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Target detection in hyperspectral mineral data using wavelet analysis

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Target detection in hyperspectral mineral data using wavelet...

IEEE International Symposium on Geoscience and Remote Sensing (IGARSS)

作者： Michael Mitchley Michael Sears Steven Damelin School of Computer Science University of the Witwatersrand Johannesburg South Africa School of Computational and Applied Mathematics University of the Witwatersrand Johannesburg South Africa Department of Mathematical Science Georgia Southern University Statesboro GA USA

A method for the automatic supervised detection of multiple mineral targets in hyperspectral mineral data is presented in this paper. The method makes use of wavelet analysis, wavelet-based denoising using thresholding of wavelet detail coefficients, and feature reduction based on sequential forward selection, which utilises an extension of receiver operating characteristic curves to fuzzy set membership in order to measure discriminating capability. The method is shown to run in time linear to the number of hyperspectral bands, per pixel. Furthermore, an extension of this method to linear unmixing is presented, based on minimising the least-squares error between abundance estimates and actual spectra by varying a thresholding parameter to eliminate outliers and imposing a sum-to-one constraint on the abundances.

关键词： Object detection Hyperspectral imaging Minerals Wavelet analysis Data analysis Hyperspectral sensors Feature extraction Human computer interaction Wavelet domain Africa

Doping-induced antiferromagnetic bicollinear insulating state and superconducting temperature of monolayer FeSe systems

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Physical Review B 2018年第1期98卷 014504-014504页

作者： Michael C. Lucking Fawei Zheng Myung Joon Han Junhyeok Bang Shengbai Zhang Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute Troy New York 12180 USA Institute of Applied Physics and Computational Mathematics Beijing 100088 China Department of Physics Korea Advanced Institute of Science and Technology (KAIST) Daejeon 305-701 Korea Spin Engineering Physics Team Korea Basic Science Institute (KBSI) Daejeon 305-806 Korea

First-principles calculations of ionic-liquid-gated (Li,Fe)OHFeSe suggest a metal-insulator transition at a nominal Li/Fe ratio of 75/25 in the (Li,Fe)OH layer. While doping increases Fermi energy, the formation of an antiferromagnetic bicollinear phase is the key for the transition. It is expected that this insulating phase also exists in other FeSe systems upon heavy electron doping, and its presence can hinder the increase of superconducting temperature. These results offer clues on how to optimize superconductivity amid its interplay with magnetic properties in FeSe systems.

关键词： Electronic structure High-temperature superconductors Monolayer films Pnictides Density functional theory

Explicit corrector in homogenization of monotone operators and its application to nonlinear dielectric elastomer composites

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arXiv 2023年

作者： Dang, Thuyen Gorb, Yuliya Bolaños, Silvia Jiménez Department of Statistics/Committee on Computational and Applied Mathematics University of Chicago 5747 S. Ellis Avenue ChicagoIL60637 United States National Science Foundation 2415 Eisenhower Avenue AlexandriaVA22314 United States Department of Mathematics Colgate University 13 Oak Drive HamiltonNY13346 United States

This paper concerns the rigorous periodic homogenization for a weakly coupled electroelastic system of a nonlinear electrostatic equation with an elastic equation enriched with electrostriction. Such coupling is employed to describe dielectric elastomers or deformable (elastic) dielectrics. It is shown that the effective response of the system consists of a homogeneous dielectric elastomer described by a nonlinear weakly coupled system of PDEs whose coefficients depend on the coefficients of the original heterogeneous material, the geometry of the composite, and the periodicity of the original microstructure. The approach developed here for this nonlinear problem allows us to obtain an explicit corrector result for the homogenization of monotone operators with minimal regularity assumptions. Two Lp−gradient estimates for elastic systems with discontinuous coefficients are also *** Codes 35B27, 74E30, 74F10, 76M50, 78M40 © 2023, CC BY.

关键词： Nonlinear equations

Improved variable coefficient square functions and local smoothing of fourier integral operators

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arXiv 2019年

作者： Gao, Chuanwei Miao, Changxing Yang, Jianwei-Urbain Graduate School of China Academy of Engineering Physics P. O. Box 8009 Beijing100088 China Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing100088 China Department of Mathematics Beijing Institute of Technology Beijing100081 China

We establish certain square function estimates for a class of oscillatory integral operators with homogeneous phase functions. These results are employed to deduce a refinement of a previous result of Mockenhaupt Seeger and Sogge [24] on the local smoothing property for Fourier integral operators, which arise naturally in the study of wave equations on compact Riemannian manifolds. The proof is an adaptation of the bilinear approach of Tao and Vargas [30], and based on bilinear oscillatory integral estimates of Lee [21].35S30, 35L15 Copyright © 2019, The Authors. All rights reserved.

关键词： Fourier analysis

Anomalous thermal transport across the superionic transition in ice

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arXiv 2023年

作者： Qiu, Rong Zeng, Qiyu Wang, Han Kang, Dongdong Yu, Xiaoxiang Dai, Jiayu Department of Physics National University of Defense Technology Changsha410073 China Hunan Key Laboratory of Extreme Matter and Applications National University of Defense Technology Changsha410073 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China

Superionic ices with highly mobile protons within the stable oxygen sub-lattice occupy an important proportion of the phase diagram of ice and widely exist in the interior of icy giants and throughout the universe. Understanding the thermal transport in superionic ice is vital for the thermal evolution of icy planets. However, it is highly challenging due to the extreme thermodynamic conditions and dynamical nature of protons, beyond the capability of the traditional lattice dynamics and empirical potential molecular dynamics approaches. In this work, by utilizing the deep potential molecular dynamics approach, we investigate the thermal conductivity of ice-VII and superionic ice-VII" along the isobar of p = 30 GPa. A non-monotonic trend of thermal conductivity with elevated temperature is observed. Through heat flux decomposition and trajectory-based spectra analysis, we show that the thermally-activated proton diffusion in ice-VII and superionic ice-VII" contribute significantly to heat convection, while the broadening in vibrational energy peaks and significant softening of transverse acoustic branches lead to a reduction in heat conduction. The competition between proton diffusion and phonon scattering results in anomalous thermal transport across the superionic transition in ice. This work unravels the important role of proton diffusion in the thermal transport of high-pressure ice. Our approach provides new insights into modeling the thermal transport and atomistic dynamics in superionic materials. © 2023, CC BY.

