esa-sceva/satcom-chunk-collection huggingface dataset:
# Use of Covariance Analysis in Electroencephalogram Reveals Abnormalities in Parkinson's Disease
## 3 Mathematical Background for Cross Wavelet Analysis
### Wavelet Filtering  
Because the original electroencephalographic data showed muscle activity artifacts in the signal, mainly from the ocular and jaw muscles, the inverse Continuous Wavelet Transform (iCWT) was applied as a filter to remove artifacts. For this process, CWT were initially applied to the original data of each subject to separate the time series in the time-frequency spaces. The signals were reconstructed with the iCWT from 2 to 50 Hz. Artifacts are reduced by iCWT because this technique has an advantage over traditional filtering in that it removes noise at all frequencies and can be used to isolate single events that have a broad power spectrum or multiple events that have varying frequency [26; 38]. Thus, signals are reconstructed within a specified frequency range without losing intrinsic information of each EEG. Figure 1A shows the 21 original time series from the CL subject identified as 01 (CL01) <60. Figure 1B shows the continuous wavelet spectra from channels Fp1 and O2 of the same subject. After the filtering process, we eliminated the first and the last seconds of each time series to avoid the edge effects and then 21 periods of 90 s free of artifacts were intercepted for each CL and PD patient. Figure 1C shows the 21 reconstructed time series from the CL01 subject. The brainwave frequency ranges used in this research were as follows (in Hz): \(\delta\) (2-3.9); \(\theta\) (4-7.9); \(\alpha\) (8-12.9); \(\beta\) (13-29.9); \(\gamma\) (30-50).  
All EEG were processed with the MATLAB software (version 9.7.0.1471314, R2019b; RRID:SCR_001622).
# Inversion of Rayleigh Wave Dispersion Curve Extracting from Ambient Noise Based on DNN Architecture
## 2 Materials and Methods  
### Generate Training Dataset  
The S-wave velocity and its corresponding dispersion curve dataset constitute the training sample data pair for DNN. The diversity and sufficiency of the sample dataset determine the performance of deep learning. Sample data can be obtained via logging experiments, laboratory tests after sampling, and field Rayleigh wave measurements. However, these methods are time-consuming and expensive. An alternative approach is forward modeling by providing geological models and then calculating the corresponding dispersion data. In this method, establishing a large number of representative geological models will be very important.
###### Abstract  
In this paper, a method of obtaining parameters of one-column Jansen-Rit model was proposed. Methods present in literature are focused on obtaining parameters in an on-line manner, producing a set of parameters for every point in time. The method described in this paper can provide one set of parameters for a whole, arbitrarily long signal. The procedure consists of obtaining specific frequency features, then minimizing mean square error of those features between the measured signal and the modeled signal, using genetic algorithm. This method produces an 8-element vector, which can be treated as an EEG signal feature vector specific for a person. The parameters which were being obtained are maximum postsynaptic potential amplitude, maximum inhibitory potential amplitude, ratio of the number of connections between particular neuron populations, the shape of a nonlinear function transforming the average membrane potential into the firing rate and the input noise range. The method shows high reproducibility (intraclass correlation coefficient for particular parameters ranging from 0.676 to 0.978) and accuracy (ranging from 0.662 to 0.863). It was additionally verified using EEG signal obtained for a single participant. This signal was measured using Emotiy EPOC+ NeuroHeadset.  
EEG modeling; Jansen model; Rit model; Jansen-Rit model; neural mass model; one-column model; genetic algorithm; biofeedback; EEG classification; EEG frequency features; model parameters estimation
## 3 Results
### Spatial Resolution with the LaGEMPix
#### 3.2.2 Line Spread Function (LSF)  
For the LSF response, we used a 3 mm thick copper plate placed at 7 mm from the Mylar window (see Figure 7a). Various holes of 5 mm diameter spaced by 3 to 20 mm, edge to edge were drilled in the plate. The average image profile on a single hole is Gaussian. The spatial resolution was, therefore, estimated by fitting the distribution by a Gaussian function. The obtained FWHM for a 5 mm diameter hole is 6.73 \(\pm\) 0.08 mm.  
Figure 6: Edge response profile for 40 kV X-rays using a 2.5 cm thick lead block. The red line represents a logistic function fit to the data.  
Figure 7: (a) The 3 mm-thick copper plate used for the evaluation of the spatial resolution using the LSF method. The numbers written on the plate represent the space between the holes in millimeters. (b) Heat map of the copper mask for 40 kV X-rays. A ROI (green rectangle) was set on the holes separated by 3 mm. The spatial resolution was estimated by fitting the profile in the ROI by a Gaussian function.  
