esa-sceva/satcom-chunk-collection huggingface dataset:
# A Direct Search Algorithm for Global Optimization
## 3 A Direct Search Algorithm for Global Optimization
### The Basic Algorithm
#### 3.4.3 Expansive Translation  
This operation aims to position the point with lowest value of the transformed cost function found so far at the right vertex. Let \(\mathcal{V}\) be the vertex set of an isosceles right \(n\)-simplex with edge length \(\Delta\), and let \(\xi_{i}\in\mathcal{V}\) be such that \(\phi(\xi_{i})\leq\phi(\xi_{j})\) for \(\xi_{j}\in\mathcal{V}\); then, the expansive translation of the right \(n\)-simplex \(\mathcal{V}\) with respect to the vertex \(i\) is given by the following expression:  
\[\xi_{j}^{\prime}=\xi_{i}+\rho(\xi_{j}-\xi_{0}),\ \xi_{j}\in\mathcal{V} \tag{16}\]  
where \(1\leq\rho<\infty\). If the vertex set of the current simplex is given by \(\mathcal{V}=\text{vset}(\xi_{0},\Delta)\), then the transformed \(n\)-simplex has the vertex set \(\mathcal{V}^{\prime}=\text{vset}(\xi_{j},\Delta^{\prime})\), where \(\Delta^{\prime}=\rho\Delta\), and its edge length is \(|\Delta^{\prime}|\). The new \(n\)-simplex, after the expansive translation, preserves its shape, but increases its content by a factor of \(\rho^{n}\). From a practical point of view, it is convenient to choose the expansive factor \(\rho\) close to one, but slightly greater, because this avoids obtaining candidate points that were already visited in previous iterations, in the next rotation operation.  
Let \(c\) be an arbitrary positive constant; if \(\phi(\xi_{i}^{\prime})<\phi(\xi_{0})-c\Delta^{2}\) for some \(\xi_{i}^{\prime}\in\mathcal{V}^{\prime}\), then the algorithm proceeds to a new iteration and performs an expansive translation operation. Otherwise, the algorithm executes a rotation operation.  
The introduction of the positive term \(c\Delta^{2}\) guarantees that the iteration is considered successful only if it provides a point with a sufficient decrease of the cost function.
## 2 Materials and Methods
### UV (RGB) Image Redundancy  
Since the camera is a color RGB camera, the UV image may contain redundant information. The UV image is the result of the interaction of monochromatic light with biological structures. It is usually close to monochromatic light, that allows the use of a more optimal color space than RGB. In order to verify whether the UV (RGB) image can be converted to a UV image in shades of gray, the PCA algorithm [31] (Principal Component Analysis) was used. The PCA algorithm enables the estimation of a new non-redundant color space for the input RGB image [32; 33; 34]. This is important for the training algorithm, because if the output image can be a grayscale image, the number of parameters (weights) to be trained will be smaller. RGB color image requires three times more weights in the last layer and reducing the number of parameters is important for the speed of convergence and the reduction of false color generation.  
An example of removing redundancy from a UV RGB image is shown in Figure 4. In order to improve the image quality of the first three main components, a random sample for 1% of the pixels is shown.  
Figure 4: Exemplary pair of acquired images, sample of PC (Principal Component) and UV main component image used for training.
# Cross-Coupled Contouring Control of Multi-DOF Robotic Manipulator
## 2 Dynamic Model and New Cross-Coupled Control Law
### Contour Error of End-Effector  
To obtain accurate contour trajectories is a fundamental requirement for modern high precision manufacturing. The contour error can be used to evaluate the quality of contour tracking, and it is defined as an orthogonal component of the derivation of an actual contour from the desired one. Figure 1 shows the relationship and difference between a tracking error and a contour error for an \(XY\) planar contour.  
Assume small joint errors are obtained during the contour tracking process, tracking errors in the joint level and at the end-effector of an n-DOF serial planar robot can be calculated as follows:  
\[\begin{array}{l}e_{qi}\left(t\right)=q_{id}\left(t\right)-q_{i}\left(t\right) \\ e_{x}\left(t\right)=-\sum\limits_{i=1}^{n}l_{i}\sum\limits_{j=1}^{i}e_{qj} \left(t\right)\sin\left(\sum\limits_{j=1}^{i}q_{j}\left(t\right)\right)\\ e_{y}\left(t\right)=\sum\limits_{i=1}^{n}l_{i}\sum\limits_{j=1}^{i}e_{qj} \left(t\right)\cos\left(\sum\limits_{j=1}^{i}q_{j}\left(t\right)\right)\end{array} \tag{2}\]  
where \(q_{id}\left(t\right)\) and \(l_{i}\) are the desired joint position and the length of link \(i\), respectively.  
