esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Results and Analysis
### b-Value and \(\gamma\)-Value
#### 3.2.2 Calculation of AE \(\gamma\)-Value  
A potential precursor indicator for studying the compressive failure process of rocks is known as the FNS method. It follows a power-law form of \(1/f^{\prime}\), where \(f\) represents frequency, and \(\gamma\) is a characteristic parameter of frequency. This \(\gamma\)-value can capture variations in complex systems within time series data. When \(\gamma=1\), the AE signal follows the pattern of \(1/f\) noise, which is also known as \"pink noise\". When rocks produce a significant number of AE, it indicates an unstable state and the AE signal consistently exhibits the \(1/f\) characteristic in the power spectrum. When rocks generate fewer AE, it implies better rock integrity, and the sample is in a stable state, with \(\gamma\) approaching 0.  
The calculation method for the characteristic parameter \(\gamma\)-value is as follows: Assuming the waveform of AE at any time \(t\) is represented by \(f(t)\), then the Fourier transform of AE is described as Equation (5):  
\[F(f)=\int_{-\infty}^{\infty}f(t)e^{-jft}dt, \tag{5}\]  
where \(f\) is frequency. The power spectral density (PSD) is given by Equation (6):  
\[PSD(f)=\left|F(f)\right|^{2}, \tag{6}\]  
Taking the natural logarithm of both sides of Equation (6):  
\[log_{10}(PSD)=c+\gamma\cdot log_{10}(f). \tag{7}\]  
In Equation (7), the \(\gamma\)-value is the parameter we are seeking.  
Figure 5: Calculation Process of \(b\)-Value: Data with time window **(a)**; Fitting the curve according to Equation (4), a negative slope represents the \(b\)-value **(b)**.  
According to Equation (7), the \(\gamma\)-value can be calculated using the power spectrum of AE. By linearly fitting \(log_{10}(PSD)\) and \(log_{10}(f)\), the negative slope of the line is the \(\gamma\)-value. To demonstrate the trend of \(\gamma\)-value over time, time windows were applied to the experimental AE waveform data. The power spectrum was calculated for each time window, and \(\gamma\)-value were determined sequentially. The calculation process is illustrated in Figure 6.
## 1 Introduction
These findings suggest that while HHP offers advantages in maintaining overall flavor quality in fruit and vegetable juices, it may facilitate the loss of specific C6/C9 aldehyde aroma-active compounds, thereby affecting the perception of the grassy note. Current research on sterilization methods for red raspberry juice has primarily focused on microbial inactivation, enzyme passivation, and anthocyanin degradation [16]. However, to the best of our knowledge, the impact of sterilization on the loss of key C6 aldehyde aroma compounds in red raspberry juice has not been extensively explored. In this regard, this study aims to (1) accurately quantify the contents of key C6 aldehyde compounds in HHP and HTST-treated red raspberry juice using an external standard method; (2) clarify the potential impact of aroma loss on the overall sensory quality of red raspberry juice by quantitative descriptive analysis (QDA); and (3) reveal the loss pathway of C6 aldehyde compounds by the non-targeted metabolome of fatty acids.
