esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 High-Dynamic Atmospheric Turbulence Compensation Algorithm
### Computing Controlling Voltages  
Due to the nonlinearity of model as well as the overdetermination of the equation set, multiplying a pseudo-inverse of the model coefficients matrix on the left of the detected wavefront value vector could not determine an agreeable vector of controlling voltages.  
Therefore, the Gauss-Newton method which has the advantages of low computational complexity and excellent convergence performance is adopted.  
Consider the following overdetermined equation set with \(2\times N\) equations and \(M\) variables  
\[\mathbf{offset}_{Target}=f(\mathbf{s})+\mathbf{e} \tag{9}\]  
where \(\mathbf{offset}_{Target}\) is the information vector collected from SHWS, and \(f(\mathbf{s})\) is a \(2\times N\) model value vector,  
\[\mathbf{s}=\begin{bmatrix}s_{1}&s_{2}&\cdots&s_{M}\end{bmatrix}^{T} \tag{10}\]  
symbolises independent variables, while \(\mathbf{e}\) stands for an error vector.  
Furthermore, the equation below is used in order to evaluate the global error of the overdetermined equation set under a certain set of solutions.  
\[F(\mathbf{s})=\frac{1}{2}\times\mathbf{e}^{T}\mathbf{e} \tag{11}\]  
The Gauss-Newton method solves the following optimization problem.  
\[\begin{split}\underset{\mathbf{s}}{\text{min}}& F(\mathbf{s})\\ \text{s.t.}&\mathbf{e}=\mathbf{offset}_{Target}-f(\mathbf{s})\end{split} \tag{12}\]  
By repeatedly computing the step length in Equation (13) and adding it to Equation (10) until it reaches the convergence condition of Equation (11) or iteration chances are exhausted, the final Equation (10) would be deformed and configured to the electrodes of wavefront correctors.  
\[\Delta\mathbf{s}=-\Big{(}J^{T}J\Big{)}^{-1}J^{T}\mathbf{e} \tag{13}\]  
\(J\) in Equation (13) is expressed as follows,  
\[J=\begin{pmatrix}\frac{\partial\mathbf{c}_{1}}{\partial s_{1}}&\cdots&\frac{ \partial\mathbf{c}_{1}}{\partial s_{M}}\\ \vdots&\ddots&\vdots\\ \frac{\partial\mathbf{c}_{2N}}{\partial s_{1}}&\cdots&\frac{\partial\mathbf{c}_{2N}} {\partial s_{M}}\end{pmatrix}. \tag{14}\]  
In practical applications, the Gauss-Newton method runs as Algorithm 1  
```
1:Initializing \(\mathbf{s}\) to zero vector.
2:Acquiring \(offset_{Target}\) from SHWS.
3:Computing \(f(\mathbf{s})\) according to model and \(\mathbf{s}\).
4:Computing \(\mathbf{e}\) in Equation (9).
5:Checking whether \(\mathbf{e}\) reaches the convergent criterion. If it does, exiting the algorithm and configuring controlling voltages to electrodes, otherwise computing \(J\) in Equation (14).
6:Computing \(\Delta\mathbf{s}\) in Equation (13) then updating \(\mathbf{s}\) in Equation (10).
7:Checking whether it exhausts iteration chances. If it does, exiting the algorithm and configuring controlling voltages to electrodes, otherwise returning back to process 3.
```  
**Algorithm 1** A description of the Gauss-Newton method
# Underlying Security Transmission Design for Orthogonal Time Frequency Space (OTFS) Modulation
## 4 Secret Key Generation Algorithm
### Characteristic Analysis for Secret Key
#### 4.2.1 Lempel-Ziv Complexity  
The Lempel-Ziv (LZ) complexity is a simple algorithm for calculating sequence complexity by calculating the rate at which new patterns appear in a sequence. It was first proposed by [PERSON] and [PERSON]. Since this method is applicable to symbol sequences, the data sequence must be quantized in advance. That is, the average value of all data must be calculated. Data larger than the average value are set to one, and data smaller than the average value are set to zero. The brief idea of LZ complexity is as follows: \(c(n)\) is defined as the complexity count of a given symbol sequence \(S=(s_{1},s_{2},\cdots,s_{n})\). \(b(n)\) is the progressive behavior of a random sequence. \(b(n)=\lim_{n\rightarrow\infty}c(n)=n/\log_{2}n\), and \(C_{LZN}(n)=c(n)/b(n)\). As we all know, the complexity of completely random sequences tends toward one, while the regular sequence tends toward zero [27]. That is, the larger the \(C_{LZ}\) is, the weaker the periodicity of the symbol sequence. The more new patterns there are, the higher the complexity becomes. As can be seen in Figure 6, the complexity of the sequence generated by the GOST algorithm we used is the highest.  
