esa-sceva/satcom-chunk-collection huggingface dataset:
# Adaptive Facial Imagery Clustering via Spectral Clustering and Reinforcement Learning
## 3 Experiments
### Manual Investigation of Parameter Settings  
We assume that the best number of clusters is unknown. However, for 400 facial images, we reasonably consider that they are divided into no more than 80 categories (i.e., the expected maximum number of clusters). Thus, the number of clusters \(K\) ranges from 0 to 80. In addition, the dimension reduction of spectral clustering should not exceed the original maximum dimension and retain the primary information of the face representations. Generally, it is reasonable to reserve no more than 50% of the original dimensions, that is to say, due to the original dimension 128, the dimension reduction (dim) can range from 0 to 60.  
We observe several settings of \(K\) and dim using the variable-controlling approach. Specifically, when one parameter changes within its range, the other is an invariable parameter. Due to this investigation over a wide range of parameters, we make a rough global observation in which the interval of the changing parameters is five and the invariable parameter is 10. The observation results of the manual investigations are illustrated in Figures 6 and 7.  
Figure 6: The obtained \(DBI\) under the different settings of cluster number K.  
Figure 7: The observation of dimension reduction dim. Dim is regarded as the changing parameter, while \(K\) is the invariable parameter. When \(K\in[10,40]\), first, the \(DBI\) value decreases, and then increases with an increase in the dim value. When \(K\in[50,80]\), the \(DBI\) value decreases with an increase in the dim value.  
As shown in Figure 6, different parameter settings result in the difference of the performance evaluation \(DBI\). Specifically, the optimal value of \(K\) is about 40 because most of the dimension settings at this value make the clustering performance better (smaller \(DBI\)). In fact, this conclusion is of practical significance due to the fact that the ORL Face Database is indeed comprised of 40 different persons.  
As shown in Figure 7, there are some valuable conclusions. First, the clustering performance deteriorates barely when the reserved dimension of the face representations is less than 15. Second, more reserved dimensional information does not mean that the performance of clustering is better. On the contrary, it becomes worse, especially when dim is over 50 in most curves. Third, we can see that the red curve, which has the invariable parameter setting \(K=40\), in fact, corresponds to the optimal setting of \(K\). The curve indicates that changing dim has less impact on the ideal \(K\) within the range of dim from 20 to 45. It implies that the closer \(K\) gets to the optimal value, the less dim changes. Therefore, it requires a smaller step size in the optimal field when we use searching methods for the parameter setting.
# Compensation of Measurement Uncertainty in a Remote Fetal Monitor
## 3 Uncertainty Estimation Approach
### Distribution Function Estimation of the Perturbations and Correlation Function  
For each patient, a stochastic model is determined, which describes the perturbation present in the fetal heart rate signal, which exists due to the individual anatomical characteristics of the patients, amniotic fluid, body fat, etc.  
The stochastic model is obtained from data acquired by clinical studies using the patient's fetal heart rate monitor. Each clinical study (sample) is a set of measurements \((y_{k},\ k=1,\ 2,\cdots,n)\).  
Using the data-normalized histogram, the probability density function (PDF) is estimated for \(n\) samples \(f_{\Xi_{n}}\), numerically integrating and using some interpolator an estimator is obtained for the probability distribution function \(F_{\Xi_{n}}\) of the perturbations, which is used to build a \(\xi\) simulator required in the Monte-Carlo method. Each sample that is added improves the probability distribution function estimation, so that, the more samples available, the better the estimator.  
