Auxiliary Mapping Research Articles

On Cauchy Problem Solution for a Harmonic Function in a Simply Connected Domain with Multi-Component Boundary

Here, we present an investigation of the Cauchy problem solvability for the Laplace equation in a simply connected plane domain with a multi-component boundary. We reduce our investigation to solution of two singular integral equations. If the problem is resolvable, then we restore its solution via the integral Cauchy formula. We present the examples of the solvable problems. The construction involves an auxiliary approximate conformal mapping or the solution of certain singular integral equations.

Weak and strong convergence theorems for a new class of enriched strictly pseudononspreading mappings in Hilbert spaces

Let Ω be a nonempty closed convex subset of a real Hilbert space H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathfrak{H}$\\end{document}. Let ℑ be a nonspreading mapping from Ω into itself. Define two sequences {ψn}n=1∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\{\\psi _{{n}}\\}_{n=1}^{\\infty}$\\end{document} and {ϕn}n=1∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\{\\phi _{{n}}\\}_{n=1}^{\\infty}$\\end{document} as follows: {ψn+1=πnψn+(1−πn)ℑψn,ϕn=1n∑nt=1ψt,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $$\\begin{aligned} \ extstyle\\begin{cases} \\psi _{n+1}=\\pi _{n}\\psi _{{n}}+(1-\\pi _{n})\\Im \\psi _{{n}}, \\\\ \\phi _{{n}}=\\dfrac{1}{n}\\underset{t=1}{\\overset{n}{\\sum}}\\psi _{t}, \\end{cases}\\displaystyle \\end{aligned}$$ \\end{document} for n∈N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$n\\in \\mathit{N}$\\end{document}, where 0≤πn≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$0\\leq \\pi _{n}\\leq 1$\\end{document}, and πn→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\pi _{n} \\rightarrow 0$\\end{document}. In 2010, Kurokawa and Takahashi established weak and strong convergence theorems of the sequences developed from the above Baillion-type iteration method (Nonlinear Anal. 73:1562–1568, 2010). In this paper, we prove weak and strong convergence theorems for a new class of (η,β)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(\\eta ,\\beta )$\\end{document}-enriched strictly pseudononspreading ((η,β)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(\\eta ,\\beta )$\\end{document}-ESPN) maps, more general than that studied by Kurokawa and W. Takahashi in the setup of real Hilbert spaces. Further, by means of a robust auxiliary map incorporated in our theorems, the strong convergence of the sequence generated by Halpern-type iterative algorithm is proved thereby resolving in the affirmative the open problem raised by Kurokawa and Takahashi in their concluding remark for the case in which the map ℑ is averaged. Some nontrivial examples are given, and the results obtained extend, improve, and generalize several well-known results in the current literature.

Inquisition of optical soliton structure and qualitative analysis for the complex-coupled Kuralay system

This study seeks to explore the integrable dynamics of induced curves through the utilization of the complex-coupled Kuralay system. The importance of the coupled complex Kuralay equation lies in its role as a fundamental model that contributes to the understanding of intricate physical and mathematical concepts, making it a valuable tool in scientific research and applications. The soliton solutions originating from the Kuralay equations are believed to encapsulate cutting-edge research in various important domains such as optical fibers, nonlinear optics, and ferromagnetic materials. Analytical techniques are employed to derive traveling wave solutions for this model, given that the Cauchy problem cannot be resolved using the inverse scattering transform. In the quest for solitary wave solutions, the extended modified auxiliary equation mapping (EMAEM) method is employed. We derive several novel families of precise traveling wave solutions, encompassing trigonometric, hyperbolic, and exponential forms. Moreover, the planar dynamical system of the concerned equation is created, all probable phase portraits are given, and sensitive inspection is applied to check the sensitivity of the considered equation. Furthermore, after adding a perturbed term, chaotic and quasi-periodic behaviors have been observed for different values of parameters, and multistability is reported at the end. Numerical simulations of the solutions are incorporated alongside the analytical results to enhance comprehension of the dynamic characteristics of the solutions obtained. This study’s outcomes can offer valuable insights for addressing other nonlinear partial differential equations (NLPDEs). The soliton solutions obtained in this study offer important insights into the intricate nonlinear equation being examined.

