esa-sceva/satcom-chunk-collection huggingface dataset:
# A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications
###### Abstract  
Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. The concepts of the regularity and degree of a node play a significant role in both the theory and application of graph theory in the neutrosophic environment. In this work, we describe the utility of the regular neutrosophic graph and bipartite neutrosophic graph to model an assignment problem, a road transport network, and a social network. For this purpose, we introduce the definitions of the regular neutrosophic graph, star neutrosophic graph, regular complete neutrosophic graph, complete bipartite neutrosophic graph, and regular strong neutrosophic graph. We define the \(d_{m}\)- and \(td_{m}\)-degrees of a node in a regular neutrosophic graph. Depending on the degree of the node, this paper classifies the regularity of a neutrosophic graph into three types, namely \(d_{m}\)-regular, \(td_{m}\)-regular, and \(m\)-highly irregular neutrosophic graphs. We present some theorems and properties of those regular neutrosophic graphs. The concept of an \(m\)-highly irregular neutrosophic graph on cycle and path graphs is also investigated in this paper. The definition of busy and free nodes in a regular neutrosophic graph is presented here. We introduce the idea of the \(\mu\)-complement and \(h\)-morphism of a regular neutrosophic graph. Some properties of complement and isomorphic regular neutrosophic graphs are presented here.  
Keywords:neutrosophic graph; complete neutrosophic graph; bipartite neutrosophic graph; complement neutrosophic graph; road transport network; wireless multihop network and social network Pacs:J0101 +
Footnote †: journal: Journal of mathematics
## 2 Results  
### SPME/GC-MS Chemical Composition  
Using the SPME/GC-MS technique, a total of eighteen volatile compounds, listed in Table 1, were detected and identified and the identifiers were also reported (Table S1). The volatile fraction of the dried leaves was dominated by the presence of sesquiterpenes (85.8%). Among them, \(\alpha\)-humulene (27.8%), \(\beta\)-caryophyllene (19.2%), and \(\alpha\)-copaene (12.9%) were the most abundant. These principal components were followed by \(\gamma\)-muurolene, \(\delta\)-cadinene, and \(\beta\)-eudesmene, whose average percentage values ranged from 4.3 to 7.6%. The relative chromatogram is reported in Figures S1-S3.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{N}^{\circ}\) & **COMPONENT 1** & **LR1 2** & **LR1 3** & **Chinook (\%)** \\ \hline
1 & isobutyric acid & 762 & 765 & 1.4 \(\pm\) 0.04 \\
2 & propionic acid & 968 & 972 & 0.7 \(\pm\) 0.02 \\
3 & 5-heptem-2-one, 6-methyl- & 981 & 986 & 1.9 \(\pm\) 0.03 \\
4 & 2-methylbutyl isobutyrate & 986 & 989 & 8.6 \(\pm\) 0.03 \\
5 & \(\beta\)-myrcene & 988 & 991 & 0.4 \(\pm\) 0.02 \\
6 & amyl isovalerate & 1090 & 1093 & 0.8 \(\pm\) 0.02 \\
7 & \(\beta\)-cyclodextrin & 1192 & 1197 & 0.4 \(\pm\) 0.01 \\
8 & ylangene & 1368 & 1376 & 3.4 \(\pm\) 0.02 \\
9 & \(\alpha\)-copaene & 1385 & 1392 & 12.9 \(\pm\) 0.05 \\
10 & \(\beta\)-bourbonene & 1392 & 1390 & 0.5 \(\pm\) 0.01 \\
11 & \(\beta\)-caryophyllene & 1438 & 1440 & 19.2 \(\pm\) 0.09 \\
12 & \(\alpha\)-humulene & 1475 & 1473 & 27.8 \(\pm\) 0.11 \\
14 & \(\gamma\)-muurolene & 1480 & 1486 & 7.6 \(\pm\) 0.02 \\
13 & \(\beta\)-eudesmene & 1490 & 1488 & 4.3 \(\pm\) 0.03 \\
15 & \(\alpha\)-selinene & 1495 & 1493 & 1.8 \(\pm\) 0.02 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Chemical volatile composition (percentage mean value \(\pm\) standard deviation) of the dried hop leaves as determined by SPME/GC–MS.
