esa-sceva/satcom-chunk-collection huggingface dataset:
# Accelerate Incremental TSP Algorithms on Time Evolving Graphs with Partitioning Methods
## 3 Algorithms
### Incremental Algorithm  
In our previous work, the inputs of an I-TSP and Ig-TSP algorithm include the complete graph, the results from the previous time interval, and the update event. The objective is to reduce the amount of recomputations in the updated graph for the current time interval. All the TSP tours of a graph are represented by a search tree [14], as shown in Figure 2. Each tour in a search tree will be a path. The intuition of I-TSP is to only recompute the paths that are affected by the update event. The pseudocode is shown in Algorithm 1. I-TSP and Ig-TSP differ from each other in their method of propagation. Where the I-TSP algorithm propagates messages to all the neighbors, Ig-TSP being a greedy algorithm that propagates only to the closest neighbor.  
Figure 1: Top three imagesshow TEGs with various update events, and the bottom three images are their respective TSP tours.  
Figure 2: Search tree with all the possible permutations of TSP tours in a four-vertex graph. Each tour begins with source vertex 0 and ends at source vertex 0. For a four-vertex graph, there will be six possible tours. The purple area shows the region affected by the update event.  
```
1:\(\Delta G_{l}(u,v,C(u,v))\), pathList.
2:A TSP tour, T
3:preProcessing(pathList)
4:\(id(source)\longrightarrow sendMessage(U,initialVertexMessage)\)
5:for vertex v do\(\triangleright\) Parallel for loop
6:for message do
7:if (\(S\
eq 1\) && message.last \(\
eq id(v)\) && message.length \(\
eq n+1\) && message[path] \(\
ot\subset validPathList\)) then
8:if\(id(v)\
otin message\)then
9:updateMessage(message)
10:endif
11:if (mode == brute) then
12: propagateAll(message)
13:else
14: propagateGreedy(message)
15:endif
16:else
17: sendMessage(id(source), message)
18:endif
19:endfor
20: computeTSPTour()
21:endfor
22:functionpreProcessing(pathList)
23:for path in pathList do
24:for p in path do
25:if ((\(p[j]==id(v^{\prime})\) && (\(p[j-1]\) or \(p[j+1]==id(u)\)) then
26:invalidPathList += path && \(j>1\)) then
27:else
28: validPathList += path
29:endif
30:endfor
31:for path in invalidPathList do
32:for p in path do
33:if ((\(p[j]==id(v^{\prime})\) or \(id(u^{\prime})\)) && \(j>1\)) then
34: truncatedPathList += path.sublist(1,j)
35:endif
36:endfor
37:endfor
38:endfor
39:for Y in truncatedPathList do
40:if (y.last = = id(v)) then
41: initialVertexMessage += y
42:endif
43:endfor
44:endfunction
```  
**Algorithm 1** Incremental distributed TSP Algorithms: I-TSP and Ig-TSP [14].
## 5 Performance Evaluation and Simulation  
In this section, we present three subsections: (A) experiment settings and measurements and (B) TL method, and (C) simulation performance. The first discusses the simulation environments, parameters, and hyper-parameters used in the paper. The second discusses the TL technique and its significance. The third explains the results and compares the simulation to other benchmarks.
## 4 Intelligent Prediction of Link States
### Convolutional Neural Networks (CNN)s  
The CNN consists of two Conv1D (one-dimensional convolutional layers) combined with a fully connected layer and an attention mechanism. It merges a MaxPooling layer and a Rectified Linear Unit (ReLU) layer between two consecutive convolutional modules to fully capture spatial dependencies [8]. A Conv1D operation with input channel 1, output channel 16, convolution kernel length 3, and step size 1 is applied to the sample set in the first convolutional layer to filter the noise and extract the valid information. Figure 2 shows an example of a simple one-dimensional convolution operation. Denote \(y_{t}^{(i,b)}\) as the input matrix of the \(0^{th}\) convolutional layer in the \(i^{th}\) region matrix at time \(t\). Then, the \(k^{th}\) network layer is represented as shown in Equation (9):  
\[y_{t}^{(i,k)}=\sum_{i\in x_{t}}f(y_{t}^{(i,k-1)})\otimes W_{i,t}^{k}+b_{t}^{k}, \tag{9}\]  
where \(x_{t}\) denotes a set of input data, \(W_{i,t}^{k}\) is the convolution kernel, \(f\) is the nonlinear (rectified linear unit) activation function, \(\otimes\) is the elemental product, and \(b_{t}^{k}\) and \(y_{t}^{(ijk)}\) denote the deviation of the convolution module \(k\) and the output value, respectively [18].  