Figure 5: Flowchart of obtaining permutation index vector.
## 3 Results and Analysis  
### Data Description and Process Schemes  
In order to test the proposed weighting approach for GPS/GALILEO RT PPP with ionospheric constraints, both static and kinematic experiments are conducted at single- and dual-frequencies. Three data processing methods, as listed in Table 1, were established to evaluate the impact on convergence time and positioning with different variances of ionospheric constraint. The first is using the GPS/GALILEO raw observations without ionospheric constraints, and the estimated parameter vector can be expressed as Equation (4). The second method is to determine the weight between observations and ionospheric constraints using priori variances by Equation (10). The third method is to determine the weight using the proposed approach. The estimated parameter vector of the second and the third method can be expressed as Equation (5). As shown in Figure 3, the observation data of 31 MGEX stations for 30-days (23 January 2018 to 23 February 2018) are selected. All these stations can track GPS/GALILEO satellites. The station coordinates were estimated every 30 s. The strategy of RT GPS/GALILEO PPP is summarized in Table 2. The RT precise orbit/clock correction and code/phase biases products in CLK92 stream from the CNES caster are used. Moreover, the correction of receiver PCO (phase center offset) and PCV (Phase Center Variations) for GALILEO are assumed to be the same as that of GPS.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Nodes** & **Details** \\ \hline Without constraint & GPS/GALILEO observations without ionospheric constraints \\ Priori variance & GPS/GALILEO observations+ionospheric constraints with a priori variance \\ New method & GPS/GALILEO observations+ionospheric constraints with proposed method \\ \hline \hline \end{tabular}
\end{table}
Table 1: List of Data Processing Methods.  
Figure 3: The distribution of MGEX stations in the experiment.
## 2 Development of Sensor Module
### Single-Sensor Performance Test  
A single Time-of-Flight (ToF) distance sensor can detect and map its surroundings by generating virtual representations based on its selected resolution mode. Figure 3 illustrates the sensor operating in 8 \(\times\) 8 mode, where it captures 64 individual distance measurements within its field of view. The red points represent locations on the target object where distance measurements are taken, while the green lines indicate the corresponding distance from each measured point to the sensor. In this study, the Robot Operating System (ROS) was used to visualize sensor data in real-time via the RViz interface, using ROS-Serial for communication between the microcontroller and ROS.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Feature** & **Detail** \\ \hline Model number & VL53L8 CX \\ Manufacturer & STMicroelectronics \\ Package & Optical LGA16 \\ Size & 23 \(\times\) 13 \(\times\) 1.75 mm \\ Ranging & 2 cm–400 cm (per zone) \\ Operating voltage & 3.3 V (AVDD), 1.2/1.8 V (IOVDD) \\ Power consumption & -46 nW \\ Operating temperature & \(-\)30 \({}^{\circ}\)C to 85 \({}^{\circ}\)C \\ Sample rate & Up to 60 Hz \\ FoV & 45 \(\times\) 45 degree \\ I2C and SPI interface & I2C (1 MHz), SPI (3 MHz) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Sensor technical specifications [27].  
Figure 2: Zone mapping: (**a**) 4 \(\times\) 4 resolution mode provides 16 distance measurements; (**b**) 8 \(\times\) 8 resolution mode provides 64 distance measurements.  
In the example shown in Figure 4, a single sensor detects a box placed in front of a wall. The red dashed line shown in Figure 4 represents the sensor's field of view (FoV). These measurements are visualized in 3D in Figure 4, where the red points represent the box and the white points represent the wall. The corresponding raw distance measurements are shown in Figure 4. This illustrates the sensor's capability to distinguish objects at different depths within its field of view. The sensor includes an integrated noise filtering mechanism based on digital signal processing (DSP) [28], which enhances the accuracy and stability of distance measurements by reducing signal noise and fluctuations.  
Figure 4: Sensor performance test: (**a**) detection of a box positioned near a wall using a single sensor; (**b**) 3D point cloud representation of the box and wall based on sensor output; (**c**) raw distance measurement in centimeters.  
Figure 3: VL53L5 CX ToF distance sensor object detection mechanism.
## 4 Simulation Results
### The IEEE 118 Bus Power System  
The IEEE 118 bus test system [44], has been used for the next two cases to confirm the effectiveness of the HIC-GWA approach. The active and reactive power demand are 4242 MW and 1439 MVAR.  