## 2 Research Methodology
### BFGS Parameter Inversion Algorithm  
The BFGS (Broyden-Fletcher-Goldfarb-Shanno) method transforms the objective function into an unconstrained optimization problem by constructing the objective function, determining the Hessian matrix approximation array through the first derivatives, then iterating afterward, continuously updating the search direction and the step size to determine the variables, and then gradually approximating the minimum value of the objective function, thereby achieving robust and stable parameter inversion [32; 33]. The specific steps are as follows:  
(1) To approximate the minimum value, the objective function f is first constructed according to the probability integral formula. The objective function formula is as follows:  
\[f=\sum_{i=1}^{N}[W(x,y)-W_{i}]^{2}+\sum_{i=1}^{N}\Bigl{[}U(x,y)_{\varphi}-U_{ i}\Bigr{]}^{2} \tag{14}\]In the formula presented, N is the number of ground observation points; \(W(x,y)\) and \(U(x,y)_{\varphi}\) are the predicted values of subsidence and horizontal movement of the ith point; \(W_{i}\) is the subsidence measurement value; and \(U_{i}\) is the horizontal movement measurement value.  
(2) At which time, the gradient of each probability integral parameter, the partial derivative \(G_{k}\), is calculated. Using the BFGS update rule, the search direction d is calculated in each iteration step. Where the initial Hessian matrix \(H_{0}\) is the identity matrix,  
\[d=-H_{k}\times G_{k} \tag{15}\]  
(3) Armijo line search is utilized to determine the step size \(\alpha\), to obtain feasible and significantly improved points in the search direction. The Armijo line search rule is as follows:  
\[f(X_{k}+\alpha d_{k})\leqq f(X_{k})+c\alpha{G_{k}}^{T}d_{k} \tag{16}\]  
In the formula presented, \(c\in\) (0,1), and \(X_{k}\) is the parameter vector after the kth iteration.  
(4) The current iteration point \(X_{k+1}\) is updated:  
\[X_{k+1}=X_{k}+\alpha\times d \tag{17}\]  
(5) The gradient \(G_{k+1}\) is updated, the BFGS is set to find the convergence parameter \(\varepsilon\), and the BFGS computation iteration is stopped when the norm of the gradient is less than \(\varepsilon\) stops from the BFGS computation iteration.  
(6) The Hessian matrix approximation array is updated by BFGS update rule.  
\[H_{k+1}=H_{k}+\left(1+\frac{{Y_{k}}^{T}\times{H_{k}}\times{Y_{k}}}{v}\right) \times\frac{{S_{k}}\times{S_{k}}^{T}}{v}-\frac{{S_{k}}\times{Y_{k}}^{T}\times{ H_{k}}+{H_{k}}\times{Y_{k}}\times{S_{k}}^{T}}{v} \tag{18}\]  
In the formula presented, \(Y_{k}=G_{k+1}-G_{k}\), \(S_{k}=X_{k+1}-X_{k}\), if \({S_{k}}^{T}\times{Y_{k}}>0\), then \(v={Y_{k}}^{T}\times{S_{k}}\), otherwise \(H_{k+1}=H_{k}\).  
(7) Let \(k=k+1\), and go back to step (2).
# Surgical Phase Recognition: From Public Datasets to Real-World Data
## 2 Methods
### Phase Recognition Models  
We consider two different architectures in this work, MSTCN-based [16] and a recent transformer-based architecture, Trans-SVNet [15].  
These architectures are composed of a backbone for extracting features from single frames, and a temporal model which combines features from consecutive frames to predict the surgical phase for each frame.  
