esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Numerical Models
### xFEM's Formulation  
Here, a brief description of the xFEM formulation is presented. Consider a domain, noted \(\Omega\), that includes a crack represented by a surface discontinuity \(\partial\Omega\), as shown in Figure 2. In xFEM, the following distance function (i.e., the function mapping the position of the closest points to the discontinuity), is used to represent the crack in \(\Omega\):  
\[f(\underline{x})=\min_{\underline{x}\in\partial\Omega}\|\underline{x}- \underline{\hat{x}}\|sign[\underline{u}\cdot(\underline{x}-\underline{\hat{ x}})], \tag{8}\]  
where \(\underline{x}\) is the position vector, \(\underline{\hat{x}}\) is the position of the closest point that is projected onto the discontinuity surface \(\partial\Omega\), and \(\underline{u}\) is the unity vector normal to \(\partial\Omega\). Therefore, the discontinuity is represented by \(f(\underline{x})=0\), and the sign of the function refers to each part of the domain, with positivity determined by \(\underline{u}\).  
In order to account for the presence of the discontinuity, the element formulation is enriched for the elements concerned by the crack. Let \(I\) be the set of all the nodes within the domain \(\Omega\) and \(J\) be the set of all the nodes belonging to the enriched elements, excluding the one containing the crack tip, which is assigned to the set \(K\). The nodal variable (e.g., displacement) can, therefore, be represented by [1]:  
\[\underline{u}(\underline{x})=\sum_{i\in\Gamma(\bar{J}\cup K)}N_{i}(\underline {x})\underline{u}_{i}+\sum_{i\in J}N_{i}^{*}(\underline{x})\underline{u}_{i}^ {*}+\sum_{i\in K}N_{i}^{**}(\underline{x})\underline{u}_{i}^{**}, \tag{9}\]  
where \(\underline{u}_{i}\), \(\underline{u}_{i}^{*}\) and \(\underline{u}_{i}^{**}\) are the regular and enriched nodal variables and \(N_{i}\), \(N_{i}^{*}\) and \(N_{i}^{**}\) are the regular and enriched shape functions. The enriched shape functions are as follow:  
\[N_{i}^{*}=N_{i}[H(f(\underline{x}))+H(f(\underline{x}_{i}))], \tag{10}\]  
and  
\[N_{i}^{**}=N_{i}\sum_{k=1}^{4}[\beta_{k}(\underline{x})-\beta_{k}(\underline {x}_{i})], \tag{11}\]  
where \(H\) is the Heaviside function and \(\beta(r,\theta)=\left\{\sqrt{r}\cos\frac{\theta}{2},\sqrt{r}\sin\frac{\theta} {2},\sqrt{r}\sin\theta\sin\frac{\theta}{2},\sqrt{r}\sin\theta\cos\frac{\theta }{2},\right\}\), with \(r\) and \(\theta\) given in Figure 2.  
Note that the previously defined cohesive material behavior is used to obtain the crack opening displacement, and either the maximum principal stress or the maximum shear stress can be used as a criterion to establish the onset of crack propagation and its direction (noting that the former criterion is used in our models). When the criterion is reached within the element containing the current crack tip, the element is considered as failed and the crack tip is advanced by one element.  
Figure 2: Illustration of the extended finite element method (xFEM) approach.
## 4 Stochastic Finite Element Methods  
Standard stochastic finite element methods can be divided into intrusive and non-intrusive ones. Nonintrusive ones have the benefit of preserving the existing software infrastructure and investment. Intrusive approaches at the moment appear to have some benefits if adaptivity is available. To date, adaptivity in domain uncertainty problems has not been studied. There are two important issues affecting the choice of approach: the cost of integration of the parameter-dependent part, and the properties of the parametrisation, that is, how does the domain change as a function of the random input.  
The stochastic collocation method considered here is based on the assumption that the dependence on the abstract variable \(\omega\) can be parameterised using a countable set of mutually independent random variables. Such a parametrisation can sometimes be known a priori or it can be estimated statistically.
# Learning with Errors: A Lattice-Based Keystone of Post-Quantum Cryptography
## 3 Lattices
### Computational Lattice Problems  
The structure of lattices makes them preferable in cryptography, and some lattices' problems are believed to be effortless while others are considered intractable. For example, given a set of vector \(\{u_{1},u_{2},\ldots,u_{n}\}\in\mathbb{R}^{n}\), which generates a lattice \(L\), it is straightforward with an algorithm to compute a basis \(\{b_{1},b_{2},\ldots,b_{n}\}\in\mathbb{R}^{n}\) of \(L\).  