Multi-fidelity simulation of aeroengine for far-off-design conditions using iterative coupled method based on auxiliary maps

Iterative coupled methods are widely used in multi-fidelity simulation of rotating components due to the simple implementation, which iteratively eliminates the errors between the computational fluid dynamics models and approximate characteristic maps. However, the convergence and accuracy of the iterative coupled method are trapped in characteristic maps. In particular, iterative steps increase sharply as the operation point moves away from the design point. To address these problems, this paper developed an auxiliary iterative coupled method that introduces the static-pressure-auxiliary characteristic maps and modification factor of mass flow into the component-level model. The developed auxiliary method realized the direct transfer of static pressure between the high-fidelity models and the component-level model. Multi-fidelity simulations of the throttle characteristics were carried out using both the auxiliary and traditional iterative coupled methods, and the simulation results were verified using the experimental data. Additionally, the consistency between the auxiliary and traditional iterative coupled methods was confirmed. Subsequently, multi-fidelity simulations of the speed and altitude characteristics were also conducted. The auxiliary and traditional iterative coupled methods were evaluated in terms of convergence speed and accuracy. The evaluation indicated that the auxiliary iterative coupled method significantly reduces iterative steps by approximately 50% at the near-choked state. In general, the auxiliary iterative coupled method is preferred as a development of the traditional iterative coupled method in the near-choked state, and the combined auxiliary-traditional iterative coupled method provides support for successful multi-fidelity simulation in far-off-design conditions.

Mapped material point method for large deformation problems with sharp gradients and its application to soil‐structure interactions

AbstractThe material point method (MPM) is often applied to large deformation problems that involve sharp gradients in the solution field. Representative examples in geomechanics are interactions between soils and various “structures” such as foundations, penetrometers, and machines, where the displacement fields exhibit sharp gradients around the soil‐structure interfaces. Such sharp gradients should be captured properly in the MPM discretization to ensure that the numerical solution is sufficiently accurate. In the MPM literature, several types of locally refined discretizations have been developed and used for this purpose. However, these local refinement schemes are not only quite complicated but also restricted to certain types of basis functions or update schemes. In this work, we propose a new MPM formulation, called the mapped MPM, that can efficiently capture sharp gradients with a uniform background grid compatible with every standard MPM basis function and scheme. The mapped MPM is built on the method of auxiliary mapping that reparameterizes the given problem in a different domain whereby sharp gradients become much smoother. Because the reparameterized problem is free of undesirably sharp gradients, it can be well solved with the standard MPM ingredients including a uniform background grid. We verify and demonstrate the mapped MPM through several numerical examples, with particular attention to soil‐structure interaction problems.

Exact wave solutions of new generalized Bogoyavlensky–Konopelchenko model in fluid mechanics

In this paper, we examine a novel generalized [Formula: see text]-dimensional Bogoyavlensky–Konopelchenko (gBK) model analytically via application of five mathematical methods, namely called Extended Simple Equation (ESE) method, Modified Extended Auxiliary equation mapping (MEAEM) method, [Formula: see text]-expansion method, [Formula: see text]-expansion method and modified F-expansion method, respectively, to obtain different types solitary wave solutions in the form of trigonometric, hyperbolic, rational and exponential functions as compared to solutions exist in [S. T. Chen and W. X. Ma, Math. China 13 (2018) 525; A. Sonia, A. Jamshad, S.-U. Rehman and A. Ali, Int. J. Appl. Comput. Math. 9 (2023)]. The research focuses on physical systems, physiology, mathematical applications, engineering fields, and the chemical processes of species in the porous nanoparticles, examining the impact of various parameters on the nonlinear model. The graphs of some solutions are plotted in the form of two-dimensional and three-dimensional by assigning the particular values to the paraments with the assistance of mathematica software which illustrated the physical behavior of the concern model. The derived solution has numerous applications in fluid dynamics and the interaction of Riemann waves and long waves.