To guarantee that the bias of the expectation estimate is zero, the correlation between the perturbation and the regression vector used in the least-squares model must be verified as zero. For this, a correlation degree estimate is made [20; 22] that exists between the perturbations and the measured signal. The correlation is defined as follows  
\[\rho_{XY}(k):=\frac{E\Big{\{}X_{j+k}Y_{j}\Big{\}}}{\sqrt{E\Big{\{}X_{j+k}^{2} \Big{\}}E\Big{\{}Y_{j}^{2}\Big{\}}}}, \tag{19}\]  
where \(\rho_{XY}\) represents the correlation function between the random variables \(X\) and \(Y\). This magnitude is estimated using  
\[\hat{\rho}_{XY}(k)=\frac{\frac{1}{n}\sum_{j=1}^{n}X_{j+k}Y_{j}}{\sqrt{\frac{1} {n}\sum_{j=1}^{n}X_{j+k}^{2}\frac{1}{n}\sum_{j=1}^{n}Y_{j}^{2}}}. \tag{20}\]  
If there is a substantial correlation, a filter must be designed so that the perturbation behaves with white noise features.
# Reverse-Net: Few-Shot Learning with Reverse Teaching for Deformable Medical Image Registration
## 3 Materials and Methods
### Pixel Alignment Network
#### 3.3.3 Inverse Deformation Field  
In most previous deep-learning-based deformable registration methods, researchers would divide the input image into a fixed image and a moving image, and only consider a single mapping from the fixed image to the moving image, ignoring the inverse transformation [39]. In our framework, we try to eliminate the division between fixed images and moving images. We divide the input image into S and T and have to implement not only \(\varphi_{ST}\) but also \(\varphi_{TS}\). Inspired by previous inverse-consistent methods [40], we introduce the new inverse-consistent method, which does not require a complex network structure to achieve accurate registration results.  
\[\varphi\xrightarrow{decompose}\varphi_{x},\varphi_{y} \tag{6}\]  
\[\left(\varphi_{x},\varphi_{y}\right)\circ\varphi=\left(\varphi_{x}^{\prime}, \varphi_{y}^{\prime}\right)\xrightarrow{combine}\varphi^{\prime} \tag{7}\]  
\[\varphi^{\prime}\times(-1)=\varphi^{-1} \tag{8}\]  
Figure 5: The detailed construction of our U-net.  
where the above formula is the process of inverse deformation field formation. \(\varphi\) is the deformation field, \(\varphi_{x}\) and \(\varphi_{y}\) are the horizontal and vertical offsets, respectively, and \(\circ\) is the transformation operator.
# Diagnosing and Balancing Approaches of Bowed Rotating Systems: A Review
## 1 Introduction  
A drastic level of vibration produces noise and reduces machine performance; it diminishes the machine's service life and reliability and can even result in dangerous difficulties. As a result, many sophisticated companies tend to have optimized maintenance schedules [1]. Assembly fault, asymmetric geometry, material inhomogeneity, and manufacturing tolerance are all possible causes of a defect [2].  
For a variety of reasons, the shaft that serves as the primary transmission component in various rotor systems is not always as straight as it should be. Sometimes the shaft is assembled from a line to a curve in high-load-carrying rotor-bearing systems, such as marine propulsion sharing, to reduce the load on bearings that are close to the heavy propeller, so the shaft is subjected to additional bend forces that run parallel to the section [3]. On the other hand, unwanted bends in shafts can occur owing to a variety of factors, including creep, thermal distortion, or a strong imbalance force. Excessive heat, length, or physical bend can all cause the shaft bending. Figure 1 shows a schematic of a simple rotor-bearing-disk system that suffers a bowed shaft and its cross-sectional view. An unexpected failure of spinning machines due to a bent shaft might result in considerable financial losses. Depending on the extent and location of the bend, a bent shaft causes excessive vibration in a machine [3,4]. In industry, approximately 35% of breakdowns of rotating devices have resulted from bowed shafts and misalignment [5,6]. As a result, a proper shaft bow diagnosis, as well as a balancing/correction procedure, appear mandatory.  
This paper proposes, for the first time, an extensive review of the state of the art on bowed rotor systems, and it can be considered as a guide for researchers who are interested to expand modern procedures in distinguishing and balancing bowed rotary devices.  
