esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Material and Methods
### Parallel Bayesian Optimization
#### 2.2.1 Gaussian Process Regression  
Usually, a GP surrogate model is used. The latter assumes a linear relation between inputs \(\mathbf{x}\) and outputs \(y\), such that \(y=\mathbf{\omega}^{T}\mathbf{x}+\epsilon\). The observation/output is often considered noisy, hence the \(e\) error term, which is assumed Gaussian (\(\epsilon\sim\mathcal{N}(0,\sigma^{2})\)). As explained in [42], a Bayesian approach assumes a prior distribution over weights \(\mathbf{\omega}\), which is also Gaussian (\(\mathbf{\omega}\sim\mathcal{N}(0,\Sigma)\)) and constitutes the prior belief. Starting from that belief, it is possible to update the prior distribution with knowledge of the data \((\mathbf{X},\mathbf{y})\), which is defined as the posterior distribution. Using the Bayes rule the posterior is expressed as  
\[\text{posterior }=\frac{\text{likelihood }\times\text{prior}}{\text{evidence}}. \tag{1}\]  
With previous notations, Equation (1) becomes  
\[p(\mathbf{\omega}|\mathbf{X},\mathbf{y})=\frac{p(\mathbf{y}|\mathbf{X},\mathbf{\omega})p(\mathbf{\omega}) }{p(\mathbf{y}|\mathbf{X})}=\frac{p(\mathbf{y}|\mathbf{X},\mathbf{\omega})p(\mathbf{\omega})}{\int_{ \mathbf{\omega}}p(\mathbf{y}|\mathbf{X},\,\mathbf{\omega})p(\mathbf{\omega})d\mathbf{\omega}}. \tag{2}\]  
The evidence \(p(y|\mathbf{X})\) is also referred to as the normalizing constant and can be expressed as the marginal likelihood by marginalizing over the weights \(\mathbf{\omega}\). Often, input data \(\mathbf{X}\) are projected into a feature space using a set of basis functions \(\Phi(\mathbf{x})=(\phi_{1}(\mathbf{x}),\dots,\phi_{k}(\mathbf{x}))^{T}\) which leads to the following model: \(y=\mathbf{\omega}^{T}\Phi(\mathbf{x})+\epsilon\). Denoting \(\mathbf{\Phi}=\Phi(\mathbf{X})\), we can simply replace \(\mathbf{X}\) by \(\mathbf{\Phi}\) in Equation (2). Knowing the distribution of the posterior \(p(\mathbf{\omega}|\mathbf{\Phi},\mathbf{y})\sim\mathcal{N}\Big{(}\frac{1}{\sigma^{2}}A^{- 1}\mathbf{\Phi}\mathbf{y},A^{-1}\Big{)}\) with \(A=\sigma^{-2}\mathbf{\Phi}\mathbf{\Phi}^{T}+\Sigma^{-1}\), it is possible to make inference. The predictive distribution of a design point \(\mathbf{x}^{*}\) writes  
\[p(y^{*}|\mathbf{\Phi},\mathbf{y}  
where \(K=\mathbf{\Phi}^{T}\Sigma\mathbf{\Phi}\) is known as the covariance matrix and \(K^{(1)(2)}=\Phi(\mathbf{x}^{(1)})^{T}\Sigma\mathbf{\Phi}(\mathbf{x}^{(2)})=k\Big{(}x^{(1)},x^ {(2)}\Big{)}\). The \(k\) function is referred to as the covariance kernel and \(K=\big{(}k(\mathbf{x}_{i},\mathbf{x}_{j})\big{)}_{i,j\in\{1,\ldots,n\}}\) and is chosen by the user among other hyperparameters. Following previous notation, we denote \(\big{(}k(\mathbf{x}^{*},\mathbf{x}_{j})\big{)}_{j\in\{1,\ldots,n\}}=K^{*,^{\prime}}= (\Phi^{*})^{T}\Sigma\mathbf{\Phi}\).
