esa-sceva/satcom-chunk-collection huggingface dataset:
# An Algorithm for Painting Large Objects Based on a Nine-Axis UR5 Robotic Manipulator
## 4 The Inverse Solution Model of Kinematics of the 9-Axis UR5 Robot
### The Inverse Solution Model for Non-Recommended Regions
#### 4.2.2 The Solution Process of the SQP Algorithm  
The SQP algorithm decomposes the problem into the quadratic programming (QP) sub-problem, obtaining the descending direction \(d\) by solving the current angle sequence \(\theta_{k}\) in the QP problem and updating \(\theta_{k+1}\) via \(d\) until the Karush-Kuhn-Tucker (KKT) condition is satisfied or the maximum number of iterations is reached. The specific solving process of the algorithm is described below.  
(1) The Lagrange function \(L(\theta_{k},\lambda)\) of the current angular sequence \(\theta_{k}\) is constructed, and the expression of \(L(\theta_{k},\lambda)\) is shown in Equation (23).  
\[L(\theta_{k},\lambda)=f(\theta_{k})+\lambda g(\theta_{k}) \tag{23}\]  
where \(\lambda\) is the Lagrangian multiplier, and \(\lambda\geq 0\).  
(2) The descending direction \(d\) of the current angular sequence \(\theta_{k}\) is obtained. Equation (23) is converted into the solution to \(d\), which is shown in Equation (24).  
\[\begin{array}{c}\min_{d}\
abla f(\theta_{k})^{T}d+\frac{d^{T}H_{k}d}{2}\\ st:\ \ g(\theta_{k})+\
abla g(\theta_{k})^{T}d\leq 0\end{array} \tag{24}\]  
In Equation (24), \(H_{k}\) represents the Hassel matrix of the Lagrangian function \(L(\theta_{k},\lambda)\).  
(3) The angle sequence in which \(\theta_{k+1}\) equals \(\theta_{k}\) plus \(d\) is updated, and whether the result of the solution satisfies the KKT condition or reaches the maximum number of iterations is determined. If the KKT condition is satisfied, the iteration is stopped. Step 2 is repeated if the KKT condition is not satisfied. The KKT condition is shown in Equation (25) [25].  
\[\begin{array}{c}\
abla f(\theta_{k})+\lambda g(\theta_{k})=0\\ \lambda\geq 0\\ g(\theta_{k})=0\\ \lambda g(\theta_{k})=0\end{array} \tag{25}\]  
In the KKT condition, the third condition means that the result of the solution satisfies the constraint. If \(g(\theta_{k})\) equals 0, the KKT condition becomes \(\bigtriangledown f(\theta_{k})\), which equals 0. If \(g(\theta_{k})\) is smaller than 0 and \(\lambda\) equals 0, the KKT condition also becomes \(\bigtriangledown f(\theta_{k})\), which equals 0.
# Three Dimensional CS-FEM Phase-Field Modeling Technique for Brittle Fracture in Elastic Solids
## 2 Methods  
### Governing Equations of a 3D Elastic Solid with Discontinuity  
Consider a three-dimensional (3D) arbitrary, homogeneous, linear elastic domain \(\mathbf{\Omega}\) bounded by \(\mathbf{\Gamma}\) such that \(\mathbf{\Gamma}=\mathbf{\Gamma}_{u}\cup\mathbf{\Gamma}_{t}\), \(\mathbf{\Gamma}_{u}\cap\mathbf{\Gamma}_{t}=\mathbf{0}\) and an internal traction free crack \(\mathbf{\Gamma}_{c}\), as shown in Figure 1, where \(\mathbf{\Gamma}_{u}\) and \(\mathbf{\Gamma}_{t}\) are the displacement and traction boundary surfaces, respectively. The equilibrium equations are given as [1,4]:  
\[\
abla\cdot\boldsymbol{\sigma}+\boldsymbol{f}^{b}=0 \tag{1}\]  
where \(\
abla\) is the divergence operator, \(\boldsymbol{\sigma}\) is the Cauchy stress tensor and \(\boldsymbol{f}^{b}\) is the body force.  