For the purpose of online calculation of the contour error \(e_{c}\), the following simple formulae presented in [1,2] is used in this paper. For a straight-line contour, the contour error \(e_{c}\) can be expressed as:  
\[e_{c}=-C_{x}e_{x}+C_{y}e_{y}\text{ with }C_{x}=\sin\theta,\quad C_{y}=\cos\theta \tag{3}\]  
where \(\theta\) is the angle between the desired straight line and the \(X\)-axis, \(e_{x}\) and \(e_{y}\) are the tracking errors of the end effector in the \(X\) and \(Y\) axes, respectively. It can be seen that the contour error coefficients \(C_{x}\) and \(C_{y}\) are constant for linear contour tracking.  
Figure 1: Tracking and contour errors for a planar contour.  
On the other hand, for a circular contour, the contour error coefficients are not constant and can be obtained by the following Equation [2]:  
\[e_{c}=-C_{x}e_{x}+C_{y}e_{y}\text{ with }C_{x}=\text{sin}\theta-\frac{e_{x}}{2R}, \quad C_{y}=\text{cos}\theta+\frac{e_{y}}{2R} \tag{4}\]  
It should be mentioned that the angle \(\theta\) is not constant but a variable for a circular contour, related to the location of the desired circle contour.
## 4 Experimental Results and Discussion  
### CLP Data Preparation and Feature Selection  
Based on the data preparation process, the CLP value was normalized, using Equation (2). As a result of normalization, the CLP value was between 0 and 1, and greater CLP indicates better labor productivity for the project. After imputing missing values and removing factors with zero standard deviation, the number of factors was reduced to 108. By eliminating  
Figure 2: Overview of particle swarm optimization (PSO).  
outliers from the CLP data set, 7 data points were removed as outliers, and the total number of data points became 85. Therefore, the CLP data set after the preparation process had 85 data points, 108 CLP factors, and a CLP value.  
Next, the number of features was reduced by the proposed HFS method. For this study, the threshold of 0.25 was defined for ReliefF. All features with weights greater than or equal to 0.25 were selected as essential features in the next HFS stage. From 108 factors in the final CLP data set, ReliefF selected 43 as essential features. In the next stage of HFS, which is the integration of SVM and GA as a wrapper method, the GA parameter settings were a population size of 50, GA maximum iteration of 60, crossover rate of 0.83, and mutation rate of 0.2. The SVM penalty factor \(C\) was 10, the kernel type was RBF, and the kernel cache was 200. These parameters were obtained by trial and error and are the optimum values for this case. The termination criteria were a maximum of 60 generations or no improvement of performance over 5 generations. The proposed wrapper method was developed considering these parameters, and it selected 14 of the 43 factors identified by ReliefF. The set of 14 factors was selected when the RMSE of the run of the wrapper model was lowest. Table 1 presents the selected CLP factors resulting from HFS. As shown in Table 1, the first 11 factors are all from the activity level, and the next three factors belong to the project level, which shows the significant impact of activity-level factors on predicting CLP. From the selected factors, \"Level of interruption and disruption\", \"Complexity of task\", \"Working condition (dust and fumes)\", \"Location of work scope (elevation)\" and \"Congestion of work area\" are factors that negatively influence CLP. In other words, after normalization, when negatively influencing factors have values close to zero, they result in greater CLP, compared to when their values are close to 1. The other selected factors are positively influencing factors, and when their values are close to 1, they result in greater CLP.
# Joint Resource Allocation and Learning Optimization for UAV-Assisted Federated Learning
## 2 System Model and Problem Formulation
### Computing and Communication Model  
The energy consumption of users directly affects the user experience. Therefore, this paper focuses on the energy consumption of users in the FL process, including the training and communication energy consumption.
## 3 Numerical Examples
### Shock-Tube Problems
The results computed in physical space exhibit significant oscillations, indicating an inability to accurately capture the shock wave, a common challenge in numerical simulations of compressible flows. In contrast, the schemes reconstructed in eigenspace show excellent agreement with the exact solution. This is particularly important in problems involving strong discontinuities, which are often difficult to resolve with conventional methods. Comparatively speaking, the URLBFS scheme has better performance in solving shock waves and contact discontinuities in Lax and Sod problems. Figure 9: Density distributions of the Lax problem at t = 1.4 were obtained using the LF, ROE, and URLBFS schemes compared to the exact solution. The results illustrate the differences in accuracy and resolution between these schemes. Panels (**a**,**c**) show the results using the WENO5 and WENO7 reconstruction methods, respectively, while panels (**b**,**d**) provide partial zoom\(-\)ins of key areas to visualize the differences better.