# Single-Shot Compressed Imaging via Random Phase Modulation
## 2 Fundamentals of Compressed Sensing
### Nonlinear Recovery Algorithm
#### 2.3.1 L0-Norm Minimization Recovery  
Intuitively, we can solve the problem in Equation (2) by \(\ell_{0}\) norm minimization using the following optimization.  
\[\begin{split}\hat{\mathbf{x}}&=\operatorname*{argmin}_{ \mathbf{x}}\lVert\mathbf{x}\rVert_{0}\\ \text{s.t.}&\mathbf{y}=\mathbf{\Phi}\mathbf{x}=\mathbf{\Phi}\mathbf{ \Psi}\mathbf{\alpha}\end{split} \tag{4}\]  
Unfortunately, solving Equation (4) relies on an exhaustive search, which has combinatorial computational complexity. Therefore, the goal is to find a computationally feasible algorithm that can successfully recover the sparse signal \(\mathbf{x}\) from the measurement \(\mathbf{y}\).
# Stability and Control of Surrounding Rock of a Trapezoidal Roadway Retained with Hard Roof Cutting
## 5 Discussion
### Surrounding Rock Control Mechanisms  
Controlling surrounding rock in trapezoidal top-cutting roadways is challenging due to irregular stress and deformation. This study demonstrates effective strategies: creating a cantilever beam structure through pre-splitting and top-cutting reduces load on the roof, enhancing stability. The roof's arch-like structure aids in stress redistribution, with the support system bearing the load to control deformation and increase stability. Top-cutting allows stress release and controlled fracturing near the cut, preventing uncontrolled damage.  
High-strength prestressed long anchor cables for roof reinforcement, combined with retractable U-shaped steel and windproof cloth for rib coal protection, significantly boost roadway stability and safety. The simulation and real-world data confirm the effectiveness of these measures in curbing excessive roof subsidence and deformation.
## 2 Materials and Methods  
### Materials  
In this study, Ordinary Portland Cement (OPC) was used in all the RC members. To investigate the effect of mineral admixtures on the flexural behavior of RC members, the cement part was replaced with a mineral admixture at a water-binder ratio of 45%. The mineral admixture type was Fly Ash (FA) and Blast Furnace Slag (BFS). The physical and chemical compositions of the binders are shown in Table 1.  
Crushed gravel was used as coarse aggregate with the maximum aggregate size, Gmax of 20 mm. The specific gravity and absorption ratio of the coarse aggregate were 2.68% and 1.35%, respectively. River sand having a fineness modulus of 2.79 was used as a natural fine aggregate in the RC member. The specific gravity and absorption ratio of this fine aggregate were 2.6% and 1.07%, respectively. Furthermore, crushed heavyweight waste glass was used as fine aggregate.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Binders Properties** & **Binders Type** & **OPC** & **FA** & **BFS** \\ \hline \multirow{2}{*}{Physical} & Specific gravity & 3.15 & 2.34 & 2.82 \\ \cline{2-5}  & Blaine (cm\({}^{2}\)/g) & 3200 & 3700 & 4000 \\ \hline \multirow{5}{*}{Chemical (\%)} & SiO\({}_{2}\) & 21.36 & 52.83 & 31.85 \\ \cline{2-5}  & Al\({}_{2}\)O\({}_{3}\) & 5.03 & 18.08 & 14.55 \\ \cline{2-5}  & Fe\({}_{2}\)O\({}_{3}\) & 3.31 & 7.74 & 0.59 \\ \cline{2-5}  & CaO & 63.18 & 5.95 & 34.95 \\ \cline{2-5}  & MgO & 2.89 & 1.43 & 5.63 \\ \cline{2-5}  & SO\({}_{3}\) & 2.30 & 0.01 & 2.97 \\ \cline{2-5}  & LOI & 1.40 & 6.14 & 0.60 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical and chemical compositions of the binders.
