esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 The Time Source Techniques
### Pulsar Star
#### 3.3.1 Timing Mechanism  
Pulsar emission is modulated by the star's rotational frequency, \(\
u=\frac{\Omega}{2\pi}\) (where \(\Omega\) is the angular velocity), which is exceptionally stable and enables microsecond-level precision in measuring the pulsed signal [58]. There is one type of pulsar called millisecond pulsar (MSP), which rotates extremely rapidly with periods of less than 10 milliseconds. MSP is even more stable. For example, the period drift rates of the millisecond pulsars PSR B1937+214 can reach \(6.74\times 10^{-17}\,\mathrm{s}^{-1}\)[59]. Additionally, pulsars exhibit long-term stability that extends over millions of years, significantly surpassing the stability of terrestrial atomic clocks [60], as shown in Figure 3.  
Observations can uncover the rotational evolution of pulsars using a technique called pulsar timing, which monitors the neutron star's rotation on a turn-by-turn basis [58]. Pulsar timing is a technique that involves comparing the observed pulse arrival times with the predicted arrival times, which are calculated using a physical model of the pulsar's signal and its propagation to the observatory [61]. This technique enables the pulsar to be used as a time source, especially for MSP.  
Figure 3: Derived frequency stability for a range of different frequency sources [59].  
Figure 2: Pulsar beams.  
The periodic pulse signals that the pulsars emit can be observed by radio telescopes. However, pulsars are weak radio sources, and their flux densities are relatively low and fluctuating with time [62]. It makes the pulses indiscernible with noise and interference; as shown in Figure 4, the timing signal with the waveform is highlighted [63]. In addition, during the transmission, the pulse signals are affected by the frequency-dependent transmission speed in the interstellar medium [64], which results in dispersion in the received observation data and degrades the time resolution of the pulse signal, as shown in Figure 5. As a result, it is impossible to use the pulse signals for timing directly. Signal processing is necessary to detect and recover the pulse signals from distortion, noise, and interference [62].  
The entire processing procedure, shown in Figure 6, starts from the output of the Analog-to-Digital Converter (ADC) in the radio telescope and ends with the Pulse-Per-Second (PPS) signal generation [62].  
Although pulsar timing signals exhibit high long-term stability, the short-term stability is less precise due to multiple sources, such as noise and interference from outer space, the atmosphere, the antenna, and signal processing errors. To address this, a local clock with good short-term stability is used, combined with a locking and control module, to ensure accurate pulse signal generation as referenced in [63].  
Figure 4: MSP J1939+2134 received waveform and pulse profile.  
Figure 5: Pulses at different frequencies with effect of dispersion.
# Joint Trajectory and Communication Design for Buffer-Aided Multi-UAV Relaying Networks
## 4 Numerical Results
Next, we demonstrate the convergence behavior of Algorithm 1 in Figure 5. The average throughput of this network during different periods is illustrated. From this figure, it can be observed that with the number of iterations of the proposed algorithm increasing, the average throughput of this network gradually converged, and the convergence was achieved at about six iterations. Therefore, the curves satisfied our expectation and verified the effectiveness of the proposed algorithm in maximizing average throughput. Furthermore, it can be found that the system average throughput could be increased by prolonging the period time.
## 6 Conclusions  
In this article, an RFR-GA-BLS model is proposed and is applied to the infrared fault diagnosis of bearings. The model can obtain the optimal parameters and minimum features while achieving high standard fault diagnosis. The innovations of this article are as follows:  
1. The infrared images of rolling bearings are collected as the original signals for fault diagnosis, and the visualization of faults is realized.
2. There is a changing the previous feature selection method and replacing it with RFR feature sorting. Thus, the problem of too much or too little feature selection is avoided.
3. Optimization of BLS by using GA to obtain three parameters, N1, N2 and N3, and the best accuracy was achieved, combined with RFR fusion into RFR-GA-BLS fault diagnosis model to obtain the optimal number of features.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Times** &
\begin{tabular}{c} **Consumption Time** \\ **Indicator (BLS is 1)** \\ \end{tabular} & **Accuracy** \\ \hline SVM & 3.32 s & 18 & 0.92222 \\ RF & 2.19 s & 12 & 0.87778 \\
1 DCNN & 37.35 s & 207 & 0.93333 \\
2 DCNN & 1831.45 s & 10,147 & 0.98889 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of broad-learning, machine-learning and deep-learning methods.  
