text{peak}}T_{1}^{2}+V_{\text{peak}}(t-t_{5})-\frac{A_{ \text{peak}}}{2}(t-t_{5})-\frac{A_{\text{peak}}}{2}(t-t_{5})^{2},&t_{5}\leq t <t_{6}\\ V_{\text{peak}}(2T_{1}+T_{2}+T_{3})-\left(\frac{1}{4}-\frac{1}{2\pi^{2}}\right)A _{\text{peak}}T_{1}^{2}+\frac{A_{\text{peak}}T_{1}}{2}(t-t_{6})-\frac{A_{ \text{peak}}}{4}(t-t_{6})^{2}+\frac{A_{\text{peak}}T_{1}^{2}}{2\pi^{2}}\cos \frac{\pi}{T_{1}}(t-t_{6}),&t_{6}\leq t<t_{7}\end{array} . \tag{8}\]  
The terminal displacement at the end time of motion is represented as follows:  
\[ \begin{array}{l}d_{end}=d(t_{7})=V_{peak}(2T_{1}+T_{2}+T_{3})=A_{peak}(T_{ 1}+T_{2})(2T_{1}+T_{2}+T_{3})\\ =\frac{2I_{peak}T_{1}}{\pi}(T_{1}+T_{2})(2T_{1}+T_{2}+T_{3})\end{array} . \tag{9}\]  
To achieve fast, smooth, and precise movements, the profile parameters should be properly designed to minimize the motion duration while considering various constraint conditions, including the desired displacement, actuator specifications, residual-vibration suppression, and robustness against system uncertainties. Once these parameters are determined, the setpoints of the motion profile can be computed using the aforementioned expressions.
# Potential and Limitations of Open Satellite Data for Flood Mapping
## 3 Materials and Methods
### Multispectral Data
#### 3.2.1 Medium-Low Resolution Multispectral Data  
For our analysis, we used MODIS (Moderate Resolution Imaging Spectroradiometer) and PROBA-V (PRoject for On-Board Autonomy-Vegetation) data. MODIS is a system of two sun-synchronous, near-polar orbiting satellites called Aqua and Terra that daily acquire images all over the world [7] that can be visualized on the NASA Worldview portal [8]. Terra collects images in the late morning and Aqua in the early afternoon; they also have a night-time pass when they acquire in thermal bands. We used the MYD09 (Aqua) and MOD09 (Terra) Atmospherically Corrected Surface Reflectance 5-Min L2 Swath 500 m [68], downloaded from the Level-1 and Atmosphere Archive and Distribution System (LAADS [69]). These products include seven bands (RGB; NIR and SWIR) with a spatial resolution of 500 m. We also downloaded 250 m spatial resolution Red and NIR band MOD09/MYD09 through the SCP plug-in of QGIS [11] to calculate the NDVI.  
MODIS images were used for the Po basin and Ebro areas, for which co-flood data not affected by extensive cloud cover and post-flood data were available. In the Ebro valley, MODIS images were available for all three of the flood events that occurred in February-March 2015.  
For the Ebro valley and Po basin floods, we also used data acquired by the ESA PROBA-V, mission launched in 2013 for vegetation monitoring [70]. This satellite has four bands (Blue, Red, NIR, and SWIR) with spatial resolution ranging from 100 m (revisit time of 5-6 days) to 300 m (daily revisit time). We used the Level 2A--radiometrically corrected segments, projected in plate carree, Top-of-Atmosphere with 100 m of spatial resolution downloaded from the ESA Proba-V portal [71]. The small area of Arahal is not suitable for analysis with the coarse spatial resolution of MODIS and Proba-V.