# On the Needs and Requirements Arising from Connected and Automated Driving
## 4 Technical Requirements: from Automotive to Network Perspective
### 5 GCAR Use Case Technical Requirements
#### 4.3.1 Lane Merge  
We consider the scenario that is depicted in Figure 1 left, as an illustration for the lane merge use case. It represents two vehicles (Veh\({}_{2}\) and Veh\({}_{3}\)) driving in the main road and a third vehicle (Veh\({}_{1}\)), which plans to merge into the traffic. The right-hand image in Figure 1 shows a recorded image of the video-based lane merge observation scenario [17], where the vehicle on the merging lane should decelerate to provide a larger headway in order to allow this maneuver. The deceleration should be below a certain value (e.g., 3 m/s\({}^{2}\)) to be comfortable for the driver and the passengers. The most relevant automotive requirements for this use case are vehicle localization accuracy, completion time, minimum inter-vehicle distance, relevance area, mobility, and the overtake time. Accuracy below one meter should be reached for future autonomous driving to give precise trajectories for the vehicle [10]. For the planning and execution of a smooth lane merge maneuver at 100 km/h, a range of approximately 350 m should be covered [4]. The completion time is computed for the lane change when considering a lateral speed of 1 m/s and a four-meter lane width, which results in around four seconds. The inter vehicular time (_Time Inter Vehicle_, TIV) must be two seconds between any two vehicles [15]. The transmitted data includes vehicle dynamics (position, speed, orientation, etc.), maneuver recommendations, and their feedback from the vehicles. If vehicle trajectories are included in the messages, the date rate is up to 1.28 Mbps per vehicle; if not, only safety messages with approximately 1200 bytes per message are transmitted [10]. A maximal latency of 30 ms is assumed to achieve a fast response time [10]. Often, the connectivity provides a line of sight where the on-board sensors cannot. Thus, reliable information is required (such as 99.9% reliability [18]) in order to be useful for the lane merge decision. The availability requirements are set to medium equal to 99% due to the fact that the trajectory contains a lot of redundant information.
## 4 Discussion
### Limitations  
This study represents a feasibility investigation with a small sample size due to the design used, which prioritizes feasibility outcomes as the primary objective. Consequently, this study is a secondary analysis of the secondary objectives of the original study (preliminary information on efficacy), which limits the generalizability of the results. The findingsare preliminary and need to be validated through larger, confirmatory studies to establish broader applicability. Another limitation of the original study is the absence of an active control group. An influencing factor might also be the imbalance in the sample for sex after age stratification, which will need to be better balanced in phase III.
# Adaptive Algorithm for Fast 3D Characterization of Magnetic Sensors
## 2 Materials and Methods
### Field Generation
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Equalization Target Coil** & **Normalization Impedance \(\mathbf{Z_{0}}\)** & **Resulting Gain Factor \(\mathbf{\beta}\)** \\ \hline Inner—x & \(62.1076\,\Omega\) & \(1.0\) \\ \hline Mid—y & \(62.3548\,\Omega\) & \(1.1549\) \\ \hline Outer—z & \(54.5292\,\Omega\) & \(1.1419\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Equalizer parameters. Figure 3: Magnitude of the different unity gain equalization filters. The frequency axis is scaled logarithmically as the chosen design limit up to which the impedances are emulated (the marked \(2\,\mathrm{kHz}\)), while measurement was performed up to \(\frac{\ell}{2}=24\,\mathrm{kHz}\). The described hardware together with the equalization procedure then enables the generation of very similar individual homogeneous fields with the different coils using the same excitation signal. This, in turn, means that we are able to produce arbitrarily directed fields by defining an elevation and azimuth angle--\(\theta\) and \(\varphi\), respectively. These are relative to the center of the coil system and transformed from these spherical coordinates to Cartesian coordinates to scale the excitation signal for the individual coil channels. For this, we chose a uniformly distributed white noise signal \(x(n)\) to enable characterization of all sensing frequencies at once. With specific given angles \(\theta_{0},\ \varphi_{0}\), this leads to the coil channel excitation signals  