After experimental comparison, the RFR feature ranking method is obviously better than others. The GA-BLS optimization algorithm can achieve fast and accurate fault diagnosis. The infrared fault diagnosis of bearings using RFR-GA-BLS has certain advantages.  
However, in this article, only the parameters of the BLS are optimized, and no improvements are made to the internal BLS. In addition, in real life, the bearing failure data are mostly unbalanced. Therefore, the data design aspect needs to be improved. The BLS also needs to be improved according to the data distribution problem. These are all issues that need to be addressed in subsequent studies.  
Conceptualization, L.L. and J.Z.; methodology, L.L.; software, L.L.; validation, L.L., X.S. and X.Y.; formal analysis, X.Y.; investigation, X.S.; resources, X.S.; data curation, L.L.; writing--original draft preparation, L.L. and J.Z.; writing--review and editing, X.S. and X.Y.; visualization, X.S.; supervision, X.Y.; project administration, L.L.; funding acquisition, J.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 51865010, and the Science and Technology Project of Jiangxi Provincial Department of Education, grant number GJJ210639.  
Not applicable.  
The authors declare no conflict of interest.
# FPT Algorithms for Diverse Collections of Hitting Sets
## 3 A Framework for Maximally Diverse Solutions
### Faster Augmentation  
We can obtain faster algorithms by using more advanced network algorithms from the literature. We will derive one such algorithm here. The best choice depends on the relation between \(n\), \(k\), and \(r\). We will apply the following result about \(b\)_-matchings_, which are generalizations of matchings: Each node \(v\) has a given _supply_\(b(v)\), specifying that \(v\) should be incident to at most \(v\) edges.  
**Proposition 2** ([24]).: _A maximum-weight \(b\)-matching in a bipartite graph with \(N_{1}+N_{2}\) nodes on the two sides of the bipartition and \(M\) edges that have integer weights between \(0\) and \(W\) can be found in time \(O(N_{1}M\log(2+\frac{N_{1}^{2}}{M}\log(N_{1}W)))\)._  
We will describe below how the network flow problem from above can be converted into a \(b\)-matching problem with \(N_{1}=r+1\) plus \(N_{2}=n\) nodes and \(M=2 rn\) edges of weight at most \(W=2r\). Plugging these values into Proposition 2 gives a running time of \(O(r^{2}n\log(2+\frac{r}{n}\log(r^{2})))=O(r^{2}n\max\{1,\log\frac{r\log r}{n}\})\) for finding an optimal augmentation. This improves over the run time \(O(r^{2}nk)\) from the previous section unless \(r\) is extremely large (at least \(2^{k}\)).  
From the network of Figure 1, we keep the two layers of nodes \(T_{i}\) and \(V_{j}\). Each vertex \(T_{i}\) gets a supply of \(b(T_{i}):=k\), and each vertex \(V_{j}\) gets a supply of \(b(V_{j}):=r\). To mimic the piecewise linear costs on the arcs \((V_{j},t)\) in the original network, we introduce \(r\) parallel _slack edges_ from a new source vertex \(s^{\prime}\) to each vertex \(V_{i}\). The costs are as follows. Let \(g_{1}>g_{2}>\cdots>g_{r}\), with \(g_{y}=f_{y}-f_{y-1}\) denote the costs in the last layer of the original network, and let \(\hat{g}:=r\). Since \(g_{1}=r-1\), this is larger than all costs. Then, every edge \((T_{i},V_{j})\) from the original network gets a weight of \(\hat{g}\), and the \(r\) new slack edges entering each \(V_{j}\) get positive weights \(\hat{g}-g_{1},\hat{g}-g_{2},\ldots,\hat{g}-g_{r}\). We set the supply of the extra source node to \(b(s^{\prime}):=rn\), which imposes no constraint on the number of incident edges.  
Now, suppose that we have a solution for the original network in which the total flow into vertex \(V_{j}\) is \(y\). In the corresponding \(b\)-matching, we can then use \(b(V_{j})-y=r-y\) of the slack edges incident to \(V_{j}\). The \(r-y\) maximum-weight slack edges have weights \(\hat{g}-g_{r},\hat{g}-g_{r-1},\ldots\hat{g}-g_{y+1}\). The total weight of the edges incident to \(V_{j}\) is therefore  
\[r\hat{g}-g_{r}-g_{r-1}-\cdots-g_{y+1}=r\hat{g}+(g_{1}+g_{2}+\cdots+g_{y}),\]  
using the equation \(g_{1}+g_{2}+\cdots+g_{r}=f_{r}-f_{0}=0\). Thus, up to an addition of the constant \(nr\hat{g}\), the maximum weight of a \(b\)-matching agrees with the maximum cost of a flow in the original network.