Figure 2: One-dimensional convolution example.  
The convolutional layer is followed by a nonlinear activation function ReLU to improve the model's ability to learn complex structures, as shown in Equation (10).  
\[f(x)=max(0,x), \tag{10}\]  
A MaxPooling layer is added to the CNN model, which is a downsampling method that reduces the spatial dimensionality value of the feature attribute map by half and retains the most important features [19]. The pooling operation is shown in Equation (11), and the input data feature set is partitioned into connected \(1\times 2\) modules by means of the window free-sliding. An activation function accelerates the convergence of the model.  
\[y_{t}^{(l,k)}=subsampling(y_{t-1}^{(ijk)}), \tag{11}\]  
The second layer of convolution is similar to the first layer, by applying a Conv1D convolution operation with 16 input channels, 32 output channels, convolution kernel length of 3, and step size of 1. This layer increases the complexity of the features and further reduces the data dimensions.
# Recursive Optimal Finite Impulse Response Filter and Its Application to Adaptive Estimation
## 2 Recursive Optimal FIR Filter and Adaptive FIR Filter
### Optimality and Unbiasdness of Recursive Optimal FIR Filter
\begin{array}{rcl}P_{k-N}^{-1}&=&\tilde{\mathcal{C}}_{k-1}^{T}\Pi_{k-1}^{-1} \tilde{\mathcal{C}}_{k-1}\\ &=&\tilde{\mathcal{C}}_{k-1}^{T}\bigg{\{}\tilde{R}_{N,1}^{-1}-R_{N,1}^{-1} \tilde{\mathcal{C}}_{k-1}\Big{(}\tilde{G}_{k-1}^{T}\tilde{R}_{N,1}^{-1}\tilde {\mathcal{C}}_{k-1}+\tilde{Q}_{N,1}^{-1}\Big{)}^{-1}\tilde{G}_{k-1}^{T}\tilde {R}_{N,1}^{-1}\bigg{\}}\tilde{\mathcal{C}}_{k-1}\\ &=&W_{1k}-W_{2k}W_{3k}W_{2k}^{T},\\ P_{k-N}^{-1}\tilde{x}_{k-N}&=&P_{k-N}^{-1}p_{k-N}^{-1}\tilde{x}_{k-1}^{T}\Pi_{ k-1}^{-1}\\ &=&\tilde{\mathcal{C}}_{k-1}^{T}\bigg{\{}\tilde{R}_{N,1}^{-1}-\tilde{R}_{N,1}^ {-1}\tilde{G}_{k-1}\Big{(}\tilde{G}_{k-1}^{T}\tilde{R}_{N,1}^{-1}\tilde{G}_{k- 1}+\tilde{Q}_{N,1}^{-1}\Big{)}^{-1}\tilde{G}_{k-1}^{T}\tilde{R}_{N,1}^{-1}\bigg{\}} \\ &=&\tilde{\mathcal{C}}_{k-1}^{T}\tilde{R}_{N,1}^{-1}Y_{N,k-1}-W_{2k}W_{3k}^{-1} \tilde{\mathcal{C}}_{k-1}^{T}\tilde{R}_{N,1}^{-1}Y_{N,k-1},\end{array}  \tag{51}\]  
respectively. Then, we can obtain the following relations by applying (51) to the right side of Equation (38):  
