esa-sceva/satcom-chunk-collection huggingface dataset:
# Whole-Body Motion Planning for a Six-Legged Robot Walking on Rugged Terrain
## 2 Methods
### Support Planning
#### 2.2.2 Torso Posture  
The so-called torso posture mainly refers to the inclination of the body in space, which can be expressed by yaw \(\alpha\), pitch \(\beta\) and roll \(\gamma\), respectively. Among them, the yaw \(\alpha\) is determined by the robot's moving direction, so the posture planning in this section is mainly the pitch \(\beta\) and roll \(\gamma\) of the torso. In order to obtain the target posture of the robot torso, the following steps are adopted:  
Step 1: Derive the target supporting polygon by fitting the target footholds and calculate the pitch \(\beta_{SP}\) and the roll \(\gamma_{SP}\) of the supporting polygon;  
Step 2: Calculate the desired pitch \(\beta_{d}\) and roll \(\gamma_{d}\) according to the following formula  
\[\left\{\begin{array}{l}\beta_{d}=0.5(\beta_{SP}+\beta_{a})\\ \gamma_{d}=0.5(\gamma_{SP}+\gamma_{a})\end{array}\right. \tag{3}\]  
where, \(\beta_{a}\) and \(\gamma_{a}\) are the current inclination parameters of the robot torso collected by the pose sensor.  
So far, we have obtained the initial and termination values of the six-dimensional motion of the robot torso. Since the torso is passive and has no active driving ability, its movement is completely propelled by supporting legs. Therefore, the torso motion needs to be transferred to the joint space of each supporting leg of the robot. For this purpose, \(N\) path points are collected from all directions of the torso, and then the path points of each supporting leg joint are obtained by means of kinematic transformation and calculation. Next, these path points are interpolated by cubic spline curve to obtain smooth joint trajectories. Let \(\theta_{1}^{j},\theta_{2}^{j},\cdots\theta_{N}^{j}\) be the corresponding path points of each supporting leg joint, where \(l\) is the number of supporting legs, \(j\) = 1, 2 and 3 are the three joints of a certain supporting leg, and \(N\) is the number of path points. For any joint \(j\) of a supporting leg \(l\), the cubic spline curve \(S\) is constructed to meet the path points and continuity conditions, namely:\[\left\{\begin{array}{ll}S(t_{i})=\theta_{i}^{lj},&i=1,2,\cdots N\\ \underset{t\to t_{i}}{\text{lim}}S(t)=S(t_{i}),&i=2,3,\cdots N-1\\ \underset{t\to t_{i}}{\text{lim}}S^{\prime}(t)=S^{\prime}(t_{i}),&i=2,3,\cdots N -1\\ \underset{t\to t_{i}}{\text{lim}}S^{\prime}(t)=S^{\prime}(t_{i}),&i=2,3,\cdots N -1\\ \underset{t\to t_{i}}{\text{lim}}S^{\prime}(t)=S^{\prime}(t_{i}),&i=2,3,\cdots N -1\\ \end{array}\right. \tag{4}\]  
where \(t_{i}\) is the motion time variable corresponding to each path point. In addition, in order to solve the equation, the boundary conditions are further set up:  
\[\left\{\begin{array}{ll}S^{\prime}(t_{1})=0\\ S^{\prime}(t_{N})=0\\ \end{array}\right. \tag{5}\]  
With a total of \(4(N-1)\) boundary conditions, the unique joint interpolation trajectories can be obtained.
## 3 Methodology and Materials
### Applying with Attention Mechanisms
#### 3.2.2 Applying Self-Attention with Novel Cycling Layer
The design goal of the cycling layer is to encode these timestamps to make the cyclical information explicit and usable by the model. The cycling position features are the cornerstone of the cycling layer's functionality. They are derived from the radian-converted timestamps using sine and cosine functions, creating a pair of values for each point in time. This duality allows the model to capture the cyclical nature of time, ensuring that it recognizes the continuity at the cycle's boundaries--such as the transition from the end of one day to the beginning of the next. The sine and cosine values are concatenated along the tensor's last dimension, effectively doubling this dimension's size. This concatenation preserves the original timestamp information while augmenting it with cyclical encoding, providing a dual representation of linear time and its inherent cycles. Figure 1: Difference between the positional layer and cycling layer: in the positional layer, the arrows show that the attention trend is based on mathematical properties and focuses on subsequent directions that are not fixed; in the cycling layer, the arrows reveal a periodic pattern in finding the next direction of focus. The color intensity reflects the weight of attention given to each sequence. The final step in the cycling layer's process is concatenating the original features with these newly created cyclical position features. The result is a combined feature vector that retains all information from the original data enriched with a clear, cyclical context. This enriched representation is then fed into the self-attention mechanism, which can now take advantage of the cyclical patterns alongside the raw data features.