# On Finding Two Posets that Cover Given Linear Orders
## 2 Definitions  
We first define here the terms and notations used in the discussion of results.  
Definition 1: ancestors(v,P)  
Given a poset \(P=(V,<_{P})\) and \(v\in V\), the ancestors\((v,P)\) is the set of elements in poset \(P\) that precedes \(v\), i.e., ancestors\((v,P)=\{a\in V|a<_{P}v\}\).  
Definition 2: descendants(v,P)  
Given a poset \(P=(V,<_{P})\) and \(v\in V\), the descendants\((v,P)\) is the set of elements in poset \(P\) that succeeds \(v\), i.e., descendants\((v,P)=\{d\in V|v<_{P}d\}\).  
Definition 3: cover relation \(\prec_{P}\)  
Given a poset \(P=(V,<_{P})\), its cover relation is \(\prec_{P}=\{(u,v)|u<_{P}v\) and there is no \(w\in V\) where \(u<_{P}w<_{P}v\}\).  
Definition 4: cover  
The term cover is used in many instances for different objects in the discussion.  
Given two elements \(u,v\in V\) of poset \(P\), we say that \(u\) covers \(v\) if and only if \(u\prec_{P}v\). In this instance, \((u,v)\) are also said to be cover pairs in \(P\).  
Given a set of linear orders \(\Upsilon\) and poset \(P\), we say that \(P\) covers \(\Upsilon\) if and only if \(\mathcal{L}(P)=\Upsilon\).  
Given a set of linear orders \(\Upsilon\) and a set of posets \(P^{*}\), we say that \(P^{*}\) covers \(\Upsilon\) if and only if \(\bigcup_{P_{i}\in P^{*}}\mathcal{L}(P_{i})=\Upsilon\).  
Definition 5: Hasse Diagram of Poset \(H(P)\)  
A poset \(P=(V,<_{P})\) corresponds to a Hasse diagram \(H(P)\), which is a directed acyclic graph \(G\) with the elements in \(V\) as nodes and pairs in the cover relation of \(P\) as edges, i.e., \(G=(V,\prec_{P})\).  
Definition 6: Tree Poset  
A tree-poset \(P=(V,<_{P})\) is a poset whose Hasse diagram is a rooted directed tree with each non-root node being covered by exactly one node.  
Definition 7: parent(v,P)  
Given a tree-poset \(P=(V,<_{P})\) and \(v\in V\) such that \(v\) is not the root node, \(parent(v,P)\) is the element \(u\) that covers \(v\), i.e., \(parent(v,P)=u\) if and only if \(u\prec_{P}v\).  
Definition 8: 2-Poset Cover Problem  
Instance: A set \(\Upsilon=\{L_{1},L_{2},...,L_{m}\}\) of linear orders over the set \(V=\{1,2,3,...,n\}\).  
Question: Does there exist a pair of distinct posets \(P_{1}=(V,<_{P_{1}})\) and \(P_{2}=(V,<_{P_{2}})\) such that \(\mathcal{L}(P_{1})\cup\mathcal{L}(P_{2})=\Upsilon\) and \(\mathcal{L}(P_{1})\) is neither a subset nor a superset of \(\mathcal{L}(P_{2})\)?  
Definition 9: 2-Tree-Poset Cover Problem  
Instance: A set \(\Upsilon=\{L_{1},L_{2},...,L_{m}\}\) of linear orders over the set \(V=\{1,2,3,...,n\}\).  
Question: Does there exist a pair of distinct tree-posets \(P_{1}=(V,<_{P_{1}})\) and \(P_{2}=(V,<_{P_{2}})\) such that \(\mathcal{L}(P_{1})\cup\mathcal{L}(P_{2})=\Upsilon\) and \(\mathcal{L}(P_{1})\) is neither a subset nor a superset of \(\mathcal{L}(P_{2})\)?  