\[\begin{array}{l}M_{k}\bigg{[} \begin{array}{cc}W_{1k}+P_{k-N}^{-1}&W_{2k}\\ W_{2k}^{T}&W_{3k}\end{array} \bigg{]}^{-1}\Bigg{(} \begin{bmatrix}P_{k-N}^{-1} \\ 0\end{bmatrix} \delta_{k-N}+ \begin{bmatrix}\tilde{\mathcal{C}}_{k-1}^{T}\\ \tilde{G}_{k-1}^{T}\end{bmatrix} \tilde{R}_{N,1}^{-1}Y_{N,k-1}\\ =&M_{k}\bigg{[} \begin{array}{cc}W_{1k}+P_{k-N}^{-1}&W_{2k}\\ W_{2k}^{T}&W_{3k}\end{array} \bigg{]}^{-1}\Bigg{[} \begin{array}{cc}2\tilde{ \mathcal{C}}_{k-1}^{T}\tilde{R}_{N,1}^{-1}Y_{N,k-1}-W_{2k}W_{3k}W_{3}^{-1} \tilde{G}_{k-1}^{T}\tilde{R}_{N,1}^{-1}Y_{N,k-1}\\ \tilde{G}_{k-1}^{T}R_{N,1}^{-1}Y_{N,k-1}\end{array} \bigg{]}\\ =&M_{k}\bigg{[} \begin{array}{cc}W_{1k}+P_{k-N}^{-1}&W_{2k}\\ W_{2k}^{T}&W_{3k}\end{array} \bigg{]}^{-1}\Bigg{[} \begin{array}{cc}2\tilde{ I}&W_{2k}W_{3k}^{-1}\\ 0&I\end{array} \bigg{]}\bigg{[} \begin{array}{cc}\tilde{\mathcal{C}}_{k-1}^{T}\\ \tilde{G}_{k-1}^{T}\end{bmatrix}\tilde{R}_{N,1}^{-1}Y_{N,k-1}\\ =&M_{k}\bigg{[}\begin{array}{cc}W_{1k}&W_{2k}\\ W_{2k}^{T}&W_{3k}\end{array}\bigg{]}^{-1}\Bigg{[}\begin{array}{cc}\tilde{ \mathcal{C}}_{k-1}^{T}\\ \tilde{G}_{k-1}^{T}\end{array}\bigg{]}\tilde{R}_{N,1}^{-1}Y_{N,k-1},\end{array}  \tag{52}\]  
This completes the proof.
# Simulation Analysis of a Three-Degree-of-Freedom Low-Frequency Resonant Mixer
## 3 Dynamic Analysis of the Three-Degree-of-Freedom Low-Frequency Resonant Mixer
### Harmonic Response Analysis of the Three-Degree-of-Freedom Low-Frequency Resonant Mixer
#### 3.2.1 Phase-Frequency Response of the Three-Degree-of-Freedom Low-Frequency Resonant Mixer  
Phase-frequency characteristics refer to the phase difference between the response and the excitation as the excitation frequency changes [23], characterizing the phase-frequency characteristics of forced vibration [24].  
To produce a vertical acceleration of 600 m/s\({}^{2}\) at the payload assembly that meets the working requirements, this study inputs a sine excitation force with an amplitude of F = 5800 N, vertically acting on the bottom plate of the excitation assembly, and proceeds with the calculation.  
As can be seen from Figure 1, by studying the force exerted by the three-degree-of-freedom system on the framework, the external influence of the equipment can be indirectly reflected, and the vibration isolation mechanism can be investigated. This study analyzes the phase-frequency response of the equipment's assemblies near the first three natural frequencies to determine the relative direction of motion of the assemblies, and thus the relative direction of the force exerted by the three-degree-of-freedom system on the framework. The phase-frequency response curves from the viewer's work results are shown in Figure 4.  