Another undemanding problem is assessing if a given vector \(u\) belongs to the lattice \(L\). On the other hand, there are problems in lattice theory, that are believed to be hard.
## 5 Conclusions  
In this paper, an issue concerning the execution of measurements on a CNC machine during the production of aircraft gearbox covers is presented. It was solved by using a method belonging to the spectrum of artificial intelligence methods.  
Owing to the input use of variable E\({}_{A-2}\) containing information on cover deformations, it was possible to eliminate the need to carry out measurements of the produced elements in the measurement laboratory on the CMM. This is the main achievement of the paper and at the same time the fulfillment of the set aim. Simultaneously, it becomes possible to apply CDT for the production of aircraft gearbox casings.  
The main findings of the studies presented are as follows:  
* Errors between measurements carried out on the CMM and the CNC are up to 0.032 mm for bearing seat 2 and up to 0.034 mm for bearing seat 6, and when ANFIS is used, they are up to 0.014 mm for bearing seats 2 and 6;
* The average errors between measurements carried out on the CMM and the CNC are 0.013 mm for bearing seat 2 and 0.015 mm for bearing seat 6, and when ANFIS is used, they are 0.008 mm for bearing seat 2 and 0.007 mm for bearing seat 6;
* After using ANFIS, the average errors for bearing seat 2 account for 62% of the original average measurement error, and the average errors for bearing seat 6 account for 44% of the original average measurement error.  
A further stage of the work will consist in the implementation of the system for aircraft production which at the current stage may operate in parallel to the existing quality control system. This solution will allow for verification of system operation over a longer period of time, continuous extension of the set of data obtained from the production process, and additional ANFIS training.  
Conceptualization, G.B., A.O., P.G. and M.M.; formal analysis, G.B. and A.O.; methodology, P.G. and M.M.; investigation, G.B.; validation P.G.; writing--original draft, G.B. and P.G.; writing--review and editing, P.G. and A.O.; supervision, P.G. and M.M.; funding acquisition, G.B. and A.O. All authors have read and agreed to the published version of the manuscript.  
This project was financed by the National Centre for Research and Development of the Republic of Poland, within the \"Intelligent Development\" program for years 2014-2020. Project number POIR.01.01.01-00-0016/19, amount granted PLN 2,202,478.  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflict of interest.  
Figure 15: Summary of errors \(\delta_{6}\) and E\({}_{6}\) for the data from the test set for bearing seat 6.
# Real-Time Geo-Localization for Land Vehicles Using LIV-SLAM and Referenced Satellite Imagery
## 3 Materials and Methods  
### System Overview  
The overall framework of our system is illustrated in Figure 2, consisting of four main components: LIV-SLAM, local image real-time generating (Section 3.2), fast cross-modal image matching (Section 3.3), and AKF (Section 3.4).  
In our system, an existing LIV-SLAM framework is utilized for pose estimation and environment reconstruction. During the mapping process, the newly updated RGB point cloud, as shown in Figure 3a, is fed into a local image real-time generating algorithm. This method effectively addresses the cross-view challenge by incrementally projecting the local observations into a vertical downward-view image, as shown in Figure 3b. The fast cross-modal image matching module then aligns the projected image with the referenced image to get an absolute position in the referenced frame, as shown in Figure 3c. Finally, the AKF module fuses the horizontal speed estimated by LIV-SLAM with the global position obtained from the fast cross-modal image matching algorithm. This integration provides a refined position expressed in the coordinate frame of the referenced image.  
Notably, the LIV-SLAM module can be implemented using various state-of-the-art methods, such as Fast-LIO [33; 34], R\({}^{3}\)LIVE [3], R\({}^{3}\)LIVE++ [4], Fast-LIVO [6; 7] and so on. Although Fast-LIO is primarily a LiDAR-inertial odometry, the RGB point cloud map can be rendered through the extrinsic parameters obtained by the calibration between LiDAR and camera. The referenced satellite imagery used in our method is p  
Figure 3: Cross-modal matching-based localization. (**a**) 3D RGB point cloud reconstructed by LIV-SLAM; (**b**) The corresponding projection image; (**c**) The matching result (highlighted by the yellow box) of the projection image and the referenced image, and the red cross indicates the current location.  