## 4 Discussion
### Surgical Considerations  
The passive implants only introduced one additional suturing step, which added, at most, 15 minutes to the surgery. Anatomically, tendon excursion and alignment with the forearm and carpal tunnel are similar to end-to-end or end-to-side tendon transfers [21; 22; 23; 24; 25]. Importantly, surgical revision, if required, would simply mean removing the implant.  
The implant could also allow customizing the range of motion and force production of the fingers. This could be achieved by changing the implant's geometry to form a non-isosceles triangle with the tendons, or by altering the rest angle of the implant, or even modifying the FDP tendon length attached to the implant. The rod implant also accommodated for small variations and inaccuracies in measuring tendon lengths prior to suturing without loss of function as would be the case in suture-based approaches. This would simplify the surgery and potentially improve outcomes. The rod implant, with its one-piece monolithic design was also easier to install and suture compared to the U implant.  
At flexed postures, we recorded the translations of the implants' centers along with their mediolateral shifts (see Table 2). The implants' rotations were also measured. This was repeated with both fingers unconstrained and with only the index finger constrained. Comparing the two cases, the implants' rotation more than compensated their reduced translation (when compared to the baseline suture case) as a result of the constraints on the index finger. This allowed the middle finger to continue flexing (see Figure 2)--as is the purpose of the implant. This was not the case with the current state-of-the-art suture-based approach since it did not have the rotational degree-of-freedom introduced by the implant.  
The mediolateral translation of the rod implant ranged from 0.5 mm to 5.08 mm--unequal finger constraints increased it. However, for the U implant, constraining the index finger reduced the mediolateral translation from 7.06 mm to 3.72 mm. It is important to note for surgical technique that mediolateral translations are also influenced by the routing of the donor tendon.
# Enhanced Ant Colony Algorithm Based on Islands for Mobile Robot Path Planning
## 3 Brief Introduction of ACO
### Island Division Strategy
#### 4.1.2 Islands Selection  
To determine the location of the intermediate islands within the auxiliary map, it is essential to calculate the radius of the search circle (\(r_{s}\)). This radius can be expressed as follows:  
\[r_{s}=\frac{d_{SE}}{N-1}, \tag{13}\]  
where \(d_{SE}\) signifies the Euclidean distance between \(S\) and \(E\), and \(N\) refers to the total number of islands, including grids \(S\) and \(E\). A search circle is defined with its center located at the grid corresponding to the starting grid S and a radius of \(r_{s}\). The free grids within the search circle are designated as candidate grids. For each candidate grid, the sum of the Euclidean distances to both the starting and ending points is calculated independently. The detailed formula for this calculation is presented below:  
\[D_{I}=\sqrt{\left(x_{I}-x_{S}\right)^{2}+\left(y_{I}-y_{S}\right)^{2}}+\sqrt{ \left(x_{I}-x_{E}\right)^{2}+\left(y_{I}-y_{E}\right)^{2}}\quad I\in A_{I}, \tag{14}\]  
where \(D_{I}\) indicates the sum of the Euclidean distances from the candidate grid, which is identified by the sequence number \(I\) to the starting point \(S\) (\(S=L_{1}\)) and the endpoint \(E\) (\(E=L_{N}\)), and \(A_{I}\) signifies the set of sequence numbers for selectable grids. The candidate grid with the minimum \(D_{I}\) value is selected, and its sequence number \(I\) is designated as the next island \(L_{2}\). Taking the grid center of \(L_{2}\) as the reference point, the above steps are repeated until the search circle includes the endpoint \(E\) (\(E=L_{N}\)), thereby determining the sequence of all islands as follows:  
\[L_{order}=[L_{1},L_{2}\cdots,L_{z},\cdots L_{N}], \tag{15}\]  
where \(L_{z}\) indicates the serial number of the \(z\)th island.  
Figure 5: Auxiliary map corresponding to Figure 1.  