**Case 11: Fuel cost**  
The function modeled by the quadratic cost curve given in Equation (14) is considered to minimize the total fuel cost of power generation. The simulation results, illustrated in Table 16, show that the HIC-GWA has significantly reduced the fuel cost compared with MSA, MDE, MPSO, FPA, and MFO approaches.  
In this case, the proposed metaheuristic has a better convergence than recently published optimization methods.  
**Case 12: Fuel cost with renewable energy sources (Wind/PV)**  
The objective in this case is to use the HIC-GWA to minimize the fuel cost \((F_{1})\), wind cost \((F_{2})\), and PV cost \((F_{3})\) for a system that includes renewable sources like WE and PV. The conventional power plants 12, 31, 66, 72, and 100 are replaced by five wind power units, and the conventional power plants 34, 36, 46, and 62 are replaced by four PV units. The simulation results are illustrated in Table 17.  
The total cost convergence curve for case 12 is presented in Figure 5. The proposed HIC-GWA approach converged in less than 100 iterations.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Solutions** & **MSA** & **MDE** & **MPSO** & **FPA** & **MFO** & **HIC-GWA** \\ \hline Fuel cost (\$/h) & 129640.72 & 130444.57 & 132039.21 & 129688.72 & 129708.08 & 129633.70 \\ \(P_{\text{loss}}\) (MW) & 73.26 & 71.64 & 112.85 & 74.32 & 74.71 & 76.80 \\ VD (p.u.) & 3.07 & 1.31 & 1.15 & 2.54 & 2.38 & 3.13 \\ L index & 0.06 & 0.07 & 0.07 & 0.06 & 0.06 & 0.06 \\ \hline \hline \end{tabular}
\end{table}
Table 16: Comparison of HIC-GWA results with the literature for case study 11.  
\begin{table}
\begin{tabular}{c c} \hline \hline Fuel cost (\$/h) & 112,545.51 \\ Wind cost (\$/h) & 5340.42 \\ PV cost (\$/h) & 4211.38 \\ \(P_{\text{loss}}\)(MW) & 76.64 \\ VD (p.u.) & 3.13 \\ L index & 0.06 \\ \hline \hline \end{tabular}
\end{table}
Table 17: Optimal solution of IEEE 118 bus power system for case study 12.  
Figure 5: Total cost convergence curve for case 12.
## 3 Materials and Methods
### Testing Procedures
#### 3.5.1 Surface Roughness  
Surface roughness was measured using the Mitutoyo Surftest SJ-210 profilometer. Five evenly spaced scans were taken on each flat plate, and the arithmetic mean roughness (\(R_{a}\)) was calculated with a cut-off length of 0.8 mm. This method ensures repeatability and consistency in surface finish evaluation.
# Vitamin D and Rehabilitation after Stroke: Status of Art
## 3 Genetic and Epigenetic of Vitamin D Pathway
### Gene Polymorphisms
#### 3.1.4 Vdr  
Several SNPs have been identified in both non-coding and coding regions of the _VDR_; some of these, Fok I (rs2228570), Apa I (rs7975232), Bsm I (rs1544410), and Taq I (rs731236) have a physiological and pathological role in different pathologies such as cancer, diabetes and cardiovascular diseases [49; 50; 51]. Moreover, _VDR_ knockout mice showed hypertension or cardiac hypertrophy and they are more susceptible to oncogene- or chemocarcin-induced tumors without developing cancer spontaneously [79].  
A recent meta-analysis on 5259 cases with risk of coronary artery disease (CAD) and 1981 controls showed that Fok I, Bsm I, Taq I, and Apa I polymorphisms in the _VDR_ might not be associated with CAD [52].  
These data are in agreement with a Mendelian randomization study where there is no association between the reduction in levels of 25(OH)D and increased risk of heart disease or myocardial infarction [53].  
[PERSON] et al. evaluated the association between Fok I, Apa I, Taq I and Bsm I variants and ischemic stroke in the Asian Indian population (313 ischemic stroke patients vs. 244 healthy controls) [20]. The authors found that only Fok I is associated with ischemic stroke in a gender-specific manner [20].