An additional measurement was made by selecting a ROI (green region in Figure 7b) at the center of the 5 mm holes spaced by 3 mm. Figure 8 shows the response of two holes spaced by 3 mm (edge to edge), featuring two peaks with a dip in the intensity. The response was again obtained by averaging all pixel values in the same column from the averaged background-subtracted image. The so-called FWHM criterion states that the minimum distance that any detector is able to resolve is equal to the FWHM value of the Gaussian distribution. The relevant values in this case are the center-to-center distance between the holes, 8 mm, and the FWHM, 7.10 \(\pm\) 0.30 mm. Following this criterion, the two holes can be resolved.
# Asymmetric Quantum Multicast Network Coding: Asymmetric Optimal Cloning over Quantum Networks
## 2 Materials and Methods
### Classical Multicast Network Coding
Then, after all edges have transmitted an alphabet, the target node \(t_{i}\) has \(m_{i}\)-alphabets \(y_{j}^{(i)}\in\mathbb{F}_{q}\) (\(j=1,\cdots,m_{i}\)), where \(y_{j}^{(i)}\) is an alphabet sent through the \(j\)th incoming edge to \(t_{i}\). A classical linear multicast network code \(\{f_{e}\}_{e\in E^{\prime}}\) is called _solvable_ if there exists a set of decoding operations \(\{g_{i}\}_{i=1}^{N}\) such that \(g_{i}:\mathbb{F}_{q}^{m_{i}}\rightarrow\mathbb{F}_{q}^{r}\) satisfies the following equation for all \(i\):  
\[\vec{x}=g_{i}\Big{(}y_{1}^{(i)},\cdots,y_{m_{i}}^{(i)}\Big{)}, \tag{16}\]  
where \(\vec{x}\in\mathbb{F}_{q}^{r}\) is the input message. If a classical linear multicast network code is solvable, any decoding operation \(g_{i}\) can be chosen as a linear map. There is a necessary and sufficient condition for the existence of a classical linear multicast network code [37; 38]. Suppose that \(C_{i}\) is the size of the minimum cut between \(s\) and \(t_{i}\). Then, there exists a classical linear multicast code with source rate \(r\) on \(G^{\prime}\) over a sufficiently large field \(\mathbb{F}_{q}\) if and only if \(C_{i}\geq r\) for all \(i\). This is nothing but a generalization of the famous max-flow min-cut theorem to a multicast network communication.
## 3 Method Verification
### Modal Analysis  
The first 15 order modes were selected for modal analysis. In addition to the six rigid body modes, the first four order vertical bending modes, the first three order torsional modes and the first two order horizontal bending modes were obtained. The mode shapes selected in this paper are shown in Figures 2-4, and the natural frequencies are shown in Table 2.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Physical Quantity** & **Value** \\ \hline Length (m) & 200 \\ Breadth (m) & 50 \\ Depth (m) & 9.5 \\ Draught (m) & 5 \\ Center of gravity (m) & (100, 0, 6.17) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main parameters of the single module.  
Figure 1: Dual-module platform.  
Figure 4: Torsional mode shapes.  
Figure 2: Vertical bending mode shapes.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Mode Type**} & \multicolumn{2}{c}{**Frequency (Hz)**} \\ \hline \multirow{3}{*}{Vertical bending mode} & 2-node & 0.00 \\ \cline{2-3}  & 3-node & 0.53 \\ \cline{2-3}  & 4-node & 0.80 \\ \cline{2-3}  & 5-node & 1.45 \\ \hline \multirow{3}{*}{Torsional mode} & 1-node & 0.53 \\ \cline{2-3}  & 2-node & 1.50 \\ \cline{2-3}  & 3-node & 1.83 \\ \hline \multirow{2}{*}{Horizontal bending mode} & 2-node & 0.58 \\ \cline{2-3}  & 3-node & 1.75 \\ \hline \end{tabular}
\end{table}
Table 2: Natural frequency.  
Because the connector releases the relative pitch between the two modules, the two-node vertical bending mode (shown in Figure 2a) actually represents the relative pitch of the platform, whose natural frequency is 0 Hz. Similarly, due to the relative pitch released by the connector, the four-node vertical bending mode (shown in Figure 2c) exhibits a 'double U' shape, and there is almost no transition in this mode shape at the joint between the two modules, which is in the form of'sharp corner'. It can be seen from Figures 3 and 4 that the horizontal and torsional modal shapes are similar to those of the single-module platform. This result means that releasing one DOF (degree of freedom) will have a great influence on the corresponding modal shapes, whereas it has little influence on the other modal shapes.  