Figure 2: System overview.  
locally on the onboard computer. No online map services or downloads are required during runtime.
## 8 Seismic Performance Evaluation
### Effect of Vertical Acceleration  
Significant damage to structures due to vertical excitation has been reported in previous earthquakes such as Northbridge [36]. However, many of the building failures were attributed to brittle failure in the reinforced concrete due to direct compressive failure resulting from the large vertical actions experienced, which is widely disregarded in the seismic design of bridges ([PERSON] et al., [37]). The effect of the vertical acceleration on the dynamic responses of a bridge subjected to the Kobe ground motion at Takarazuka station (PGA = 0.71) and Tabas motion at Ferdows station (PGA = 0.42), representing near and far-field earthquakes, respectively, was therefore investigated in this study. For better understanding, the time-history analysis was performed both with and without taking into account the vertical component of the ground motion. The maximum displacement of the deck and arch crown are presented in Table 8.  
The DCR values for a bridge subjected to the Kobe earthquake without taking into account the vertical component is also indicated in Table 8. In this case, the highest discrepancies of about 8%, 10.2% and 72.2% were obtained for displacements in the longitudinal, transverse and vertical direction. When the vertical component of ground motion was taken into account there was a significant impact on the DCR values of the bridge, with a maximum discrepancy of 17% being reached in pier P6, and the same pattern was shown in the results for far-field earthquake ground motion (Tables 6 and 7). This indicates that the vertical acceleration plays an important role in the seismic behavior of a bridge and hence it is strongly recommended that all three orthogonal components of ground motion should be included in seismic analyses and design of RC arch bridges.  
Figure 13: Percentage of input energy dissipated by modal damping and hysteretic dissipation. (**a**) Near-field earthquakes; (**b**) Far-field earthquakes.
# A Multi-Agent Optimization Approach for Multimodal Collaboration in Marine Terminals
## 4 Solution Methodology
### Prioritized Search  
MOEAs are relatively straightforward to implement and can effectively yield a satisfactory set of solutions for multi-objective optimization problems. However, achieving the set of all Pareto efficient solutions can be challenging due to the problem's complexity and high dimensionality. A significant drawback is the excessive generation of redundant observations, as the operators used to create new solutions focus on diversity but lack a robust mechanism to incorporate local knowledge into the search process. For example, certain berths may be incompatible with specific vessels, yet the search algorithm evaluates these infeasible solutions, which, despite incurring minimal computational cost, detracts from overall optimization efficiency. To address these limitations, we propose a novel algorithm based on prioritized planning, which utilizes local knowledge to minimize redundancy and improve solution quality. The berth allocation variable \(x\) is assigned sequentially for each vessel according to \(y\), leveraging _priority trees_, and outlined in Section 4.2.1. Subsequently, our approach employs a _search algorithm_, as described in Section 4.2.2, to determine the priority list \(y\).
## 4 Adaptive Sample-Size Unscented Particle Filter with Partitioned Sampling
### Partitioned Sampling
With the same model, the complexity of the traditional method is \(N\times(T_{f}+T_{h})\), whereas the partitioned sampling one is \(N\times(T_{f}+3T_{h})/9\), which has the same order of complexity but less computational time than the former. When \(T_{f}\gg T_{h}\), the algorithm complexity is dominated by the state one-step prediction time, as the complexity of the state model increas, and the operation time of the algorithm with partitioned sampling can be reduced to a minimum of 12% of the original method. In fact, partitioned sampling can also be used for general two-dimensional target tracking. Similar to the above analysis for three-dimensional high-maneuvering targets, the state vector of a general two-dimensional maneuvering target is 6-dimensional, and the two-dimensional motion space could be decomposed into two independent subspaces. At this time, the number of particle species is \(N_{x}\times N_{y}\) rather than \(N_{x}+N_{y}\), and when \(T_{f}\gg T_{h}\), as the complexity of state model increases, the operation time of the algorithm with partitioned sampling can be reduced to a minimum of 25% of the original method. Obviously, this method still maintains its advantage for the general two-dimensional target, but with the decrease of state dimension, this advantage will not be as significant as in three-dimensional high-maneuvering target tracking. Therefore, partitioned sampling can be interpreted as a method applicable for any high-dimensional problems with a high dimensional decomposable space model; as the space dimension is higher and the decomposable subspace is smaller, its advantage will be more significant.
