esa-sceva/satcom-chunk-collection huggingface dataset:
# A Method for Identifying the Wear State of Grinding Wheels Based on VMD Denoising and AO-CNN-LSTM
## 2 Grinding Wheel Wear State Recognition Based on VMD Denoising and AO-CNN-LSTM
#### 2.2.1 Aquila Optimizer
### VMD Algorithm for Denoising AE Signals  
The VMD algorithm is employed for the purpose of non-recursively decomposing a set of signals into K Intrinsic Mode Functions (IMFs) characterized by quasi-orthogonality and specific sparsity, ensuring effective signal separation. Rooted in concepts such as Wiener filtering, Hilbert transformation, and frequency mixing [11], the VMD algorithm constructs a variational problem. The key constraint in this approach is that the sum of all components must be consistent with the original signal. The constrained variational expression is given by:  
\[\left\{ \begin{matrix}\underset{\{u_{k}\},\{\omega_{k}\}}{\text{min}}\left\{ \sum\limits_{k}\|\partial_{t}\Big{[}\Big{(}\delta(t)+\frac{j}{\pi t}\Big{)} \times u_{k}(t)\Big{]}e^{-j\omega_{k}t}\|_{2}^{2}\right\}\\ s.t.\sum\limits_{k}^{K}u_{k}=f(t)\end{matrix} \right. \tag{1}\]  
In Equation (1), \(\{u_{k}\}\) represents the K IMFs obtained after VMD decomposition \(\{u_{1},u_{2},\ldots,u_{k}\}\); \(\{\omega_{k}\}\) denotes the center frequencies of the K IMFs \(\{\omega_{1},\omega_{2},\ldots,\omega_{k}\}\); \(f(t)\) is the original signal; \(\partial_{t}\) represents the gradient operator; \(\delta(t)\) is the Dirac delta function; * denotes the convolution operator; \(s.t.\) denotes the constraint term. To resolve the variational constraint problem and convert it from a constrained problem to an unconstrained one, the augmented Lagrange function is introduced [12]. Through the incorporation of the augmented Lagrange function, the transformed expression is derived, namely,  
\[ \begin{matrix}\|\partial_{t}\Big{[}\Big{(}\delta(t)+\frac{j}{\pi t}\Big{)} \times u_{k}(t)\Big{]}e^{-j\omega_{k}t}\|_{2}^{2}\\ L(\{u_{k}\},\{\omega_{k}\},\lambda)=\alpha\sum\limits_{k=1}^{K}\qquad\quad+ \|f(t)-\sum\limits_{k=1}^{K}u_{k}(t)\|_{2}^{2}\\ \qquad\quad+<\lambda(t),f(t)-\sum\limits_{k=1}^{K}u_{k}(t)>\end{matrix}  \tag{2}\]  
In Equation (2), \(\lambda\) represents the Lagrange operator, ensuring the strictness of the constraint conditions. \(\alpha\) serves as a quadratic penalty factor to guarantee the accuracy of signal reconstruction. To update the constraint parameters and find the saddle point of Equation (2), we first initialized \(u_{k},\omega_{k},\lambda\), and \(n\). Then, based on Equations (3)-(5), we iteratively updated it to obtain \({u_{k}}^{n+1},\omega_{k}^{n+1}\), and \(\lambda^{n+1}\) until the iterative constraint conditions in Equation (6) were satisfied.
## 4 Analysis of Prediction Results
(RMSE = 0.8662) > F-GCN (RMSE = 0.9749) > BiGRU (RMSE = 1.0486) > BiLSTM (RMSE = 1.1552). Models based on GCNs were better at capturing complex geological structures for local information processing when dealing with sequential data. These models were adept at accommodating the intricate geological structures and data interdependencies present in the logging data. BiGRU (RMSE = 1.0486) and BiLSTM (RMSE = 1.1552) showed poorer performance; these two models are common variants of RNNs and are relatively strong in handling long-term dependencies in sequential information. These models might not have completely captured the intricate data patterns, due to insufficient local sequence feature extraction. Therefore, models based on GCNs had smaller relative errors and better performance, and were more capable of approaching the true values. The ADF-GCN model (RMSE = 0.4873), which considered both deep sequences and temporal-related graphs, and used an attention mechanism to generate an adaptive adjacency matrix, not only captured the correlations between deep sequences and features but also addressed the limitations of pre-built adjacency matrices, making its performance the best. Figure 7 presents a scatter plot of the relative error intervals, alongside relative frequency histograms for the deep learning model. These charts were pivotal for assessing the model performance, providing insights into the model's behavior across various error  
Figure 6: Scatter plot of relative error of deep learning models. ranges, which aided in a more nuanced evaluation and refinement of the model. The chart's x-axis denotes the relative error intervals, reflecting the gap between consecutive relative error values. The y-axis presents the relative frequency histogram, indicating the proportion of samples in each relative error interval against the total sample count. This dual-dimensional analysis enabled a thorough review of model performance on the chart. Notably, chart peaks suggest a concentration of samples in certain error intervals, hinting at the model's stability and accuracy within those ranges. From the chart, it can be seen that the ADF-GCN (MAE = 0.4746) performed the best. This may be because it could better handle deep sequence data and capture complex geological structural information. Models based on GCNs generally have peaks closer to 0 than the RNN variants, including BiGRU (MAE = 0.7830) and BiLSTM (MAE = 0.9035). This suggests that even though RNNs variants are good at processing long-term dependent sequence information, undirected graphs are more suitable for capturing correlations between data, making them more applicable for identifying and combining logging data with high affinity or similarity. Figure 7: Histograms of the relative error interval and relative frequency of the deep learning models.