Furthermore, by comparing the natural frequencies in Table 2, it can be seen that the horizontal bending stiffness is greater than the torsional stiffness and the torsional stiffness is greater than the vertical bending stiffness. Among the first 15 order modes, the number of vertical modes is the most, whereas the number of horizontal bending modes is the least, which conforms to the distribution law of flat barge structural modes.
# Improved Direct Linear Transformation for Parameter Decoupling in Camera Calibration
## 2 Parameter Coupling Analysis  
### Camera Model  
The camera model is shown in Figure 1. A 3D point is denoted by \(P_{i}=\left[\begin{array}{cc}X_{i}&Y_{i}&Z_{i}\end{array}\right]^{T}\). A 2D image point is denoted by \(p_{i}=\left[\begin{array}{cc}u_{i}&v_{i}\end{array}\right]^{T}\). The relationship between 3D point \(P_{i}\) and its image projection, \(p_{i}\), is given by:  
\[\begin{array}{c}u_{i}=u_{0}+a_{x}\frac{r_{11}X_{i}+r_{12}Y_{i}+r_{13}Z_{i}+t _{x}}{r_{31}X_{i}+r_{32}Y_{i}+r_{33}Z_{i}+t_{z}}\\ \\ v_{i}=v_{0}+a_{y}\frac{r_{12}X_{i}+r_{22}Y_{i}+r_{23}Z_{i}+t_{y}}{r_{31}X_{i}+ r_{32}Y_{i}+r_{33}Z_{i}+t_{z}}\end{array} \tag{1}\]  
where \(a_{x}=f/d_{x}\), \(a_{y}=f/d_{y}\) and \(f\) is the camera focal distance. In addition, \(d_{x}\), \(d_{y}\) are pixel sizes in the horizontal and vertical directions; (\(u_{0}\), \(v_{0}\)) is the optical center point of the image; and \(R\), \(T\) are the rotation matrix and translation vector, respectively, which relate the world coordinate system to the camera coordinate system. Furthermore, \(r_{ij}\) is the \(i\)-th row and \(j\)-th column element of \(R\), and \(t_{x}\), \(t_{y}\), \(t_{z}\) are the elements of \(T\). For simplicity, the rotation matrix is represented by Euler angles, \(\psi\), \(\theta\), \(\phi\), which represent the rotation around the respective \(x\), \(y\) and \(z\) axes.  
Figure 1: Camera model.  
Owing to the influence of image noise and distortion, the calibration parameters, image points and space points do not completely conform to Equation (1). Thus, we have:  
\[\begin{split}\Delta u_{i}&=u_{i}-u_{0}-a_{x}\frac{r_{ 11}X+r_{12}Y+r_{13}Z+t_{x}}{r_{31}X+r_{32}Y+r_{33}Z+t_{z}}\\ \Delta v_{i}&=v_{i}-v_{0}-a_{y}\frac{r_{12}X+r_{22}Y+ r_{23}Z+t_{y}}{r_{31}X+r_{32}Y+r_{33}Z+t_{z}}\\ \text{min}f(u,\
u)&=\sum_{i=1}^{n}{(\Delta u_{i}^{2}+ \Delta v_{i}^{2})}\end{split} \tag{2}\]  
Equation (2) describes the calculation of image re-projection errors. Small re-projection errors are desired, which means that the calibration results satisfy Equation (3). However, the question arises of if a small image re-projection error will lead to the high calibration accuracy of the camera parameters. Analysis of the relationship between the image re-projection error and the calibration accuracy is therefore required.
## 2 Related Works
The estimation of the CCI and desired power have been proposed (adopting the different bandwidth of the CCI and desired signals). When the desired and the CCI signals are the broadband OFDM and narrowband signals, respectively, the estimation of the narrowband signal power based on the Welch periodogram is proposed [37]. The estimation of the desired and undesired signal powers based on the pilot signal has been proposed [38]. Because the narrowband signal has the weakness of multipath fading owing to the lack of frequency diversity, the accuracy of the narrowband signal power is degraded. When the desired and CCI signals are the continuous wave and the frequency modulation (FM) signals, respectively, the estimation scheme of the continuous wave and FM signal power is proposed [39]; however, the estimation of the modulated signal is unavailable. The estimation scheme of the collision-free period, which is equal to the unoccupied time period by the other system, under the frequency sharing between the Bluetooth low energy and the IEEE 802.15.4 is proposed [40]. The estimation depends on the computer simulation and, thus, performing the computer simulation; changing the situation involves large computational complexity. The spectrum sensor for TV white space is considered [41]. It achieves low computational complexity owing to the simple detection of CCI but cannot estimate the power of CCI. To the best of our knowledge, the estimation scheme of the desired power, CCI power, and COR with high accuracy under spectrum sharing among other systems has not yet been considered.