The feature extraction backbone is based on the Resnet-50 [20] architecture. The features extracted from the final Resnet block yield a vector of 2048 dimensions for each frame. Per-frame extracted features of a video are stacked to form a sequence, which is then fed into the temporal model.  
As a temporal model, we consider (i) the online trained MSTCN model, which was named TeCNO [9], and (ii) the offline trained MSTCN model, which we named TeCNO-Off in this work.  
MSTCN consists in cascading multiple stages of temporal convolutional networks (TCNs) [21]. This cascade prediction scheme allows every stage to refine the predictions of the previous stage. Every stage contains multiple layers of TCNs, which use dilated convolutions and skip connections. Dilated convolutions offer a larger temporal receptive field with fewer parameters. Hence, this results in faster training and inference, which helps process long surgical videos.  
While the TeCNO online model performs causal convolutions in its TCN layers, whereas its offline version, TeCNO-Off, performs acausal convolutions. In other words, to predict the phase for each frame, the offline version considers all surrounding frames (preceding and succeeding), while the online model considers only preceding frames.  
Additionally, we considered Trans-SVNet [15], which fuses the temporal features extracted from MSTCN and spatial features extracted from Resnet-50 in its transformer layers. This spatial and temporal information fusion yielded top results on Cholec80 dataset [15]. We trained two versions of this model, one with cross-entropy loss and one with weighted cross-entropy loss (see details in Section 2.3.1).
###### Abstract  
This paper introduces an enhancement technique for three-dimensional computational integral imaging by utilizing a post-processing method. Despite the advantages of computational integral imaging systems, the image quality of the systems can suffer from scattering artifacts due to occluding objects during image reconstruction. The occluding objects in out-of-focus locations, especially, can offer scattering artifacts to other objects at in-focus locations. In this study, we propose a novel approach to remove scattering artifacts in reconstructed images from computational integral imaging reconstruction (CIIR). Unlike existing methods such as synthetic aperture integral imaging systems with pre-processing methods, our technique focuses on a post-processing method to remove scattering artifacts. Here, the scattering artifacts are analyzed using a dehazing model with spectral analysis. To enhance the quality of reconstructed images, we introduce a visibility model and an estimation method for a visibility coefficient, a crucial parameter of the dehazing model. Our experimental results from computer simulations indicate that the proposed method is superior to existing computational integral imaging reconstruction (CIIR) methods.  
three-dimensional integral imaging; computational integral imaging reconstruction; scattering artifacts; image quality enhancement; dehazing Article
# Photovoltaic Cell and Module I-V Characteristic Approximation Using Bezier Curves
## 2 Definition of the Bezier Curves  
A quadratic Bezier curve (Figure 2) can be specified by three control points [15]: the curve goes through the ends \(P_{0}\) and \(P_{2}\) and approximates \(P_{1}\).  
The curve equation is as follows [20]:  
\[B_{2}(t)=(1-t)^{2}P_{0}+2t(1-t)P_{1}+t^{2}P_{2} \tag{1}\]  
where \(t\) varies between 0 and 1. Equation (1) can be expressed for the \(x\) and \(y\) coordinates:  
\[\left\{\begin{array}{l}x(t)=(1-t)^{2}x_{0}+2t(1-t)x_{1}+t^{2}x_{2}\\ y(t)=(1-t)^{2}y_{0}+2t(1-t)y_{1}+t^{2}y_{2}\end{array}\right. \tag{2}\]  
The derivative of (1) is:  
\[B_{2}^{\prime}(t)=2(1-t)(P_{1}-P_{0})+2t(P_{2}-P_{1}) \tag{3}\]  
At the end points, (3) becomes (4):  
\[\left\{\begin{array}{l}B_{2}^{\prime}(t)\big{|}_{t=0}=2P_{1}-2P_{0}\\ B_{2}^{\prime}(t)\big{|}_{t=1}=2P_{2}-2P_{1}\end{array}\right. \tag{4}\]  
A cubic Bezier curve (Figure 3) can be specified by four control points [15]: the curve goes through the ends \(P_{0}\) and \(P_{3}\) and approximates \(P_{1}\) and \(P_{2}\). The analytical expression of the curve is a cubic polynomial. The curve is tangent at \(P_{0}\) to \(\overline{P_{0}P_{1}}\) and at \(P_{3}\) to \(\overline{P_{3}P_{2}}\).  