# Development and Simulation of Motion Control System for Small Satellites Formation
## 2 Satellite Formation Modeling
Using (3), this term can be expressed in the following form:  
\[\dfrac{\mu}{\gamma}r_{\mathrm{c}}-\dfrac{\mu}{r_{\mathrm{c}}^{2}} =\mu\left(\dfrac{r_{\mathrm{c}}}{\left(1+\frac{2}{r_{\mathrm{c}}}x+\dfrac{x^{ 2}+y^{2}+z^{2}}{r_{\mathrm{c}}^{2}}\right)^{3/2}}\dfrac{1}{r_{\mathrm{c}}^{3} }-\dfrac{1}{r_{\mathrm{c}}^{2}}\right) \tag{5}\] \[=\dfrac{\mu}{r_{\mathrm{c}}^{2}}\left(\left(1-\left(-\dfrac{2}{r_ {\mathrm{c}}}x-\dfrac{x^{2}+y^{2}+z^{2}}{r_{\mathrm{c}}^{2}}\right)\right)^{- \frac{3}{2}}-1\right) \tag{6}\]  
Let us define  
\[\xi\equiv-\dfrac{2}{r_{\mathrm{c}}}x-\dfrac{x^{2}+y^{2}+z^{2}}{r_{\mathrm{c}} ^{2}}=\left(-\dfrac{2}{r_{\mathrm{c}}}-\dfrac{x}{r_{\mathrm{c}}^{2}}\right)x +\left(-\dfrac{y}{r_{\mathrm{c}}^{2}}\right)y+\left(-\dfrac{z}{r_{\mathrm{c}} ^{2}}\right)z \tag{7}\]  
Then, by negative binomial series and (5), (7) becomes:  
\[\dfrac{\mu}{\gamma}r_{\mathrm{c}}-\dfrac{\mu}{r_{\mathrm{c}}^{2}}=\dfrac{\mu} {r_{\mathrm{c}}^{2}}\left((1-\xi)^{-\frac{3}{2}}-1\right)=\dfrac{\mu}{r_{ \mathrm{c}}^{2}}\left(1+\dfrac{3}{2}\Psi\xi-1\right)=\dfrac{3}{2}\dfrac{\mu} {r_{\mathrm{c}}^{2}}\Psi\xi \tag{8}\]  
Figure 1: Reference systems. where \(\Psi\) is defined as a series \(\Psi\equiv 1+\psi_{1}+\psi_{2}+\cdots\), where:  
\[\psi_{1}\equiv\frac{\left(\frac{3}{2}+1\right)}{2}\xi,\quad\psi_{2}\equiv\frac{ \left(\frac{3}{2}+2\right)}{3}\psi_{1}\xi,\quad\psi_{3}\equiv\frac{\left(\frac{ 3}{2}+3\right)}{4}\psi_{2}\xi,\quad\ldots\]  
Consequently, (1) becomes:  
\[+\left[ \begin{array}{ccccc}0&0&0\\ 0&0&0\\ 0&0&0\\ \frac{1}{m_{f}}&0&0\\ 0&\frac{1}{m_{f}}&0\\ 0&0&\frac{1}{m_{f}}\end{array} \right]\left[ \begin{array}{c}u_{1}\\ u_{2}\\ u_{3}\end{array} \right], \tag{9}\]  
where state variables \(x_{1}\), \(x_{2}\), \(x_{3}\), \(x_{4}\), \(x_{5}\) and \(x_{6}\) are \(x\), \(\dot{x}\), \(y\), \(\dot{y}\), \(z\) and \(\dot{z}\) in the LVLH coordinates, respectively. Equation (9) has the form of (4).
# Error Distribution Pattern Analysis of Mobile Laser Scanners for Precise As-Built BIM Generation
## 3 Experiment Design and Analysis Method
### Mock-Ups  
The objective of the experiment is to analyze error distribution patterns in MLS point clouds. To achieve this, analysis targets were installed in the experimental room [15; 16; 17]. In this experiment, column-shaped objects (Column A and Column B) were used as analysis targets. Figure 1 presents the dimensional design diagrams of the Columns. The dimensions of Column A are 497 mm \(\times\) 505 mm \(\times\) 1500 mm, while those of Column B are 500 mm \(\times\) 500 mm \(\times\) 1500 mm. Both Columns were installed in the experimental room with their vertical alignment adjusted to match the gravity direction (\(z\)-axis) as closely as possible.  
The objective of this study is to identify error distribution patterns that are biased from the actual surface of objects, and to examine whether the resulting error pattern can contribute to improving the accuracy of BIM reconstruction using MLS point clouds. Columns are one of the primary building components found in indoor construction environments. In addition, they provide four surfaces with sufficient area, making them suitable for our  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **TLS** & **MLSs** \\ \cline{2-4}
**Specifications** & **TLS-01** & **MLS-01** &
\begin{tabular}{c} **MLS-02 and** \\ **MLS-03** \\ \end{tabular} \\ \hline Point (range) accuracy & \(\pm\)1 mm & 10 mm & 10–30 mm \\
3D accuracy & 2 mm @ 10 m, 3.5 mm @ 25 m & - & - \\ Relative accuracy & - & \(\leq\)10 mm & Up to 6 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specifications of terrestrial laser scanner (TLS) and mobile laser scanners (MLSs) used in this study.  
experiment, which involves extracting and analyzing data at the planar-segment level. For these reasons, column-type mock-ups were used in our experiments as the analysis targets.  