# Second Harmonic Revisited: An Analytic Quantum Approach
## 2 Results
### Quantum Regime
#### 2.2.2 Conversion Probability  
Achieving an analytic expression for the probability of converting \(2k\) photons of the fundamental field into \(l\leq k\) SH photons is generally a hard task because the number of perturbative terms in the expansion of the SH state (see Equation (29)) is generally not enough to recognize the convergence to a known analytic function. Moreover, there is no guarantee at all that such a function exists. However, there are some simple cases where a large number of perturbative orders (up to 30) can be retrieved and found to be the terms of the perturbative expansion of known analytical functions. In particular, this is the case if the input photon-number is small and \(l=1\). We found out that the probability \(p_{1}(N,\tilde{\gamma})\) of generating a single SH photon from \(2\leq N<6\) input photons converges, up to the order 30, to a periodic function, i.e.,  
\[p_{1}(N,\tilde{\gamma}) = |\langle N-2,1|\psi(\tilde{\gamma})\rangle\rangle|^{2}=\frac{N!} {(N-2)!}\frac{1}{\tilde{\zeta}}\sin^{2}(\sqrt{\tilde{\zeta}}\tilde{\gamma}) \tag{39}\]  
where:  
\[\zeta=\sum_{k=1}^{N/2}k\frac{[N-2(k-1)]!}{(N-2k)!}.\]  
The interplay among multiple creation and annihilation processes and their superposition is periodic up to six input photons, as shown in Figure 1. For \(N\geq 6\), this is no longer true, but still, \(p_{1}(N,\tilde{\gamma})\) converges to an analytic function. The reason for the aperiodic behavior of \(p_{1}(N,\tilde{\gamma})\) for \(N\geq 6\) is due to the contribution of a larger number of processes at every order, resulting in a squared sum of different periodic functions. The ratio between the periods of these functions turns out to be incommensurable, so that their sum is not a periodic function.
# The Iterative Solution to Discrete-Time \(H_{\infty}\) Control Problems for Periodic Systems
## 2 Iterative Methods for Stabilizing Solution
### The Iterative Procedure with One Matrix Sequences
Our iteration is:(\(i=1,2,\)...)  
\[Y^{(i)}(\theta)=\mathbb{Q}(Y^{(i-1)}(0))\,,\,\,\,Y^{(i)}(\theta-1)=\mathbb{Q}( Y^{(i)}(\theta))\,,\,\,\,\,\cdots\,,\,\,\,\,\,Y^{(i)}(0)=\mathbb{Q}(Y^{(i)}(1)) \tag{14}\]  
The iteration process stops with \(\max_{t}\,\,\,\,\|\tilde{Y}^{(i_{0})}(t)-\mathbb{Q}(\tilde{Y}^{(i_{0})}(t))\| \leq\textit{eps}\). The following algorithm is applied so as to execute the iterative procedure described by Equation (11):  
**Algorithm OMS** (One Matrix Sequence). 1. We take \(X^{(0)}(t)=0,t\in\mathbb{Z}\), \(\epsilon\) as a small positive number. 2. We compute \(X^{(1)}(\cdot)\) as \(\theta\)-periodic and stabilizing solution of the following Riccati equation:  
\[X^{(1)}(t) =A^{T}(t)X^{(1)}(t+1)A(t)-\left[A^{T}(t)X^{(1)}(t+1)B_{2}(t)+C^{T} (t)D_{2}(t)\right]+C^{T}(t)C(t)\] \[\times\left[D_{2}^{T}(t)D_{2}(t)+B_{2}^{T}(t)X^{(1)}(t+1)B_{2}(t) \right]^{-1}\left[A^{T}(t)X^{(1)}(t+1)B_{2}(t)+C^{T}(t)D_{2}(t)\right]^{T}\]  
3. For \(k=2,3,4,\ldots\) we compute the stabilizing solution \(X^{(k)}(\cdot)\) of the discrete-time Riccati equations with a defined sign Equation (11). This step might be performed with one of the following approaches:  
3.1. A Block Stein Iteration presented via Equation (13).
## 4 Discussion
### Limitations and Perspectives  
Landsat NDVI has a higher spatial resolution than MODIS NDVI and is less affected by spatial compositing and mixed pixels, making it better suited to capturing surface details and for characterizing flux tower footprints [46]. However, the 16-day revisit cycle and problems with frequent cloud contamination and snow limit the amount of Landsat data, and therefore Landsat available data are often insufficient for research on vegetation seasonal variability [47; 48]. Although gap-filling and reconstruction are widely used methods for improving the quality of Landsat data, the effects of gap-filling and reconstruction on the Landsat data were small for GPP estimates [15; 49].  
It is often more appropriate to use MODIS NDVI than Landsat NDVI data, despite the coarser resolution of the former, owing to its high revisit frequency and low cloud proportion of cloud-affected pixels [50]. In the future, blending high spatial resolution data (i.e., Landsat) with high temporal resolution (i.e., MODIS) could provide an alternative data source with high temporal resolution and high spatial resolution that would be better able to capture spatiotemporal patterns in ecosystem dynamics [51]. If combined with higher temporal-resolution data in this way, the 30-m resolution Landsat NDVI could be used to simulate GPP at regional or global scales. The advantage of using remote sensing data with high resolution when simulating GPP for heterogeneous landscapes is the superiority of the resulting general GPP monitoring at medium or coarse resolution--which could then capture more detailed GPP dynamics and responses to heterogeneous landscape changes such as cropland agriculture, land use change, and human activities.