## 4 Experimental Validation
### Data Verification  
In order to further verify the broad validity of the damage index. The damage index of the randomly acquired damage continuous image is extracted. Additionally, the fitting relationship is established, as show in Figure 10.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Damage Index** & **Texture Characteristics** \\ \hline ASM & Image texture width \\ CLS & Image texture uniformity \\ \hline \hline \end{tabular}
\end{table}
Table 6: Texture characteristics of damage indicators.  
Figure 10: _Cont._  
There is a specify positive correlation between ASM and the development trend of injury. Additionally, CLS is identify negatively correlated with the development of fatigue damage. CLS and ASM have the same trend and fantastic stability after comparison with multiple experimental images. The verification results show that the CLS and ASM can used as indicators of damage sensitivity characteristics of crack damage monitoring. This indicator can comprehensively monitor the damage status of cracks and accurately predict the health trend of the structure.
## 5 Conclusions  
The COVID-19 pandemic led to the closure of traditional face-to-face teaching institutions and the rise of the online education system. Although online education serves as the backbone of education during the pandemic, its effectiveness and suitability have serious concerns from stakeholders such as parents, teachers, and students. For this reason, such concerns must be analyzed to find the problems faced by students and suggest modifications to utilize the full potential of online education. This study investigates the effectiveness of online education by analyzing the sentiments of its stakeholders' using social media data. The dataset used in this study has been obtained by the Twitter API using the keywords related to the topic. Various text preprocessing methods, such as stemming, normalization, tokenization, and stop words removal, etc., have been used to clean the tweets. Afterwards, lexicon-based approaches have been used to find the sentiments and label tweets. Two feature engineering techniques BoW and TD-IDF are used to classify positive, negative, and neutral reviews using several machine learning algorithms. Results indicate that using the data balancing with SMOTE enhances the classification accuracy. DT, SVM, and RF perform very well and achieved an accuracy of 0.95 using Bow and SMOTE, while SVM achieves 0.95 accuracy using TF-IDF with SMOTE. VADER and SentiWordNet techniques are also used for performance comparison with TextBlob, and results indicate that TextBlob shows superior results for data annotation as compared to VADER and SentiWordNet. Deep learning models are used in comparison with machine learning models, and results suggest the superior performance of machine learning models, primarily due to the small size of the dataset. Topic modeling through LSA suggests that the uncertainty of opening date institutions is among the most concerning topics for students. Additionally, lack of technical skills and network challenges in rural areas are major concerns for the students.  
Conceptualization, M.M. and F.R.; Data curation, E.L. and F.R.; Formal analysis, M.M. and P.B.W.; Funding acquisition, E.L.; Investigation, P.B.W. and F.R.; Methodology, E.L. and F.R.; Resources, S.U. and A.A.R.; Software, P.B.W. and S.U.; Supervision, M.M. and I.A.; Validation, A.A.R.; Visualization, S.U. and I.A.; Writing--review and editing, I.A. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Florida Center for Advanced Analytics and Data Science funded by Ernesto.Net (under the Algorithms for Good Grant).  