\[v_{\mathrm{x}}(n) =\beta_{\mathrm{x}}\Big{(}h_{\mathrm{z}_{\mathrm{x}}}*\big{[}x(n )\sin(\theta_{0})\cos(\varphi_{0})\big{]}\Big{)}, \tag{7}\] \[v_{\mathrm{y}}(n) =\beta_{\mathrm{y}}\Big{(}h_{\mathrm{z}_{\mathrm{y}}}*\big{[}x(n )\sin(\theta_{0})\sin(\varphi_{0})\big{]}\Big{)},\] (8) \[v_{\mathrm{z}}(n) =\beta_{\mathrm{z}}\Big{(}h_{\mathrm{z}_{\mathrm{x}}}*\big{[}x(n )\cos(\theta_{0})\big{]}\Big{)}, \tag{9}\]  
which are calculated programmatically and then passed as voltages to the DAC. Practically, we designed the software system to calculate the desired directions and resulting Cartesian weights automatically from given inputs. When a single direction (1D) is desired, this is typically measured in-plane with the plate in the center of the coils and a singular offset angle can be introduced. This is also possible for a planar \(360^{\circ}\) (2D) characterization around a fixed axis (e.g., \(x\)-axis) with a number of equal, discrete angular steps \(N_{\varphi}\). The reference axis for both 1D and 2D characterization can also be changed. In a full 3D characterization scenario, the number of discrete steps can be set for azimuth and elevation (\(N_{\theta}\)) separately. The used angle pairs are derived from the division of \(360^{\circ}\) and \(180^{\circ}\), respectively, which results in a total number of directional steps of \(N_{\mathrm{steps}}=N_{\theta}N_{\varphi}\).
# Laser-Induced Breakdown Spectroscopy for Determination of Spectral Fundamental Parameters
## 1 Introduction  
Laser-induced breakdown spectroscopy (LIBS) [1] is a spectroanalytical technique that is attracting a wide interest for its applications to in situ industrial processes [2; 3; 4; 5], environmental analysis [6; 7; 8], the study of geological materials [9; 10; 11] and cultural heritage objects [12; 13; 14] and planetary exploration [15; 16; 17], to mention a few. At the laboratory level, excellent results have been obtained in microanalysis and elemental mapping [18; 19; 20]. The advantages with respect to other more assessed microanalytical techniques were mainly exploited especially in geological [21; 22; 23], cultural heritage [24; 25; 26] and biomedical applications [27; 28; 29].  
Another important field where LIBS analysis has been applied, although sometimes neglected with respect to the large variety of practical applications, is the study of the complex processes occurring in the plasma during its formation and evolution [30]. This kind of fundamental approach has involved the study of the process of laser ablation [31; 32], the generation of shock waves [33; 34] and the analysis of the emitted radiation [35].  
This latter phenomenon is the base of the analytical application of LIBS. Consequently, studies about the fundamental parameters of the plasma radiation (transition probabilities or, equivalently, oscillator strengths [36] and Stark broadening and shift coefficients [37; 38]) are of paramount importancefor the development of LIBS as an analytical technique, as well as for the more general studies on the process of plasma emission.  
These parameters are traditionally determined in plasma physics studies involving pulsed or continuous plasma sources (linear pulsed discharges, arcs) and conventional emission, absorption or fluorescence spectroscopic techniques. All these methods are considerably more complex with respect to LIBS, which has the further advantage, with respect to traditional methods, of working on potentially all the kinds of materials, conducting or insulating, in gas, liquid or solid form. However, the simplicity of the experimental setup is compensated, in LIBS, by the complex physicochemical processes occurring in the laser-induced plasma. LIBS plasmas are characterized by fast spatial and temporal changes; they are by nature transient, inhomogeneous and out of thermal equilibrium. Therefore, a deep knowledge of the phenomena occurring inside the laser-plasma and their effect on the emitted radiation is needed for a correct interpretation of the experimental results.  