Figure 2: A quadratic Bézier curve representation. \(P_{0}\) and \(P_{2}\) are the end points, the control point \(P_{1}\) is approximated and the curve is tangent to \(\overline{P_{0}P_{1}}\) and \(\overline{P_{2}P_{1}}\) segments at \(P_{0}\) and \(P_{2}\) respectively.  
The equation for the Bezier cubic curve is [20]:  
\[B_{3}(t)=(1-t)^{3}P_{0}+3t(1-t)^{2}P_{1}+3t^{2}(1-t)P_{2}+t^{3}P_{3} \tag{5}\]  
The previous equation can be expressed for the \(x\) and \(y\) coordinates:  
\[\left\{\begin{array}{l}x(t)=(1-t)^{3}x_{0}+3t(1-t)^{2}x_{1}+3t^{2}(1-t)x_{2}+ t^{3}x_{3}\\ y(t)=(1-t)^{3}y_{0}+3t(1-t)^{2}y_{1}+3t^{2}(1-t)y_{2}+t^{3}y_{3}\end{array}\right. \tag{6}\]  
The derivative of (5) is:  
\[B_{3}^{\prime}(t)=3(1-t)^{2}(P_{1}-P_{0})+6t(1-t)(P_{2}-P_{1})+3t^{2}(P_{3}-P_{ 2}) \tag{7}\]  
At the end points, (7) becomes (8):  
\[\left\{\begin{array}{l}B_{3}^{\prime}(t)\big{|}_{t=0}=3P_{1}-3P_{0}\\ B_{3}^{\prime}(t)\big{|}_{t=1}=3P_{3}-3P_{2}\end{array}\right. \tag{8}\]
## 4 Sensitivity Analysis
### Effect of Ambient Temperature  
The temperature of the air cooler outlet stream varies according to ambient temperature. Therefore, the sensitivity analysis conducted to investigate the effect of ambient temperature on the exergy efficiency of each process and the results are illustrated in Figure 13. The air cooler discharge temperature is defined to be 10 \({}^{\circ}\)C higher than the ambient temperature. With an increasing ambient temperature value in the range of 0-40 \({}^{\circ}\)C with 5 \({}^{\circ}\)C step sizes, the exergy efficiency decreases in all three processes. The increase in the ambient temperature leads to an increment of the duties of the compressor and  
Figure 11: Effect of the natural gas compositions on the product cost of each process.  
Figure 12: Effects of the natural gas compositions on the variable cost of each process.  
the rise in the inlet temperatures of the MCHEs. Therefore, the required energy for liquefying the same natural gas capacity increases accordingly. The largest differences in the exergy efficiency can be observed in SMR (34.4%), followed by dual nitrogen expansion (22.3%) and propane pre-cooled self-refrigeration (5.08%). Each process has a certain temperature ranges that make the process infeasible because of the compressor duty constraint. The SMR process can operate over the wide range (10-40 \({}^{\circ}\)C) because it can adjust the MR composition according to the ambient temperature changes. However, the operation availability range of propane pre-cooled self-refrigeration is relatively small because of the refrigeration duty of the main compressor.  
The effects of ambient temperature on the product cost are illustrated in Figure 14. As stated earlier, an increase in the required energy affects the energy cost that leads to an increase in product cost. The largest difference in product cost can be observed for SMR, 5.9%; this is followed by dual nitrogen expansion (4.5%) and propane pre-cooled self-refrigeration (1.1%). Overall, the effect of the ambient temperature on the product cost does not seem to be significant.  