Not applicable.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
## 3 Results and Discussion
### Monostatic and Multistatic Radar Application for Material and Structure Recognition  
One of the project hypotheses declares that the multistatic radar has to have advantages over the monostatic radar in object material and structure recognition with AI. This topic was studied, and is described in detail in [29; 30]. Outcomes summary:  
* The object detection accuracy was worst in the case of the monostatic radar [29];
* In the case of the multistatic radar, the detection accuracy increased by 6% in comparison to monostatic or bistatic radar cases;
* Switching from monostatic to multistatic radar increases the detection accuracy for a variety of tested NNs and for simple NN architectures, and reduces the mistakenly classified object count up to four times [30].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Represent.** & **SNR** & **Error in Prediction \(\times\) 10\({}^{-3}\)** & **Data Used** \\ \hline PCA & 20 & 0.71 \(\pm\) 0.01 & \\ PCA & 10 & 1.03 \(\pm\) 0.01 & Both \\ (\(\epsilon_{r}\)) & 6.67 & 2.84 \(\pm\) 0.02 & training \\  & 5 & 10.19 \(\pm\) 0.09 & and \\ \hline PCA & 20 & 0.09 \(\pm\) 0.5\({}^{-3}\) & evaluation \\ PCA & 10 & 0.13 \(\pm\) 0.9\({}^{-3}\) & on data \\ (\(tan\delta\)) & 6.67 & 0.28 \(\pm\) 1.2\({}^{-3}\) & with noise \\  & 5 & 0.74 \(\pm\) 2.4\({}^{-3}\) & \\ \hline PCA & 20 & 122.73 \(\pm\) 21.14 & Training \\ PCA & 10 & 148.93 \(\pm\) 25.81 & on data \\ (\(\epsilon_{r}\)) & 6.67 & 229.98 \(\pm\) 55.51 & without \\  & 5 & 772.45 \(\pm\) 195.42 & added noise, \\ \hline PCA & 20 & 5.82 \(\pm\) 0.09 & evaluating \\ PCA & 10 & 7.55 \(\pm\) 0.13 & only on data \\ (\(tan\delta\)) & 6.67 & 10.43 \(\pm\) 0.27 & with noise \\  & 5 & 18.87 \(\pm\) 0.41 & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Parameter estimation error with noise added to the generator signal.  
Figure 9: Dielectric loss estimation of data with different noise levels.  
These findings can by explained by additional information carried in signals that have been passed through or scattered from objects [29].
## 3 Popular ANN Architectures Employed for Time Series Forecasting Purposes
### Radial Basis Function Networks  
Radial basis function networks (RBFNs) are based on function approximation theory. RBFNs were first formulated by [PERSON] and [PERSON] [42]. We outlined in Section 3.1 how FFNNs with sigmoid activation functions (one hidden layer) can approximate functions. RBFNs are slightly different from FFNNs, but they are also capable of universal approximation [43]. In principle, FFNNs arise from the need to classify data points (clustering), while RBFNs rely on the idea of interpolating data points (similarity analysis). An RBFN has a three-layer structure, similar to the structure of an FFNN. The difference lies in the implementation of a Gaussian function instead of a sigmoid activation function in the hidden layer of the RBFN for every neuron. These Gaussian functions are also called _radial basis functions_, because their output value depends only on the distance between the function's argument and a fixed center.  
In order to understand the training process of an RBFN, let us recap the concept of _exact interpolation_, mentioned earlier in Section 3.1.2. Given a multidimensional space \(D\), the exact interpolation of a set of \(N\) data points requires that the dimensional input vectors \(\vec{x}^{(p)}=\langle x_{1}^{(p)},\ldots,x_{D}^{(p)}\rangle\) will be mapped to the corresponding target output \(t^{(p)}\)\(\forall p=1,\ldots,N\). The objective is to propose a function \(f(x)\) such that \(f(\vec{x}^{(p)})=t^{(p)}\). The _naive_ radial basis function method uses a set of basis functions \(N\) of the form \(\phi(\|\vec{x}-\vec{x}^{(p)}\|)\), where \(\phi(\cdot)\) is a nonlinear function. A linear combination of the basis functions \(f(\vec{x})=\sum_{p=1}^{N}w_{p}\phi(\|\vec{x}-\vec{x}^{(p)}\|)\) can be obtained as a result of the mapping, for which it is required to find the \"weights\" \(w_{p}\) such that the function passes through the data points. The most famous and recommended basis function is the Gaussian function:  
\[\phi(r)=\exp\left(-\frac{r^{2}}{2\sigma^{2}}\right) \tag{6}\]  
with width parameter \(\sigma>0\). Figure 2 shows an RBFN under this naive approach. Please observe that, in this architecture, the \(N\) input patterns \(\{\vec{x}^{(p)},p=1,\ldots,N\}\) determine the input to the hidden layer weights directly.  
Figure 2: Radial basis function network under the naïve radial basis function approach.  