The Dirichlet and Neumann boundary conditions are given as:  
\[\boldsymbol{u}(\boldsymbol{x},t)=\bar{\boldsymbol{u}}(\boldsymbol{x},t) \quad\text{on}\quad\mathbf{\Gamma}_{u} \tag{2}\]  
\[\boldsymbol{\sigma}\cdot\boldsymbol{n}=\boldsymbol{f}^{t}\quad\text{on}\quad \mathbf{\Gamma}_{t} \tag{3}\]  
\[\boldsymbol{\sigma}\cdot\boldsymbol{n}=\mathbf{0}\quad\text{on}\quad\mathbf{ \Gamma}_{c} \tag{4}\]  
where \(\boldsymbol{n}\) is the outward unit normal vector on the boundary area \(\mathbf{\Gamma}\) and \(\bar{\boldsymbol{u}}\) is the prescribed displacement on the boundary \(\mathbf{\Gamma}_{u}\).  
The stress-strain relation is given by the constitutive equation  
\[\boldsymbol{\sigma}=\boldsymbol{C}\cdot\boldsymbol{\epsilon} \tag{5}\]  
where \(\boldsymbol{C}\) is the matrix of elastic constants.  
Figure 1: An arbitrary discontinuous three-dimensional body.  
Assuming small displacements and strain, we can define the compatibility relation between strain and displacement as:  
\[\mathbf{e}=\
abla^{s}\mathbf{u}(\mathbf{x}) \tag{6}\]  
The elastic strain energy density is given by  
\[\psi_{\epsilon}(\mathbf{e})=\frac{1}{2}\lambda\mathbf{e}_{ii}\mathbf{e}_{jj}+\mu\mathbf{e}_{ij} \mathbf{e}_{ij} \tag{7}\]  
where \(\lambda\) and \(\mu\) are the Lame constants.
## 3 Experimental Results and Discussion
### Experimental Platform
#### 3.2.3. Experimental Evaluation Metrics  
The experiments use the intersection and integration ratio (IOU), Precision, Recall, mean average precision (mAP), F1 value, Params, and Gigafloating point operations per second (GFLOPs) as the key performance evaluation metrics. The _IOU_ refers to the ratio of area overlap between the obtained detection results and the true value frame, which can be denoted as  
\[IOU=\frac{A\cap B}{A\cup B} \tag{26}\]  
Precision is the proportion of true instances (true to positive category) among all samples classified as positive instances (positive category). It measures the risk of the classifier misclassifying negative examples (negative categories) as positive examples. The formula for the precision rate (Precision Rate = True Examples/True Examples + False Positive Examples) can be expressed as follows:  
\[P=\frac{TP}{TP+FP} \tag{27}\]  
In the formula, _TP_ (True Example) is the prediction of a positive example, and if the true result is positive, the prediction is correct. _TN_ (False Positive Example) is the prediction of a positive example, and the true result is negative, so the prediction is incorrect.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Configure** & **Version** \\ \hline CPU & 16 vCPU Intel(R) Xeon(R) Platinum 8481C \\ GPU & RTX 4090D (24 GB) \\ Python & 3.8 (ubuntu20.04) \\ PyTorch & 2.0.0 \\ Cuda & 11.8 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameter configuration.  
Recall is the proportion of positive cases that are classified out of all samples that are true positive cases. It measures the ability of the classifier to correctly detect positive examples. Recall is calculated as true examples/(true examples + false negative examples):  
\[R=\frac{TP}{TP+FN} \tag{28}\]  
In the formula _FP_ (False Negative Example), if the prediction result is negative and the true result is positive, the prediction is wrong. _FN_ (True Negative Example) is the prediction result is negative, and the true result is negative, so the prediction is correct.  
\(F\)1 value is the index that combines the precision and recall:  
\[F1=\frac{2\times(P\times R)}{P+R} \tag{29}\]  
Compared to \(F\)1 values, Mean Average Precision Mean (_mAP_) synthesizes performance across all categories and provides a more comprehensive assessment of the model's accuracy and recall on the target detection task.  
\[mAP=\frac{1}{N}\sum_{i=1}^{N}Api \tag{30}\]  
Params and GFLOPs represent the parameter size and computational complexity of the model, respectively, which are key indicators of model complexity and resource requirements. In addition, the FPS value of frames per second is used to evaluate the inference speed of the model, indicating how many images the model can process per second. Higher FPS values reflect the model's ability to handle real-time detection tasks.
## 3 Results and Discussion
### Material Characterization
#### 3.1.3 Specific Surface Area (BET)  
Figure 3 shows the specific surface area for the Hap series samples (Hap-H1, Hap-H2, Hap-H3, and Hap-H3 750), calculated from N\({}_{2}\) adsorption isotherms using the BET (Brunauer-Emmett-Teller) method.  