Figure 14: Effects of ambient temperature on product cost of each process.  
Figure 13: Effects of ambient temperature on exergy efficiency of each process.
## 4 Description and Numerical Analysis of Failure Characteristics of Test Block
### Breakage and Numerical Analysis of Test Block under Different Apertures  
As shown in Figure 5, the failure of the test block with different borehole diameters shows that the failure of the test block is mainly crack propagation, surface shedding, and hole wall collapse. By observing the whole process of the failure of the test block under uniaxial compression, during the failure process of the test block with different apertures, a tensile microcrack first appears above the hole, and as the axial stress continues to increase, the tensile crack extends along the axial direction, forming a crack through the hole. After entering the stress peak stage, the micro-cracks on the surface of the test block begin to increase, and, finally, the main control crack propagation test block was quickly and completely destroyed [22]. From the failure state of the test blocks with different apertures in Figure 5, the surface of the test blocks with apertures of 6 mm and 10 mm (such as Figure 5a,b) presents slight shedding, the crack propagation is not obvious, the damage degree is low, and the hole wall collapse is not obvious. The surface of the test block with borehole diameters of 15 mm, 20 mm, and 25 mm (Figure 5c-f) showed obvious shedding, and the main control crack propagation, damage degree, and hole wall collapse gradually became obvious. Combined with FLAC3D simulation Figures 6-8, and the vertical stress values of the monitoring points in Figure 7 from the shallow to the deep are counted in Figure 8a,b, respectively. It can be seen that with the increase in pore size, the radius of the plastic zone around the hole is larger, and the vertical stress at both ends of the hole, top and bottom, gradually decreases, but there is a peak stress concentration not far from the borehole.  
Figure 5: (**a**) is the failure diagram of the sample with a borehole diameter of 6 mm, (**b**) is the failure diagram of the sample with a borehole diameter of 10 mm, (**c**) is the failure diagram of the sample with a borehole diameter of 15 mm, (**d**) is the failure diagram of the sample with a borehole diameter of 20 mm, (**e**) is the failure diagram of the sample with a borehole diameter of 25 mm, and (**f**) is the failure diagram of the sample with a borehole diameter of 40 mm.  
Figure 6: Plastic zone diagram of different borehole diameters.  
Figure 7: Vertical stress nephogram of different borehole diameters. (**a**) 6 mm; (**b**) 10 mm; (**c**) 15 mm; (**d**) 20 mm; and (**e**) 25 mm.
## 2 Background and Rationale
### Rationale
Thus, the energy of nodes on the same path may still be depleted compared to the energy of the nodes on the unchosen paths. Therefore, both early filtering of the fabricated reports and balancing the workload on the chosen filtering nodes and along the routing path are of utmost importance in improving the energy efficiency and increasing the lifetime of WSNs. In a WSN, the radio unit on the sensor consumes the most energy. In single hop communication based WSNs, CHs located far from the BS have a larger energy burden due to the long-haul communication link. Therefore, multi-hop cluster head communication is more energy efficient, and the CHs collaborate with each other to forward their data to the BS [25]. Thus, data forwarding on a multi-hop path through intermediate CHs is more realistic in this case [25]. The cluster head selection can be periodically rotated with in a cluster to balance the energy consumption. MR-LEACH [32] is a multi-hop routing strategy for energy conservation in WSNs in which an intermediate CH serves as a relaying node. In MR-LEACH, the intermediate nodes are only the CHs forming a tree rooted at the BS, and member nodes serve as leaves. The context aware architecture for probabilistic voting-filtering scheme in [29] also presupposes a multi-hop cluster head-based data forwarding technique due to its inherent energy conserving feature. LEACH provides extended network lifetimes [33]. Similarly, in our proposed scheme, the role of the CH can be rotated with in the cluster to achieve energy balancing as proposed in [25; 26; 32; 34]. However, a discussion of such CH rotation techniques is beyond the scope of this paper.