Optical soliton solutions of fokas system and (2 + 1) Davey-Stewartson system by mapping method

In this article, a very effective technique called generalized auxiliary equation mapping method has been employed to investigate some very important nonlinear equations in optical fibers such as Fokas system and (2+1) Davey-Stewartson (DS) system. Under different situations, the obtained solutions exhibit various wave pattern like bright and dark soliton, kink soliton, periodic wave soliton and singular solitons. These solutions are novel and interesting and prove the efficiency of the method. The accuracy of the obtained results provides the competence of the method and ensures that it can be used for other mathematical models involved in optical fibers. Graphical simulation of some reported results has been discussed here to visualize and support the mathematical results in terms of 3D, 2D and contour plots.

Auxiliary Information Guided Self-attention for Image Quality Assessment

Image quality assessment (IQA) is an important problem in computer vision with many applications. We propose a transformer-based multi-task learning framework for the IQA task. Two subtasks: constructing an auxiliary information error map and completing image quality prediction, are jointly optimized using a shared feature extractor. We use visual transformers (ViT) as a feature extractor for feature extraction and guide ViT to focus on image quality-related features by building auxiliary information error map subtask. In particular, we propose a fusion network that includes a channel focus module. Unlike the fusion methods commonly used in previous IQA methods, we use the fusion network, including the channel attention module, to fuse the auxiliary information error map features with the image features, which facilitates the model to mine the image quality features for more accurate image quality assessment. And by jointly optimizing the two subtasks, ViT focuses more on extracting image quality features and building a more precise mapping from feature representation to quality score. With slight adjustments to the model, our approach can be used in both no-reference (NR) and full-reference (FR) IQA environments. We evaluate the proposed method in multiple IQA databases, showing better performance than state-of-the-art FR and NR IQA methods.

3sXcsNet: A framework for face presentation attack detection using deep learning

Face Recognition is a widely used authentication method deployed for accessing personal digital devices like mobiles and laptops, digital door locks, or various security applications. However, presentation attacks in form of print, video and mask can circumvent such authentication methods. Several solutions based on texture features are proposed in the state-of-the-art; nevertheless, they are sensitive to varying illumination conditions and are less resilient against 2D and 3D attacks. In this paper, we propose a novel 3-stream compact Xception framework (3sXcsNet) consisting of four input streams RGB, MSRCR, MSRCP, and a depth map to form two specific 3-stream fusion (CRF and CPF) to mitigate the illumination scenarios. These streams provide discriminative features. RGB images have rich texture features; MSRCR and MSRCP images are illumination invariant and preserve better chromaticity applied on a color or intensity channel, respectively. In addition, an auxiliary depth map that provides depth information for each pixel makes it easier to analyze features and recognize whether the input image is from a real person or a spoof medium. The 3-stream CRF and CPF represent the features differently and feed independently to a deep CNN compact Xception with a CBAM network. These feature maps are fused using an average fusion mechanism for classification of real and spoof faces. We utilize both 2D and 3D attack datasets namely, REPLAY-ATTACK, CASIA-FASD, OULU-NPU, and 3DMAD to evaluate the effectiveness of the proposed framework. We attain an EER of 1.27% and 0.19% for CRF fusion, as well as 1.48% and 0.20% for CPF fusion when assessing performance on the CASIA-FASD and REPLAY-ATTACK datasets, respectively. On the OULU-NPU dataset, we obtain the most favorable results for two protocols while employing CRF fusion, resulting in ACER metrics of 0.7% and 3.2±2.7%, respectively. On the other hand, CPF fusion outperformed with an ACER of 1.8±1.0% for one protocol. Our findings on intra-database outperform the current state-of-the-art. We also perform cross-database testing to assess the generalization capability of the framework on 2D and 3D attack datasets. Furthermore, the proposed method outperforms both fusion procedures in terms of error rate HTER for intra-database and cross-database testing on the 3DMAD dataset.

The dynamical structures of the Sharma–Tasso–Olver model in doubly dispersive medium

In this article, the Sharma–Tasso–Olver model is investigated which characterizes the nonlinear double-dispersive evolution dispersive waves’ dynamical propagation in heterogeneous mediums. To study the dynamical nature of moving waves with a periodic and isolated nature analytically, the governing model is converted into an ordinary differential equation via a wave transformation to employ the extended modified auxiliary equation mapping approach and the G′G2 expansion method. In order to validate the computations, the stability of the obtained results is also established. It has been found that the model supports nonlinear solitary waves, periodic waves, shock waves and stable oscillatory waves. For a set of appropriate parameters, Mathematica is used to represent the dynamics of various wave structures as 3D, 2D and contour visualizations. Additionally, we may remark that the results discussed here are novel and innovative.