Referring to the data in Table 2, it can be observed from Figure 4 that at the first-order natural frequency of 14.47 Hz and the second-order natural frequency of 38.42 Hz, the phase difference between the motion of the payload assembly and the vibration-isolating assembly remains zero. As can be seen from Figure 1, the payload assembly and the vibration-isolating assembly are connected to the framework through springs, and at this time, the inertial forces of the payload assembly and the vibration-isolating assembly, which are in the same direction, act simultaneously on the framework, which is not conducive to the vibration isolation of the equipment. At the third-order natural frequency of 58.95 Hz, the phase difference between the payload assembly and the vibration-isolating assembly is consistently maintained at 180\({}^{\circ}\). Referring to Figure 1, it can be seen that at this point, the frame is only subjected to the forces from two springs k\({}_{2}\) and k\({}_{4}\), as well as the force exerted by the ground. The frame is directly connected to the payload assembly and the vibration damping assembly through the two springs. Compared to when the two assemblies move in the same direction, when they move in opposite directions, the resultant force transmitted to the frame via the springs will relatively decrease, and the force exerted by the ground on the frame will also decrease accordingly. In this state, the low-frequency resonance mixing equipment has a minimal impact on external vibrations.  
Figure 4: _Cont._
## 5 Result and Discussion
### Comparative Analysis
From the 4-5 columns of the table, we can see that energy consumption cost one increases while energy consumption cost two decreases. However, the energy consumption cost shows a decreasing trend, indicating that the energy consumption of the pure electric bus is much lower than that of the fuel vehicle. On the premise of ensuring the completion of the operation task, the energy consumption of the increased pure electric bus is lower than that of the reduced fuel vehicle. Therefore, considering the energy consumption alone, it is better to keep the higher the proportion of the electric bus. 3. The total cost is shown as concave in column 7 of Table 7, with decreasing energy costs and increasing passengers cost. It indicates that when the number of electric buses increases to a certain proportion, the saving costs on energy are not enough to make up for the rising passengers cost. There is a balance between the two costs in order to achieve the optimal (the lowest total cost). Therefore, it is not acceptable to merely consider energy consumption reduction from the perspective of the total cost. How to choose depends on which aspect the bus enterprises focus on, and at the same time, they should respond to the national policy. 4. As is shown in column 8 of Table 7, increasing charging times is inevitable in the process of increasing the proportion of pure electric buses, which requires the expansion of charging infrastructure. 5. The total number of vehicles in column 1 of Table 7 shows that in the process of replacing fuel buses by pure electric buses, the size of buses keeps increasing, so the capacity of the parkingyard and charging equipment need to be expanded. The current discussion on energy consumption saving is mostly concentrated in reducing the number of cars and formulating policies on reducing car use, but the studies on public transit are less. Based on the characteristics of energy-intensive for the traditional buses, blindly advocate public transit may save energy but it is not the best solution. The application of the electric bus in a reasonable ratio can achieve the reduction on public transport energy consumption. The current situation is that the environmental-friendly electric buses are gradually replacing the fuel vehicles. Although the replacement is not entire, the scale is gradually expanding. Therefore, the study on the schedule of the bus driving plan to reduce the energy consumption is particularly important. The variation of the single bus type operation is not reasonable, which may easily lead to the waste of capacity during flat peak periods and the shortage of capacity during peak periods. Different types of buses can carry different passenger loads, so different bus type matching ratios should be considered according to the passenger flow.
## 2 Materials and Methods
### Estimation of LST  
The satellite's LST provides crucial data for assessing the influence of urbanization [45]. Landsat satellite thermal band images were utilized to uncover the surface heat's locative scattering, in addition to measuring the LULC effect on LST within the research region. Concerning the LST calculation, the method used was explained by [PERSON] et al. [46]. The temperature information was acquired by making use of Landsat's (TM and ETM+) digital number (DN) (0-255) and the Landsat's OLI (DN 0-65,536) thermal bands. The DN was then transformed to Kelvin temperature in two actions. Initially, the DN value to spectral radiance made use of the next method [47; 48]:  
\[L_{\lambda}=M_{L}\times QCal+A_{L} \tag{1}\]  
\[L_{\lambda}=\frac{Lmax_{\lambda}-Lmin_{\lambda}}{QCal_{max}-QCal_{min}}\times \left(QCal_{max}-QCal_{min}\right)+Lmin_{\lambda} \tag{2}\]  
In which \(L_{\lambda}\) denotes the spectral radiance W/(m\({}^{2}\) sr \(\upmu\)m), \(M_{L}\) is a multiplicative element for scaling the thermal bands' radiance, \(QCal\) represents the digital number, \(A_{L}\) is an additive element for the band radiance scaling, \(QCal_{max}=255\), \(QCal_{min}=1\), and \(Lmax_{\lambda}\) and \(Lmin_{\lambda}\) denote the thermal bands' spectral radiance at DN = 255 and 1, respectively (given in W/m\({}^{2}\) ster \(\upmu\)m) [14].  