## 2 Geometric Noise Analysis
### Lever Arm Noise  
After geometric calculation, the lever arm noise is  
\[\Delta a=\overrightarrow{B_{3}B_{2}}=\frac{d\cos\varphi_{2}}{\cos(2\varphi_{1}+ \varphi_{2})}-d \tag{1}\]  
When \(\varphi_{2}\) approaches 0, the detector alignment error is ignored, and the lever arm noise is  
\[\Delta a=d\frac{(1-\cos(2\varphi_{1}))}{\cos(2\varphi_{1})} \tag{2}\]  
Perform numerical fitting on the trigonometric function part, as shown in Figure 2 below.  
Figure 1: TTL coupling: (**a**) Analysis diagram of TTL coupling; (**b**) Partial enlargement (O: Center of rotation. \(M_{1}\): Static mirror. \(M_{2}\): Dynamic mirror. A: Laser. \(P_{1}\): The incident point of the laser on \(M_{1}\). \(P_{2}\): The incident point of the laser on \(M_{2}\). \(P_{3}\): The intersection of the laser and the actual detector. \(\Delta X\): Lateral jitter. \(\Delta Y\): Longitudinal jitter. \(B_{0}\): The intersection of the emergent laser and the detector when the mirror is stationary. \(B_{1}\): The intersection of the auxiliary emergent laser and the detector parallel to \(\overrightarrow{P_{1}B_{0}}\). \(B_{2}\): The intersection of the actual dynamic emergent light and the detector. \(B_{3}\): With \(P_{2}\) as the center and \(d\) as the radius, drawing the intersection of the arc and \(\overrightarrow{P_{2}B_{2}}\) (\(\overrightarrow{P_{1}B_{0}}|=d\)). \(\Delta a\): Lever arm error. \(\Delta b\): Piston error. \(\varphi_{1}\): Mirror angle jitter. \(\varphi_{2}\): Angle error of the detector. \(\alpha\): The angle of incidence).  
Figure 2: Numerical fitting graph of lever arm noise.  
It can be determined that the lever arm noise is approximately  
\[\Delta a\approx 2{\varphi_{1}}^{2}d \tag{3}\]  
It can be seen from Formula (3) that the lever arm noise has a first-order correlation with the distance from the reflected light to the detector. The lever arm noise can be suppressed by reducing the distance of the reflected light to the detector. The relationship between lever arm noise and angle jitter exhibits a second-order dependency.
## 3 Experimental Results
### Deflagration Fracturing  
The experimental failure results of deflagration fracturing for different cases of D1-D4 are illustrated in Figure 10. For single-borehole specimens, the one under the room temperature condition exhibited a greater number of fractures. In contrast, the granite sample heated to 150 \({}^{\circ}\)C displayed only two prominent main fractures, approximately aligned with the \(X\)-axis and \(Y\)-axis. Similarly, the fractures induced by deflagration in the double-borehole under high-temperature conditions were also more regular. Besides the fracture traversing both boreholes along the \(X\)-axis, the deflagration with less deflagration agent per borehole unexpectedly generated two fractures parallel to the \(Y\)-axis, which penetrated the entire specimen. Compared to the cracks created by hydraulic fracturing, the fractures resulting from deflagration exhibited significantly larger fracture widths, commonly on the order of millimeters.  
Figure 9: Fluid pressure within the wellbore changes with time. The insets depict the fluid pressure distribution across the flowplane at different time points, which also reflect the fracture state of the fracture plane.