Some new wave solutions and modulation instability of a Hamiltonian amplitude equation in optical fibres

The nonlinear Schrödinger equation (NLSE) is one of the most important physical models for explaining the dynamics of optical soliton proliferation in optical fibre theory. Due to an extensive variety of applications for ultrafast signal routing systems and short light pulses in communications, optical soliton propagation in nonlinear fibres is a topic of substantial present interest. To overcome the ill-posedness of the unstable NLSE, a new term Lxt is introduced which leads to the Hamiltonian amplitude equation. In this work, we study exact wave solutions to the nonlinear complex model by utilizing a set of analytical approaches namely as the exp(−ξ(δ)) method, the improved F-expansion technique, and the extended modified auxiliary equation mapping method. Numerous solutions, including singular periodic, multi-periodic, single bell-shaped, and multi-bell-shaped wave frameworks were found. The proposed plan of action is swift, strong, as well as offers the requirements needed to verify the origin of these solutions. Additionally, a dynamics representation of the fascinating behaviour of several solidarity using 2D, 3D, and contour graphs is provided, also we discuss the stability analysis and modulation instability of the proposed model.

Integrative data system for monitoring biota and natural habitats in the Israeli Eastern Mediterranean marine environment.

An integrative data system for monitoring the biota of the Mediterranean waters of Israel as well as selected records from adjacent Levantine basin regions is presented here, aimed at providing data and research tools for long-term bio-geographic and ecological studies and more important, providing background data for assisting governmental regulators to establish educated habitat-oriented environmental policy. The system relies on the geographic information system (GIS) online map-based platform and contains at present the following components: biotic database of ~ 170,000 recorded sampling events; uniform habitat maps of 63 benthic habitats and 2 pelagic ones, constructed using relevant bathymetric features and biotic community compositions; bathymetric hill-shade map; depth contours; raster depth grid and human interference map. Other informative auxiliary maps are planned to be added (e.g., map of potential pockmark sites, detailed maps of tiny carbonate crust nolls and more). A number of 883 cited documents were listed by us for potential extraction of sampling efforts, most of them areavailable to us as PDFs andare available also to the users, excluding copyright-protected ones. Forty-three major projects were depicted in addition to a variety of small studies (e.g., university theses). Thirty-five sampling devices were documented and described, and 3187 species-level identifications were already recorded. In addition, the system provides access to description of sampling devices and pictures of species and seascapes. New data is continuously deposited to the system and the system is flexible, allowing future addition of new types of information. The system site is accessible through the link: https://experience.arcgis.com/experience/40e86605ff4d4e5096ed2c901fec2a2f .

On the solitonic wave structures and stability analysis of the stochastic nonlinear Schrödinger equation with the impact of multiplicative noise

The nonlinear Schrödinger equation (NLSE) is a fundamental and significant physical model that plays a crucial role in demonstrating the dynamics of optical solitons in the theory optical fibers. The propagation of solitons in nonlinear optical fibers has garnered substantial interest due to its broad spectrum of applications, particularly in ultrafast signal routing systems and short light pulses for communications. This article focuses on investigating the impact of multiplicative noise on the solutions of this governing model. To achieve this, three distinct methods, namely the enhanced modified extended tanh expansion (METE) method, the generalized Kudryashov (GK) approach and the extended modified auxiliary equation mapping (EMAEM) method are employed to obtain a new variety of stochastic solutions. The perception of how noise intensity impacts the transmission of waves is a fundamental and critical issue in various fields. In the context of this study, an equation describes an exact wave pattern under the condition that s (representing noise intensity) equals zero. In such cases, the observed pattern remains undisturbed and matches the expected theoretical wave pattern. However, as the strength of noise s increases, the observed pattern begins to deviate from the ideal wave pattern and exhibits signs of damage or distortion. Furthermore, the stability analysis for the stochastic NLSE is performed, providing valuable insights into the behavior solutions as the strength of multiplicative noise increases. The validation of computational results through stability analysis enhances the confidence in the findings of the study. All the mathematical calculations, as well as graphical representations, have been meticulously achieved to present a comprehensive and detailed understanding of the impact of multiplicative on soliton propagation in nonlinear optical fibers.