## 3 Results
### Synergistic Anti-Biofilm Activity  
The hydroethanolic extracts of 0.1 mg/mL _N. officinal_ + 0.1 mg/mL _P. guajava_, and 0.1 mg/mL _N. officinal_ + 0.5 mg/mL _P. guajava_ were effective in reducing biofilm formation in both the standard and clinical strain 4 of _E. faecalis_, with a statistically significant difference compared to the control group (\(p<0.0001\)). Additionally, the 0.1 mg/mL _N. officinal_ + 0.1 mg/mL _P. guajava_, and 0.1 mg/mL _N. officinal_ + 0.2 mg/mL _P. guajava_ hydroethanolic extracts also significantly reduced biofilm formation in the standard and clinical strain 2 of _E. faecalis_ (\(p<0.0001\)), as shown in Figure 2.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{_E. faecalis_} & \multicolumn{2}{c}{**Isolated MBC mg/mL**} & \multicolumn{2}{c}{**Combined MBC mg/mL**} & \multicolumn{2}{c}{**Result**} \\ \cline{2-7}  & _N. officinal_ & _P. guajava_ & _N. officinal_ & _P. guajava_ & **FBCI** & **Effect** \\ \hline \multirow{4}{*}{ATCC} & 12.5 & 0.52 & 0.1 & 0.1 & 1.5 & Synergistic \\ \cline{2-7}  & 12.5 & 0.52 & 0.1 & 0.5 & 1.25 & Synergistic \\ \cline{2-7}  & 12.5 & 0.52 & 0.1 & 0.5 & 5.5 & Additive \\ \cline{2-7}  & 12.5 & 0.52 & 0.05 & 0.5 & 5.2 & Additive \\ \hline \multirow{4}{*}{Clinical strain 2} & 12.5 & 0.52 & 1.5 & 0.2 & 9.5 & Synergistic \\ \cline{2-7}  & 12.5 & 0.52 & 1.5 & 0.1 & 8.5 & Synergistic \\ \cline{2-7}  & 12.5 & 0.52 & 0.1 & 1 & 10.5 & Additive \\ \cline{2-7}  & 12.5 & 0.52 & 0.05 & 1 & 10.25 & Additive \\ \hline \multirow{2}{*}{Clinical strain 4} & 12.5 & 0.52 & 0.1 & 0.1 & 1.5 & Synergistic \\ \cline{2-7}  & 12.5 & 0.52 & 0.1 & 0.05 & 1.25 & Synergistic \\ \hline \end{tabular}
\end{table}
Table 1: The results obtained from the Fractional Bactericidal Concentration Index calculation.  
Figure 2: _Cont._
## 2 Materials and Methods
### Reflectivity Spectrum Extrapolation Method
The forward modeling of the data spectral constraint (real part and imaginary part separately) and the sinusoidal elements of varying frequency periodicities now within the same spectral limit can be given as Equation (13):  
\[\varphi=\beta\alpha+\varepsilon \tag{13}\]  
where \(\varphi\) is the deconvolved data spectrum, \(\beta\) is the kernel matrix of sinusoidal atoms, \(\alpha\) is the reflection coefficients vector including \(r_{e}\) and \(r_{o}\), and \(\varepsilon\) denotes the prediction error [19; 38]. The kernel has a dimension of \(\mu\times K\), where \(\mu\) is the number of frequencies determined by the available bandwidth and the sampling rate in frequency, \(K\) is the number of layers and hence the number of even or odd pairs stated by Equation (10) above, and can be varied to encompass all possible frequency periodicities. By solving the objective function (Equation (14)), basis pursuit concurrently minimizes both the L2 norm of the error term and the L1 norm of the solution, creating sparsity in the solution vector. The L1 norm is defined as the sum of the seismic trace's absolute values. The square root of the sum of the squares of the seismic trace values is the L2 norm, on the other hand. The parameters are solved using linear programming. \[min\left[\mid\mid\varphi-\beta\alpha\mid\mid_{2}+\lambda\mid\mid m\mid\mid_{1}\right] \tag{14}\]  
Lambda (\(\lambda\)) in Equation (14) is the trade-off parameter between sparsity and accuracy of the solution. The regularization parameter \(\lambda\) balances the inverted reflectivity resolution and noise. Increasing \(\lambda\) decreases the resolution of inverted reflectivity and decreasing \(\lambda\) may cause noise amplification [17; 51]. In this study, the \(\lambda\) value was determined empirically. After the bandwidth is extended, we can calculate the resulting reflectivity series by inverting the reflectivity spectrum (in the frequency domain) to the time domain using Equation (15) [20; 52], since it shares the same coefficient with Equation (10). \[Sr(t)=\sum_{n=0}^{k-1}((re(n)+ro(n))b(t+n.dt)+(re(n)-ro(n))b(t-n.dt)) \tag{15}\]
# Semantic Traffic Sensor Data:
## 3 Traffic Modelling in TRAFAIR
### Modeling of Data Provided by Traffic Sensors  
Traffic data can be measured by using different types of sensors, such as detectors located along the roadside, which use various technologies to detect the presence of vehicles [46; 47]. More specifically, traffic count technologies can be split into two categories: intrusive methods and non-intrusive methods. On the one hand, intrusive methods usually consist of a data recorder and a sensor placed on the road like pneumatic road tubes or induction loops. On the other hand, non-intrusive techniques are based on remote observations, such as manual counting, microwave radars, or video image detection. These techniques allow the detection of different types of data, such as the volume of traffic (counts of the numbers of vehicles on different road segments in a city), travel speeds, and in some cases even the specific types of vehicles (cars, motorbikes, buses, vans, pickup trucks, trailer trucks, large trucks, articulated lorries, etc.), occupancy rates, etc.  