# Algebraic Point Projection for Immersed Boundary Analysis on Low Degree NURBS Curves and Surfaces
## 4 Methodology of Algebraic Point Projection
### Algebraic Point Projection for a NURBS Curve
#### 4.1.3 Improvement to First Order Algebraic Point Projection  
As illustrated in Figures 8 and 9, when the test point is far from the curve, first-order algebraic point projection is inaccurate. In immersed boundary analysis, point projection is only required at quadrature points near the boundary since the physical influence of the boundary on the underlying domain is local. For quadrature points that are far from the boundary, a recursive first-order algebraic point projection must be adopted for accuracy. The main idea is to treat the footpoint estimate of the previous step of first-order algebraic point projection as the starting point for the next step, and to recursively proceed until convergence. If a point is far from the boundary, we combine the distance to the curve \(d\) in Equation (14) and distance to convex hull of Bezier segment \(\phi\) to get the composed distance \(\bar{d}\) and its gradient \(\
abla d\) as follows:  
\[\bar{d}=\sqrt{d^{2}+\frac{(|\phi|-\phi)^{2}}{4}} \tag{27}\]  
\[\
abla\bar{d}=\begin{cases}\
abla d,&\phi\geq 0\\ \dfrac{2\
abla d+2\
abla\phi}{\sqrt{d^{2}+\phi^{2}}},&\phi<0\end{cases} \tag{28}\]  
The composed distance together with its gradient is then used for estimating the footpoint in Equation (20). The result after recursive execution is illustrated in Figure 10. Comparing against original first-order algebraic point projection in Figure 8(b), one can observe that the improved first order procedure is better.  
Figure 9: Point projection for cubic Bézier curve in two-dimensional physical space using the developed algebraic method as well as Newton–Raphson iterations for: (**a**) test distance \(\bar{d}=0.1\); and (**b**) test distance \(\bar{d}=0.3\). From left to right, Newton–Raphson method, first-order algebraic point projection, and second-order algebraic point projection are shown. The inset image shows that first-order point projection fails to converge onto footpoints on the curve when distances are larger.
## 4 Hybrid Thematic Analysis: Key Findings from NLP and Expert Review
### Foundational Technologies and Advanced Methodologies
#### 4.4.2 Optimization of Algorithms for Predictive Monitoring  
Advanced algorithms underpin next-generation predictive monitoring. Deep neural networks have been employed to analyze vibrations and temperatures in turbines [7, 56], utilizing LSTM-CNN hybrids for precise, real-time assessments. Hybrid methods that integrate analytical models with AI have enhanced bit-wear predictions in mining, improving operational performance [6, 74].  
Recent proposals emphasize the utility of domain adaptation methods to handle varying operational modes, including off-peak or startup conditions, which may drastically impact fault signals [5, 69]. In belt-driven systems, advanced wavelet transforms combined with machine learning classifiers have shown promise in automatically detecting cracks, misalignments, and unbalance, especially under transient loading [23, 69]. Researchers also highlight that interpretability can be bolstered by applying Shapley Additive Explanations (SHAP) to identify dominant fault features [32, 87]. This approach ensures that models remain transparent and trusted in high-stakes operational environments.  
Advanced polynomial chaos expansions [8, 9, 10] have been utilized to quantify uncertainties in sensor measurements, enabling more robust optimization of operating parameters [11, 12, 13]. Additionally, Bayesian networks have facilitated dynamic risk assessment in conveyor operations [22, 23, 26], allowing operators to balance throughput with system health.  
Digital twins have been integrated with deep learning for high-fidelity scenario simulations. Automatic feature selection has improved fault detection in bearings, while explainable AI has enhanced clarity in real-time industrial decision-making. Furthermore, recent developments in attention-based RNN architectures have improved long-horizon predictions for complex dynamics, reducing the risk of unexpected downtime in large mining plants.
