esa-sceva/satcom-chunk-collection huggingface dataset:
## 4 Uncertainty Quantification
### Determination of Orthogonal Polynomial Basis  
If there is only one random variable (i.e., \(n=1\)), the gPC expansion for the random output can be directly constructed using Equation (26), where the orthogonal basis is the same as for the random input variable. However, the orthogonal basis for a multidimensional random vector results in tensor products of different polynomials representing each uncertain variable. For instance, let the random input variable \(\xi_{1}\) follow the normal distribution with corresponding Hermite polynomials as \(H(\xi_{1})\), and let \(\xi_{2}\) follow a uniform distribution represented by Legendre polynomials denoted as \(L(\xi_{2})\). Then, the polynomials of the random output are obtained by (cf. [41] for more details)  
\[\psi(\xi_{1},\xi_{2})=H(\xi_{1})\otimes L(\xi_{2}). \tag{29}\]  
When the above random two-dimensional system (i.e., \(n=2\)) is used for a second-order gPC expansion (i.e., \(m=2\)), the orthogonal polynomials are represented as  
\[\left\{\begin{array}{ll}\psi_{0}(\xi_{1},\xi_{2})=H_{0}L_{0}=1,&\psi_{3}( \xi_{1},\xi_{2})=H_{2}L_{0}=\xi_{1}^{2}-1,\\ \psi_{1}(\xi_{1},\xi_{2})=H_{1}L_{0}=\xi_{1},&\psi_{4}(\xi_{1},\xi_{2})=H_{1} L_{1}=\xi_{1}\xi_{2},\\ \psi_{2}(\xi_{1},\xi_{2})=H_{0}L_{1}=\xi_{2},&\psi_{5}(\xi_{1},\xi_{2})=H_{0}L_ {2}=\frac{1}{2}(3\xi_{2}^{2}-1)\end{array}\right. \tag{30}\]  
The uncertain parameter \(Y\) is then approximated as  
\[Y(\xi_{1},\xi_{2})=y_{0}+y_{1}\xi_{1}+y_{2}\xi_{2}+y_{3}(\xi_{1}^{2}-1)+y_{4} \xi_{1}\xi_{2}+\frac{1}{2}y_{5}(3\xi_{2}^{2}-1). \tag{31}\]
# Exploring Carbon-Fiber UAV Structures as Communication Antennas for Adaptive Relay Applications
## 2 Materials and Methods
### Experimental Setup for Antenna Characterization
#### 2.1.4 Regions Around the Antennas  
An additional important aspect is the identification of the regions surrounding the antenna. Figure 4 illustrates the three main spatial regions around an antenna, each defined by a specific formula. These regions are [19]: the reactive near-field region, the radiating near-field (or transition) region, and the far-field region (also known as the radiation zone). Each zone is characterized by its distance from the antenna and exhibits distinct electromagnetic and electric field distribution properties, which significantly influence how the antenna interacts with its surrounding environment.  
The reactive near-field region starts at the surface of the antenna and extends to a specific distance, calculated using the following relation:  
\[R=0.6\sqrt[3]{\frac{D^{3}}{\lambda}}=0.0834\text{ m} \tag{2}\]  
where \(D\) is the maximum dimension of the antenna as seen from the observation point (in this case, 0.169 m), and \(\lambda\) is the wavelength corresponding to the frequency of 1.2 GHz--chosen based on the justification provided in the previous section--and computed using the formula \(\lambda=c\textit{f}\).  
Beyond this distance, specifically starting from 0.0834 m, the radiating near-field (Fresnel) region begins and extends up to another distance, defined by:  
\[R_{0}=\frac{2D^{2}}{\lambda}=0.2285\text{ m} \tag{3}\]  
Figure 4: Regions around the antennas [20].  
All points located at distances greater than 0.2285 m from the antenna are considered in the far-field region (Fraunhofer zone), which is the true radiation zone.  
All points beyond \(R_{0}\) = 0.2285 m fall within the far-field region, where the following conditions must be satisfied [21]: \(R_{0}\gg D\) and \(R_{0}\gg\lambda\).  