Secondly, thermal infrared information was then developed by extracting the brightness temperature (\(T_{B}\)) from the above-calculated spectral radiance. The transformation method can be explained as follows [14; 47]:  
\[T_{B}=\frac{K_{2}}{Ln\left[\frac{K_{1}}{L_{\lambda}}+1\right]} \tag{3}\]  
where \(T_{B}\) is the \(T_{B}\) (given in \({}^{\circ}\)K), and \(K_{1}\) and \(K_{2}\) represent thermal band's conversion constants. For Landsat 4 (TM), \(K_{1}\) is 607.76 and \(K_{2}\) is 1260.56; for Landsat 7 (ETM+), \(K_{1}\) is 666.09 and \(K_{2}\) is 1282.71; for Landsat 8 (OLI), \(K_{1}\) is 774.89 and \(K_{2}\) is 1321.08. All \(K_{1}\) and \(K_{2}\) values are given in mW/cm\({}^{2}\)/sr/\(\upmu\)m and Kelvin, respectively.
# Multi-Granularity User Anomalous Behavior Detection
## 6 Discussion
### Complexity Analysis  
Assuming that the initial number of training samples for MG-UABD is \(D\), the maximum number of features among all types of behaviors is \(M\), the number of decision trees in the random forest algorithm is set to \(T\), and the depth of the decision trees is \(d\), the time complexity of training a coarse-grained classification module is \(O(D\times logD\times M\times T)\). If anomalous users which are detected in the coarse-grained anomaly detection stage is \(n\), the maximum number of behavior samples corresponding to these users is \(P\), and the time complexity of training the fine-grained detection module is \(O(P\times logP\times M\times T)\). The time complexity of both coarse-grained and fine-grained modules during the detection  
Figure 13: Detection effectiveness for each type of behavior.  
phase is \(O(d)\). As for the spatial complexity, if the number of nodes in each decision tree in the random forest is \(v\), the spatial complexity of the coarse-grained detection module is \(O(v\times T)\), and the spatial complexity of the fine-grained detection stage is \(O(n\times vs.\times T)\).  
It is obvious that MG-UABD builds detection models for each user in the fine-grained detection stage, which increases the computational time and space resources. The time complexity is directly proportional to the maximum number of anomalous user behavior samples detected in the coarse-grained detection stage, and the space complexity is directly proportional to the number of anomalous users. Therefore, it should be selected as needed in practical applications. Fortunately, the two modules of this model can be decoupled, and companies can choose which module to use based on their employee size and cost calculation. In addition, further research can explore the quantitative evaluation of the degree of user anomaly in the coarse-grained detection stage, and design a fine-grained detection model based on the degree of user anomaly, which is more targeted and cost-effective.
