esa-sceva/satcom-chunk-collection huggingface dataset:
# Studies on the Electrochemical Behavior of Sulfite on Incoloy 800 in a Neutral Environment
## 3 Results
### Chronamperometric Studies  
The chronoamperometric measurements had as a starting point the linear voltammetry studies. Based on these studies, six values of the potential steps were chosen. (0.40, 0.75, 1.00, 1.25, 1.50, and 1.75 V) to highlight the anodic processes that occur at the surface of the working electrode. When the anodic process is conducted at the first five chosen potential values, the only process that takes place on the surface of the Incoloy 800 electrode is the anodic oxidation of sulfite. At the value of 1.75 V, the release of oxygen takes place on the anode, simultaneously with the main process (the shape of the amperogram represented in Figure 4b, being typical for a gas evolution process on the electrode surface). This fact is justified by the different slope of the chronoamperometric plot in Figure 4b. From the chronoamperometric data, it can be seen that when the potential shifts towards more positive values, the current density values increase accordingly, which implicitly has the effect of an intensification of the useful process of oxidizing sulfite ions to sulfate. The slightly different shape of the specific chronoamperometric plots for concentrations of 5 \(\times\) 10\({}^{-1}\) and 1 mol L\({}^{-1}\) when the measurements are carried out at the same value of the potential is justified by the existence in the immediate vicinity of the interface of a very large number of sulfite anions (Figure 4a), correlated with the recording of some values of higher current densities, values that decrease due to the emergence of the need to bring sulfite ions from the mass of the electrolyte to the electrode-electrolyte interface.  
From the CA studies, it can be stated that for both sulfite concentrations, in the first 900 s, the anodic oxidation of sulfite is controlled by the charge transfer, whereas in the following period, the mass transfer of sulfite ions in the speed-determining step, and over  
Figure 4: Chronoamperometric plots for the Incoloy 800 electrode in neutral solution at different sulfite concentrations at +1.00 V (**a**) and in 1 mol L\({}^{-1}\) Na\({}_{2}\)SO\({}_{4}\) + 10\({}^{-1}\) mol L\({}^{-1}\) Na\({}_{2}\)SO\({}_{3}\) (**b**).  
this interval, the mechanism of the useful process is controlled by the mass transfer of sulfur ions to the steel electrode.  
Based on a chronoamperometric data recorder in the tested system, the following conclusions may be drawn:  
1. characteristic potential range for SO3\({}^{2-}\) oxidation in neutral solution is between +0.40 and +1.50 V
2. at more positive potential values, SO3\({}^{2-}\) oxidation and oxygen evolution reactions occur simultaneously and chronoamperometric curves have a typical shape;
3. current densities increase with the increasing sulfite concentration added in neutral electrolyte (1 M Na2 SO4).
# A Multi-Scale Deep Back-Projection Backbone for Face Super-Resolution with Diffusion Models
## 2 Related Work  
### Single-Scale Deep Back-Projection Networks  
SISR is a challenging task that aims to reconstruct an HR image from an LR image. This task has many applications in various fields, such as satellite imagery [29], monitoring equipment [30], remote sensing images [31], medical imaging [32], and so on. However, SISR is an ill-posed problem because one LR image can correspond to multiple HR images. Therefore, it requires sophisticated methods to recover the missing details and enhance the image quality.  
Deep learning methods have become popular for SISR in recent years. [PERSON] et al. [7] proposed DBPN, which uses iterative up and down sampling layers to provide an error feedback mechanism for projection errors at each stage. It improves SR performance for large scaling factors by bringing high-level information back to the previous layer and refining low-level information. Based on DBPN [7], [PERSON] et al. [33] proposed an enhanced back-projection network that provides an up and down sampling process with error feedback to capture various spatial correlations and introduced the residual block in the sampling process to alleviate the difficulty of training deep networks.  
By constructing interconnected upward and downward sampling stages, the DBPN can handle different types of image degradation and recover HR components. To conclude, the DBPN offers three valuable insights for SISR: (1) jump connection; (2) continuous up and down sampling; and (3) sampling with convolution.