Due to the room's height and the limitations of handheld MLS devices, the ceiling and floor planes of these columns were not captured in the resulting MLS point clouds. Consequently, the MLS point clouds of the Columns appear as closed shapes in the xy-plane. This characteristic plays a crucial role in the proposed method for analyzing the error distribution patterns in MLS point clouds. The detailed analysis procedure is described in Section 3.4.
###### Abstract  
In this study, we show an effective data-driven identification of the State-of-Health of Lithium-ion batteries by Nonlinear Frequency Response Analysis. A degradation model based on support vector regression is derived from highly informative Nonlinear Frequency Response Analysis data sets. First, an ageing test of a Lithium-ion battery at 25 \({}^{\circ}\)C is presented and the impact of relevant ageing mechanisms on the nonlinear dynamics of the cells is analysed. A correlation measure is used to identify the most sensitive frequency range for ageing tests. Here, the mid-frequency range from 1 Hz to 100 Hz shows the strongest correlation to Lithium-ion battery degradation. The focus on the mid-frequency range leads to a dramatic reduction in measurement time of up to 92% compared to standard measurement protocols. Next, informative features are extracted and used to parametrise the support vector regression model for the State of Health degradation. The performance of the degradation model is validated with additional cells and validation data sets, respectively. We show that the degradation model accurately predicts the State of Health values. Validation data demonstrate the usefulness of the Nonlinear Frequency Response Analysis as an effective and fast State of Health identification method and as a versatile tool in the diagnosis of ageing of Lithium-ion batteries in general.  
Keywords: lithium-ion batteries; state-of-health; nonlinear frequency response analysis; battery degradation; machine learning; support vector regression +
Footnote †: journal: Applied Soft. 2018, 8, 821; doi:10.3390/app8050821
# Data Fusion of Multivariate Time Series: Application to Noisy 12-Lead ECG Signals
## 4 Application of NDFA in 12-Lead ECG Signals
### Synthetic Signals Experiments  
#### 4.1.1 Ideal Synthetic Signals Experiments  
As realistic ECG signals are recorded in clinical environment, the signals would be contaminated inevitably by the noise and artifacts with different magnitudes. To solve this problem, synthetic ECG signals were widely applied in estimating the performance of the algorithm. In [30], [PERSON] et al. proposed a dynamical model for generating synthetic ECG signals. Based on the idea of systems dynamics, [PERSON] et al. [31] and [PERSON] et al. [32] developed an improved dynamical model, which can generate 12-lead synthetic ECG signals. In the experiment, ideal VCG signals were obtained via the model, as shown in Figure 3 and it will be employed for testing the performance of NDFA.  
Figure 4a-c represent the reconstructed trajectories of \(V_{x}\), \(V_{y}\) and \(V_{z}\), respectively. Figure 4d represents the fused signal of VCG signals \(s\). From the morphology of reconstructed trajectory perspective, it is clear that there are needle-like features (Feature 1) on the three trajectories. Meanwhile, the longer closed trajectory (Feature 3) and disordered feature of the closed trajectory within a small space (Feature 2) are shown distinctly in Figure 4a-c. In Figure 4a, the local trajectories of Features 2 and 3 essentially reflect the P wave and QRS complexes in ECG signal, respectively. Evidently, the three features of original VCG signals are well described by the fused trajectory \(s\).  
Figure 3: Synthetic ECG signals.  
Correlation Coefficient and Procrustes distance [33; 34; 35] are widely used in similarity measure. Although ECG signals possess the non-stationary characteristic, the signals within a short time span are stationary and predictable relatively. Therefore, in order to manifest the advantage of NDFA more objectively, Correlation Coefficient (_Cor_) is introduced to assess the performance of our algorithm. _Cor_ is defined as:  
\[Cor(a,b)=\frac{C(a,b)}{\sqrt{C(a,a)C(b,b)}} \tag{16}\]  
where the similarity of two reconstructed trajectories can be described quantitatively by parameter _Cor_.  