Definition 10: comparable and incomparable  
Given a poset \(P=(V,<_{P})\) and elements \(u,v\in V\), \(u\) and \(v\) are comparable, denoted by \(u\perp v\) if \(u<_{P}v\) or \(v<_{P}u\). Otherwise, \(u\) and \(v\) are incomparable, denoted by \(u||_{P}v\).
# Evaluation and Prediction of Ecological Benefits in Song-Liao River Basin
## 4 Discussion
### Analysis of Ecological Quality Assessment  
Generally, the EQI in SRB showed a gradual upward trend from 1990 to 2020, consistent with the research results based on trend analysis and Nonparametric tests in Northeast China [69]. The ecological quality in most areas remained stable, and the decline mainly occurred around the city and in coastal areas. The research based on the city scale points out that LUCC dramatically influences the temporal and spatial characteristics of EQI, which is consistent with the main findings of this study [70]. Comparing Figures 6 and 8, it could be found that LUCC also influences the spatial distribution of EQI in this study. Best and Good are mainly distributed in the Woodland in the north, northeast, and west of the study area, and Normal is mainly located in the transitional areas of Cropland and Woodland in the middle and east. Bad and Worst are mainly distributed in Grassland, Barren, and Residence in the central and western regions. The research is based on RSEI but uses different data sources to evaluate the EQI of SRB, which is consistent with the findings of our study [71]. This study believes that the low EQI in the central and southern regions may be the concentrated heavy industry base and human land in this region. The composition of EQI shows that the value of EQI is higher in the area with high vegetation coverage (Figure 2i-2l) and sufficient water but lower in the area with broad impervious layers or sparse vegetation. Human activities (urban expansion, farmland development, and forest disturbance) will affect the natural state of EQI [72].  
On the other hand, natural factors will also affect the temporal and spatial characteristics of EQI. The EQI of Hulunnaoer in the west of the study area has been low for many years, and the LUCC in this area is mainly Grassland and Water. From the altitude point of view, the warm and humid airflow from the southeast sea passes through Changbai Mountains and the Greater Khingan Mountains twice, making it difficult for water vapor to reach this area [73]. Figure 2a-d show that the annual average temperature in this area is significantly higher than in the surrounding areas. The comprehensive effect of these factors leads to the low humidity in this area, which is positively correlated with EQI. This phenomenon is consistent with the research results based on driving factors in this area [74]. They also found that land use type, slope, and elevation are the main driving factors for forming ecological quality patterns in northeast China. Another south-central region (Hunshandake Sandy Land) has held low EQI for many years. LUCC in this area is a crisscross state of Grassland, Cropland, and Barren, and it is a region with widespread desertification [75].
## 2 Background
### Automatic Interpretation Based on Neural Network  
Machine learning algorithms, especially supervised learning algorithms, use evaluated well data for training to achieve an intelligent evaluation of cementing quality. A major advantage of supervised learning is that it does not require manual decision making. The algorithm will establish the relationship with the cementing quality after training enough amplitude variable density logging data. If the training is correct, the supervised learning algorithm can reasonably explain the data not seen in the training process.  
Many scholars have applied machine learning algorithms in the field of logging interpretation. [PERSON] (2018) et al. [14] used neural networks to obtain information from open-hole logging data and reconstruct open-hole acoustic logging data. [PERSON] (2018) et al. [7] used neural networks to identify reservoir locations from logging data, and [PERSON] (2019) et al. [15] used support vector machines and neural networks to automatically identify ultrasonic waveform characteristics, which can predict additional information about the longitudinal wave velocity of annular materials in cased wells. [PERSON] et al. [9] (2020) established different machine learning algorithms, such as random forest and neural network prediction based on CBL-VDL, and ultrasonic imaging data, to output the prediction results of cementing quality. [PERSON], [PERSON] et al. [10] (2021) used the Gaussian process regression algorithm for training and generated new characteristic curves based on CBL and VDL logging data to accurately evaluate the cementing quality.  
Cementing quality evaluation based on CBL-VDL is very similar to the general image classification task. In the classification task, the variable density image is segmented and input into the neural network for training, and the cementing quality is classified in this way. Relevant scholars have conducted a large amount of research on image classification algorithms. At present, the best method is based on convolutional neural networks (CNNs) [16]. Therefore, the work of this paper is also based on a convolutional neural network to complete the classification task. However, in this problem, the VDL is not a simple image recognition task. In the VDL evaluation, it is necessary to integrate the overall and local features of the image, that is, the evaluation results of cementing quality are not only based on the light and dark features of a single strip, but also refer to the shape and density of all strips. Thus, this paper builds a multi-dimensional feature extraction convolution neural network to classify the cementing quality.
