esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Proposed Methods
### Reasoning-Based Scheduling Method  
According to the coupling relationship between subsystems, the target selection strategy for satellites in different coupling states is different. Therefore, the scheduling framework constructed in this paper consisted of three parts: (1) satellite state prediction based on the satellite's initial state and the distribution of targets and ground stations; (2) rule-based reasoning using satellite state prediction results and obtain the targets selection strategy; (3) the observation and data transmission scheduling according to the selected target selection strategy.
## 2 Methods
### Estimator  
For computational purposes, the estimator of the areas where the accuracy of the solution would benefit more to have smaller elements should be cheap to compute. We use a straightforward local estimator based on [34], although other good alternatives are [35; 36; 37]. We compute the estimator individually for each element \(m\) with a _volumetric_ residual \(\mathcal{R}_{\text{Vol}}^{(m)}\), defined through \[\mathcal{R}_{\text{vol}}^{(m)}=\mathbf{\
abla}\times\mu_{r}^{-1}(\mathbf{\
abla}\times\mathbf{ E}_{\text{FEM}}^{(m)})-k_{0}^{2}\epsilon_{r}\mathbf{E}_{\text{FEM}}^{(m)}-\mathbf{F}, \tag{9}\]  
and a _face_ residual \(\mathcal{R}_{\text{face}}^{(m)}\) that changes if a boundary condition is present in that face. Thus, we define the residuals \(\mathcal{R}_{\text{D}}\), \(\mathcal{R}_{\text{N}}\), and \(\mathcal{R}_{\text{C}}\) for the Dirichlet, Neumann, and Cauchy boundary conditions, respectively, as  
\[\mathcal{R}_{\text{D}}^{(m)}=\mathbf{\hat{n}}^{(m)}\times(\mathbf{E}_{ \text{FEM}}^{(m)}\times\mathbf{\hat{n}}^{(m)})-\mathbf{\
abla}_{\text{D}},\] on \[\Gamma_{\text{D}}\], (10a) \[\mathcal{R}_{\text{N}}^{(m)}=\mathbf{\hat{n}}^{(m)}\times\mu_{r}^{-1} (\mathbf{\
abla}\times\mathbf{E}_{\text{FEM}}^{(m)})-\mathbf{\
abla}_{\text{N}},\] on \[\Gamma_{\text{N}}\], (10b) \[\mathcal{R}_{\text{C}}^{(m)}=\mathbf{\hat{n}}\times\mu_{r}^{-1}(\mathbf{ \
abla}\times\mathbf{E}_{\text{FEM}}^{(m)})-jk_{0}\mathbf{\hat{n}}^{(m)}\times(\mathbf{E} _{\text{FEM}}^{(m)}\times\mathbf{\hat{n}}^{(m)})-\mathbf{\
abla}_{\text{C}},\] on \[\Gamma_{\text{C}}\]. (10c)  
We also use the tangential continuity of the magnetic field (not imposed explicitly) as the face residual \(\mathcal{R}_{\text{neigh}}\) for faces that belong to both elements \(m\) and \(n\), i.e.,  
\[\mathcal{R}_{\text{neigh}}^{(m)}=\mathbf{\hat{n}}^{(m)}\times\mu_{r}^{-1}(\mathbf{ \
abla}\times\mathbf{E}_{\text{FEM}}^{(m)})+\mathbf{\hat{n}}^{(n)}\times\mu_{r}^{-1} (\mathbf{\
abla}\times\mathbf{E}_{\text{FEM}}^{(n)}), \tag{11}\]  
so \(\mathcal{R}_{\text{face}}^{(m)}=\mathcal{R}_{\text{D}}^{(m)}\cup\mathcal{R}_{ \text{N}}^{(m)}\cup\mathcal{R}_{\text{C}}^{(m)}\cup\mathcal{R}_{\text{neigh}}^ {(m)}\) for each face in the \(m\)-th element.  