In the right aforementioned figure, \(\theta_{r}\), \(\theta_{m}\), and \(\theta_{c}\) are the phase angles of the residual bow vector, disk unbalancing vector, and the shaft center line vector with respect to the reference axis, respectively. \(m\), \(c\), and \(o\) are the indicators of the mass center of the disk, center of the shaft, center of the bow, respectively. Furthermore, the shaft elastic deflection, residual bow, and unbalancing deflection vectors are represented by \(\overrightarrow{\rho}_{c}\), \(\overrightarrow{\rho}_{o}\), and \(\overrightarrow{\rho}_{m}\), subsequently.
# Shape Memory Alloy Reinforced Self-Healing Metal Matrix Composites
## 2 Classification of Self-Healing Metal Matrix Composites  
SHMMCs are classified on the basis of self-healing mechanism, phase transformation involved during healing, characteristic length scale of the healed damage, and autonomy. SMA clamp-and-melt-based self-healing, solder tube/capsule-based self-healing, and nano-SMA dispersoid-based self-healing are among the self-healing mechanisms studied so far for metal matrix composites. SHMMCs are classified by [PERSON] [66] based on the type of phase transformation involved during healing, such as solid-state or liquid-assisted healing. According to this classification, SMA clamp and melt and solder tube/capsule-based self-healing are classified as liquid-assisted healing, whereas nano-SMA dispersoid-based self-healing is classified as solid-state healing. [PERSON] et al. [67] have classified the SHMMCs based on the characteristic length scale of the healed damage. According to their classification, nano-SMA dispersoid-based healing is classified as nanoscale healing, whereas SMA clamp and melt and solder tube/capsule-based healing is classified as nanoscale healing. Based on autonomy, SHMMCs can be classified as autonomous or nonautonomous [67]. The autonomous SHMMCs do not require external intervention to repair the damage, whereas nonautonomous SHMMCs do require external intervention, such as the application of heat. According to this classification, nano-SMA dispersoid-based healing is classified as autonomous healing, whereas SMA clamp and melt and solder tube/capsule-based healing is classified as nonautonomous healing. Table 1 shows the classification of self-healing metal matrix composites. The SMA clamp-and-melt-based self-healing concept stands out as the most promising among the macroscale mechanisms because of its ability for limitless repetition. In contrast, the solder tube/capsule-based self-healing approach utilizes encapsulated solder materials that are released to fill and repair cracks. While offering localized healing, its success depends on the careful selection of host matrix and solder materials. The nano-SMA dispersoid-based self-healing mechanism offers a precise nanoscale healing potential but relies on specific material combinations to achieve the desired nanosized coherent particles with shape-memory effects [67].
# Time-Evolving Graph Convolutional Recurrent Network for Traffic Prediction
## 3 Proposed Method
### Example of the Prediction Process of TEGCRN  
In this section, we will explain the entire process of TEGCRN and take the prediction for traffic speed as an example. Given the historical speed observations of \(P\) steps \([\mathbf{X}_{t-P+1},\cdots,\mathbf{X}_{t}]\), the prediction targets are the speeds of the next \(Q\) steps. In this case, \(\mathbf{X}_{t}\in\mathbb{R}^{N\times F}\) represents the speed of all the \(N\) nodes at time slot \(t\) and \(F=1\). As shown in Figure 3, we first employ Equations (2) and (4) to generate tensor \(\mathbf{A^{te}}\) and obtain the time-evolving graphs of the corresponding time slots \([\mathbf{A^{te}_{l-p+1}},\cdots,\mathbf{A^{te}_{l}}]\) and \([\mathbf{A^{te}_{l+1}},\cdots,\mathbf{A^{te}_{l+Q}}]\) for the encoder and decoder, respectively. Next, for each historical time slot, the speed snapshot \(\mathbf{X}_{t}\) and the corresponding time-evolving graph \(\mathbf{A^{te}_{l}}\) are input to the TCGCRU encoder step-by-step, as the calculations show in Equation (8). The graph convolution operations in Equation (8) are formulated by Equations (6) and (7). The output in the last step of the encoder is used to initialize the hidden state of the decoder. Then, following the calculations similar to the encoder, in each step, the decoder takes the prediction of the previous step as input and generates the speed predictions \([\mathbf{\hat{X}}_{t+1},\cdots,\mathbf{\hat{X}}_{t+Q}]\) step-by-step.