## 5 Discussion
### Spectral Alteration Zonation  
Traditional zoning, based on mineral assemblage and a symbiotic relationship, has been widely used to solve many problems. The spectral features can reveal some features of mineralogy more deeply, so spectral alteration zonation is proposed. In this paper, the relative content changes of chlorite and garnet are used as indicators for identifying minerals. Therefore, the alteration information of Fe\({}^{2+}\) in alteration rocks was extracted separately, and the spectral alteration zoning was studied according to the microscopic alteration phenomenon, which is used as the micro prospecting standard for the Gongchangling magnetite deposit. It is divided into three spectral alteration zones, the shorter-wavelength zone, the transitional zone and the longer-wavelength zone.  
The combination of traditional and spectral alteration zones can better indicate the regular change of alteration rock during mineralization. In Gongchangling deposit, magnetite mineralization and wall rock alterations are consistent in both time and space, and each are relatively reductive environments, which was revealed by the HySpex spectrum data and results of traditional geological methods and is in consistent with the previous studies, including fluid inclusions, whole rock geochemistry analysis and rare earth trace elements analysis [27; 29; 36; 40]. Hence, the alteration zonation results according to the HySpex spectrum are credible.  
According to the real geological background, the shorter-wavelength zone corresponds to the high-grade iron ore, while the longer-wavelength zone corresponds to distal alteration of the wall rock, which is a visual indicator and estimates marking on the macroscopic scale for the HySpex spectrum. It can not only indicate the existence of blind ore bodies, but also predict the locations of ore bodies according to the types and characteristics of altered rocks.
# A New Algorithm Based on Colouring Arguments for Identifying Impossible Polyomino Tiling Problems
## 2 Preliminaries
There are various ways to do this and the resulting even parity constructions are parity equivalent \(n\)-ominoes. Although all the odd parity polyominoes have minimal area with respect to their parity, some of them cannot be continued in the sequence (labelled 'dead-end'). If a white square is not accessible, then the only way the parity can be increased by one unit is by adding one white square and two black squares, resulting in a polyomino that no longer has minimal area (e.g., the third polyomino with \(p=+4\)). Even if a white square _is_ accessible, we cannot always add a single black square to increase the parity by a single unit. For example, in the fifth polyomino construction with \(p=+6\), adding a black square to the single accessible white square is not permitted as this yields a shape that is not simply-connected, contradicting our definition of a polyomino. Thus, in this case, and similar ones, the only way to legitimately increase the parity is by adding three squares (two black and one white), again resulting in a polyomino that no longer has minimal area. As we progress down more levels of the tree the same pattern of polyomino constructions continue, although when the parity is even we get more parity equivalent \(n\)-ominoes. The sequence of polyominoes also have maximal parity with respect to their area. If this were not true then it would be possible to reduce the area of a polyomino without changing its parity. To do this we would have to remove an equal number of black squares and white squares. However, we cannot remove a single white square from any of the polyominoes as the resulting shape would no longer be simply-connected, contradicting our definition of a polyomino. Theorem 1 leads to a simple upper bound for the parity of a polyomino with respect to its area as shown in the following corollary. **Corollary 1**. : _Consider a polyomino \(P_{i}\) with area \(c_{i}\) and parity \(\pm p_{i}\)\((p_{i}\in\mathbb{N})\). Then for all \(p_{i}\in\mathbb{N}\) we have_  
\[p_{i}\leq \begin{cases}c_{i}/2&\text{if $p_{i}$ is even,}\\ (c_{i}+1)/2&\text{if $p_{i}$ is odd.}\end{cases} \]  
Proof. : From Theorem 1 the least possible area for a polyomino \(P_{i}\) with area \(c_{i}\) and parity \(\pm p_{i}\) is given by  
\[c_{\text{min}}=2p_{i}-\mathrm{mod}(p_{i},2)\leq c_{i}\quad\text{for all $p_{i}\in \mathbb{N}$},\]  
and if the parity is zero then \(c_{i}\geq 2\). Thus, for all \(p_{i}\in\mathbb{N}\)  
\[p_{i}\leq\frac{c_{i}+\mathrm{mod}(p_{i},2)}{2}= \begin{cases}c_{i}/2&\text{if $p_ {i}$ is even,}\\ (c_{i}+1)/2&\text{if $p_{i}$ is odd,}\end{cases} \]  
as required. A proof of the less sharp result \(p_{i}\leq(c_{i}+1)/2\) is given in ([18], p. 42) using a different argument.