# Control of Porosity in Parts Produced by a Direct Laser Melting Process
## 3 Results and Discussion  
### Characteristics of Single-Track Melting Test  
The soundness of a fabricated part depends on the characteristics of the melting and solidification of metallic powder. This soundness can be observed directly in a single-track melting test, as shown in Figure 8. Full melting of the powder bed and formation of a continuous fused metal line was achieved by means of a single track-melting test.  
Single-track melting was performed using laser powers of 150 and 200 W, scan rates of 36.6 to 220 mm/s, and a hatching distance of 0.06 mm. The depths and widths of the bead produced by various process parameters were measured using an image analysis program. In general, a height/width ratio of approximately 0.5 is considered to be optimal for the bead shape [23]. Figure 9 illustrates the bead shapes of powders 1 and 2 at different scan speeds. The bead size decreased with an increasing scan rate, owing to the reduced heat input.  
Figure 8: Schematic of single-track melting.  
Figure 7: Cross-sectional microscopic view of powder 3: (**a**) image obtained from optical microscope and (**b**) image following binarization process.  
Figure 10 shows the height/width ratio of a single-track bead with an increasing scan rate for powders 1 and 2. The optimum bead shapes for powders 1 and 2 were obtained at laser scan rates of 110 mm/s and 73 mm/s, respectively. This difference in scan rates means that the powder morphology significantly affects the bead shape in DLM, which agrees with the results of [PERSON] [24]. The differences in powder packing density, heat conduction, laser diffraction, and layering height are considered to be the main causes of the varying behaviors for powders 1 and 2.
## 2 Definitions  
In this section we give some preliminary definitions that will be useful in the rest of the paper. First, in this paper, we will consider only undirected graphs. Consider a set of colors \(C=\{1,\ldots,c\}\). In the paper we denote by \(c\) the cardinality of \(C\). A \(C\)-edge-colored graph (or simply an edge-colored graph when the set of colors is clear from the context) is defined as \(G=(V,\mathcal{E})\), where \(V\) denotes the set of vertices of \(G\) and \(\mathcal{E}=\{E_{1},\ldots,E_{c}\}\) denotes a collection of edge sets, where the set \(E_{i}\), with \(i\in C\), represents the set of edges colored with color \(i\). Notice that, for a given pair of vertices \(v_{i}\), \(v_{j}\), there may exist more than one edge between \(v_{i}\) and \(v_{j}\) (each of these edges is associated with a distinct color of \(C\)).  
A path \(\pi\) in \(G\) is called a _uni-color_ path if all the edges of \(\pi\) have the same color, that is they belong to the same set \(E_{i}\) (for some \(i\in C\)). Given two vertices \(x,y\in V\), an \(xy\)-path is a path between vertices \(x\) and \(y\). Two paths \(\pi^{\prime}\) and \(\pi^{\prime\prime}\) are _internally disjoint_ (or, simply, _disjoint_) if they do not share any internal vertex, while a set of paths are internally disjoint if they are pairwise internally disjoint.  
Next, we introduce the formal definitions of the problems we deal with in this paper, namely the optimization problem Max CDP, the decision problem (CDP) naturally associated with Max CDP, and the corresponding length-bounded variants \(\ell\)-LCDP and \(\ell\)-LCDP\({}_{p}\).  
**Problem 1**.: Maximum Colored Disjoint Paths (Max CDP).  
_Input_: a set \(C\) of colors, a \(C\)-edge-colored graph \(G=(V,\mathcal{E})\), and two vertices \(s,t\in V\).  
_Output_: the maximum number of disjoint uni-color \(st\)-paths.  
**Problem 2**.: Colored Disjoint Paths (CDP).  
_Input_: a set \(C\) of colors, a \(C\)-edge-colored graph \(G=(V,\mathcal{E})\), a non-negative integer \(p\), and two vertices \(s,t\in V\).  
_Output_: Do there exist at least \(p\) disjoint uni-color \(st\)-paths in \(G\)?  
The \(\ell\)-Length Colored Disjoint Paths (\(\ell\)-LCDP) problem is a variant of Max CDP where the length of the paths in the solution is bounded by an integer \(\ell\geq 1\). The \(\ell\)-LCDP\({}_{p}\) problem is the decision version of \(\ell\)-LCDP which asks if there exists a solution of \(\ell\)-LCDP with cardinality at least \(p\).