There are problems with the exact interpolation (naive radial basis function) approach. First, when the data are noisy, it is not desirable for the network outputs to pass through all data points because the resulting function could be highly oscillatory and would not provide adequate generalization. Second, if the training dataset is very large, the RBFN will not be computationally efficient to evaluate if we employ one basis function for every training data point.
# Methods and Applications of Space Understanding in Indoor Environment--A Decade Survey
## 2 Review Methodology and Conduction
### Research Questions (RQ)  
The main goal of this study was to create an overview of the room segmentation and classification methods that could be easily visualized. Questions we raised in this section were formulated to organize the results into a set of taxonomy diagrams. Each diagram represents knowledge gathered from answering one of the questions asked. To make the taxonomies cover a possibly wide range of solutions, they had to be generic enough to cover many possible relevant answers. At the same time, the questions had to be precisely formulated so as not to include too many papers unrelated to the topic.  
**RQ1: What input data structures are in use?** The approach chosen for the entire survey was to be primarily data-driven. It created the need for a list of input data structures, which are typically available and used in room segmentation and classification tasks. We expected to find data structures of multiple dimensions, such as 2D-floor plan images or 3D point cloud models. Additional subtype divisions were specified as needed.  
**RQ2: What is the high-level abstraction category of the performed process?** After identifying the input data structure, we separated different classes of solutions. Found methodologies proved to be highly diverse and incomparable between one another without additional grouping. We included instance segmentation or multi-class classification to the expected categories.  
**RQ3: What is the accomplished task?** The third taxonomy was dedicated to the actual practical application of the analyzed methodology. We expected the same category of performed process to be used in multiple, often very different types of tasks, like 3D model reconstruction, floor plan prediction, or robot localization.  
We answered all three of the stated research questions for each of the papers found during the conducted survey. This way, the preparation of the taxonomies and proper paper classification was faster and more likely to be truly objective. Gathered research papers were automatically organized by the answers given, going top to bottom by (1) input data type, (2) solution category, and (3) implemented task.
## 2 Preliminaries  
### Graph Construction  
The construction of the association graph is the process of extracting the original numerical and feature information and converting it into a graph, which includes the relationship between each node and the data characteristics of each node [25]. The constructed graph structure determines the performance of the model.  
Let G(V, E) represent a graph, V represent a node in the graph, and E represent an edge in the graph. Generally, a sample of the original data is regarded as a node, and the characteristics of the nodes in the graph are defined by the sample characteristics. Adjacency matrix \(A\) is used to represent the structural information between nodes. It contains zero and one, which are expressed as follows:  
\[A_{ij}=\left\{\begin{array}{ll}1&\quad\text{if }v_{i}\ \rhd\v_{j}\\ 0&\text{if not }v_{i}\ \rhd\v_{j}\end{array}\right. \tag{1}\]  
where \(v_{i}\ \rhd\v_{j}\) indicates that \(v_{i}\) and \(v_{j}\) are connected.  
To provide accurate information for the subsequent model, nodes of the same category in the graph should be connected. Nodes of the same category often have high similarity; therefore, common graph construction methods calculate the similarity between every two nodes and determine whether the nodes are connected by an edge. Among these methods, the KNN graph construction method is one of the most common. Its principle is to connect the k nodes most similar to the central node. The similarity between nodes can be represented by the Euclidean distance, as expressed by Equation (2):  
\[D\big{(}v_{i},v_{j}\big{)}=\sqrt{\sum_{l=1}^{n}\big{(}v_{i}^{l}-v_{j}^{l}\big{)}^{ 2}} \tag{2}\]  
where \(D\big{(}v_{i},v_{j}\big{)}\) represents the Euclidean distance between \(v_{i}\) and \(v_{j}\), n represents the number of all features of the node, and \(v_{i}^{l}\) and \(v_{j}^{l}\) represent the l-th feature of \(v_{i}\) and \(v_{j}\), respectively. If \(i\) and \(j\) satisfy Equation (3) or (4),  
\[D_{ij} =\underset{k}{\text{min}}D_{i} \tag{3}\] \[D_{ij} =\underset{k}{\text{min}}D_{j} \tag{4}\]  
the adjacency matrix can be expressed as  
\[A_{ij}=1 \tag{5}\]  
where \(A_{ij}\) indicates the connection status of the edge between \(v_{i}\) and \(v_{j}\) at row i and column j of the adjacency matrix; \(D_{ij}\) is the Euclidean distance between \(v_{i}\) and \(v_{j}\); and \(\underset{k}{\text{min}}D_{i}\) denotes the top-k smallest Euclidean distances between \(v_{i}\) and all other nodes.