## 1 Introduction
Since there are huge spatial disparities in economic level, industrial structure, technologies, and education in particular, population aging will likely become a bottleneck to hinder green transformation and high-quality development. Population aging also varies from one region to another [6], which implies that a \"one size fits all\" policy will not work in China. One approach, when designing and implementing measures and policies, would be to prioritize precise region-targeted measures and policies during the design phase in the context of aging; such an approach is likely to help promote overall rapid high-quality development in China. The paper contributes to the issues set out in three distinct ways. First, we apply a geo-visualization technique to map the spatiotemporal variations of population aging in 30 Chinese provinces from 2002 to 2018 with the aim of displaying the changes in the intensity of spatial clustering of aging over time and better understanding the role of aging in GTFP in a spatial dimension. Second, we use the global Malmquist-Luenberger index (GMLI) method proposed by [PERSON] [7] based on traditional total factor productivity (TFP) to calculate the GTFP scores of the 30 provinces from 2002 to 2018. The spatiotemporal distribution of GTFP is also discussed. We notice huge differences in the GTFP scores across provinces. The implication of this finding is that, once again, more effective region-oriented measures and policies should be formulated in accordance with local conditions. Third, from the spatial distribution of GTFP and population aging, we observe strong spatial clustering. Thereafter, both the spatial spillovers of GTFP and population aging are incorporated to build a fixed effects spatial Durbin model (SDM) able to quantify the direct and indirect effects of population aging on GTFP. The use of SDM can be regarded as the most valuable part of our research. This is because it can fill a research gap in the existing literature, in that as far as we know no study has quantified the spatial spillover effect of aging in neighboring regions on GTFP in specific regions. The most important finding of our work is to confirm a positive spatial spillover effect of aging on GTFP, implying that population aging in neighboring provinces can help increase the GTFP of a given province due to competition caused by population mobility between adjacent provinces. Moreover, the main findings will help policymakers design and implement region-targeted measures and policies to alleviate the negative impacts of aging on high-quality development, but such policies and measures will also help to achieve the sustainable development goal in China. The structure of this paper is organized such that Section 2 is a literature review. Section 3 introduces methods and data sources. Section 4 presents the spatiotemporal variations of GTFP and aging and the estimation results of classical and spatial econometric models. Conclusions and policy implications round out the paper in Section 6.
## 3 Results
### Statistical and Geostatistical Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline  & **PM10** & **PM2.5** & **CO** & **PM4** & **PM1** & **NO\({}_{2}\)** & **SO\({}_{2}\)** & **O\({}_{3}\)** & **H\({}_{2}\)S** & **VOC** & **CO\({}_{2}\)** & **NO** \\  & **ug/m\({}^{3}\)** & **ug/m\({}^{3}\)** & **ppm** & **ug/m\({}^{3}\)** & **ug/m\({}^{3}\)** & **ug/m\({}^{3}\)** & **ug/m\({}^{3}\)** & **ppm** & **ug/m\({}^{3}\)** & **ug/m\({}^{3}\)** & **ug/m\({}^{3}\)** \\ \hline Mean & 214 & 119 & 5 & 133.6 & 58.4 & 35 & 288 & 0.014 & 0.25 & 0.07 & 23.3 & 1.5 \\ Minimum & 78 & 28 & 2 & 38 & 11 & 9 & 110 & 0.01 & 0.07 & 0 & 4.7 & 0.2 \\ Maximum & 307 & 187 & 10 & 245 & 136 & 64 & 510 & 0.02 & 0.95 & 0.23 & 65 & 3.9 \\ Std. deviation & 79 & 58 & 2.8 & 62.5 & 44.2 & 15.5 & 108 & 0.005 & 0.23 & 0.06 & 15.7 & 0.99 \\ Skewness & \(-\)0.22 & \(-\)0.28 & 0.36 & 0.2 & 0.52 & 0.54 & 0.45 & 0.24 & 1.9 & 1.1 & 1.4 & 0.99 \\ Kurtosis & \(-\)0.7 & \(-\)0.7 & \(-\)0.3 & \(-\)0.2 & \(-\)0.1 & \(-\)0.55 & 0.05 & \(-\)0.2 & 0.7 & 1 & 1.9 & 0.74 \\ NAAQS & 150 & 35 & 35 & & 100 & 1300 & 0.075 & & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Descriptive statistics of air parameters. PM10 and NO2 concentrations showed a continuous increase from 2016 to 2019. However, they clearly decreased during the spring of 2020 by 62% and 78%, respectively, due to the lockdown imposed during the coronavirus pandemic, as shown in Figure 9, wherever human activity decreased dramatically. The southern part of the study area suffers from pollution, mainly particulate matter from factories and dust storms. In addition, vehicles are one of the main causes of air pollution and emissions of carbon from PM2.5 [21]. Ad-Dar Al-Baida, Taybah, and Al-Mansuriah are the least affected due to their distance from the industrial area. Despite that, Ad-Dar Al-Baida residents complain of pollution, and remedial measures must be adopted to reduce the seriousness of the situation. More studies should be conducted in the study area to determine the general direction of the concentrations of oxides and to identify the chemical composition of the particulate matter. Moreover, citizens may change their lifestyle to mitigate the sources of air pollution, such as transportation and energy consumption [40]. Figure 8: _Cont_. Figure 8: Ordinary kriging map of particulate matter and gases.