According to theory, two additional conditions must be satisfied to ensure measurements are truly conducted in the far field: the observation distance \(R_{0}\) must be much greater than both \(D\) and \(\lambda\). In practice, the convention \(R_{0}>20\cdot D\) is often applied. Although, in our case, these conditions are near the lower limit, due to the physical constraints of the testing laboratory, the measurements can still be considered valid within the far-field (Fraunhofer) region.
## 3 Experimental Results and Analysis
### Strain Rate Effect of the Specim  
The average strain rate of the sandstone sample under the coupling effect of temperature and water changes with axial pressure, as shown in Figure 10.  
Figure 10 illustrates that the average strain rate of the sandstone samples increases with an increase in axial pressure. The average strain rate of the sample without axial  
Figure 10: The average strain rate of the specimen changes with axial pressure.  
Figure 9: The elastic modulus of the sample changes with axial pressure.  
pressure is 67.61 s\({}^{-1}\), the average strain rate of the sample with axial pressure of 0.5 MPa is 73.98 s\({}^{-1}\), and the average strain rate of the sample with axial pressure of 4 MPa is 138.90 s\({}^{-1}\), which reflects an increase of 64.92 s\({}^{-1}\). This phenomenon is due to the fact that the internal structure of the sandstone sample deteriorates when subjected to axial pressure, which causes the dynamic compressive strength of the sandstone sample to decrease and the average strain rate to increase. In this way, the dynamic compressive strength of the sandstone sample decreases, and the average strain rate increases. With an increase in axial pressure, new cracks are generated and gradually expand inside the specimen, making the deterioration damage to the internal structure more severe and more likely to occur, resulting in a rapid decrease in the dynamic compressive strength of the sandstone specimen and an exponential increase in the average strain rate. The average strain rate of the sandstone sample with an increase in axial pressure of the temperature-water coupling is an exponential function of growth, showing an obvious strain rate effect. The fitted functional relationship is shown in Equation (4), and the correlation coefficient is 0.9798, with an obvious positive correlation:  
\[\dot{\epsilon}(P)=67.61e^{0.18p}\ \ (R^{2}=0.9798) \tag{4}\]  
where \(\dot{\epsilon}(P)\) represents the average strain rate of the sandstone sample under the coupling effect of temperature and water.
## 4 Conclusions
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Prediction Protocol** & **Core Factor** & **Linear Regression Line** & \
\begin{tabular}{c} **Correlation** \\ **Coefficient (R2)** \\ \end{tabular} &
\begin{tabular}{c} **Corresponding** \\ **Figure** \\ \end{tabular} \\ \hline \multirow{3}{*}{Equation (1). PIM} & Polarizability [Å3] & \(y=3x+2.037\) & 0.94 & \multirow{3}{*}{Figure 3d} \\  & Ionization energy [eV] & \(y=-0.312x+11.875\) & 0.05 & \\  & Molecular weight [g mol\({}^{-1}\)] & \(y=82.24x+21.111\) & 0.92 & \\ \hline \multirow{3}{*}{Equation (2). re-PIM} & Polarizability [Å3] & \(y=2.24x+2.924\) & 0.94 & \multirow{3}{*}{Figure 4c} \\  & Ionization energy [eV] & \(y=-0.280x+11.814\) & 0.04 & \\  & Molecular weight [g mol\({}^{-1}\)] & \(y=80.99x+25.267\) & 0.94 & \\ \hline \multirow{3}{*}{Equation (3). PIMN} & Polarizability [Å3] & \(y=2.53x+2.822\) & 0.85 & \multirow{3}{*}{Figure 5c} \\  & Ionization energy [eV] & \(y=-0.167x+11.629\) & 0.01 & \\  & Molecular weight [g mol\({}^{-1}\)] & \(y=73.18x+36.187\) & 0.91 & \\ \cline{2-5}  & Number of electrons & \(y=35.97x+17.230\) & 0.94 & \\  & Molar volume [cm\({}^{3}\) mol\({}^{-1}\)] & \(y=27.509x+32.502\) & 0.82 & \\ \cline{2-5}  & HOMO [eV] & \(y=-0.12x-9.312\) & 0.01 & \\  & Formation energy [a.u.] & \(y=-0.827x-0.137\) & 0.73 & \\ \cline{2-5}  & HOMO–LUMO gap [eV] & \(y=-0.103x+8.779\) & 0.03 & \\  & Electronic spatial extent gap [a.u.] & \(y=2.708x+6.578\) & 0.03 & \\ \hline \multirow{3}{*}{Equation (4). OPT} & Number of electrons & \(y=34.459x+18.84\) & 0.97 & \multirow{3}{*}{Figure 6c} \\  & Molecular weight [g mol\({}^{-1}\)] & \(y=72.137x+36.101\) & 0.96 & \\ \cline{1-1}  & Molar volume [cm\({}^{3}\) mol\({}^{-1}\)] & \(y=25.90x+32.641\) & 0.79 & \\ \cline{1-1} \cline{2-5}  & Polarizability [Å3] & \(y=2.486x+2.836\) & 0.88 & \\ \cline{1-1}  & Formation energy [a.u.] & \(y=-0.712x-0.301\) & 0.71 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Linear regression lines and correlation coefficients (\(R^{2}\)) of the correlation between the dielectric strength and each core factor for each prediction protocol. **Author Contributions:** Writing--review and editing, and supervision, K.C.K. ; validation, formal analysis, investigation, and data curation, M.K.C. All authors have read and agreed to the published version of the manuscript. This work was also supported by the Korea Electric Power Corporation (Grant number: R21X001-4). Not applicable. **Data Availability Statement:** No data is shared by the authors. **Conflicts of Interest:** The authors declare no conflict of interest.
# Chromium(III) Removal from Wastewater by Chitosan Flakes
## 4 Conclusions  
The present study indicated the suitability of chitosan in applications aimed at removing chromium(III) ions from aqueous solutions. Chitosan is a low-cost reagent and its utilization is novel, non-toxic, and environmentally compatible. Although its effectiveness has been proven in the adsorption of several metal ions, such as Cu, Ag, Cd, Zn, Mo, V, Pb, and Cr(VI), Cr(III) has been poorly investigated. Moreover, among the usable forms of chitosan, flakes are the least studied. In this work, the adsorption of Cr(III) on chitosan flakes was investigated considering concentrations (up to 2000 mg L\({}^{-1}\)) that are much higher than those reported in the few studies present in literature. This made it possible to highlight a much higher adsorption capacity of chitosan (up to 138.45 mg g\({}^{-1}\)), well beyond the values observed so far.  
The pH significantly influences the adsorption capacity of the biopolymer, the latter increasing with the pH of the solution. The adsorption process is rather rapid: it was found that 2 h of contact time are sufficient to reach about 95% of the adsorption equilibrium; the Langmuir equation provided the best fit over the entire concentration range, thus suggesting a monolayer interaction of chromium on the adsorbent.  
The adsorption capacity for Cr(III) in dynamic tests was found to be penalized by the competition between ions, and particularly influenced by the presence of zinc and cadmium due to their strong affinity with chitosan. The recovery of Cr(III) ions (and the consequent regeneration of chitosan) can be obtained by desorption with a 0.1 M EDTA solution, with the latter being recoverable by precipitation in an acidic medium.  
Since chitosan is basically a low-cost and environmentally friendly material, its use as it is produced (i.e., flakes) is desirable, especially considering the greater theoretical adsorbent capacity due to a major availability of both amino and hydroxyl groups, but involves some critical issues. In particular, since the shape and size characteristics of commercial chitosan flakes introduce hydrodynamic limitations such as column clogging, a batch reactor is probably more appropriate as a experimental setup. Further investigations are therefore underway to quantify the effectiveness of alternative operating solutions.  