Taking the auxiliary map of Figure 1 as an example, as shown in Figure 6, 3 and 100 represent the starting position and target position, respectively. Assuming that the map requires five islands, the final path planning sequence is given by \(I_{order}=[3,25,47,68,100]\). The EACI algorithm sequentially generates the local optimal path between the two adjacent sequence numbers. Connecting all local optimal paths from start to end yields the global optimal path for the entire complex map.
## 3 Proposed Methodology
### Proposed Architecture Using Concatenating Features
#### 3.3.1 Logistic Regression  
LR is a statistical method that models a binary dependent variable using a logistic function. This well-known machine learning algorithm has been used in many different contexts [56].  
We chose Logistic Regression (LR) as our baseline classifier due to its proven effectiveness in text classification tasks and its ability to handle multi-class problems through one-vs.-rest strategy. LR offers several advantages for offensive language detection: interpretability of feature weights, efficient training with large feature sets, and probabilistic outputs that can be threshold-adjusted [57]. Previous studies have demonstrated its success in hate speech detection, achieving competitive results while maintaining computational efficiency [31; 32]. LR is a statistical method that models a binary dependent variable using a logistic function.  
We have defined l2 regularized LR for OLD using Equation (21) as:  
\[\min\sum_{i=1}^{N}\log\Bigl{(}1+\exp\Bigl{(}-l_{i}\Bigl{(}\mathbf{w}^{T}\mathbf{ f}_{i}+\theta\Bigr{)}\Bigr{)}\Bigr{)}+\lambda\|\mathbf{w}\|_{1} \tag{21}\]  
The classifier used for classifying test data with labels \(l\in\{0,1,2\}\) with weight vector \(w\) and other model parameters \(\lambda>0\).  
\[\Pr(l=0\mid\mathbf{f})=\frac{1}{1+\exp(-(\mathbf{w}^{T}\mathbf{f}+\theta))} \tag{22}\]  
Equation (22) provides the probability estimate for class label \(l=0\), where \(Pr(l=0\mid\mathbf{f})\) represents the probability of the class 0 on given input feature f. In the LR model, w denotes weight vector, f is the input feature vector, and \(\theta\) is the bias term. Similarly for the other classes, we have calculated the probability using Equations (23) and (24).  
\[\Pr(l=1\mid\mathbf{f})=\frac{1}{1+\exp(\mathbf{w}^{T}\mathbf{f}+\theta)} \tag{23}\]  
\[\Pr(l=2\mid\mathbf{f})=\frac{1}{1+\exp(\mathbf{w}^{T}\mathbf{f}+\theta)} \tag{24}\]
## 3 Experimental Study  
In this study, to evaluate the combined effects of rubber content by volume and the aspect ratio (i.e., the ratio of median particle sizes of the rubber and the gravel, \(AR\)\(=D_{50,R}/D_{50,G}\)[38, 39, 40, 41, 42]) on the physical properties and mechanical response of GRMs, a poorly-graded rounded gravel (G) and two coarse-sized recycled granulated rubber types--namely, large rubber (RL) and small rubber (RS)--were tested. Their particle size distribution (PSD) along with photos are shown in Figure 3, while their index properties are reported in Table 1. The specific gravity (\(G_{\text{s}}\)) was measured as 2.71 (G), 1.15 (RL), and 1.14 (RS)--the rubber was free of steel wires and fiber reinforcements. The aspect ratio of G-RL was \(AR\)\(=\) 0.67 and that of G-RS was \(AR\)\(=\) 0.33.  
Figure 3: Material tested in this study: (**a**) Particle size distribution; and physical aspect of (**b**) gravel, (**c**) large rubber particles, and (**d**) small rubber particles (adopted from [16]).  
Several mixtures were prepared at various volumetric rubber content (_VRC_) of 0%, 10%, 25%, 40%, and 100% by mixing RL and RS with G. Note that, _VRC_ is defined as the ratio of the rubber particle volume (\(V_{\text{R}}\)) to the total volume of solid particles (\(V_{\text{TOT}}=V_{\text{R}}+V_{\text{G}}\), where \(V_{\text{G}}\) is the volume of gravel grains), according to Equation (1):  
\[VRC=\frac{V_{\text{R}}}{V_{\text{R}}+V_{\text{G}}}\ (\times 100) \tag{1}\]  
Dry specimens were prepared by tamping method at a degree of compaction of 90% or above (based on standard Proctor tests--refer to details in Section 4.1). Segregation in the specimens was avoided by minimizing any vibration and preventing granular flow.  