The N\({}_{2}\) adsorption-desorption isotherms for the Hap series samples are depicted in Figure 3. The isotherms reveal that all samples are characterized as type IV, indicating initial monolayer formation within the pores followed by multilayer formation at higher relative pressures, typical of mesoporous materials [11]. The Hap series samples also display H3-type hysteresis, commonly associated with plate-like pores within a pore size range from 2 to 50 nm [37]. Specific surface area measurements obtained via the BET method show the highest value for the Hap-H3 750 sample at 128.41 m\({}^{2}\)/g, followed by Hap-H3 (41.46 m\({}^{2}\)/g), Hap-H2 (24.72 m\({}^{2}\)/g), and the lowest for Hap-H1 (4.51 m\({}^{2}\)/g).  
Pore volume and pore diameter, calculated using the BJH (Barrett-Joyner-Halenda) model, are summarized in Table 1. The largest pore diameter was observed in the Hap-H2 sample (36.73 nm) with a pore volume of 0.41 cm\({}^{3}\)/g, followed by Hap-H1 (35.16 nm) with a pore volume of 0.05 cm\({}^{3}\)/g, Hap-H3 (31.63 nm) with a pore volume of 0.47 cm\({}^{3}\)/g, and  
Figure 3: N\({}_{2}\) adsorption–desorption isotherms for the Hap series samples.  
finally, Hap-H3 750 (20.95 nm) with the highest pore volume of 0.86 cm\({}^{3}\)/g, contributing to its increased specific surface area.  
Notably, the only difference between Hap-H3 and Hap-H3 750 lies in the thermal treatment applied to Hap-H3 750 after synthesis. Consequently, based on the X-ray diffraction results and the (211) peak (Figure 1), a reordering effect is observed in Hap-H3 750, leading to an increase in crystal size. As a result, pore diameter decreased while pore volume increased, enhancing the specific surface area from 41.46 m\({}^{2}\)/g in Hap-H3 to 128.41 m\({}^{2}\)/g in Hap-H3 750.
# Evolving Dispatching Rules for Dynamic Vehicle Routing with Genetic Programming
## 7 Discussion  
### Scalability  
To estimate the applicability of this approach in the case of larger VRP instances, we apply a previously evolved priority function to different problem instances of increasing size. The data in the tested instances were obtained by using a VRPTW setting and randomly generating the input values for a given number of customers. A serial meta-algorithm was then used to build the entire solution from scratch for the given instance. The aim here was not to test the feasibility of the VRP solution, but rather to illustrate the speed at which a single solution can be built using the proposed approach. The results of this experiment are given in Table 11.  
It can be seen that the total duration approximately matches the quadratic dependency on the number of customers, which follows from the complexity of the meta-algorithm. Note that these results do not include the calculation of customer distances, which is presumed to be available beforehand, and can also be approximated with other existing methods.
# Microalgae: Potential for Bioeconomy in Food Systems
## 3 Nutritional Composition
### Vitamins, Pigments, and Antioxidants  
Microalgae also produce other compounds of high commercial value, such as pigments, vitamins, and antioxidants. Chlorophyll, carotenoids, and phycobilins are the most abundant pigments in microalgae and cyanobacteria [15, 48]. In addition to providing coloration, they possess health-promoting properties with potential in the pharmaceutical industry as antioxidants, vitamin precursors, neuroprotection, and immunological stimulants [49]. The most used pigments, including beta-carotene, lutein, chlorophyll a and b, astaxanthin, and phycocyanin, are produced by _Botryococcus braunii_, _C. vulgaris_, _Chlorococcecum_ sp., _Scenedesmus_ sp., _Arthospira platensis_, and _Haematococcus pluvialis_[15].  
Some microalgae are excellent sources of micronutrients, such as vitamin B12 (_Cylindospermum_ sp., _Tylpotthrix tennis_, _Nostoc muscorum_, and _Hapalosiphon fontinalis_), vitamin C (_Protothea moriformis_, _Chlorella_ sp., _Arthospira_ sp., and _Dunaliella_ sp.) [15, 29], vitamin E (_Euglena gracilis_ and _D. tertiolecta_) [15, 33], and other B-complex vitamins (B1, B3, B5, B6 in _Tetraselmis suecia_) [33].  
Phenolic antioxidants such as rutin, hesperidin, morin, caffe acid, catechol, and catechhin are produced by some microalgae (_Nostoc_ sp., _Chlorella_ sp., _Anabena_ sp., _Tylpotthrix_ sp., and _Chlamydomonas_ sp.) as secondary metabolites. Phenolic compounds act as free radical scavengers, hydrogen atom donors, and metal chelators. In view of these essential functions, they are used in food supplements [49, 50].