Here, to illustrate the similarity of these signals integrally, the mean values of the VCG signals and the fused signal \(s\) need to be calculated. Via Equation (16), the mean value \(Cor_{xyz}\) of correlation coefficients \(Cor(Vx,Vy)\), \(Cor(Vx,Vz)\) and \(Cor(Vy,Vz)\) is 0.3540. Analogously, the mean value \(Cor_{s}\) of correlation coefficients \(Cor(s,Vx)\), \(Cor(s,Vy)\) and \(Cor(s,Vy)\) is 0.5517. The results illustrate that the three features of original signals \(Vx\), \(Vy\), and \(Vz\) are well preserved in the fused signal.
# A Variational Neural Network Based on Algorithm Unfolding for Image Blind Deblurring
## 2 Related Work
### Blur Kernel Estimation Model  
To more accurately estimate the blur kernel, we adopt the two-stage total variation (TV) model proposed by [PERSON] et al. (2019). This model effectively balances the sparsity of the blur kernel with the smoothness of image restoration through a phased approach. This method not only improves the accuracy of the blur kernel estimation but also results in visually more naturally restored images. In blind deblurring models, an \(L_{1}\) regularizer is commonly employed as a constraint to enhance the sparsity of the blur kernel estimation,thereby improving the overall quality of image restoration. Equation (2) can be rewritten as follows:  
\[E(u,k)=\frac{1}{2}\|k*\
abla u-\
abla y\|_{2}^{2}+\lambda\|\
abla u\|_{1}+\frac{ \gamma}{2}\|k\|_{2}^{2}\|k\|_{1}=1,\ k\geq 0 \tag{3}\]  
where \(\|\cdot\|_{p}\) is denoted as the \(L_{p}\) regularization term, and \(\lambda\) and \(\gamma\) are penalty parameters. To improve stability, the gradient information is constrained using the \(L_{1}\) regularizer. Similarly, the blur kernel for estimation normalization is constrained using the \(L_{2}\) regularizer.  
In Equation (3), the \(L_{1}\) regularizer is used to constrain the gradient information, aiming to tend toward producing a sparse solution. However, due to its properties such as non-convexity and excessively sparse solutions, it becomes difficult to estimate the true blur kernel.
## 3 Object Detection Performance Evaluation Results
### Object Detection Performance Evaluation Metrics  
To analyze the effect of droplet contamination on object detection performance, we utilized mean average precision (mAP) as an evaluation metric. The mAP is a widely used performance metric in computer vision fields such as object detection and image segmentation [40]. By utilizing mAP, we can estimate the overall performance of algorithms in detecting and classifying the locations and types of objects. Specifically, the mAP is an essential evaluation metric in applications like autonomous driving, video surveillance systems, and medical image analysis, where accurate object detection is critical. The mAP is calculated as the area under the precision-recall curve for all object classes, allowing us to evaluate the model's performance across various threshold settings [41; 42]. Precision is a metric used to evaluate the ability of a model to correctly predict positive instances, while recall evaluates the ability of the model to correctly identify all True Positive cases in a dataset. The precision and recall are calculated using Equations (3) and (4), respectively, while AP and mAP are calculated using Equations (5) and (6), where k is the number of the class. The concepts of True Positive (TP), False Positive (FP), False Negative (FN), and True Negative (TN), which are used in the calculation of precision and recall, are detailed in Table 2.  
\[\mathrm{P}=\left(\frac{\mathrm{True\ Positive}}{\mathrm{True\ Positive}+ \mathrm{False\ Positive}}\right) \tag{3}\]  
\[\mathrm{R}=\left(\frac{\mathrm{True\ Positive}}{\mathrm{True\ Positive}+ \mathrm{False\ Negative}}\right) \tag{4}\]  
\[\mathrm{AP}=\int_{0}^{1}\mathrm{P(R)dR} \tag{5}\]  
\[\mathrm{mAP}=\frac{1}{\mathrm{k}}\sum_{i=1}^{\mathrm{k}}\mathrm{AP_{i}} \tag{6}\]  
The intersection over union (IOU), utilized to evaluate object detection performance by comparing the ground truth bounding box to the predicted bounding box, was set at 0.5. To verify the degradation of object detection performance, we used mAP\({}_{\mathrm{loss}}\), as shown in Equation (7). A larger mAP\({}_{\mathrm{loss}}\) indicates that the performance of the object detection algorithm is significantly degraded due to droplet contamination.  