# Modulus Stretch-Based Circular SAR Imaging with Contour Thinning
## 3 Experimental Results
### Simulated Data Imaging
#### 3.1.2 Double-Line Target Imaging  
The target was two lines consisting of dense points with an interval of 0.1 between \(x=-5\) and 5. The \(y\) coordinates of the two lines were \(\pm 0.2\), \(\pm 0.15\) and \(\pm 0.1\), that is, the distance between the two lines was 0.4, 0.3 and 0.2, as shown in Figure 5.  
Figure 6a-c is the imaging result of a traditional backprojection algorithm with a synthetic aperture of 5\({}^{\circ}\) when two lines are 0.4, 0.3 and 0.2 apart. Figure 6d-f is the imaging results of Figure 6a-c after piecewise linear transformation based on a 5\({}^{\circ}\) synthetic aperture. It can be seen that the traditional backprojection algorithm can distinguish the two lines when they are 0.4 apart. When the distance is shortened to 0.3, it is more difficult to distinguish the two lines. When the distance is shortened to 0.2, the imaging results of the traditional backprojection algorithm are completely indistinguishable from the two lines. However, the imaging results after piecewise linear transformation can distinguish the two lines in all cases.  
Figure 7a-c is the imaging result of traditional backprojection algorithm with full synthetic aperture when two lines are 0.4, 0.3 and 0.2 apart. Figure 7d-f corresponds to Figure 7a-c imaging results of full aperture after piecewise linear transformation at each slow time \(\tau_{n}\). As can be seen from Figure 7, the two lines can be distinguished from the imaging results after piecewise linear transformation in three cases, while the traditional backprojection algorithm cannot distinguish the two lines when the distance is less than 0.2.  
Figure 5: Double-line target location map. The distance between the two lines is (**a**) 0.4; (**b**) 0.3; (**c**) 0.2.  
Figure 6: Double-line target imaging with a synthetic aperture of \(5^{\circ}\). The piecewise linear transformation parameters are \(T=0.95\), \(k_{1}=1.2\), \(k_{2}=0.1\): (**a,d**) The distance between the two lines is 0.4; (**b,e**) The distance between the two lines is 0.3; (**c,f**) The distance between the two lines is 0.2.  
Figure 7: Double-line target imaging with full synthetic aperture. The piecewise linear transformation parameters are \(T=0.95\), \(k_{1}=1.2\), \(k_{2}=0.1\): (**a,d**) The distance between the two lines is 0.4; (**b,e**) The distance between the two lines is 0.3; (**c,f**) The distance between the two lines is 0.2.  
The above simulation results show that the imaging result after piecewise linear transformation is better than that of the traditional backprojection algorithm. The imaging results after piecewise linear transformation can distinguish the very close targets which are mixed together in the traditional backprojection algorithm imaging.
## 3 Results and Discussion  
### Particle Size Distribution  
TPW samples ground under different conditions resulted in significantly different particle size distribution (Figure 2). Prolonged grinding (40 s of grinding) resulted in a significant decrease in the median diameter from 732 um (no grinding) to 210 um but did not affect the span which ranged from 2.34 to 2.47 in all ground samples.  
Figure 2: Particle size distribution of TPW after 0, 5, 9, 18, and 40 s of grinding. Dx 10: the particle diameter below which 10% of the sample’s total volume of particles is found; Dx 50: median diameter; Dx 90: the diameter below which 90% of the sample’s total volume of particles is found.
# Bayesian Estimation of Simultaneous Regression Quantiles Using Hamiltonian Monte Carlo
## 2 Simultaneous Quantile Regression
### Bayesian Linear Quantile Regression  
Consider the following quantile regression model:  
\[Y=\mathbf{x}^{\prime}\mathbf{\beta}_{\tau}+\epsilon. \tag{5}\]  
We assume that the error \(\epsilon\) and \(\mathbf{x}\) are independent, and \(\epsilon\sim F\), \(F\) is unknown, but \(F(0)=\tau\). Hence, \(\mathbf{x}^{\prime}\mathbf{\beta}_{\tau}\) denotes the \(\tau\)-th quantile of \(Y|\mathbf{x}\). For all \(\mathbf{x}_{t}\in\mathbb{R}\), suppose the relationship between \(\mathbf{\iota}_{\tau}(\mathbf{x}_{i})\) and \(x_{i}\) could be modeled as \(\mathbf{\iota}_{\tau}(\mathbf{x}_{i})=x_{i}\mathbf{\beta}_{\tau}\), where \(\mathbf{\beta}_{\tau}\) is a vector with unknown interest parameters. From i.i.d \((\mathbf{x}_{t},Y_{t})_{t=1,\ldots,T}\) issued from the model defined in Equation (5), we are interested in estimating quantiles of the \(Y|\mathbf{x}\) law via the Bayesian approach. It then suffices to estimate \(\mathbf{\beta}_{\tau}\).  