Conceptualization, L.P.; methodology, L.P. and A.P.; validation, L.P. and I.F.; investigation, I.S. and M.S.; data curation, M.V.; writing--original draft preparation, L.P. and M.V.; writing--review and editing, L.P. and M.V.; project administration, L.P.; funding acquisition, L.P. All authors have read and agree to the published version of the manuscript. This research received no external funding. The authors declare no conflict of interest.
# Exploring Frontiers of 4D X-ray Tomography
## 2 High-Speed X-ray CT
### X-ray Imaging
Note that the absorption of X-rays is described by the imaginary part of the complex refractive index, which is about \(10^{-8}\) to \(10^{-9}\) several orders of magnitude smaller. Four typical optical systems that have been proposed as methods for realizing X-ray phase-contrast imaging are compared in Figure 2. The method in Figure 2a is called \"crystal interferometry\" [6; 7; 8; 9], which uses a Mach-Zehnder interferometer using Bragg reflection by a single crystal. Figure 2b shows diffraction enhanced imaging (DEI) [10; 11; 12], a method using an analyzer crystal, which detects the slight refraction of X-rays by an object by utilizing the very small angular width of the Bragg reflection of a single crystal (about 10 \(\upmu\)rad). The imaging methods in Figure 2a,b require monochromatic X-rays, so the measurement time for obtaining a projection image is generally on the order of seconds even when highly brilliant synchrotron radiation X-rays are used. The methods in Figure 2c,d are called the \"propagation-based method\" [13; 14; 15; 16] and \"grating interferometry\" [17; 18; 19; 20; 21; 22; 23; 24], respectively, and can use X-rays with a wide energy bandwidth (continuous X-rays) and spherical waves, which means that high-intensity X-rays can be used. Therefore, they are suitable for imaging with a high temporal resolution. The propagation-based method can be realized with a very simple configuration consisting only of a sample and an image detector. Images with enhanced edges can be obtained on the basis of the interference between slightly refracted X-rays inside and outside the boundaries of the structures in a sample. However, the pseudo-homogeneous assumption [16] is required for the quantitative analysis of the phase shift. Grating interferometry, in comparison, allows for quantitative imaging without any special assumptions. Another advantage of grating interferometry over the propagation-based method is its multi-modality; three independent projection images, absorption, differential-phase, and visibility-contrast images [23; 24] can be obtained, as shown in Figure 3.  
Figure 1: (**Left**) Schematic diagram of how X-rays pass through object. Dashed line shows X-ray wave without object, and solid with object. (**Right**) Dependence of interaction cross section on atomic number for X-rays (solid, dashed, and dot-dash curves correspond to those for X-ray wavelengths of 0.2 Å, 0.6 Å, and 1.0 Å, respectively). Upper curves in graph: cross section corresponding to X-ray phase shift. Lower curves in graph: cross section corresponding to X-ray absorption.
# Temporal Encoding to Reject Background Signals
## 2 Results
### Data Rates
Additionally, efficiency improvements will be possible through use of PPM style transmission, to transmit multiple bits per correlation peak.
## 4 Methodology
### Feature Selection Methods
#### 4.1.1 Variance-Based Feature Selection  
First-order feature selection refers to basic techniques that use straightforward statistics to identify the most important features in a dataset. Instead of diving deep into complex models, it relies on metrics such as variance and correlation to quickly gauge which features stand out. These methods can remove less relevant or redundant information early, making subsequent analyses more focused and efficient. Variance analysis examines the extent to which a feature's values vary within the dataset. If a feature shows almost no change, it is unlikely to help predict the outcome. By removing features with extremely low variance, inputs that do not add meaningful information to the model are eliminated. This simple step helps streamline the data, reduce the noise risk, and make the model training process more efficient. Equation (1) denotes the variance. In this study, a parameter-wise variance function calculates a variance matrix containing scalar values. Finally, parameters with low variance are removed from the feature list. The remaining features will be passed on to the next analysis.  
\[Var(x)=\frac{\sum_{s=0}^{n}{(x_{s}-\overline{x})^{2}}}{n-1} \tag{1}\]  
where \(n\) is the number of measurements, \(x\) is the observed parameter, and \(\overline{x}\) is the mean of all observations' mean.