Adding up all the residuals, we introduce the residual for each element \(m\), which is introduced through  
\[\mathcal{R}^{(m)}=h^{(m)}\Big{(}\mathcal{R}_{\text{vol}}^{(m)},\mathcal{R}_{ \text{vol}}^{(m)}\Big{)}_{m}+\sum_{k}^{5}K_{k}h_{k}^{(m)}\Big{\langle}\mathcal{ R}_{\text{face,$k$'}}^{(m)}\mathcal{R}_{\text{face,$k$}}^{(m)}\Big{\rangle}_{k}, \tag{12}\]  
where \(K_{k}\) is \(\frac{1}{2}\) and \(1\) for triangular and rectangular faces, respectively. Moreover, \(h\) is the diameter of the entity (volume or face). Note that the sesquilinear forms are local to the element \(m\) or a given face \(k\).
## 2 Problem Description and Modeling
### SEC Network  
The SEC network is depicted in Figure 2a; \(n\) satellites are represented as \(\mathbf{S}=\{\mathrm{s}_{i},\,i\in\mathbb{N}_{n}\}\), which consists of \(Z_{o}\) adjacent orbital planes with \(Z_{s}\) satellites in each orbital plane, and we have \(n=Z_{o}\times Z_{s}\). Each satellite is equipped with an edge server for executing tasks, and edge servers are represented by \(\mathbf{U}=\{u_{k},\,k\in\mathbb{N}_{n}\}\).  
Furthermore, satellites are continuously connected to their four adjacent satellites via ISLs [46], which comprise the two intra-plane satellites and the two inter-plane satellites. As illustrated in Figure 2b, satellite \(\mathrm{s}_{5}\) is connected to satellites \(\mathrm{s}_{2}\) and \(\mathrm{s}_{8}\) through intra-plane ISLs (represented in orange), while inter-plane ISLs (represented in green) connect satellites \(\mathrm{s}_{4}\) and \(\mathrm{s}_{6}\) to \(\mathrm{s}_{5}\).  
The length of the ISLs are continuously changing as satellites move along their orbits. To model the SEC network accurately, we derived an approximate formula detailed in the supplementary file [47], by which the ISL distance \(l_{i,j}^{a}\) between satellites \(s_{i}\) and \(s_{j}\) at time \(a\) can be obtained based on the satellite orbit elements. Specially, if no ISL exists between  
\begin{table}
\begin{tabular}{l l} \hline \hline  & \multicolumn{2}{c}{**Solution Components**} \\ \hline \(\theta=\{\theta_{1},\,\theta_{2},\,\ldots,\,\theta_{n}\}\) & Task assignments for all edge servers. \\ \hline \(\Delta=\{\aleph;\,\Upsilon\}\) & Individual of MOWPS, where \(\aleph\) implies the execution sequence of tasks and \(\Upsilon\) represents assignment results. \\ \hline \(\Psi_{all}\) & Set of individuals. \\ \hline \(\Psi_{nd}\) & Set of nondominated individuals. \\ \hline \(N_{p}\) & Number of individuals in a population. \\ \hline \((N,M_{0},\,\theta)\) & Petri net amended based on solution \(\theta\). \\ \hline \(\pi_{\Delta}\) & Transition sequence extracted from \(\Delta\). \\ \hline \(\Psi_{\epsilon}\) & Set of elite individuals. \\ \hline \(\phi\) & Strengthened dominance relation sort. \\ \hline \(\xi\), & Proportion of elite individuals. \\ \hline \(\varepsilon\) & Proportion of extracted individuals. \\ \hline \(P_{reserve}\) & Probability of retaining elements. \\ \hline \(P_{bias}\) & Probability of biased selection. \\ \hline \(\varphi_{i}\) & Utility value for Lamarckian learning method. \\ \hline \(K_{max}\) & Maximum number of iterations. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Notations.  
Figure 2: (**a**) An SEC network with 36 satellites; (**b**) example of ISL connections.  
and \(s_{j}\), we set \(I_{i,j}^{a}=\infty\). Then, the communicate topology of satellites at time \(a\) is represented by a \(n\times n\) matrix \(L_{a}\), where \(L_{a}[i,j]=I_{i,j}^{a}\).