# DTS-Net: Depth-to-Space Networks for Fast and Accurate Semantic Object Segmentation
## 3 Proposed Method
### Efficient Sub-Pixel Convolutional Neural Networks  
Efficient sub-pixel CNN [1] was originally proposed for image and video super-resolution, in which high-resolution images are constructed from lower-resolution images through DTS aggregation. In this approach, pixels with the same location in the low-resolution image channels are mapped and re-ordered to form a super-pixel in the high-resolution image. DTS aggregates small feature maps of dimension \(h\times w\times r^{2}\) to form a  
Figure 3: (**a**) Xception block. There are three depth-wise separable convolutions, each having prior ReLU activation. A residual connection connects the block start and end in the entry-flow stage. A \(1\times 1\) convolution is implemented in the middle-flow stage. (**b**) MobileNetV2 block. An expansion module is followed by a Depth-wise separable convolution layer, then a projection module was added with a residual connection between the beginning and the end of the block.  
final high-resolution dense map of size \(rh\times rw\) (as a segmentation or depth map), where \(h\), \(w\), and \(r^{2}\) are the feature-map width, height, and depth, respectively. The feature maps extracted from the feature extractor CNN are passed to the \(1\times 1\times r^{2}\) convolutional layer, which gives a total activation patterns of \(r^{2}\) with size \(\frac{W}{r}\) and \(\frac{H}{r}\), where \(W\) and \(H\) are the width and height of the input image, respectively. The final reconstructed dense map is also produced. The DTS module then rearranges the elements of the tensor \(\frac{W}{r}\times\frac{H}{r}\times r^{2}\) to a tensor of shape \(r\), \(\frac{W}{r}\times r\), \(\frac{H}{r}\), which is equivalent to the input image size of \(W\times H\). This operation is illustrated visually in Figure 2. In this method, fast one-step up-sampling is performed, which can be mathematically expressed as  
\[MAP_{x,y}=F_{[x/r],[y/r],mod(y/r)+mod(x,r)}, \tag{1}\]  
where \(MAP_{x,y}\) is the constructed dense map, \(F\) represents the feature maps extracted from the CNN and passed to the \(1\times 1\times r^{2}\) convolutional layer, \(r\) is the feature map depth, and operation \(mod\) is the modulus, which maps the pixels from the low-resolution feature maps to the super-pixel in the final dense map when \(mod(x,r)=0\) or \(mod(y,r)=0\).  
In our implementation, we use \(r=32\), as the Xception or MobileNetV2 feature extractors down-sample the features using the convolution and max-pooling to \(1/32\) of the input image size. Therefore, to reconstruct the final dense map at the same size as the input image, we use the \(1\times 1\times 1024\) convolutional layer, where \(r^{2}=1024\), to obtain a final feature map count equal to \(r^{2}\). This reconstruction layer can be trained simply with a regression loss (we use the mean absolute error), while inference (a rounding operation) is used to round the predicted pixels in the dense layer to the nearest integer in the case of semantic segmentation.
# Study on Shear Performance of Web-Embedded Composite Shear Connector
## 2 Push-Out Test
### Load-Slip Curve  
To study the USBC of each part in the WECSC, the load-slip curves of four specimens were obtained (Figure 11). Additionally, the USBCs and corresponding displacements are listed in Table 3.  
Figure 11: Load–slip curves of four different specimens.  
Figure 10: Damage pattern through steel bars.  
In Figure 11, three stages were observed in the load-slip curve: elastic, nonlinear, and descending. In the elastic stage, the load changes significantly albeit with less slip, meaning that the WECSC was a rigid shear connector, and most of the load was borne by the shear capacity of the concrete bowel.  
Before entering the nonlinear stage, the maximum load values of P-0, P-18, P-18-S, and P-18-S# were 150.36, 531.44, 590.16, and 700.65 kN, respectively, accounting for 67.41, 76.54, 71.84, and 65.02% of USBC, respectively. After entering the nonlinear stage, the development trends of the four curves were similar. The slope of the curve tended to be flat, the load growth was slow in this stage, and the slip gradually increased. This is because the load was slowly transferred from concrete to steel members at this stage. When the peak load was reached, the curve entered the descending stage. At this time, the concrete bowel was crushed, and the load was fully borne by the shear action of penetrating rebars because the steel member had good ductility leading to obvious slip. Owing to the large rigidity of the specimen, the internal steel members were not cut; thus, when the load dropped to a certain range, it was no longer reduced.  