# A Managerial Approach to Investigate Fall Risk in a Rehabilitation Hospital
## 3 Results  
Table 2 shows all the parameters (anamnestic and clinical) considering only patients at their first fall and excluding recurrences. The collected data are referred to \"alert and fall analysis reports\" referring to the period January 2020-December 2021 and occurred at _Istituti Clinici Scientifici_ Maugeri of Bari, Italy. Figure 4: Ishikawa diagram. Figure 3: Basic stream map. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Categories** & **Statistics** \\ \hline Years, mean \(\pm\) St. dev. & // & 72.6 \(\pm\) 11.9 \\ \hline \multirow{6}{*}{Mobility, n [\%]} & Bedridden & 19 [8.0] \\  & Assisted with aids & 111 [46.6] \\  & Assisted without aids & 16 [6.7] \\  & Autonomous with aids & 60 [25.2] \\  & Autonomous without aids & 32 [13.4] \\ \hline \multirow{6}{*}{State of consciousness, n [\%]} & Psychomotor agitation & 14 [5.9] \\  & Confusion & 15 [6.3] \\  & Vigilant & 209 [87.8] \\ \hline \multirow{6}{*}{Drugs acting on vital signs} & Yes & 59 [24.8] \\  & No & 179 [75.2] \\ \cline{2-3}  & Diuretics, n [\%] & Yes & 126 [52.9] \\  & No & 112 [47.1] \\ \cline{2-3}  & Hypotensive, n [\%] & Yes & 165 [69.3] \\  & No & 73 [30.7] \\ \cline{2-3}  & Hypoglycemias, n [\%] & Yes & 13 [5.5] \\  & No & 225 [94.5] \\ \cline{2-3}  & Laxatives, n [\%] & Yes & 14 [5.9] \\  & No & 224 [94.1] \\ \hline \multirow{6}{*}{Psychoactive drugs} & Hyponics, n [\%] & Yes & 21 [8.8] \\  & No & 217 [91.2] \\ \cline{2-3}  & Opioid, n [\%] & Yes & 3 [1.2] \\  & No & 235 [98.8] \\ \cline{2-3}  & Sedatives, n [\%] & Yes & 49 [20.5] \\  & No & 189 [79.5] \\ \hline \multirow{6}{*}{Syschoactive drugs} & Yes & 24 [10.1] \\  & No & 214 [89.98] \\ \cline{2-3}  & Antidepressants, n [\%] & Yes & 39 [16.4] \\  & No & 199 [83.6] \\ \cline{2-3}  & Antiepileptics, n [\%] & Yes & 32 [13.4] \\  & No & 206 [86.6] \\ \hline \multirow{6}{*}{Antiparkinsonians, n [\%]} & Yes & 7 [2.9] \\  & No & 231 [97.1] \\ \cline{2-3}  & Antiparkinsonians, n [\%] & Yes & 3 [1.2] \\  & No & 235 [98.8] \\ \hline \multirow{6}{*}{Systemic antibistamines, n [\%]} & Yes & 1 [0.4] \\  & No & 237 [99.6] \\ \cline{2-3}  & Morse, mean \(\pm\) St. dev. & // & 33.3 \(\pm\) 18.5 \\ \hline \multirow{6}{*}{Stratify, n [\%]} & 0 & 9 [13.2] \\  & 1 & 31 [45.6] \\ \cline{1-1}  & 2 & 23 [33.8] \\ \cline{1-1}  & 3 & 5 [7.4] \\ \hline \multirow{2}{*}{Risk, n [\%]} & Yes, preventive personalized measures & 69 [29.0] \\  & Yes, preventive standard measures & 169 [71.0] \\ \hline \multirow{6}{*}{Hour of fall, n [\%]} & Morning & 97 [40.8] \\  & Night & 48 [20.2] \\ \cline{1-1}  & Afternoon & 59 [24.8] \\ \cline{1-1}  & Evening & 34 [14.2] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Anamnestic and clinical parameters for all the patients considering only their first fall.