A Regional Road Network Capacity Estimation Model for Mountainous Cities Based on Auxiliary Map

The focus of sustainable urban transportation development lies in realizing the untapped capacity potential of the existing road network and enhancing its operational efficiency without expanding its physical footprint. To quantify the supply capacity of road networks in mountainous cities, this paper converts the problem of solving the capacity of road networks into the problem of solving the minimum cut set in road networks from the perspective of road network capacity, using the idea of the auxiliary diagram method in graph theory. By improving the limitation that the auxiliary map method is only applicable to the single starting point and terminal point network, a regional road network capacity estimation model of a mountain city based on the auxiliary map is constructed. Combined with the actual regional road network, the model results presented in this paper show that the road network capacity calculated by the auxiliary graph method is 30,137 pcu/h. Using the improved traffic distribution simulation method, the network capacity is 38,776 pcu/h. Compared with the traffic distribution simulation method, the regional road network capacity model based on an auxiliary map proposed in this paper is more realistic.

Optical Dromions for Spatiotemporal Fractional Nonlinear System in Quantum Mechanics

In physics, mathematics, and other disciplines, new integrable equations have been found using the P-test. Novel insights and discoveries in several domains have resulted from this. Whether a solution is oscillatory, decaying, or expanding exponentially can be observed by using the AEM approach. In this work, we examined the integrability of the triple nonlinear fractional Schrödinger equation (TNFSE) via the Painlevé test (P-test) and a number of optical solitary wave solutions such as bright dromions (solitons), hyperbolic, singular, periodic, domain wall, doubly periodic, trigonometric, dark singular, plane-wave solution, combined optical solitons, rational solutions, etc., via the auxiliary equation mapping (AEM) technique. In mathematical physics and in engineering sciences, this equation plays a very important role. Moreover, the graphical representation (3D, 2D, and contour) of the obtained optical solitary-wave solutions will facilitate the understanding of the physical phenomenon of this system. The computational work and conclusions indicate that the suggested approaches are efficient and productive.

Optical soliton solutions, bifurcation, and stability analysis of the Chen-Lee-Liu model

The Chen-Lee -Liu model has many applications in assorted fields, particularly in the study of nonlinear dynamics, chaos theory, circuit design, signal processing, secure communications, encryption and decryption of chaotic signals, as well as cryptography. The modified extended auxiliary equation mapping method has been applied to the Chen-Lee-Liu model in this article and explores new wave profiles, such as singular periodic solutions, periodic solutions, and kink-type soliton solutions. The complex wave conversion is considered to make a simple differential equation. Three- and two-dimensional images are plotted using Mathematica and MATLAB, and their dispersion and nonlinearity effects are discussed. We also discuss the bifurcation analysis of the studied model. The stability of the equilibrium points is studied, and the phase portrait of the system is presented graphically. The obtained wave profiles might play an important role in telecommunication systems, fiber optics, and nonlinear optics.

On the dynamics of the (2+1)-dimensional chiral nonlinear Schrödinger model in physics

The nonlinear Schrödinger equation is one of the significant nonlinear complex models describing the optical solitons in dispersive media. In this study, the (2+1)-dimensional chiral nonlinear Schrödinger model has been investigated analytically which is of key importantance in the field of fluid sciences. A variety of exclusive travelling waveform solutions have been established for the complex dynamical model by employing a set of eminent analytical approaches namely the extended modified auxiliary equation mapping method, the improved F-expansion method, and the unified method, respectively. We obtained different forms of solitary types solutions with the help of these technique. The outcomes are a set of bell-shaped, single periodic, optical, and multi-periodic solutions. Finally, the stability of the developed results is also established to validate the computations. The study provides a very spectacular and appropriate way to put together several interesting wave demonstrations for more complex models of current era.