In this review, we focus our attention on the main models of plasma radiation and on the different experimental strategies that may be used for the determination of the fundamental spectral parameters using LIBS.
## 3 Results
### MB Sensor Monitoring Results  
Figure 7 indicates that the varying value of the output power increased with the external force (0-100 N) on PAB in vitro and in vivo (repaired the defect in the sheep leg). The maximum value was 0.04 dbm at 100 N. The increasing trend was similar both in vivo and in vitro. Figure 8 shows the variation of the output power when the external force was changed for the three days (days 0, 7, and 15) in the alkaline medium in vitro. Figure 8 indicates that the change of output power was low on day 0 in the alkaline medium at about 0.1 dbm. Importantly, the changes were about 0.15 dbm and 0.20 dbm on days 7 and 15, respectively. The output power gradually increased with degradation. Figure 8 further shows the increasing tendency of the output power at 10, 50, and 100 N on days 0, 7, and 15. Figure 9 shows the increasing output power in the PBS medium with values of 0.04, 0.07, and 0.1 dbm for days 0, 7, and 15, respectively. Figure 9 further shows the details of the output power at 10, 50, and 100 N. The variation of the output power of PAB in the alkaline medium was higher than that in PBS.  
Figure 6: SEM images of PAB immersed in the NaOH medium at different magnifications (500\(\times\), 5000\(\times\), and 15,000\(\times\)) and degradation times (days 0, 7, and 15). The red circles indicate the degradation condition of PAB.  
Figure 7: Varying values of the output power when an external force of 0–100 N was applied to PAB in vitro and in vivo (repaired sheep leg).
# Dissolved Oxygen Modeling by a Bayesian-Optimized Explainable Artificial Intelligence Approach
## 4 Model Application and Results
### Sensitivity Analysis  
Sensitivity analysis offers insights into the robustness of models and plays a crucial role in informing decision-making. In the present work, sensitivity analysis is conducted by slightly perturbing each input variable and computing the change in the predicted outputs. Figure 8 shows the sensitivity results for different inputs. The sensitivity is measured by the average relative variation in the prediction due to the perturbations. The parameters \(T\), \(Q\), and \(G\) are constantly more sensitive than other variables, demonstrating their significance in modeling DO. This is consistent with the SHAP analysis in the previous section. The \(Q\) shows slightly higher feature importance than the \(G\), which differs from the SHAP results. This discrepancy arises presumably because sensitivity analysis is primarily a local measure, focusing on how minor variations in individual features influence the output. In contrast, Shapley values provide a global perspective by assessing each feature's contribution across all possible combinations of feature values. Additionally, Shapley values account for interaction effects between features, whereas sensitivity analysis considers each feature separately. With a perturbation of 5%-30%, the sensitivity ranges are 1.0-6.1% for \(T\), 0.9-5.2% for \(Q\), and 0.8-5.0% for \(G\). The small sensitivity values indicate the robustness of the model. The parameters pH, \(Tu\), and \(Sc\) exhibit comparatively low sensitivity to perturbations, which matches the SHAP plot. When increasing the perturbation from 5% to 30%, the sensitivity for these factors is less than 1.1%, illustrating their limited impacts on DO levels.  
Figure 7: SHAP summary plot. The \(x\)-axis displays the Shapley values for each data point, colored by the value of the corresponding feature parameter. The \(y\)-axis ranks the predictors based on their influence on the DO concentration.