# Use of Wearable Sensor Technology in Gait, Balance, and Range of Motion Analysis
## 6 Discussion
### Biofeedback  
Researchers have used objective measurements extracted from wearable sensors to provide biofeedback [23; 26]. Biofeedback information can be provided visually, auditorily, and/or tactiely. Visual biofeedback can be difficult when using wearable devices for assessment. However, using smart devices this issue can be addressed since most of the smart devices provide small and portable screens. Additionally, auditory biofeedback can be implemented in such devices by using earphones, adding the capability of having both types of feedback occurring at the same time. This dual feedback can be used with one portable device and can be very beneficial for patients who benefit from feedback, such as those with Parkinson's disease [23; 65]. On the other hand, tactile biofeedback systems are designed to provide stimulation to the surface of the skin with electrical signals or vibrations [26]. Tactile biofeedback is not recommended since applying such stimulations can be obtrusive and it can affect subject performance during the assessment; particularly, if they are performing gait, balance or other functional tasks.
# Applying Automatic Translation for Optical Music Recognition's Encoding Step
## 3 Experimental Setup
### Translating Monodic Staves
#### 3.2.2 Ambiguous Translation Cases  
The translation of the key signature is a challenge in itself for machine learning models, as they have to discriminate when a sharp or a flat is part of a key signature and when it is not. The models must learn that accidentals that are part of a key signature must be all of the same type (sharp or flats), and must be written in a specific order. In addition, they must learn which notes on the staff are affected by the key signature. When a note altered by an accidental appears next to the key signature, it can lead to ambiguous cases where the models (and even humans, in some cases), cannot tell whether the accidental preceding the note is part of the key signature or not. In general, a musician would use information from a broader context than the current staff to tell whether the accidental is part of the key (for example, the key signature found in previous staves). However, in this experimental setup, input instances consist of isolated staves, without song context, which makes it more difficult for the models to correctly translate what is related to a key signature in those cases.  
Figure 7 presents such situations. Figure 7a,b shows examples of ambiguous situations where even a human, without a larger context, would struggle to decide whether the accidental next to the note is part of the key signature or not. The other three cases exemplify situations where the models must learn to apply the key signature definition rules mentioned in the previous paragraph, and consider the accidental next to the note as not part of the key signature. These ambiguous cases are seldom found in our corpora. They are present in 0.92% of samples in FMT and 5% of Zaragoza samples. The Camera-PrIMuScorpus does not contain any of these cases, as its samples are synthetic and have been built with a meter sign between the key signature and the beginning of the first measure. Despite having so few cases in our corpora, it is interesting to know how trained models deal with these rare events.  
Figure 7: **(a,b)** Examples of ambiguous key signatures. **(c–e)** Cases where key signature definition rules must be applied to consider the accidental next to the note as not part of the key signature.  
The presence of staves with absent clef and key in the FMT-C dataset, as discussed in Section 3.1, could also be considered as ambiguous cases that models will have to struggle with, where only 25.9% of the staves in that dataset contain clef and key signature symbols.
# A Method of Discriminating Between Power Swings and Faults Based on Principal Component Analysis
## 3 Power Swing Blocking Method Using PCA
### Criterion for PSB and PSD Function  
Suppose that the instantaneous values of the three-phase voltage at time \(t\) are \(u_{\rm A}(t)\), \(u_{\rm B}(t)\), and \(u_{\rm C}(t)\). Based on the expressions of \(\xi_{1}\) and \(\xi_{2}\) in section A of this chapter, the coordinates of the three-phase voltage at this moment in \(XOY_{\rm U}\) can be calculated as follows:  
\[\left\{\begin{array}{l}x_{\rm U}=\frac{\sqrt{2}}{2}[u_{\rm C}(t)-u_{\rm A}(t )]\\ y_{\rm U}=\frac{\sqrt{6}}{6}[2u_{\rm B}(t)-u_{\rm A}(t)-u_{\rm C}(t)]\end{array}\right. \tag{17}\]  
where \(x_{\rm U}\) and \(y_{\rm U}\) represent the abscissa and ordinate, respectively.  