# A Large Capacity Histogram-Based Watermarking Algorithm for Three Consecutive Bins
## Preliminaries
### Existing Histogram-Based Watermark Embedding  
In [PERSON] et al.'s method [13], the histogram-based watermarking method primarily utilized the histogram \(H\) and mean \(\overline{A}\) to determine the embedding range \(B=[(1-\lambda)\overline{A},(1+\lambda)\overline{A}](0<\lambda<1)\) firstly; then they divided these bins into a series of groups where each of them contained two neighboring bins; lastly, they embedded watermark bits into these groups. For clarity and the ease explanation, the concrete rule of watermark embedding can be formulated as follows:  
\[\left\{\begin{array}{ll}\frac{a}{b}\geq T,&W(i)=1\\ \frac{b}{a}\geq T,&W(i)=0\end{array}\right., \tag{2}\]  
where \(a\) and \(b\) refer to the number of the two consecutive bins and \(T\) is a threshold controlling the number of modified pixels, the value of which has a direct influence on both robustness and image quality. If the numbers \(a\) and \(b\) in the adjacent bins satisfy the conditions in Equation (2), no operation is needed. Otherwise, some modifications will be made to let some pixels in one bin jump into the other. Here, a possible case is presented in Figure 1. When the watermark to be embedded is \(W(i)=1\), no change is made to the two bins since the numbers \(a\) and \(b\) in the adjacent bins have already met Equation (2). When the watermark to be embedded is \(W(i)=0\), the number of pixels in the two adjacent bins will be adjusted until satisfying the condition \(\frac{b}{a}\geq T\), as shown in Figure 1.  
However, the watermark embedding design of [PERSON] et al. [13] fails to take the approximately equal number of adjacent bins into consideration, i.e., \(W(i)=2\), as shown in the marked part with red dashed line. This will have a direct influence on the watermark embedding capacity; in turn, the watermark capacity, lowered greatly, restricts many application scenarios. To solve this issue, we design a novel histogram shape-based watermark scheme in the next section.
## 2 Materials and Methods
### The General Case of the Kalman Filter  
From the least-squares class of estimators, the KF is a recursive estimator.  
The matrices \(\mathrm{X}_{\mathrm{m}}\), \(\mathrm{M}_{\mathrm{m}}\), \(\mathrm{P}_{\mathrm{m}}\), and \(\mathrm{Z}_{\mathrm{m}}\) are presumed to be known for any \(\mathrm{m}\).  
Consider a sequence \(\Gamma_{\mathrm{m}}\), which includes all the data observations recorded until moment \(\mathrm{  
For any \(\mathrm{m}\geq 1\), let an \(\mathrm{N_{m}}\)\(\sigma\)-algebra be generated by \(\mathrm{B_{1}}\),..., \(\mathrm{B_{m}}\)[26] and  
\[\hat{\mathrm{A}}_{\mathrm{m}}\;=\;\mathrm{E}[\mathrm{A_{m}}|\mathrm{N_{m}}], \tag{10}\]  
\[\mathrm{Q_{m}}\;=\;\mathrm{E}\big{(}\big{(}\mathrm{A_{m}}\;-\;\hat{\mathrm{A} }_{\mathrm{m}}\;\big{)}\big{(}\mathrm{A_{m}}\;-\;\hat{\mathrm{A}}_{\mathrm{m} }\big{)}^{\prime}|\mathrm{N_{m}}\big{)}. \tag{11}\]  
If \(\mathrm{N_{m}}\) is known, \(\hat{\mathrm{A}}_{\mathrm{m}}\) is the best estimator of \(\mathrm{A_{m}}\) and \(\mathrm{Q_{m}}\) is the conditional variance-covariance matrix of the errors.  