## 4 Conclusions  
Based on the chaotic polarization system of optically injected cascaded VCSELs, we propose a scheme for implementing high-speed optical chaotic data selection logic operations with the performance of error detection and correction. It has been observed that the S-VCSEL can emit chaotic laser output within a broader parameter space encompassing an applied electric field and optical injection amplitude. When the applied electric field is set to 11 kV/mm or 25 kV/mm and the optical injection amplitude is around 4.4, the polarized light emitted by the PPLN exhibits strong correlation with that emitted by the S-VCSEL. Moreover, both the PPLN and S-VCSEL demonstrate identical polarization bistability characteristics: under an applied electric field of 11 kV/mm, x-PC predominates, while y-PC is suppressed. Additionally, y-PC is entirely suppressed by x-PC when the optical injection amplitude exceeds 4.7. Under an applied electric field of 25 kV/mm, the predominant polarization is y-PC, with x-PC being suppressed. Similarly, when the optical injection amplitude exceeds 4.7, x-PC is completely suppressed by y-PC. Based on the aforementioned findings, we utilize the modulation of optical injection amplitude and an applied electric field as the logic input and control logic signal, respectively. Utilizing the outstanding mean comparison mechanism, we achieve two identical logic outputs through demodulating the polarized light from the PPLN and S-VCSEL. This enables the realization of high-speed optical chaotic data selection logic operations, achieving operational speeds of up to approximately 114 Gb/s. Through an examination of noise effects on the logic outputs, it was observed that neither logic output displayed any error symbols even under a noise strength as high as 180 dBw. Furthermore, the anti-noise performance of logic output \(O_{1}\) was found to be superior to that of optical chaotic logic output \(O_{2}\). Error symbols in \(O_{2}\) can be detected and corrected by comparison with \(O_{1}\) when the noise strength does not exceed 185 dBw.  
**Author Contributions:** Conceptualization, G.X. and K.W.; methodology, G.X. and K.W.; software, G.X. and K.W.; formal analysis, K.W., L.X. and J.D.; writing--original draft preparation, K.W.; writing--review and editing, G.X.; visualization, K.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by Natural Science Research Project of Anhui Educational Committee (2022 AH051724), University-Level General Projects of Chaohu University (XLY-202204), National Undergraduate Innovation and Entrepreneurship Training Program (202310380038).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data are contained within the article.  
**Conflicts of Interest:** The authors declare no conflicts of interest.
# Elevation and Mass Changes of the Southern Patagonia Icefield Derived from TanDEM-X and SRTM Data
## 2 Materials and Methods
### Dataprocessing for DEM Production
#### 2.2.2 Postprocessing and Mosaicking  
Due to the concatenation of scenes along-track a consistent raw DEM was generated for each track. However, across orbits, the raw DEM strips needed to be mosaicked to a continuous DEM. For this step, we introduced an automatic sequence to adjust the raw DEM strips using stable points off-glacier. Stable ground was identified as pixels below a 10\({}^{\circ}\) slope threshold in the TDX DEM, after applying masks for vegetation and water bodies derived from optical data. The bias obtained from the stable points was removed by fitting a bilinear plane with a least squares approach. After this vertical offset correction, we introduced a horizontal co-registration of the TDX DEMs with the reference SRTM DEM. Following [PERSON] and [PERSON] [26], an iterative process was used to minimize shifts between both DEMs in x and y direction. Stable ground pixels were examined for direction and amplitude of elevation deviations with respect to the aspect of the DEM. We extracted the shift parameters as polar coordinates from sinusoidal least squares fitted modeling of the function describing the dh/tan(slope) to aspect dependencies found in the sample of assumed stable points (Supplementary Materials Figure S2). The sum of the consecutively derived shift parameters was applied as a global transformation of the DEM to the new origin with subsequent resampling to the reference SRTM raster parameters. An additional loop of bilinear vertical adjustment was run to correct for residual vertical offsets after horizontal co-registration. These improved TDX DEM tiles were then mosaicked to the final DEM-product. We applied a simple merge where only values of one raster dataset were considered in overlapping areas. Without any averaging, these values were referenced to one exact acquisition date for further calculations.