## 2 Materials and Methods
### Main Machine Learning Algorithms
#### 2.2.3 Random Forest  
Random forest is a versatile machine learning algorithm that can be effectively used for classification and detection tasks. In the context of classification, random forest constructs an ensemble of decision trees, where each tree is trained on a random subset of input features and data samples. The algorithm works by iteratively splitting the data based on the selected features, with the aim of maximizing the difference between classes in the resulting subsets. During the classification phase, the group of decision trees collectively votes on the class label for a given input, and the majority class label is assigned as the final prediction [46]. Random forest's ability to combine multiple decision trees and aggregate their predictions makes it robust against overfitting and noisy data. It can handle high-dimensional feature spaces and provides an estimate of feature importance, aiding in understanding the relative contributions of different features to the classification task. Random forest has been successfully applied to various classification problems, such as image recognition, text classification, and medical diagnosis, where it can accurately handle complex decision boundaries and capture non-linear relationships between features and classes. In the context of detection, random forest can be used as a robust algorithm to identify specific objects or patterns within data. For example, in object detection tasks, random forest can be used to detect objects by learning a set of features that describe the appearance or shape of the target object. Different studies suggest that random forest algorithms are used in atmospheric science. For air quality forecasting, RF algorithms are used in conjunction with meteorological models for air quality forecasting [47] or to model atmospheric concentrations of pollutants such as sulfur dioxide [48], and to analyze spatial patterns in forest attributes [49] and flood risk [50].
# Predicting the Evolution of Syntenies--An Algorithmic Review
## 5 Accounting for Gene Trees
### Minimizing Duplication Episodes
#### 5.4.2 The Clustering Model  
Given an interval assignment of each duplication node of the set of gene trees, three different duplication clustering models have been proposed in the literature. The _Episode Clustering (EC) model_ allows clustering any two duplications that can be mapped to the same location in the species tree (yellow boxes in Figure 6), while a slightly more constrained model, called the _Minimum Episodes (ME) model_, excludes cases in which a duplication and an ancestor of this node (from the same gene tree) are clustered together (orange boxes in Figure 6).  
The two problems were introduced by [PERSON] et al. [109] with the interval model being the GMS-model. These problems can be formulated as NP-hard set cover problems [111]. Alternatively, representing them as a Tree Interval Cover (TIC) Problem, polynomial-time algorithms can be designed for the EC and ME models under the GMS interval model [112; 113]. Moreover, linear time and space algorithms for the TIC Problem that applies to the EC and ME models have been developed by [PERSON] et al. [114] under every interval model. Finally, [PERSON] and [PERSON] [106] proposed a variant of the algorithm for general interval models presented in [110] that runs in linear time for the ME Problem. Solutions to the EC and ME problems for unrooted gene trees and for the PG-model were also studied [108; 115].  
Finally, in addition to the EC and ME clustering models, the _Gene Duplication Clustering (GD) model_[107] is similar to EC except that only duplications from different gene trees can be clustered in a single episode.  
Figure 6: **(1)** Two gene trees (red and blue) and a species tree \(S\). Leaves of the gene trees are labeled according to the genome the corresponding gene belongs to. The event-labeling of internal nodes correspond to the LCA-mapping (rectangles are duplications and the other nodes are speciation). The interval labeling \(Int(d)\) is given for each duplication node \(d\) (a single letter \(l\) corresponding to the interval \([l,l]\)): the black label corresponds to the LCA-mapping, the green interval to the GMS-model and the purple interval to the PG-model; **(2)** The two gene trees embedded in the species tree \(S\). The duplication positions are chosen from the GMS-model intervals, and indicated by a green arrow in **(1)**. The orange boxes correspond to the multiple duplications according to the ME model, while the yellow boxes correspond to the multiple duplications according to the EC model.  
Notice that the EC Problem for the FHS-model has a trivial outcome with one cluster. On the other hand, the GD and ME problems for the FHS interval model have been shown NP-hard [107; 116]. The unconstrained ME model has also been extended to gene losses for different costs of duplications and losses [116].