_Appl. Sci._**2015**, \(5\), 1790-1802; doi:10.3390/app5041790  
_Applied sciences_  
**ISSN 2076-3417**  
www.mdpi.com/journal/applsci  
_Article_  
**Temporal Shaping of High Peak Power Pulse Trains from a Burst-Mode Laser System**  
**[PERSON] \({}^{1,\dagger}\), [PERSON] \({}^{1,2,\dagger}\), [PERSON] \({}^{1,2,\ast}\) and [PERSON] \({}^{1,2}\)**  
\({}^{1}\) Institute of Optics and Quantum Electronics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1,  
Jena 07743, Germany; E-Mails: [EMAIL_ADDRESS] (J.K.); [EMAIL_ADDRESS] (J.R.); [EMAIL_ADDRESS] (M.C.K.)  
\({}^{2}\) Helmholtz Institute Jena, Frobelstieg 3, Jena 07743, Germany  
\({}^{\dagger}\) These authors contributed equally to this work.  
* Author to whom correspondence should be addressed; E-Mail: [EMAIL_ADDRESS]; Tel.: +49-3641-9-47209; Fax: +49-3641-9-47202.  
Academic Editor: [PERSON]  
_Received: 25 September 2015 / Accepted: 8 December 2015 / Published: 15 December 2015_  
**Abstract:** It has been shown in the past that pulsed laser systems operating in the so-called \"burst mode\" are a beneficial approach to generate high peak power laser pulses at high repetition rates suitable for various applications. So far, most high-energy burst-mode laser systems put great effort into generating a homogeneous energy distribution across the burst duration, e.g., by shaping the pump pulse. In this work, we present a new shaping technique, which is able to produce arbitrary energy distributions within the burst by pre-shaping the seed pulse burst with a Pockels cell. Furthermore, this technique allows for the precompensation of any static modulations across the burst, which may be introduced during the subsequent amplification process. Therefore, a pulse burst with a uniform energy distribution can also be generated. The method is tested with an ultra-short pulse burst mode laser amplifier system producing bursts of a 1 ms duration with a pulse repetition rate of 1 MHz and a maximum output power of 800 W during the burst. Furthermore, a method to predict the influence of the amplifier on a non-uniformly shaped burst is presented and successfully tested to produce a pre-defined pulse shape after amplification.  
**Keywords:** burst; Pockels cell; temporal shaping; Ytterbium; diode pumped; solid-state laser; cryogenically cooled; Yb:CaF\({}_{2}\); femtosecond laser
# A Wide-Angle Scanning Leaky-Wave Antenna Based on a Composite Right/Left-Handed Transmission Line
## 2 Operation Principle and Scheme of the Proposed LWA  
### OperationPrinciple  
The Floquet theorem indicates that infinite harmonic components are introduced into LWAs with a periodic structure, and the phase constant of each harmonic component can be expressed as:  
\[\beta_{n}\ =\ \beta_{0}+\frac{2\pi n}{p} \tag{1}\]  
where \(n\) is the order of the space harmonic, \(p\) is the per-unit length, and \(\beta_{0}\) is the phase constant of the fundamental mode. According to the operation principle of the periodic LWA, the radiation condition can be satisfied when the fast wave component is supported in the periodic structure. The LWA based on the CRLH TL has a quasi-uniform periodic structure and it can operate in the fundamental mode and radiate electromagnetic waves. The main beam angle from the broadside can be determined by the phase constant of the fundamental mode and is written as:  
\[\theta_{0}\ =\ \sin^{-1}(\beta_{0}/k_{0}) \tag{2}\]  
where \(k_{0}\) is the wave number in free space.  
In the frequency-dependent CRLH TL LWA, the backward to forward beam-scanning capability is achieved by varying the frequency. Similarly, the phase constant can also be changed by loading electronically controlled components, such as varactors. As a result, it can be deduced that the beam scanning capability can be achieved at a fixed frequency by controlling the DC bias voltage \(V\) of the varactors, which is equivalent to changing the propagation constant of the fundamental mode. Then, the main beam angle can be calculated by:  
\[\theta_{0}\ =\ \sin^{-1}(\beta_{0}(\ V)/k_{0}). \tag{3}\]