## 4 Experiments and Discussion
### Results  
Table 1 is a summary of the experimental results. According to the three evaluation indexes of RMSE, MAE and MAPE, DA-RNN achieves the best prediction accuracy. Regardless of the method used, the accuracy of the prediction can always be improved by inputting dynamic factors. The optimal value of the parameter \(T\) is 5, while the optimal values of the parameters m and p are both 128. This is because the influence of the values of m and p on the prediction is small relative to \(T\), and they are structural parameters of the RNN without any clear physical meaning. Taking into account the length of this article, Table 1 only lists the experimental results when \(m=p=128\).  
In Section 2, we not only used the calculation formula of the next station arrival time \(t_{i}\), but also the calculation formula of the remaining station arrival time \(t_{i+1}\) to \(t_{k}\). If the bus is located on the \(i\)-th road segment, then the dynamic factors of the (\(i\)+1)-th to \(k\)-th road segment are unknown. So \(t_{i+1}\) to \(t_{k}\) can only be predicted with a static model. First enter \(t_{i}\) into the static model to get \(t_{i+1}\). Then enter \(t_{i}\) into the static model to get \(t_{i+1}\). We performed iterative operations until \(t_{k}\) was obtained. The result under offline conditions is shown in Figure 6.
## 3 Results and Discussions
### Wall Erosion When the Value of \(\alpha\) Is Positive
Therefore, different from the case with positive \(\alpha\) shown in Figure 9, some of the ion velocities when \(\alpha\) is negative are along the direction far away from the wall, as shown in Figure 13. Moreover, as the value of negative \(\alpha\) decreases, the number of the ions whose velocity is away from the wall increases, and the maximum value of the velocity in this direction rises. Thus, the overall distribution of IVDF becomes flat. The difference in IVDF for radial components shown in Figures 9 and 13 results in different degrees of sputtering erosion on the dielectric wall. When the value of \(\alpha\) is negative, the ions entering the simulation area are slowed down or even reversely accelerated, resulting in a reduction in both the number and energy of ions that can hit the wall. The erosion rate values in Figure 14 are generally smaller than that in the cases of \(\alpha=0\) and \(\alpha>0\). Meanwhile, as the value of the negative \(\alpha\) decreases, the average velocity of the ions away from the wall increases, and the erosion rate of the dielectric wall induced by the ion sputtering decreases. Therefore, compared with the cases of \(E\bot B\) and \(\alpha>0\), having magnetic field lines convex to the anode direction enables better focusing of the ion beam and reduction of the erosion rate. Compared with the case with the electric field \(E\) perpendicular to the magnetic field \(B\), when the value of the angle \(\alpha\) is \(-15^{\circ}\), \(-30^{\circ}\), \(-45^{\circ}\), and \(-60^{\circ}\), the erosion rate decreases by 5.5%, 59%, 83%, and 90%, respectively. Figure 6:0 Ion velocity distribution function for radial component with different values of the negative \(\alpha\). According to the above conclusions, several relevant phenomena can be explained in the Hall thrusters. Firstly, the magnetic field configuration that is convex toward the anode is always chosen for application in Hall thrusters because this configuration corresponds to the case with negative \(\alpha\) in this paper. According to the numerical results, this type of magnetic field configuration benefits the convergence of ion beams and can reduce the sputtering erosion rate on the wall. Secondly, the erosion near the exit of the thruster is more serious than that inside the channel because the value of the negative \(\alpha\) near the exit is smaller than that near the anode. According to the result shown in Figure 14, the larger value of \(\alpha\) corresponds to a larger erosion rate when \(\alpha\) is negative. Therefore, in the channel with a smaller value of the negative \(\alpha\), the effect of the magnetic field on shielding ion sputtering is more effective, and the wall erosion is less severe.