## 3 Methodology and Data Collection
### Transport Corridors  
A corridor is a broad geographic area, defined by logical, existing, and forecasted travel patterns served by various modal transportation systems that provide important connections within and between regions of the State for people, goods, and services [39]. Travel within the corridor may include vehicle, rail, transit, water, air, or non-motorized means. In the same sense, a transport corridor is the area of origin and destination of traffic flows [40].  
In Mexico, transport corridors are defined by the largest movement of freight and passengers across the road network. The first transport corridors were defined through origin-destination data and cargo transported [41]. Transport corridors are placed into a hierarchy using land use models, incorporating the economic value of the freight transported. The results can then be applied to the first strategic planning for the expansion of the corridors in the country. Nowadays, the network is composed of 16 large road corridors that connect the main ports and border crossings, in addition to providing accessibility to major cities that make up the country and Mexico City. Figure 2 shows the main transport corridors in Mexico.
# Streamlining Visual UI Design: Mining UI Design Patterns for Top App Bars
## 3 The Proposed Approach
### Clustering Design Patterns  
Once the vector representations are obtained, we apply a variety of clustering algorithms to group similar representations together, enabling the identification of potential design patterns within the TAB. The choice of clustering algorithm plays a crucial role in the effectiveness of pattern identification. Here, we introduce several commonly used clustering algorithms: K-means, Gaussian Mixture Models (GMM), Balanced Iterative Reducing and Clustering using Hierarchies (BIRCH), and Spectral Clustering.  
**K-means.** K-means is a widely used clustering algorithm that partitions data into \(K\) clusters by iteratively optimizing cluster centroids to minimize the sum of squared distances between data points and their nearest centroids.  
**GMM.** GMM assumes that the data are generated from a mixture of several Gaussian distributions. Unlike K-means, which assigns each data point to a single cluster, GMM assigns probabilities to each data point belonging to each cluster.  
**BIRCH.** BIRCH is a hierarchical clustering algorithm that is particularly well-suited for large datasets. It incrementally builds a hierarchical clustering structure by clustering small subsets of data points called micro-clusters and merging them to form larger clusters.  
**Spectral.** Spectral clustering is a graph-based clustering technique that partitions data based on the eigenvectors of a similarity matrix derived from the data. Unlike traditional clustering algorithms that operate directly on the data space, spectral clustering considers the pairwise relationships between data points, making it effective for capturing non-linear and non-convex clusters.
## 2 Method
### Mapped Features Reconstruction  
In the third module of our framework, we use the decoder of the trained autoencoder \(AE\) to reconstruct the latent representations \(\hat{Z}\) obtained from the regressors, in the feature mapping network module, back to the input space \(Y^{k}\), where \(y_{i}^{k}\) approximates \(\mu^{k}\) centroid (mean sample) of the same class.  
A summary of the transformation pipeline is shown in Algorithm 2. Given a training set \(D^{T\!r}\) and a test set \(D^{T\!s}\), we first extract the features \(Z_{tr}\) of \(D^{T\!r}\) from the trained autoencoder \(AE\) and map \(Z_{tr}\), using the trained regressors in the feature mapping network \(B\), to \(Z_{tr}\), then, we use the decoder of \(AE\) to reconstruct \(\hat{Z}_{tr}\) to the input space yielding \(D^{T\!r}\). We do the same for \(D^{T\!s}\) resulting in the transformed test set \(D^{T\!s}\).  