The one-dimensional (1-D) compressibility of GRMs was evaluated up to 500 kPa vertical stress by means of a medium-size (inner diameter 250 mm; specimen height from 150 mm) compression cell. Alternatively, the shear strength was estimated by using a medium-size (100 mm \(\times\) 100 mm in cross-section and 53 mm in height) direct shear box under 30, 60, and 100 kPa normal stress levels (the horizontal displacement rate was 1 mm/min). Moreover, to evaluate the small-strain stiffness, shear modulus degradation, and damping ratio of GRMs, two series of bender element and small-strain drained cyclic triaxial tests (specimen size: diameter = 70 mm; height = 170 mm) were also carried out on dry specimens. Additionally, batch leaching tests besides conductivity, pH, total organic carbon (TOC), and inductively coupled plasma mass spectrometry (ICP-MS) analyses were performed to assess key environmental aspects of GRMs. A summary of the geo-environmental tests performed in this study is reported in Table 2.
# The Inheritance and Variation of Floral Scent Compounds in Parent-Progeny Relationships of _[PERSON]_
## 4 Discussion
### Heritability of Volatiles and Its Applications in Malus Fragment Germplasm Breeding  
Although floral scents are highly variable and sensitive to environmental factors, their biosynthesis is fundamentally governed by genetic factors [42]. As with all genetic traits, the chemical compounds contributing to floral scents may also reflect their taxonomic relationships [43]. There are certain similarities in the olfactory characteristics of breeds within the same hybrid population, while differences between hybrid populations reflect their pedigree [8]. For instance, most ancestors of Asiatic lily hybrids possess little or no scent, whereas Oriental lily hybrids are highly fragrant [8]. In this study, most compounds in the progenies were inherited from their maternal parent (60.61-75.00%). Progenies exhibited sensory characteristics similar to those of their maternal parents: earth/woody, sweet, and rose. The characteristic compounds, including geranylacetone, 6-methyl-5-hepten-2-one, 2-phenylethylanol, \(\beta\)-ionone, decanal, and so on, were similar, but their contents differed among progenies. Moreover, most common compounds were significantly downregulated through hybridization. This regularity was also found in the study of tea roses [13]. These similarities and differences of flowers among closely related germplasm could be a means for classifying _Malus_ with an unclear genetic background.  
Natural hybrids may also exude unique scent combinations that differ from those of the parental species in compound identity or quantitative ratio of compounds [44]. In this study, we found that some progenies had higher relative contents of volatile compounds. Compared with the maternal parent, the percentages of methyl caproate and methyl 2-ethylexanoate, which had a fruity odor, were increased in the progenies. Compared to the male parent, the composition of compounds in the progeny ('Brandywine') follows a similar pattern. Hybrids are superior to one parental species and can be used in unidirectional backcrossing to enhance the odor performance [10; 12]. Moreover, this study even found the presence of a high-percentage \(\alpha\)-ionone in the progenies of _M. ioensis_, 4-methylanisole, and linalool in the 'Klehm's Improved Bechtel' hybrid, which were absent in its parental germplasm, indicating an absolute difference generating from different biochemical pathway [10]. These unique combinations may be due to transgressive inheritance, in which hybrids have compounds outside the types or range of either parent species [10; 12]. The newly generated substances can enrich the diversity of _Malus_ scents and provide different flavors for breeding new cultivars.
# A Two-Stage Registration Strategy for Thermal-Visible Images in Substations
## 3 Experimental Results and Discussion
### Evaluation Matrices  
To objectively ascertain the effectiveness of the method, this paper proposes two evaluation indicators: precision and target registration error (TRE). The precision represents the proportion of the correct number of matching (CNM) correspondences in the total number of matches (TNM). The precision can be defined as follows:  
\[Precision=\frac{CNM}{TNM} \tag{6}\]  
This metric indicates the accuracy of key point matching when obtaining the transformation matrix. TRE represents the Euclidean distance between the key points after coordinate transformation and the real corresponding points. The TRE is calculated as follows:  
\[TRE=P_{g}-P_{e} \tag{7}\]  
\(P_{g}\) is the transformation map of the ground truth key points, and \(P_{e}\) is the transformation map of the key points extracted after the second registration of the image.  
However, it is impossible to find the real coordinate transformation matrix between image pairs. Therefore, this paper uses the control point selector in MATLAB to manually select 12 pairs of sub-pixel accuracy feature points in the image to generate an approximate ground truth transformation model. By employing the approximate transformation matrix, the keypoints of the matched visible image undergo a transformation process.