If \(F\) is unknown, the likelihood is not available, but the Bayesian approach requires some likelihood; hence, we use the \"working likelihood\" defined as the ALD:  
\[l(Y|\mu,\sigma,\tau)=\frac{\tau(\tau-1)}{\sigma}\exp(-\rho_{\tau}(\frac{Y-\mu }{\sigma})),\]  
where \(\mu=x_{t}^{\prime}\beta_{\tau}\) and \(\rho_{\tau}(u)\) is as defined in (3). The \(\tau\)-th quantile of this distribution is zero; hence, the pseudo posterior is  
\[\pi(\mathbf{\beta}|(\mathbf{x}_{t},Y_{t})_{t=1,\ldots,T})\propto\prod_{t=1}^{T} \text{ALD}(y_{t}-\mathbf{x}_{t}^{\prime}\mathbf{\beta}_{\tau},\sigma,\tau)\times\pi( \mathbf{\beta}_{\tau},\sigma), \tag{6}\]  
Equation (6) describes the ALD probability distribution, where \(y_{t}\) is the observed data point, \(x_{t}^{\prime}\) is the design matrix for observation \(t\), \(\beta\) is a set of parameters, \(\sigma\) is a scale parameter, and \(\tau\) is a quantile parameter. This equation provides a natural way to solve the problem of Bayesian estimation of the quantile \(q_{\tau}\) of order \(\tau\). Moreover, the relationship between minimizing the loss function (3) and maximizing a likelihood function is demonstrable. This equivalence arises when the likelihood function is constructed by combining independently distributed asymmetric densities of the Laplace distribution. Furthermore, it is noteworthy to emphasize that the simple Bayesian quantile can be regarded as a specific instance of a Bayesian regression quantile. In this particular case, the simplicity is characterized by setting \(k=1\) and considering only the variable \(x\), with the absence of additional covariables. This distinction highlights a specialized scenario within the broader framework of Bayesian quantile regression.
# MTRSRP: Joint Design of Multi-Triangular Ring and Self-Routing Protocol for BLE Networks
## 4 The Proposed MTRSRP
### Self-Routing Protocol of MTRSRP
Comparing the initial bits of the codes, as \"000\" increased to \"011,\" the transmission transitioned from the inner ring to the outer ring. Therefore, the transmission path was as follows: 00010 -> 00001 -> 00101 -> 01001 -> 01101. In designing MTRSRP, considerations were primarily focused on the connections within triangular rings and between rings. For connections within triangular rings, the design principle of the shortest path was employed by utilizing coding addressing techniques to optimize connection paths. This allows the packets to be transmitted within triangular rings via the shortest path, reducing communication latency and improving packet transmission efficiency. By contrast, a straight-line transmission approach was adopted for connections between rings, which was also based on the shortest path principle, to facilitate efficient packet transmission between rings. The combination of these approaches established self-routing paths for the entire multi-triangular ring network, which aligned with the paths of the minimum spanning trees [23], ensuring communication efficiency and performance of the entire network. Thus, the self-routing path protocol designed by MTRSRP, which utilizes the shortest paths for packet routing in conjunction with coding addressing techniques, significantly enhances the efficiency and performance of network communication, opening up new possibilities and values in the field of network communication technology development and applications.