Our proposed framework can be embedded as a preprocessing step in semi-supervised and supervised settings. In the semi-supervised setting, we use the limited training (labeled) set \(D^{T\!r}\) to train our framework and transform the test (unlabeled) set \(D^{T\!s}\) and cluster the transformed unlabeled set \(D^{T\!s}\) using a clustering algorithm. In the supervised setting, we use an off-the-shelf classifier in the following setting: the plain training set \(D^{T\!r}\) augmented with the transformed training set \(D^{T\!r}\) using our framework as shown in Algorithm 2. The augmentation of the mapped training samples increases the size of the learning data pool which is beneficial in the case of small size datasets where the lack of training samples increases the chance of overfitting. Our augmentation resembles SMOTE augmentation in that we both operate in the feature space to generate the augmented samples. However, our augmentation is different in that we do not interpolate new data samples among a number of neighboring samples, conversely, we transform the available data samples to a group of similar data samples approximating the mean sample of the target class. Also, SMOTE increases the density of samples of the same class within the same boundaries of data clusters without relocation of clusters which does not provide any improvement in the separability and compactness characteristics.  
```
Require: \(D^{T\!r}\), \(D^{T\!s}\)
1 \(Z_{tr}\gets Extract\ features\ of\ D^{T\!r}\) from the trained autoencoder \(AE\)
2 \(Z_{tr}\gets Predict\ features\ using the trained MLP regressors and \(Z_{tr}\) as input
3 \(D^{T\!r}\gets Reconstruct\ the predicted\ features\ \hat{Z}_{tr}\) using the decoder of \(AE\)
4  Repeat for \(D^{T\!s}\)
```  
**Algorithm 2** The Transformation Pipeline.
# A Model-Agnostic Algorithm for Bayes Error Determination in Binary Classification
## 3 ILD Algorithm Mathematical Framework
### True Positive, True Negative, False Positive, False Negative  
In the feature bucket \(i\), if \(p^{[i]}=0\), then only \(m_{0}^{[i]}\) observations would be correctly classified. On the other side, if \(p^{[i]}=1\), only \(m_{1}^{[i]}\) observations would be correctly classified. For each bucket \(i\) the true positive \(TP^{[i]}\) can be written as  
\[TP^{[i]}=m_{1}^{[i]}p^{[i]} \tag{6}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Bucket** & **Feature 1** & **Feature 2** & **Class 0** & **Class 1** \\ \hline
1 & \(F_{1}^{[1]}=0\) & \(F_{2}^{[1]}=0\) & \(m_{0}^{[1]}\) & \(m_{1}^{[1]}\) \\ \hline
2 & \(F_{1}^{[2]}=0\) & \(F_{2}^{[2]}=1\) & \(m_{0}^{[2]}\) & \(m_{1}^{[2]}\) \\ \hline
3 & \(F_{1}^{[3]}=1\) & \(F_{2}^{[3]}=0\) & \(m_{0}^{[3]}\) & \(m_{1}^{[3]}\) \\ \hline
4 & \(F_{1}^{[4]}=1\) & \(F_{2}^{[4]}=1\) & \(m_{0}^{[4]}\) & \(m_{1}^{[4]}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: An example of an aggregated dataset \(B\) with only two binary features.  
Figure 1: An intuitive representation of the dataset aggregation step for a dataset with two binary features \(F_{1}\) and \(F_{2}\). Observations with, for example, \(F_{1}=0\) and \(F_{2}=0\) will be in bucket 1 in the aggregated dataset \(B\). Features with \(F_{1}=0\) and \(F_{2}=1\) in bucket 2 and so on.  
In fact, if \(p^{[i]}=0\), then \(TP^{[i]}=0\), and if \(p^{[i]}=1\), then \(TP^{[i]}=m_{1}^{[i]}\). Considering the entire dataset, the true positive, true negative (\(TN\)), false positive (\(FP\)), false negative (\(FN\)) are given by  
\[TP = \sum_{i=1}^{N_{B}}TP^{[i]}=\sum_{i=1}^{N_{B}}m_{1}^{[i]}p^{[i]} \tag{7}\] \[TN = \sum_{i=1}^{N_{B}}TN^{[i]}=\sum_{i=1}^{N_{B}}m_{0}^{[i]}(1-p^{[i]})\] (8) \[FP = \sum_{i=1}^{N_{B}}FP^{[i]}=\sum_{i=1}^{N_{B}}m_{0}^{[i]}p^{[i]}\] (9) \[FN = \sum_{i=1}^{N_{B}}FN^{[i]}=\sum_{i=1}^{N_{B}}m_{1}^{[i]}(1-p^{[i]}) \tag{10}\]  
where the sums are performed over all the \(N_{B}\) buckets.