# Fault Detection and VSC-HVDC Network Dynamics Analysis for the Faults in Its Host AC Networks
## 4 Performance Analysis
### Effect of Fault Inception  
The performance of many power system protection algorithms is affected due to changes in the fault inception time. When a fault was at the zero-crossing point, then it was observed that it introduced more transients in the current signal in comparison with the fault at a peak crossing fault. The validation of this statement was tested using the proposed method. To conduct this study, a three-phase (ABC) fault was first created at a zero-crossing instant (2.530 s) for an R\({}_{\text{f}}\) value of 10 \(\Omega\) and then created at location F\({}_{1}\). Similarly, the ABC fault was created at (2.546 s) with a 20 \(\Omega\) fault resistance at location F\({}_{1}\). The load angles were set to 120\({}^{\circ}\) and 130\({}^{\circ}\) for zero and peak crossing, respectively. Figure 10 shows the current and its corresponding energy indices for both cases. From the DTE index, a gradual increase in the DTE for the peak crossing fault was observed, while for the zero crossing, there was an immediate rise in the DTE. The DTE index crossed the threshold in 2 ms for the peak crossing fault, while it took 1.3 ms to cross the threshold for the zero-crossing fault. Therefore, the results provided by the proposed method abided by the previous statement. Thus, a reliable decision can be made for the relay.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Fault Type**} & \multicolumn{3}{c}{**HHT**} & \multicolumn{2}{c}{**SST**} \\ \cline{2-6}  & **Location** & **DTE (p.u.)** & **Time (ms)** & **DTE (p.u.)** & **Time (ms)** \\ \hline AG & & 19.7 & 8.62 & 9.7 & 4.25 \\ \hline ABG & & 26.0 & 7.57 & 16.5 & 3.28 \\ \hline AB & & 38.23 & 5.32 & 32.5 & 1.25 \\ \hline ABC & & 44.0 & 4.95 & 42.0 & 1.30 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Detection time computation.  
Figure 9: TFRs obtained for ABC fault (**a**) using HHT and (**b**) using SST.
## 3 Performance Predictions of Cement-Eggshell Powder Binary System
### Evaluation of Long-Term Hydration Heat and Long-Term Hydration Degree  
After obtaining the values of parameters of the hydration model (shown in Table 1), we can calculate the long-term hydration heat and long-term hydration degree. The calculation results of the long-term hydration heat are shown in Figure 2a. At 28 days age, for the specimens with 0%, 7.5%, and 15% eggshell powder replacement, the hydration heat based on each gram of cement is 402.69, 426.88, and 446.73 J/g cement, respectively. As the eggshell powder replacement increases, we can see that the heat release based on unit mass of cement increases. This is because the physical effects of eggshell powder, namely the dilution effect and nucleation effect, accelerate the hydration reaction of cement [5]. Figure 2b shows the calculation results of the long-term hydration degree. At 28 days age, for the specimens with 0%, 7.5%, and 15% eggshell powder replacement, the cement hydration degree is 0.832, 0.882, and 0.923, respectively. The development trend of the hydration degree is similar to that of the hydration heat. In the early stage, before about 200 h, the hydration degree increased rapidly. After 200 h, the hydration degree entered a plateau period and the growth rate became slow. At the later stage of the reaction, 28 days, the hydration degree almost stopped with the increase in age. This shows that the compressive strength test age to measure Portland cement concrete based on 28 days of age is roughly reasonable. Figure 2c shows the calculation results of long-term hydration heat based on 1 g binder. At 28 days of age, for specimens with 0%, 7.5%, and 15% eggshell powder substitution, the hydration heat based on each gram of binder is 402.69, 394.86, and 379.72 J/g binder, respectively. When the hydration heat is expressed as per gram of binder, the cumulative hydration heat of 28 days decreases with the increase in eggshell powder substitution. This is because in the later stage of hydration, the dilution effect of eggshell powder plays a dominant role, reducing the cumulative hydration heat [5]. While nucleation increases the cumulative heat of hydration per gram of cement (Figure 2a), dilution decreases the heat of hydration per gram of binder (Figure 2c).