## 3 Error Model and Cross-Identification Algorithm
### Cross-Identification Method Based on LM Algorithm
#### 3.2.2 C-LM Algorithm  
In Equation (23), since the first column of the \(M_{\theta}\) is zero, the joint angle \(\theta_{1}\) cannot be identified when the optimization objective is solely the differential translation \({}_{m}^{t}d\). Similarly, due to \(M_{d}^{\prime}\) and \(M_{u}^{\prime}\) being zero, and the first three columns of \(E_{u}^{\prime}\) and \(F_{v}^{\prime}\) also being zero, the parameters such as link length \(a_{i}\), link offset \(d_{i}\), translation \([x,\ y,\ z]\) between the DCF and the MCF, and translation \([x^{\prime},\ y^{\prime},\ z^{\prime}]\) between the TCF and the FCF cannot be identified when the optimization objective is solely the differential rotation \({}_{m}^{t}\delta\). Furthermore, when attempting to simultaneously identify all geometric parameters using Equation (25) and the LM algorithm, the results are prone to becoming trapped in local optima.  
To address the aforementioned issues, this paper proposes a geometric parameter cross-identification method based on the LM algorithm. The specific steps are as follows:  
Step 1: Considering only the differential rotation \(\delta\) as the optimization objective, use the LM algorithm to solve the pose part of the linear Equation (25). This step aims to identify the nonlinear parameters related to angles, which include \(\left[\Delta\theta_{1}\ \ \ \cdots\ \ \ \Delta\theta_{n}\right]^{T}\), \(\left[\Delta\theta_{1}\ \ \ \cdots\ \ \ \Delta\theta_{n}\right]^{T}\), \(\left[\Delta\beta_{1}\ \ \ \cdots\ \ \ \Delta\beta_{n}\right]^{T}\), \(\left[\alpha,\beta,\gamma\right]\), and \([\alpha^{\prime},\beta^{\prime},\gamma^{\prime}]\).  
Step 2: Using the identified angular parameters from the previous step as the initial values, with the position error \(\Delta p\) and differential rotation \(\delta\) as the optimization targets, identify all linear and nonlinear parameters, where the linear parameters are \(\left[d_{1}\ \ \cdots\ \ \ d_{n}\right]^{T}\), \(\left[a_{1}\ \ \cdots\ \ \ a_{n}\right]^{T}\), \([x,y,z]\), and \([x^{\prime},y^{\prime},z^{\prime}]\). Note that the position error \(\Delta p\) and the differential translation \(d\) differ by a rotation matrix \(R\).  
Step 3: Repeat the above two steps until the iteration termination condition is met.  
The proposed C-LM algorithm identifies the nonlinear parameters related to the angles according to the differential rotation \(\delta\), and then uses it as the initial value to identify all the parameters to be sought. This solves the local optimal problem caused by the mutual interference of linear and nonlinear parameters when identifying geometric parameters simultaneously. Therefore, compared to the strategy of simultaneously identifying all parameters, the proposed C-LM algorithm is more likely to escape local minima, has a wider convergence range, and achieves higher identification accuracy. The flowchart of the geometric parameter cross-identification algorithm based on the LM algorithm is shown in Figure 3.  
Figure 3: Flowchart of the C-LM algorithm.
## 2 Chebyshev Graph Convolutional Neural Network Modeling Method  
The framework of the ChebyNet modeling method for rotating equipment fault diagnosis under variable operating conditions is illustrated in Figure 1 and comprises three modules: data preprocessing, feature extraction, and multi-task collaborative diagnosis.  
Figure 1: Framework diagram of ChebyNet modeling method for rotating equipment fault diagnosis under variable operating conditions. The black circle represents the reference node whose features are to be updated, and the color of other circles changes, indicating that the features of the corresponding nodes are aggregated by the reference node.  
First, the data preprocessing module includes a fast Fourier transform (FFT) unit for raw data and a data graph construction unit. The FFT unit converts the raw time domain data into frequency domain data to reveal the characteristics of the data in the frequency domain. In the data graph construction unit, the PathGraph method is used to comprehensively consider the complex interactive relationships among the data and transform them into graph data, laying the groundwork for subsequent GNN processing.  