The results in Table 3 show that different components have different effects on the growth of the USBC. The USBC of the P-0 specimen can be regarded as being provided by the shear capacity of the concrete bowel as well as the chemical bonding and friction forces of the steel-concrete interface. By contrast, the USBC of P-18 specimen increased by 471.21 kN, which was provided by the shear action of penetrating rebars. Compared with P-18, studs were added to the P-18-S specimen; therefore, the USBC increased by 127.17 kN, which was provided by the shear resistance of the stud. However, the USBC did not increase significantly, because the bearing capacity of the stud itself was lower than that of the perforating steel bar, fewer studs were arranged, and the model used in this test was small. Based on the P-18-S specimen, an end-bearing area was added to the P-18-S# specimen, and the USBC was increased by 256.09 kN, which was provided by the end concrete.
# Modeling of NOMA-MIMO-Based Power Domain for 5G Network under Selective Rayleigh Fading Channels
## 1 Introduction
Investigate the attainable rates of UP NOMA with a synchronized transmission in [31] and estimate both the upper and lower bounds of a synchronized NOMA system's possible rates, illustrating that the measured lower bound is approximately the rate achievable by conventional synchronized NOMA systems. Nonetheless, each user is provided with a relatively limited number of transmitted symbols, which may lead to inaccurate findings. The ergodic rate achievable in [23; 24] is monitored and checked to ensure optimal performance of the encoder and pre-detection systems that simplify decoding in the dual receive channels used for DL and UL transmissions. Nevertheless, the number of users is insufficient to confirm the optimal situation, and there has been no research into the method's impact on OP or BER, for example. In this paper, we examine the impact of varying the bandwidth and the number of antennas in a 5G network on the bit error rate (BER) and spectrum efficiency (SE) of the downlink, and the average capacity rate and outage probability (OP) of the uplink in a network subject to Rayleigh fading. During the analytical process, the integral expressions of the BER, SE, capacity rate, and OP were generated. In addition, modeling is used to verify all the potential configurations of the system. The following are some of the research's most significant contributions:  
* Two different bandwidths (BWs) for the NOMA system over a Rayleigh fading channel are proposed and investigated;
* Improvements in the system have been examined when NOMA and MIMO are used together to handle four users. The article addresses the NOMA technique which is considered one of the main bullets of 5G technology. Our main innovative idea in the article is remodeling NOMA-MIMO for the power domain for a higher data rate, capacity, and throughput. This has been performed by proposing a new power domain scheme for NOMA-MIMO. The remainder of the paper is structured as follows: Section 2 contains previous and related works. Section 3 discusses the proposed system mathematical model. Simulation and simulation parameters are presented in Section 4. The results and discussions are presented in Section 5 and, finally, Section 6 concludes the paper and presents further future work.
# Cluster-Centered Visualization Techniques for Fuzzy Clustering Results to Judge Single Clusters
## 5 Validation by Example
The data points of the red and black clusters are mixed. Figure 5: Artificial ambiguous data set with two clusters and the visualized results with the three CCV techniques. Figure 6: Artificial ambiguous data set with three clusters and the visualized results with the three CCV techniques. Figure 7 shows the artificially ambiguous data set with four clusters. The clustered data are located again at the top left. The center of the separated black cluster and both centers of the overlapping clusters are visible. Due to the noisy data points, the fuzzy \(k\)-means algorithm seems to be able to identify four clusters. The majority of the noisy data points are in their own cluster. With the CPC method in the top right, the four clusters are separated in the visualization. The black cluster center is in the middle of the circle, and the red, green, and blue cluster centers are on the edge. The visualization shows clearly that the black, red, and blue clusters are clearly separated. But some data points in the black cluster are attracted to the blue cluster, and vice versa. Therefore, some data points overlap toward the respective cluster center. The A2C method in the bottom left delivers a not very clear separation of the four clusters because of some mixed data points for the black and blue clusters. The green and red clusters are also overlapping. The AM method in the bottom right delivers the same mixed separation of the black and blue clusters but a significantly better separation of the green and red clusters. The use of the three newly developed CCV techniques has indicated that the results based on the \(k\)-means clustering algorithm deliver more information about the dependencies between the individual clusters when focusing on a single cluster. With two or three clusters, the separation is visible both for the artificial good and partially for the ambiguous data set. But with four clusters, the data points are overlapping between some clusters. Therefore, it is not possible to separate the data points correctly. But with only two clusters, one larger cluster is created, into which all close data points are classified. However, it should be noted that if the initial data set is better, the easier it can be clearly clustered than poorer initial data. With the black cluster as the center, all three CCV techniques achieved a good separation of the three other clusters.