关键词： Ice

Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion

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arXiv 2022年

作者： Xu, Hao Zeng, Junsheng Zhang, Dongxiao BIC-ESAT ERE SKLTCS College of Engineering Peking University Beijing100871 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Southern University of Science and Technology Guangdong Shenzhen518055 China Department of Mathematics and Theories Peng Cheng Laboratory Guangdong Shenzhen518000 China

Data-driven discovery of PDEs has made tremendous progress recently, and many canonical PDEs have been discovered successfully for proof-of-concept. However, determining the most proper PDE without prior references remains challenging in terms of practical applications. In this work, a physics-informed information criterion (PIC) is proposed to measure the parsimony and precision of the discovered PDE synthetically. The proposed PIC achieves state-of-the-art robustness to highly noisy and sparse data on seven canonical PDEs from different physical scenes, which confirms its ability to handle difficult situations. The PIC is also employed to discover unrevealed macroscale governing equations from microscopic simulation data in an actual physical scene. The results show that the discovered macroscale PDE is precise and parsimonious, and satisfies underlying symmetries, which facilitates understanding and simulation of the physical process. The proposition of PIC enables practical applications of PDE discovery in discovering unrevealed governing equations in broader physical scenes. © 2022, CC BY-NC-ND.

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A projection approach for multiple monotone regression

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arXiv 2019年

作者： Lin, Lizhen Thomas, Brian S.T. Piegorsch, Walter W. Scott, James Carvalho, Carlos Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States Department of Statistical Science Duke University DurhamNC United States BIO5 Institute Department of Mathematics University of Arizona TucsonAZ United States University of Texas McCombs School of Business AustinTX United States

Shape-constrained inference has wide applicability in bioassay, medicine, economics, risk assessment, and many other fields. Although there has been a large amount of work on monotone-constrained univariate curve estimation, multivariate shape-constrained problems are much more challenging, and fewer advances have been made in this direction. With a focus on monotone regression with multiple predictors, this current work proposes a projection approach to estimate a multiple monotone regression function. An initial unconstrained estimator – such as a local polynomial estimator or spline estimator – is first obtained, which is then projected onto the shape-constrained space. A shape-constrained estimate is obtained by sequentially projecting an (adjusted) initial estimator along each univariate direction. Compared to the initial unconstrained estimator, the projection estimate results in a reduction of estimation error in terms of both Lp (p ≥ 1) distance and supremum distance. We also derive the asymptotic distribution of the projection estimate. Simple computational algorithms are available for implementing the projection in both the unidimensional and higher dimensional cases. Our work provides a simple recipe for practitioners to use in real applications, and is illustrated with a joint-action example from environmental toxicology. Copyright © 2019, The Authors. All rights reserved.

关键词： Risk assessment

Approximation with CNNs in sobolev space: with applications to classification 22

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Approximation with CNNs in sobolev space: with applications ...

Proceedings of the 36th International Conference on Neural Information Processing Systems

作者： Guohao Shen Yuling Jiao Yuanyuan Lint Jian Huang Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong SAR China School of Mathematics and Statistics and Hubei Key Laboratory of Computational Science Wuhan University Wuhan 430072 China Department of Statistics The Chinese University of Hong Kong Shatin New Territories Hong Kong SAR China

ISBN: (纸本)9781713871088

We derive a novel approximation error bound with an explicit prefactor for Sobolev- regular functions using deep convolutional neural networks (CNNs). The bound is non-asymptotic in terms of the network depth and filter lengths, in a rather flexible way. For Sobolev-regular functions which can be embedded into the Hölder space, the prefactor of our error bound depends on the ambient dimension polynomially instead of exponentially as in most existing results, which is of independent interest. We also establish a new approximation result when the target function is supported on an approximate lower-dimensional manifold. We apply our results to establish non-asymptotic excess risk bounds for classification using CNNs with convex surrogate losses, including the cross-entropy loss, the hinge loss, the logistic loss, the exponential loss and the least squares loss. We show that the classification methods with CNNs can circumvent the curse of dimensionality if input data is supported on a neighborhood of a low-dimensional manifold.

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GELFAND-TSETLIN MODULES FOR LIE ALGEBRAS OF RANK 2

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arXiv 2024年

作者： And¯Elić, Milica da Fonseca, Carlos M. Futorny, Vyacheslav Tsylke, Andrew Department of Mathematics Kuwait University Al-Shadadiyah Kuwait Kuwait College of Science and Technology Doha District Safat13133 Kuwait Faculty of Applied Mathematics and Informatics Technical University of Sofia Kliment Ohridski Blvd. 8 Sofia1000 Bulgaria Chair of Computational Mathematics University of Deusto Bilbao48007 Spain Shenzhen International Center for Mathematics Southern University of Science and Technology China Kyiv Taras Shevchenko University Kyiv Ukraine

We explicitly construct families of simple modules for all simple Lie algebras of rank 2 on which a certain commutative subalgebra acts diagonally with a simple spectrum. In type A, these modules are the well-known ge... 详细信息

关键词： Lie groups