Secondly, the data feature extraction module includes the ChebyNet global feature extraction unit and the GAT local feature extraction unit. In the global feature extraction unit of the ChebyNet, symmetry processing enhancements are implemented to enhance its capacity for equitable information integration, thereby addressing the issue of biased information transmission. At the same time, the ChebyNet's efficient global feature extraction capabilities enable the comprehensive mining of overall features within variable operating conditions data. In the GAT local feature extraction unit, node attention is adaptively calibrated to accurately capture local details and key features within the data. This fusion method not only ensures the integrity of global features but also takes into account the accuracy of local features, thoroughly analyzing the complex interplay between global and local features.  
Finally, the multi-task collaborative diagnosis module comprises node classification tasks and a node reconstruction task. The node classification tasks offer a distinct supervisory signal to the model through the construction of a Cross-Entropy Loss function, thereby guiding it to differentiate between various fault categories. The node reconstruction task employs a self-supervised learning approach that constructs a root Mean Squared Error (MSE) Loss function to map the input, thereby compelling the model to gain a deeper understanding of the internal structure and patterns within the data and enhancing its generalization ability in managing variable operating conditions. The sum of the loss values of the two tasks is considered the total loss, and the parameters are updated according to the gradient information of the total loss to facilitate the coordinated optimization of both tasks. The maximum value of the category probability is determined using the Argmax function and presented as the model's predicted value for diagnosis.
## Appendix A Equations of Motion  
In this section, we present the step-by-step details of the derivation of (9) from the previous equations, as it constitutes the most critical part of this article.  
Starting from (8), one has first to rename the dummy index from \(k\) to \(j\), multiply both sides by \(f_{k}\), and then take the inner product. This will yield the expression  
\[\begin{array}{c}-\sum\omega_{j}{}^{2}Q_{j}(f_{k}|f_{j})=\sum\breve{Q}_{j}(f_ {k}|f_{j})-\frac{\dot{q}}{q}\sum\breve{Q}_{j}\big{[}\big{(}f_{k}|f_{j}\big{)}+ 2\big{(}f_{k}|\kappa_{j}x|g_{j}\big{)}\big{]}\\ -\frac{\ddot{q}}{q}\sum Q_{j}\Big{[}\frac{1}{2}\big{(}f_{k}|f_{j}\big{)}+ \big{(}f_{k}|\kappa_{j}x|g_{j}\big{)}\Big{]}+\frac{\ddot{q}}{q^{2}}\sum Q_{j} \big{[}\frac{3}{4}\big{(}f_{k}|f_{j}\big{)}+3\big{(}f_{k}|\kappa_{j}x|g_{j} \big{)}-\big{(}f_{k}|\kappa_{j}^{2}x^{2}|g_{j}\big{)}\big{]}.\end{array} \tag{10}\]  
Using (3), we trivially get  
\[\begin{array}{c}-\sum\omega_{j}{}^{2}Q_{j}\delta_{kj}=\sum\breve{Q}_{j} \delta_{kj}-\frac{\dot{q}}{q}\sum\breve{Q}_{j}\Big{[}\delta_{kj}+2\alpha_{kj} \Big{]}-\frac{\ddot{q}}{q}\sum Q_{j}\Big{[}\frac{1}{2}\delta_{kj}+\alpha_{kj} \Big{]}\\ +\frac{\dot{q}^{2}}{q^{2}}\sum Q_{j}\Big{[}\frac{3}{4}\delta_{kj}+3\alpha_{kj} -\beta_{kj}\Big{]},\end{array} \tag{11}\]  
which after rearrangement takes the form  
\[\breve{Q}_{k}=-\omega_{k}{}^{2}Q_{k}+\frac{\dot{q}}{q}\breve{Q}_{k}+\frac{ \ddot{q}}{2q}Q_{k}-\frac{3\dot{q}^{2}}{4q^{2}}Q_{k}+2\frac{\dot{q}}{q}\sum \alpha_{kj}\dot{Q}_{j}+\frac{\ddot{q}}{q}\sum\alpha_{kj}Q_{j}-\frac{\dot{q}^{2 }}{q^{2}}\sum\Big{(}3\alpha_{kj}-\beta_{kj}\Big{)}Q_{j}. \tag{12}\]  