Now, we consider \(\mathbf{Q}\), respectively \(\mathrm{Q_{0}}\), which is the set of symmetric matrices that are non-negatively defined (respectively positively defined) and of \(\mathrm{r}\times\mathrm{r}\) dimensions. For any \(\mathrm{Q}\in\mathbf{Q}\) and \(\mathrm{m}\geq 1\), we then define:  
\[\xi_{\mathrm{m}}(\mathrm{Q})=(\mathrm{X_{m}}\mathrm{Q}\mathrm{X^{\prime}}_{ \mathrm{m}}+\mathrm{I})(\mathrm{I}+\mathrm{S_{m}}+\mathrm{S_{m}}\mathrm{X_{m} }\mathrm{Q}\mathrm{X^{\prime}}_{\mathrm{m}})^{-1}, \tag{12}\]  
where \(\mathrm{S_{m}}=\mathrm{Z^{\prime}}_{\mathrm{m}}\mathrm{Z_{m}}\) and \(\mathrm{I}\) is the unit matrix of order \(\mathrm{r}\). It follows that \(\xi_{\mathrm{m}}\) takes \(\mathrm{P_{0}}\) into itself.  
The basic result shown above is related to the fact that the applications \(\xi_{\mathrm{m}}\), \(\mathrm{m}\geq 1\), are contractions in \(\mathrm{Q_{0}}\) if we enhance \(\mathrm{Q_{0}}\) with the Riemann measurement \(\delta\)[27], which is invariant to conjugacy. Furthermore, the contractions could be strict or uniform, depending on the controllability and observability properties of the above system (9).  
To demonstrate the results in this view, we considered the symplectic group of matrices. The matrices are invariant to \(\mathrm{P_{0}}\). In this view, they could be considered a generalization of the Perron-Frobenius theorem. In some sense, the study of [PERSON] [28] is elementary.  
The symplectic matrices utilize some of the already existing ideas [29]. The semigroup \(\Sigma\) was induced by [PERSON] [30] in a similar context. Finally, we note that the Riccati transformation [31] has a contractibility property, which is a generalization of the positive matrices under a Hilbert space metric [32].
## 4 Proposed Empirical Models for Weather Factors
### Snow Model  
The highest extinction coefficient \(\alpha_{\text{snow}}\) is observed for using dry snow, as shown in Figure 6. The explanation for this is similar to the reasoning provided for rain. For dry snow, density can be assumed to be four times smaller than for wet snow, as discussed by [27]. To attain a similar precipitation rate, the amount of dry snowflakes must be 4 times higher than for wet snow; hence, dry snow yields more scattering events than wet snow. To classify the amount of snowfall in relation to visibility, one can refer to [42], where a visibility of 100 m is considered to occur during a dry snow precipitation rate of 6 mm/h, which is considered heavy snowfall according to [43]. To calculate the missing backscattering coefficient \(\beta_{\text{snow}}\), the same approach as for fog was used, i.e., consider \(\alpha/\beta\) as invariant. The refractive index was retrieved from [44], and the particle size distribution from [45]. Following this approach, the following empirical equation is proposed:  
\[\beta_{\text{snow}}=\frac{\alpha_{\text{snow}}}{1.26} \tag{12}\]
## 6 Results
### Combinations of the Studied System Components  
In this section, the results obtained in the convergence simulation of the NPC as a fitness function using the QOBO are presented. The optimized parameter results (i.e., \(A_{pv}\), \(A_{wind}\), \(P_{dgn}\), \(P_{Cap\_but}\), \(P_{BM}\)) for all suggested combinations are listed in Table 3 with the rating of the inverter that takes the value of the peak load demand. From Figure 10, the reader can notice that using QOBO, BO, HHO, AEFA and IWO algorithms, the best minimum values of fitness function (NPC) is obtained for the second configuration, i.e., hybrid PV/biomass energy system. From the table, it is obvious that QOBO generates the minimum value of LCOE in all cases. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Hybrid Power** & **Algorithm** & **PV (m2)** & **Wind (m2)** & **Diesel** & **Battery** & **Biomass** & **Time(s)** \\ \hline \multirow{6}{*}{PV/WT/Diesel/BESS} & QOBO & 484.765 & 0 & 1.2142 & 13.4390 & // & 51,507 \\  & BO & 248.002 & 998.505 & 0.6480 & 14.8052 & // & 164,242 \\  & HHO & 513.105 & 305.293 & 0.5204 & 14.6552 & // & 30,655 \\  & AERA & 329.159 & 176.277 & 5.4696 & 18.6552 & // & 10,531 \\  & IWO & 830.791 & 136.557 & 10.296 & 5.8224 & // & 57,938 \\ \hline \multirow{6}{*}{PV/Biomass} & QOBO & 293.971 & // & // & // & 1020.18 & 32,104 \\  & BO & 293.972 & // & // & // & 1020.31 & 122,417 \\  & HHO & 298.860 & // & // & // & 2040.47 & 10,453 \\  & AEFA & 302.980 & // & // & // & 1185.76 & 3855 \\  & IWO & 365.515 & // & // & // & 2739.00 & 36,098 \\ \hline \multirow{6}{*}{PV/Diesel/BESS} & QOBO & 376.011 & // & 1.3402 & 58.9083 & // & 16,799 \\  & BO & 336.253 & // & 2.9170 & 52.1928 & // & 33,009 \\  & HHO & 482.756 & // & 1.7843 & 13.7590 & // & 13,983 \\  & AEFA & 386.692 & // & 1.6713 & 55.7583 & // & 6327 \\  & IWO & 748.387 & // & 4.0111 & 51.4565 & // & 24,630 \\ \hline \multirow{6}{*}{WT/Diesel/BESS} & QOBO & // & 2726.29 & 91.141 & 72.375 & // & 26,510 \\  & BO & // & 2823.34 & 42.637 & 72.371 & // & 66,514 \\ \cline{1-1}  & HHO & // & 2808.76 & 74.565 & 73.230 & // & 135,097 \\ \cline{1-1}  & AEFA & // & 3015.08 & 72.963 & 72.653 & // & 78,697 \\ \cline{1-1}  & IWO & // & 4318.76 & 78.218 & 82.7987 & // & 26,960 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Sizing results of different scenarios obtained from different optimization methods.
# Impact of Shifts in Vegetation Phenology on the Carbon Balance of a Semiarid Sagebrush Ecosystem
## 2 Materials and Methods
### Eddy Covariance Data  
Eddy covariance (EC) measurements of energy, water vapor, and net ecosystem CO\({}_{2}\) fluxes were made using a 3D sonic anemometer (Model CSAT3, Campbell Scientific, Inc., Logan, UT, USA) and an open-path gas analyzer (Model LI-7500A, LI-COR, Inc., Lincoln, NE, USA). The EC system was installed on the flux tower at 5 m above the ground, and the signals were sampled at a rate of 10 Hz and stored using a data logger (CR3000, Campbell Scientific, Inc.). Raw 10 Hz data were processed using EddyPro(r) software (version 7.06, LI-COR, Inc.) to determine half-hourly fluxes of CO\({}_{2}\) (NEE) and latent and sensible heat (LE and H). The 10 Hz data were filtered for out-of-range values and instrument failures and then despiked [32]. We applied the double rotation method [33] to the three-dimensional wind components. Then, block averaging was used to calculate the fluctuating parts for each 30-min interval. Covariances were calculated and corrected for the effects of high- and low-pass filtering [34; 35] and air density fluctuations [36], respectively. According to [PERSON] and [PERSON] [37], the corrected fluxes were quality-checked and flagged, and low-quality data were removed for this study. The \"REddyProc\" R package [38] was applied to determine the friction velocity (u\({}_{*}\)) threshold and fluxes under conditions of low turbulent mixing were also removed. These removed data were further gap-filled using a machine learning algorithm as described in Section 2.6.