Boundary-enhanced semi-supervised retinal layer segmentation in optical coherence tomography images using fewer labels.

Automatic segmentation of multiple layers in retinal optical coherence tomography (OCT) images is crucial for eye disease diagnosis and treatment. Despite the success of deep learning algorithms, it still remains a challenge due to the blurry layer boundaries and lack of adequate pixel-wise annotations. To tackle these issues, we propose a Boundary-Enhanced Semi-supervised Network (BE-SemiNet) that exploits an auxiliary distance map regression task to improve retinal layer segmentation with scarce labeled data and abundant unlabeled data. Specifically, a novel Unilaterally Truncated Distance Map (UTDM) is firstly introduced to alleviate the class imbalance problem and enhance the layer boundary learning in the regression task. Then for the pixel-wise segmentation and UTDM regression branches, we impose task-level and data-level consistency regularization on unlabeled data to enrich the diversity of unsupervised information and improve the regularization effects. Pseudo supervision is incorporated in consistency regularization to bridge the task prediction spaces for consistency and expand training labeled data. Experiments on two public retinal OCT datasets show that our method can greatly improve the supervised baseline performance with only 5 annotations and outperform the state-of-the-art methods. Since it is difficult and labor-expensive to obtain adequate pixel-wise annotations in practice, our method has a promising application future in clinical retinal OCT image analysis.

Developing an intelligent cloud attention network to support global urban green spaces mapping

Urban green spaces (UGS) play an important role in understanding of urban ecosystems, climate, environment, and public health concerns. Satellite derived UGS maps provide an efficient and effective tool for urban studies and contribute to targets and indicators of the sustainable development goals, at the global level, set by the United Nations. However, clouds create a challenging issue in optical satellite image processing, leading to significant uncertainty in UGS mapping. In this study, we propose an automatic UGS mapping method by integrating satellite images with crowdsourced geospatial data while aiming to reduce the uncertainty caused by cloud contamination. The proposed method consists of three parts: (1) auxiliary data pre-processing module; (2) cloud attention intelligent network (CAI-net); and (3) non-cloud scenes classification module. The auxiliary data pre-processing module was used to convert crowdsourcing geospatial data into auxiliary maps. The CAI-net was proposed to retrieve detailed UGS classes within clouds from satellite image patches and auxiliary maps, while non-cloud scenes classification module was used to extract UGS from satellite image patches. The proposed method was applied to generate spatial continuous global UGS map products, considering the uncertainty caused by cloud contamination. The results show the proposed method yielded a high-quality global UGS map with average overall accuracy as high as 92.96% when satellite images had cloud coverage ranging from 0% to 50%. The geospatial AI, specifically CAI-net, can provide more accurate UGS mapping regardless of different geographical and climatic conditions of the study areas, which is especially significant for humid tropical and subtropical regions with frequent clouds and rains.

On Kosloff Tal-Ezer least-squares quadrature formulas

In this work, we study a global quadrature scheme for analytic functions on compact intervals based on function values on quasi-uniform grids of quadrature nodes. In practice it is not always possible to sample functions at optimal nodes that give well-conditioned and quickly converging interpolatory quadrature rules at the same time. Therefore, we go beyond classical interpolatory quadrature by lowering the degree of the polynomial approximant and by applying auxiliary mapping functions that map the original quadrature nodes to more suitable fake nodes. More precisely, we investigate the combination of the Kosloff Tal-Ezer map and least-squares approximation (KTL) for numerical quadrature: a careful selection of the mapping parameter ensures stability of the scheme, a high accuracy of the approximation and, at the same time, an asymptotically optimal ratio between the degree of the polynomial and the spacing of the grid. We will investigate the properties of this KTL quadrature and focus on the symmetry of the quadrature weights, the limit relations for the mapping parameter, as well as the computation of the quadrature weights in the standard monomial and in the Chebyshev bases with help of a cosine transform. Numerical tests on equispaced nodes show that a static choice of the map’s parameter improve the results of the composite trapezoidal rule, while a dynamic approach achieves larger stability and faster convergence, even when the sampling nodes are perturbed. From a computational point of view the proposed method is practical and can be implemented in a simple and efficient way.