Define \(C\) as follows:  
\[C=m\Big{(}x_{\rm U}^{2}+y_{\rm U}^{2}\Big{)} \tag{18}\]  
where \(m\) is a coefficient which makes \(C\) equal to 100 during normal operation, and it can be calculated as \(200/\big{(}3\ M^{2}\big{)}\) in advance, according to (16).  
As the above analysis shows, the value of \(C\) reduces to a small value within a short time after a three-phase shorting fault occurs, but it changes slowly during a power swing. Therefore, by comparing the threshold value with the value of \(C\), the three-phase shorting  
Figure 2: Projection trajectories under different disturbances. (**a**) Three-phase shorting fault; (**b**) power swing.  
fault and the power swing can be discriminated. The criterion for the PSB function is as follows:  
\[C_{\rm avr}>C_{\rm set} \tag{19}\]  
where \(C_{\rm set}\) is the threshold, and \(C_{\rm avr}\) is the average value of \(C\), corresponding to three sampling points after a half-cycle delay. If the calculated result satisfies (19), the disturbance should not be regarded as a fault, and the protection relay should be blocked.  
Considering the two tasks of the PSBU, another criterion for the PSD function is also needed. Based on the above analysis, the change rate of \(C\) can be used to detect most faults under a power swing. However, in some special cases, the effect of using the change rate of \(C\) is not good. For the following case under consideration, the fault occurs at the oscillation center, whose voltage amplitude becomes close to 0 when the fault occurs. At this moment, there is no sudden change in the voltage amplitude, nor in the value of \(C\) shown in Figure 3.  
Therefore, in order to detect a three-phase shorting fault during a power swing more reliably, another index is proposed here. Similarly, the current sampling data are processed by using PCA to obtain the coordinates, denoted by \(x_{\rm I}\) and \(y_{\rm I}\). The index \(P_{\rm UI}(k)\) is defined as follows:  
\[P_{\rm UI}(k)=x_{\rm U}(k)x_{\rm I}(k)+y_{\rm U}(k)y_{\rm I}(k) \tag{20}\]  
The criterion for the PSD function is as follows:  
\[\Delta P=|P_{\rm UI}(k)-P_{\rm UI}(k-1)|>P_{\rm set} \tag{21}\]  
where \(P_{\rm set}\) is the threshold. If (21) is satisfied, the PSBU will deblock the protection relay.
# Experimental Study on Multi-Cell Counting Using an Inertial Microfluidic Device
## 2 Materials and Methods
### Experimental Parameters  
The experimental design in this study was meticulously crafted to assess the counting efficiency of microparticles within a microfluidic chip under various conditions. Key parameters, such as channel dimensions, flow rates, and particle concentrations, were systematically altered to investigate their effects on particle behavior and sorting efficiency. The design aimed to simulate physiological conditions and provide insights into the optimal configurations for particle separation.
## 2 Materials and Methods
### Model Validation
These outliers significantly impact the CV(RMSE) value. R\({}^{2}\) is a metric with a limited capacity to evaluate the model comprehensively. It assesses the overall model fit relative to variability, but a high R\({}^{2}\) value does not guarantee accuracy, as it may be misleading in the presence of systematic errors or overfitting. Moreover, R\({}^{2}\) does not provide information about the actual magnitude of errors, which is crucial for practical applications. While these metrics are effective for smaller datasets, their interpretation becomes more complex at the national scale. Although the primary objective is to calculate energy performance for large numbers of buildings rather than to represent each individual building precisely, the data are presented both at the individual building level and aggregated into groups of 100 buildings. This dual approach ensures that the model functions well for building groups without masking potential errors in specific building types or regions. Since no single metric is perfect, several are evaluated, and the graphs are analyzed so that the metrics complement each other and allow for an appropriate interpretation of the performance of the generated model. Big data models often use data partitioning for validation. This technique enables developers to train the model on one subset, validate its performance on another, and assess its generalization ability on unseen data. By partitioning, models can effectively address the challenges posed by the size and complexity of Big Data, ensuring the model does not overfit to the training data. To avoid validation biases caused by partitions that fail to adequately reflect geographic and climatic diversity, a 10-fold cross-validation approach was adopted, reducing the risk of fitting too closely to the training set. This method ensures that all building types, climates, and other determining factors are evaluated. Since cadastral data are organized by region, the entire dataset was randomly shuffled before performing the cross-validation to minimize potential biases. These cross-validation strategies, combined with the use of multiple metrics and visualizations, provide a more comprehensive approach to addressing the inherent limitations of each metric, thereby increasing confidence in the model's performance. Despite the challenges of working with large datasets and multiple building types, this methodological approach offers a reliable representation of energy predictions at both aggregate and individual building levels. To evaluate the model, all available data were used, covering the 1,246,864 residential buildings. The NMBE, CV(RMSE), and R\({}^{2}\) values were obtained for both individual buildings and aggregated buildings, along with figures showing the relationship between EPC values and the predictions. The results of the model validation are presented in Section 3.2, while a specific case study predicting data for Madrid, a region excluded from the training dataset, is detailed in Section 3.3.2.