\[\mathrm{mAP}_{\mathrm{loss}}=\mathrm{mAP}_{\mathrm{clean}}-\mathrm{mAP}_{ \mathrm{contamination}} \tag{7}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Ground Truth**} \\ \hline
**Predicted** & **Positive** & **Negative** \\ \hline Positive & True Positive & False Positive \\ Negative & False Negative & True Negative \\ \hline \hline \end{tabular}
\end{table}
Table 2: Definition of True Positive (TP), False Positive (FP), False Negative (FN) and True Negative (TN).
_Algorithms_**2012**, \(5\), 421-432; doi:10.3390/a5040421  
_algorithms_  
**ISSN 1999-4893**  
www.mdpi.com/journal/algorithms  
_Article_  
**Univariate \(L^{p}\) and \(l^{p}\) Averaging, \(0<p<1\), in Polynomial Time by Utilization of Statistical Structure**  
**[PERSON] \({}^{1,2}\)**  
1. Mathematical Sciences Division and Computing Sciences Division, Army Research Office, Army Research Laboratory, P.O. Box 12211, Research Triangle Park, NC 27709-2211, USA;  
E-Mail: [EMAIL_ADDRESS]; Tel.: +1-919-549-4253; Fax: +1-919-549-4354
2. [PERSON] Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27695-7906, USA  
_Received: 28 July 2012; in revised form: 6 September 2012 / Accepted: 17 September 2012 / Published: 5 October 2012_  
**Abstract:** We present evidence that one can calculate generically combinatorially expensive \(L^{p}\) and \(l^{p}\) averages, \(0<p<1\), in polynomial time by restricting the data to come from a wide class of statistical distributions. Our approach differs from the approaches in the previous literature, which are based on _a priori_ sparsity requirements or on accepting a local minimum as a replacement for a global minimum. The functionals by which \(L^{p}\) averages are calculated are not convex but are radially monotonic and the functionals by which \(l^{p}\) averages are calculated are nearly so, which are the keys to solvability in polynomial time. Analytical results for symmetric, radially monotonic univariate distributions are presented. An algorithm for univariate \(l^{p}\) averaging is presented. Computational results for a Gaussian distribution, a class of symmetric heavy-tailed distributions and a class of asymmetric heavy-tailed distributions are presented. Many phenomena in human-based areas are increasingly known to be represented by data that have large numbers of outliers and belong to very heavy-tailed distributions. When tails of distributions are so heavy that even medians (\(L^{1}\) and \(l^{1}\) averages) do not exist, one needs to consider using \(l^{p}\) minimization principles with \(0<p<1\).  