We may furthermore use \(\alpha_{kj}=-\frac{1}{2}\delta_{kj}+g_{kj}\) and \(\beta_{kj}=\Big{(}\frac{1}{3}k^{2}\pi^{2}-\frac{1}{2}\Big{)}\delta_{kj}+h_{kj}\) from (4) to simplify and rewrite (12) as  
\[\breve{Q}_{k}=-\omega_{k}{}^{2}Q_{k}-\frac{3\dot{q}^{2}}{4q^{2}}Q_{k}+\frac{ 3\dot{q}^{2}}{2q^{2}}Q_{k}+\frac{\ddot{q}}{q^{2}}\Big{(}\frac{k^{2}\pi^{2}}{3} -\frac{1}{2}\Big{)}Q_{k}+2\frac{\ddot{q}}{q}\sum g_{kj}\dot{Q}_{j}+\frac{\ddot {q}}{q}\sum g_{kj}Q_{j}-\frac{\dot{q}^{2}}{q^{2}}\sum\Big{(}3g_{kj}-h_{kj} \Big{)}Q_{j}, \tag{13}\]  
which by plugging in the definition for \(r_{k}\) from (10) takes the form  
\[\breve{Q}_{k}=-\omega_{k}{}^{2}Q_{k}+r_{k}\frac{\dot{q}^{2}}{q^{2}}Q_{k}+2 \frac{\dot{q}}{q}\sum g_{kj}\dot{Q}_{j}+\frac{\ddot{q}}{q}\sum g_{kj}Q_{j}+ \frac{\dot{q}^{2}}{q^{2}}\sum\Big{(}h_{kj}-3g_{kj}\Big{)}Q_{j}. \tag{14}\]  
This is exactly Equation (9).
## 3 The First Modal Inertial/Invariant Single Load Vectors Pushover Analysis Methods
### The N2 Method, Eurocode 8  
The N2 method, initially developed by [43] and later improved by [44], is a widely used nonlinear static analysis method recommended for use by EC8 [42]. It combines pushover analysis of an MDOF model and response spectrum analysis of a corresponding SDOF model to achieve a balance between reliability and applicability for everyday design use. The N2 method differs from the capacity spectrum method in that it has adopted an \(R-\mu-T\) approach rather than the over damped spectra applied in the CSM method. The detailed procedure for conducting the N2 method is outlined below,  
1. Pushover Analysis: perform the analysis to obtain the capacity curve represented in \(V_{b}\)-\(D\) terms.
2. Conversion and approximation: Convert the pushover curve of the MDOF system into the capacity diagram of an ESDOF system. Approximate this curve with an idealized elastic-perfect plastic relationship to determine the period \(T_{e}\) of the ESDOF.  
Figure 3: Illustration of the application of the ICSM method [43].  
Target displacement calculation: the target displacement is computed as follows:  
\[d_{et}^{*}=S_{a}(T_{e})\left[\frac{T_{e}}{2 TI}\right]^{2} \tag{9}\]  
where \(S_{a}(T_{e})\) represents the elastic acceleration response spectrum at the period \(T_{e}\). To ascertain the target displacement \(d_{t}^{*}\), different formulas are proposed for varying period ranges.  
In the short period range (\(T*\leq T_{C}\)), if the condition \(F_{y}/m^{\prime}\leq S_{a}(T_{e})\) holds, the response remains elastic, leading to \(dt^{\prime}=de^{\prime}t\) and \(dt=C_{0}dt^{\prime}\). If this condition is not met, the response turns nonlinear, and the ESDOF maximum displacement is given by:  
\[d_{t}^{{}^{\prime}}=\frac{d_{et}^{{}^{\prime}}t}{\sqrt{1+(qu-1)*\frac{T_{C}}{ Ie}\leq d_{et}^{{}^{\prime}}t}} \tag{10}\]  
where \(q_{u}\) is the acceleration ratio of the structure with unlimited elastic capacity, times the modal mass m* over its yield force, defined as:  
\[qu=\frac{S_{a}(T_{e})*m^{{}^{\prime}}}{F_{y}} \tag{11}\]  
In the medium and long period range (\(T^{*}\geq T_{C}\)), the target displacement for the inelastic system matches that of an elastic structure, so \(dt^{\prime}=de^{\prime}t\). The MDOF system's displacement is consistently determined as \(dt=C_{0}dt^{\prime}\).