## 4 Results and Discussion  
### Incompressible Taylor-Green Vortex  
The Taylor-Green vortex (TGV) [52] is a canonical three-dimensional flow problem which contains transition to anisotropic small-scale turbulence and subsequent decay [50]. The TGV problem is simulated in a triple periodic cube \(\Omega=[0,2\pi)^{3}\), starting from the initial condition as follows:  
\[\rho =\rho_{0}\,,\] \[u =V_{0}sin\Big{(}\frac{x}{L}\Big{)}cos\Big{(}\frac{y}{L}\Big{)}cos \Big{(}\frac{z}{L}\Big{)}\,,\] \[v =-V_{0}cos\Big{(}\frac{x}{L}\Big{)}sin\Big{(}\frac{y}{L}\Big{)} cos\Big{(}\frac{z}{L}\Big{)}\,, \tag{49}\] \[w =0\,,\] \[p =p_{0}+\frac{\rho_{0}V_{0}^{2}}{16}\left(cos\Big{(}\frac{2x}{L} \Big{)}+cos\Big{(}\frac{2y}{L}\Big{)}\right)\left(cos\Big{(}\frac{2z}{L}\Big{)} +2\right)\,,\]  
where \(\rho\), \((u,v,w)\) and \(p\) denote density, velocity vector and pressure, respectively, \(\rho_{0}\), \(V_{0}\) and \(L\) are reference density, velocity and length and are all set to 1.0. The characteristic convective time is defined as \(t_{c}=L/V_{0}\). The physical duration of the computation is set to \(t_{final}=20t_{c}\). The initial Reynolds number is defined as \(Re_{0}=\rho_{0}V_{0}L/\mu\) and is set to 1600. The Mach number is set to \(M_{0}=V_{0}/c_{0}=0.1\), with \(c_{0}=\sqrt{\gamma p_{0}/\rho_{0}}\) being the speed of sound, where \(\gamma\) is set to 1.4 and the initial pressure \(p_{0}\) is adjusted to ensure \(M_{0}=0.1\). The simulation is conducted using FR-DG scheme on uniform Cartesian grids of \(120^{3}\) degrees of freedom (DOFs) discretized by a coarse mesh of \(30^{3}\) elements with third-ordersolution polynomial (\(p3\)) and a finer mesh of \(60^{3}\) elements with first-order solution polynomial (\(p1\)). This resolution leads to a purposely under-resolved simulation for investigation of the impact of the methodologies applied in this paper.  
Figures 1-4 display the time evolution of \(E_{k}\), \(\epsilon_{total}\) and components of \(\epsilon^{\prime}\) of the Taylor-Green vortex simulation. The additional modeling dissipation terms, \(\epsilon_{ggg}\) and \(\epsilon_{a}\), are plotted in Figure 5. A DNS result of \(E_{k}\), \(\epsilon_{s}\) and \(\epsilon_{d}\) computed by [PERSON] [53] via the 13-point dispersion-relation-preserving (DRP) scheme [54] on \(512^{3}\) elements is taken as reference in Figures 1-4. Note that at the DNS solution \(\epsilon_{s}\) is accurate enough to be plotted as a reference for the total dissipation rate \(\epsilon_{total}\). The contribution of the compressible dissipation \(\epsilon_{c}\) is neglectable in this testcase and  
Figure 4: Time evolution of the pressure dilation \(\epsilon_{d}\) of TGV simulation, \(Re=1600\), \(120^{3}\) DOFs.  