## 3 Results  
### Details on the Computation  
In order to compare the predictions of the time-dependent X-ray emission rates obtained from the 3-level model with available experimental data, the calculations were performed for a copper atom and an incident X-ray photon energy close to the Cu-K-shell edge. The details of the experimental setup and the data analysis can be found in [13]. Thanks to a relatively small detuning of only 12 eV with respect to the ionization threshold, both one- and two-photon absorption channels were probed in this experiment by measuring simultaneously the X-rays from a radiative decay of the intermediate state excited through inelastic scattering of the incident photons, as well as the non-resonant K\(\alpha_{1,2}\) X-rays resulting from the two-photon absorption process. The X-ray signatures of the TPA and OPA processes were measured with a high-resolution von Hamos diffraction spectrometer. The experiment thus provided information on the flux and incident X-ray energy dependences for the TPA mechanism. In the present calculations, the photon absorption cross sections for the N\({}_{1}\rightarrow\) N\({}_{2}\) and N\({}_{2}\rightarrow\) N\({}_{3}\) excitations were taken from the reported experimental values [13], which were determined to be \(\sigma_{1,2}=5.5\times 10^{-22}\) cm\({}^{2}\) and \(\sigma_{2,3}=1.4\times 10^{-16}\) cm\({}^{2}\). Similarly, the atomic lifetimes for the N\({}_{2}\) and N\({}_{3}\) states were fixed to \(\tau_{2}=5.4\times 10^{-17}\) s and \(\tau_{3}=4.42\times 10^{-17}\) s, respectively.  
In the calculations, we assumed a Gaussian-shaped X-ray pulse, which was inserted into Equations (1)-(3) in the following form:  
\[\mathrm{I(t)}=\frac{\mathrm{I_{0}}}{\sqrt{2\pi\sigma}}\times\exp\left(-\frac{ \mathrm{(t)}^{2}}{2\sigma^{2}}\right) \tag{5}\]  
In the above equation, \(\mathrm{I_{0}}\) represent the X-ray pulse intensity, and \(\sigma\) the standard deviation of its time profile. In the computations, we assumed a Gaussian X-ray pulse full width at half maximum value of 30 fs as reported in the experiment. This approximation was made since the experiment took advantage of the self-seeded mode of operation of the LCLS XFEL [6], which transforms the broad, spiky SASE (Self-amplified Spontaneous Emission) spectral structure and reduces it to a quasi-monochromatic spectrum. The resulting X-ray pulse in time will be similarly a single pulse with limited structure [14]. The numerical calculations for the time-dependent population of states were performed in the range of \(\Delta\)t = 100 fs (i.e., about 3 times the pulse length) and with a time-step (dt) of \(10^{-4}\) fs, i.e., a value being much smaller than the pulse width and the lifetimes of the probed atomic states.
## 1 Introduction
Based on the historical data collected from 220 kV substations in a region, a historical database is established, and the characteristic quantities, classical domains and fault sets for state evaluation and fault prediction are compiled and summarized. A state evaluation model based on the improved AHP method and the matter-element extension method, and a fault prediction model based on K-means clustering are constructed. Through the analysis of actual operation cases in a certain region at a certain time, it is proved that the model can realize the real-time monitoring of the protection system state and fault prediction when the state deteriorates with an accuracy rate of more than 90%. In actual operations, it can rely on digital twin technology to update the historical database with real-time feedback and gradually improve the correct rate of fault prediction.
## 3 Results and Discussion
### Vertical down Position  
The observation of molten pool behavior with a longitudinal direction in the vertical down position is shown in Figure 8a. The dynamic arc imaging synchronization of waveforms is shown in Figure 8b. During the welding procedure, the gravity continuously pushed the molten pool flow forward and more molten pool piled up between the arc ignition and base metal, creating a cushion effect, as shown in Figure 9. The accumulation of the molten pool in the arc center caused the arc length to shorten close to the droplet on the molten pool surface. As a result, the short circuit transfer mode occasionally occurred when the wire contacts the surface of the molten pool before droplet detachment, as shown in Figure 10. This condition induced an unstable arc and more spatters occurred in the vertical down position. Due to the accumulated molten pool in the arc center, arc forces such as arc pressure, electromagnetic force, and droplet impact in OPOD transfer mode suppressed the surface of the molten pool. Under these conditions, the short circuit transfer and OPOD transfer obstructed the depth penetration because the accumulated molten pool prevented downward flow into the base metal. Therefore, the penetration depth had the smallest value of 0.8 mm and bead width had the largest value of 6.9 mm compared to other welding positions.