## 2 Materials and Methods
Wavelengths of a maximum of 2.5 cm and a minimum of 1.7 cm were considered for the measurements and scaling process. Reflectivity is defined as the reduction in reflected power caused by the introduction of a material [16; 17; 18]. This power reduction is compared to a \"perfect\" reflection, which comes very close to the reflection of a flat metal plate. The antennas can be positioned anywhere on the arc to allow performance measurements with angles of incidence not normal to the sample. The vector network analyzer is used to provide both stimulus and measurement [19]. In the present case, considering that the aim is to evaluate the reflection of metal objects in free space, the calibration is performed by measuring the resulting power reflecting off a metal plate over a wide frequency range and then over the same frequency range on a radar absorbing material (ECCOSORB HPY-60, with a reflectivity of \(-\)50 dB). The latter measure will be the \"zero\" or 0 dB level (i.e., the reference level), considering the net of errors in the NRL measurement setup, in order to simulate a radio wave that is lost in space without encountering any reflecting body [20]. The material under test is then placed on the radar absorbing material (RAM) plate, and the reflected signal is measured in dB. The time-domain gate and anechoic panels are used to eliminate antenna cross-talk and clear the error otherwise introduced by room reflections as well as noise. Using this configuration, it is possible to characterize the properties of systems in different directions. The measurement system is based on Agilent 8571E software (material measurement) and the Agilent PNA-L N5230C vector analyzer. The antennas are Q-par Angus Ltd. and are active in the 12-18 GHz range. The sample rating was set at 512 points, with a power of \(-\)15 dBm and a 1 kHz bandwidth, and the TE polarization of antennas was considered. The measurements' reliability lies within the 2 dB range with respect to the reflection properties declared in the ECCOSORB datasheet. Measurements of the fabricated samples are then performed. The antennas are placed at a 45\({}^{\circ}\) angle with respect to the sample (Figure 1). Every measure has been smoothed with a polynomial (for CubeSat and cylinder) and a mobile average (for parallelepiped and parallelepiped with appendices) trend line for a better comprehension of the VNA response.
## 6 Discussion  
The MRDP method enables a simple analytical design of a PIDA controller while ensuring nearly ideal dynamics of setpoint and disturbance step responses. If the requirement is to ensure corresponding shapes of responses even for saturating control, its resulting controller transfer function can be modified by approximate factorization (inspired by [13; 43]) with neglect of the imaginary part of numerator zeros. A further increase in dynamics is possible with the help of PPM.  
Although the parallel and series structures yield the same transient responses under linear control, the responses under limited control are significantly different. The parallel PIDA control with traditional anti-windup solutions based on conditioning techniques [47] always result in overshoot [14], while the proposed modified solutions have no or negligible overshoot. As pointed out in the first articles dedicated to the performance portrait method [44], its advantages are particularly evident when other methods fail. However, the preliminary design of the controller using the modification of the MRDP method has significantly contributed to finding intervals for the controller parameters that allow for optimal control loop dynamics.  
From the point of view of calculating the optimal value of \(T_{i}\), the solved task represents a typical compromise in engineering applications. However, it should be noted that in order to study the effect of \(T_{i}\) in combination with a nonlinear saturation block (which is a special case of sectoral nonlinearity), the control loop must be transformed into a canonical equivalent circuit with saturation and a linear part [9; 53; 54; 55]. In such a case, however, different controller parameterizations correspond to different transfer functions of the linear part, which could explain the different behavior.
## 3 Results and Discussion
### Physical Adsorption of C\({}_{6}\)H\({}_{6}\) by Activated Carbon  
No physical adsorption configuration of C\({}_{6}\)H\({}_{6}\) at the edge of activated carbon was observed in this study, despite multiple attempts at geometric optimization. This suggests that the adsorption of C\({}_{6}\)H\({}_{6}\) at the edge of activated carbon is challenging to achieve.  