Figure 5: Time evolution of the additional dissipation \(\epsilon_{\textit{SS}}\) for explicit LES and \(\epsilon_{a}\) for LES with artificial viscosity of TGV simulation, \(Re=1600\), \(120^{3}\) DOFs. (**a**) \(p1\); (**b**) \(p3\).  
Figure 3: Time evolution of the solenoidal dissipation \(\epsilon_{\textit{s}}\) of TGV simulation, \(Re=1600\), \(120^{3}\) DOFs. (**a**) \(p1\); (**b**) \(p3\).
## 4 Discussions
### Limitations and Future Work  
We made sure that the AI models such as DNN were very effective in resolving the nonlinear issues for GPP prediction. The DNN model provides a useful method to overcome the limitations of linear and process-based models. However, a limited volume of data can lead to degradation of accuracy since it may not sufficiently represent the various aspects of GPP changes [24,43]. A large database from various locations of EC measurements will be required for a more advanced DNN model. A longer time series to cover various weather events will also be necessary to cope with unexpected outlier cases. By using such big data for GPP prediction, we can produce an alternative GPP map from the improved DNN model. Moreover, a spatially continuous retrieval of forest GPP over South Korea can be achieved after the improved DNN model is combined with a higher-quality dataset. For example, the advanced versions of the MODIS products, such as gap-filled snow-free daily albedo (MCD43 GF), gap-filled daily AOD with the multi-angle implementation of atmospheric correction (MAIAC) (MCD19A2), and gap-filled daily surface radiation (MCD18A1), are now available. Additionally, the meteorological reanalysis such as Local Data Assimilation and Prediction System (LDAPS) of South Korea can be used for the local-scale land surface variables such as sensible/latent/soil heat flux, temperature, humidity, wind, and precipitation. The use of meteorological reanalysis will also help avoid the problem of the cloud-covered pixels in satellite images.
# Research on Trajectory Planning and Tracking Methods for Coal Mine Mobile Robots
## 2 Trajectory Planning Based on MINCO Trajectory Classes
### Trajectory Planning Based on MINCO Trajectories and Safe Corridors
#### 2.2.4 MINCO Trajectory-Based Planning Approach  
The cost function for the spatio-temporal deformation of a MINCO trajectory can be written as \(J(\mathbf{q}(\xi),\mathbf{T}(\mathbf{\tau}))\). The optimization of the cost \(J\) to the variables \(\xi\) and \(\mathbf{\tau}\) is an unconstrained optimization problem. By handing it over to a general-purpose optimizer, we can quickly solve \(\xi\) and \(\mathbf{\tau}\) at the minimum cost. The path point vectors \(\mathbf{q}\) and time vectors \(\mathbf{T}\) corresponding to the minimum cost are then obtained by mapping. Thus, with the customized boundary conditions \(\mathbf{q}\) and \(\mathbf{T}\), a feasible trajectory that fits the robot kinematics model with optimal control cost under the constraints of the underground coal mine environment can be obtained.  
After the above analysis, the overall process of the trajectory planning method is:  
(1) Firstly, process the underground coal mine environment constraints to obtain the voxel map containing obstacle information;  
(2) Quickly obtain a good path on the voxel map with the RRT* algorithm;  
(3) Generate a safe corridor from the path and obstacle information obtained at the front end;  
(4) Apply MINCO trajectories and their spatio-temporal deformations to generate optimal trajectories under safe corridor constraints and temporal regularity term constraints;  
(5) After obtaining the optimal trajectory, refresh the map at certain time intervals and inflate the obstacles appropriately. Perform collision detection on the trajectory after obtaining the new voxel map. If the trajectory is not safe enough or new obstacles appear on the trajectory, then repeat the above process to replan for dynamic obstacle avoidance.  
The flowchart of the MINCO trajectory planning method is shown in Figure 12:  
Figure 11: Convex polyhedron constraint variable mapping.