**Keywords:** average; heavy-tailed distribution; \(L^{p}\) average; \(l^{p}\) average; median; mode; polynomial time; radial monotonicity; statistical structure; univariate
## 3 Independent Set
### Time Complexity
Then  
\[U^{\prime}\setminus C^{\prime} \subseteq U^{\prime}\setminus(C\cap U_{2})\] \[=(U\setminus N^{+}(u_{1}))\setminus(C\cap(N^{+}(u_{2})\setminus N ^{+}(u_{1}))\cap U)\] \[=U\setminus[N^{+}(u_{1})\cup(C\cap(N^{+}(u_{2})\setminus N^{+}(u _{1})))]\] \[=U\setminus[N^{+}(u_{1})\cup C]\subseteq U\setminus C.\]  
Case 2: two vertices are excluded. Now \(U^{\prime}=U\setminus(N^{+}(u_{1})\cup N^{+}(u_{2}))\), and  
\[U^{\prime}\setminus C^{\prime}\subseteq U^{\prime}\subseteq U\setminus C.\]  
We have shown that condition (2) holds at the start of the next iteration, and so it gives a loop invariant as claimed. \(\qed\)  
A vertex \(v\) is _absorbed_ if it is processed during the loop of Algorithm 3 and then appended to the result set, \(C^{\prime}\). **Corollary 3.5**. : _A vertex can be absorbed once at most._  
**Proof. ** Let \(U,C,U^{\prime}\) and \(C^{\prime}\) be as before. Observe that if, during the iteration, vertex \(v\) is absorbed in a call to Algorithm 3, then \(v\in U\setminus C\) and \(v\
otin U^{\prime}\setminus C^{\prime}\). The Corollary now follows from the second invariant in Lemma 3.4. \(\qed\)  
**Lemma 3.6**. : _Algorithm 4 takes \(O(n^{2})\) time._  
**Proof. ** The total running time of each iteration of the main loop of Algorithm 4 besides calling Algorithm 3 is \(O(n)\). The set \(U\) decreases by at least one vertex on each iteration, so the time spent outside of Algorithm 3 is \(O(n^{2})\). From Corollary 3.5 at most \(n\) vertices are absorbed and \(O(n)\) steps are performed each time, so in total \(O(n^{2})\) time is spent in all calls to Algorithm 3 for absorbing vertices. Assume that \(v\) is processed by Algorithm 3 for the first time, but it is not absorbed and it is tested against a set \(C_{1}\). Since \(v\) is not absorbed, we may assume that Algorithm 3 has returned the pair of vertices \(vu\). At least one of \(u\) and \(v\) is removed (along with its neighbourhood) from \(U\) and moved to \(I\)If \(v\) is removed from \(U\), then no more time can be spent on it by Algorithm 3, hence the total time spent on \(v\) by Algorithm 3 is \(O(n)\). Now assume that \(u\) is removed. We have that \(C_{1}\subseteq N^{+}(u)\) and each vertex in \(N^{+}(u)\) is removed from \(U\). Hence, if \(v\) is processed again by Algorithm 3, it will be tested against a set \(C_{2}\) with \(C_{1}\cap C_{2}=\emptyset\), and therefore \(|C_{1}|+|C_{2}|=|C_{1}\cup C_{2}|=O(n)\). As we saw before, if \(v\) is absorbed or removed from \(U\), then it cannot be processed again by Algorithm 3; and thus the running time spent on \(v\) is again \(O(n)\). If \(v\) is not removed from \(U\), then \(C_{2}\) is removed from \(U\). Hence, if \(v\) is processed again by Algorithm 3, \(v\) will be tested against a set \(C_{3}\) with \(|C_{1}|+|C_{2}|+|C_{3}|=|C_{1}\cup C_{2}\cup C_{3}|=O(n)\), and so on. Thus, we see that over all these tests, each vertex is tested at most once for adjacency to \(v\), and so the total time spent on \(v\) is \(O(n)\).
# Mechanisms Underlying the Changes in Sporadic E Layers During Sudden Stratospheric Warming
###### Abstract
SSW events have profound effects on both the neutral atmosphere and the ionosphere. Studies leveraging ground-based and satellite data have shown significant alterations in various ionospheric parameters during SSW periods, including vertical plasma drift, total electron content (TEC), peak electron density, equatorial electric fields, and equatorial electrojets [19; 20; 21; 22; 23; 24]. While ionospheric changes during SSW events have been extensively studied, research specifically focusing on the E layer, particularly the sporadic E layer, remains limited. Investigating these variations during SSW events is crucial for elucidating the interaction mechanisms between the ionosphere and the neutral atmosphere and enhances our understanding of the dynamic patterns within sporadic E layers. This paper utilized data from three stations in Japan along with satellite data to explore the changes in and causes of sporadic E layers during the winter of 2008/2009. The structure of this paper is as follows: Section 2 presents the data and wavelet transform methodology. Section 3 includes discussions on (1) changes in the sporadic E layer during the 2008/2009 winter SSW; (2) analysis of wind field fluctuations; and (3) the mechanism of planetary wave modulation of sporadic E layers. Section 4 consists of the discussion.