In the rest of this section, key ideas about the modeling of data provided by traffic sensors are explained. Firstly, Section 3.2.1 presents some examples of sensors that provide traffic data for the TRAFAIR project. Then, Section 3.2.2 describes our database model for traffic data.
# LightMFF: A Simple and Efficient Ultra-Lightweight Multi-Focus Image Fusion Network
## 3 Method
### Focus Property and Edge Detection  
To provide prior guidance through an initial coarse decision map, we adopt the pixel-level spatial frequency gradient, as proposed in SESF-Fuse [30], as our initial focus measure. The computational formulation is as follows:  
\[\text{RF}_{i(x,y)}=\sqrt{\sum_{a=-r}^{r}\sum_{b=-r}^{r}\left[I_{i(x+a,y+b)}-I_{i( x+a,y+b-1)}\right]^{2}} \tag{1}\]  
\[\text{CF}_{i(x,y)}=\sqrt{\sum_{a=-r}^{r}\sum_{b=-r}^{r}\left[I_{i(x+a,y+b)}-I_{ i(x+a-1,y+b)}\right]^{2}} \tag{2}\]  
\[\text{SF}_{i(x,y)}=\sqrt{\frac{\left(\text{CF}_{i(x,y)}\right)^{2}+\left( \text{RF}_{i(x,y)}\right)^{2}}{(2r+1)^{2}}} \tag{3}\]  
where RF and CF represent the row and column frequency vectors, respectively, and \(r\) denotes the kernel radius. By computing the pixel-level spatial frequency for source images \(I_{i}\), where \(i\in\{A,B\}\), we obtain their respective spatial frequency maps \(\text{SF}_{i}\). The initial decision maps \(\text{IDM}_{A}\) and \(\text{IDM}_{B}\) are then generated through pixel-wise comparison of \(\text{SF}_{A}\) and \(\text{SF}_{B}\):  
\[\text{IDM}_{A(x,y)}=\begin{cases}1,&\text{if }\text{SF}_{A(x,y)}\geq\text{SF}_{B(x,y)} \\ 0,&\text{otherwise}\end{cases} \tag{4}\]  
\[\text{IDM}_{B(x,y)}=1-\text{IDM}_{A(x,y)} \tag{5}\]  
Additionally, to provide explicit boundary information and facilitate the refinement of decision maps, especially in edge regions, we employ the Sobel operators [47] for edge detection. For source images \(I_{A}\) and \(I_{B}\), the edge maps \(\text{Edge}_{A}\) and \(\text{Edge}_{B}\) are computed using horizontal and vertical Sobel kernels:  
\[S_{x}=\begin{bmatrix}-1&0&1\\ -2&0&2\\ -1&0&1\end{bmatrix},\quad S_{y}=\begin{bmatrix}-1&-2&-1\\ 0&0&0\\ 1&2&1\end{bmatrix} \tag{6}\]  
Figure 2: Architecture of the proposed method.  
\[\text{Edge}_{i}=\sqrt{(I_{i}*S_{x})^{2}+(I_{i}*S_{y})^{2}},\quad i\in\{A,B\} \tag{7}\]  
where \(*\) denotes the convolution operation. The edge maps highlight structural boundaries in the source images by computing the magnitude of gradients in both horizontal and vertical directions, providing crucial guidance for decision map refinement in regions where focus properties transition.