Figure 8 illustrates the adsorption configuration of C\({}_{6}\)H\({}_{6}\) on the activated carbon plane, revealing noticeable parallel-displaced \(\pi\)-\(\pi\) stacking interactions between C\({}_{6}\)H\({}_{6}\) and the activated carbon models. The distances from the center of C\({}_{6}\)H\({}_{6}\) to the marked C atom (as depicted in Figure 8) on NF, PD, and PR are 3.331a.u., 3.329a.u., and 3.371a.u., respectively. Consequently, it can be concluded that pyridine does not exert a significant influence on this distance while pyrrole functional groups lead to its increase. By comparing the electron density of the bond critical points numbered 1, 2, and 3 in Figure 8a-c, it is evident that the bond critical point formed by C\({}_{6}\)H\({}_{6}\) and PR has the lowest electron density, while the bond critical point formed by C\({}_{6}\)H\({}_{6}\) and PD demonstrates the highest electron density (excluding bond critical point 3 in PD). This implies that the presence of the pyridine functional group enhances the \(\pi\)-\(\pi\) stacking interaction between C\({}_{6}\)H\({}_{6}\) and C atoms connected to the marked C atom, whereas the pyrrole functional group diminishes this interaction. Regarding bond critical point 4, the electron density follows the order of PR \(>\) NF \(>\) PD. In other words, the pyrrole functional group strengthens interactions in proximity to bond critical point 4, while the pyridine functional group weakens them. According to the adsorption energy values given in Table 4, a comprehensive assessment can be made regarding the \(\pi\)-\(\pi\) stacking interaction between C\({}_{6}\)H\({}_{6}\) and activated carbon models. It is evident that C\({}_{6}\)H\({}_{6}\) exhibits similar adsorption energy values on PR and NF, indicating that pyrrole functional groups have minimal impact on the adsorption of C\({}_{6}\)H\({}_{6}\) onto the activated carbon plane. However, it is noteworthy that C\({}_{6}\)H\({}_{6}\) demonstrates a higher adsorption energy (\(-\)0.0379 eV) on PD, surpassing its value on NF by 0.01 eV. Hence, it can be inferred that pyridine functional groups weakly enhance the adsorption process of C\({}_{6}\)H\({}_{6}\) onto the activated carbon plane.  
Figure 8: IGMH analysis diagram depicting the adsorption of C\({}_{6}\)H\({}_{6}\) on different activated carbon surfaces: (**a**) NF plane, (**b**) PD plane, and (**c**) PR plane. Atoms are colored by 8G\({}^{\text{atom}}\). Bond critical points (orange spheres) and bond paths (brown lines) are also shown. Parts of bond critical points are labeled in red, while the electron density at these points is depicted in black.
## 2 Results and Discussion
### Post-Docking Analysis and Chemotype Selection  
We removed from the docking outputs (one pose saved for each fragment) the less stable tautomeric and ionization forms, as determined by Epik [41] (state penalty value \(\leq\) 0.6 kcal/mol). We removed duplicates from the merged outputs and ranked them by Gscore. Finally, we applied an aromatic interaction filter with Tyr308 (i.e., an aromatic ligand atom must be within 5 A from any heavy atom of the Tyr308 side chain), a key residue that, when mutated into asparagine or serine, inhibits the synthetic activity of the enzyme, and removed PAINS (pan-assay interference compounds) using the filters provided by Canvas [42,43] in order to exclude frequent hitters [44]. This work resulted in the selection of 30,126 and 30,960 fragments for the His312 and Hip312 grids, respectively. We visually inspected and assessed the top 1% of docked poses, identifying three recurrent chemotypes, i.e., benzimidazole, aminobenzic acid, and indole (for the calculated enrichment factors, see Supplementary Table S2) and three singletons (the best pose of representative fragments is shown in Figure 3 and Supplementary Figure S3). Aminobenzic acids emerged mainly from the Hip312 model and benzimidazoles mainly from the His312 model, while indoles emerged from both to a lesser extent.  
In order to maximize the chemical space explored, we performed a similarity search (Tanimoto index \(\geq\) 90%) using the PubChem database [45] and the representative structures of each chemotype as input. We applied the same screening workflow (see Supplementary Information) to the expanded set of fragments leading to the final selection of eighteen fragments for experimental validation (Figure 4).  
Prior to conducting biochemical assays, we assessed the docking poses stability by running molecular dynamics (MD) simulations. Starting from the best pose for each fragment we ran 100 ns simulations using Desmond [46] (NPT, T = 300 K, p = 1 atm, TIP3P [47], OPLS3e [48], dt = 2 fs). We considered the aromatic interaction with Tyr308 described above as the key feature to be maintained and monitored during the simulations. All the examined fragments form stable interactions with the residues involved in the binding of the GDP guanine ring in the X-ray structure, retaining, in particular, stable contact with the side chain of Tyr308, with the exception of fragments B1 and I2 that exit the binding pocket (Supplementary Figure S4).  
Figure 3: Best poses of representative structures of the three chemotypes selected for experimental validation. (**a**) aminobenzic acid **A3** docked in the Hip312 grid; (**b**) Benzimidazole **B2** docked in the His312 grid; (**c**) indole **I1** docked in the His312 grid. Fragments are shown as balls and sticks with green carbon atoms. The protein is shown in grey, with the side chain of Tyr308 highlighted.