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Topological Optimization and Optimal Transport

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By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered. ContentsPart I Geometric issues in PDE problems related to the infinity Laplace operator Solution of free boundary problems in the presence of geometric uncertainties Distributed and boundary control problems for the semidiscrete Cahn-Hilliard/Navier-Stokes system with nonsmooth Ginzburg-Landau energies High-order topological expansions for Helmholtz problems in 2D On a new phase field model for the approximation of interfacial energies of multiphase systems Optimization of eigenvalues and eigenmodes by using the adjoint method Discrete varifolds and surface approximation Part II Weak Monge-Ampere solutions of the semi-discrete optimal transportation problem Optimal transportation theory with repulsive costs Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations On the Lagrangian branched transport model and the equivalence with its Eulerian formulation On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows Pressureless Euler equations with maximal density constraint: a time-splitting scheme Convergence of a fully discrete variational scheme for a thin-film equatio Interpretation of finite volume discretization schemes for the Fokker-Planck equation as gradient flows for the discrete Wasserstein distance


Book
Optimal transport methods in economics
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ISBN: 1400883598 9781400883592 0691172765 9780691172767 9780691183466 0691183465 Year: 2016 Publisher: Princeton, N.J. Princeton University Press

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Optimal Transport Methods in Economics is the first textbook on the subject written especially for students and researchers in economics. Optimal transport theory is used widely to solve problems in mathematics and some areas of the sciences, but it can also be used to understand a range of problems in applied economics, such as the matching between job seekers and jobs, the determinants of real estate prices, and the formation of matrimonial unions. This is the first text to develop clear applications of optimal transport to economic modeling, statistics, and econometrics. It covers the basic results of the theory as well as their relations to linear programming, network flow problems, convex analysis, and computational geometry. Emphasizing computational methods, it also includes programming examples that provide details on implementation. Applications include discrete choice models, models of differential demand, and quantile-based statistical estimation methods, as well as asset pricing models.Authoritative and accessible, Optimal Transport Methods in Economics also features numerous exercises throughout that help you develop your mathematical agility, deepen your computational skills, and strengthen your economic intuition.The first introduction to the subject written especially for economistsIncludes programming examplesFeatures numerous exercises throughoutIdeal for students and researchers alike


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Learning to Understand Remote Sensing Images,
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ISBN: 3038976997 3038976989 Year: 2019 Publisher: MDPI - Multidisciplinary Digital Publishing Institute

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With the recent advances in remote sensing technologies for Earth observation, many different remote sensors are collecting data with distinctive properties. The obtained data are so large and complex that analyzing them manually becomes impractical or even impossible. Therefore, understanding remote sensing images effectively, in connection with physics, has been the primary concern of the remote sensing research community in recent years. For this purpose, machine learning is thought to be a promising technique because it can make the system learn to improve itself. With this distinctive characteristic, the algorithms will be more adaptive, automatic, and intelligent. This book introduces some of the most challenging issues of machine learning in the field of remote sensing, and the latest advanced technologies developed for different applications. It integrates with multi-source/multi-temporal/multi-scale data, and mainly focuses on learning to understand remote sensing images. Particularly, it presents many more effective techniques based on the popular concepts of deep learning and big data to reach new heights of data understanding. Through reporting recent advances in the machine learning approaches towards analyzing and understanding remote sensing images, this book can help readers become more familiar with knowledge frontier and foster an increased interest in this field.

Keywords

metadata --- image classification --- sensitivity analysis --- ROI detection --- residual learning --- image alignment --- adaptive convolutional kernels --- Hough transform --- class imbalance --- land surface temperature --- inundation mapping --- multiscale representation --- object-based --- convolutional neural networks --- scene classification --- morphological profiles --- hyperedge weight estimation --- hyperparameter sparse representation --- semantic segmentation --- vehicle classification --- flood --- Landsat imagery --- target detection --- multi-sensor --- building damage detection --- optimized kernel minimum noise fraction (OKMNF) --- sea-land segmentation --- nonlinear classification --- land use --- SAR imagery --- anti-noise transfer network --- sub-pixel change detection --- Radon transform --- segmentation --- remote sensing image retrieval --- TensorFlow --- convolutional neural network --- particle swarm optimization --- optical sensors --- machine learning --- mixed pixel --- optical remotely sensed images --- object-based image analysis --- very high resolution images --- single stream optimization --- ship detection --- ice concentration --- online learning --- manifold ranking --- dictionary learning --- urban surface water extraction --- saliency detection --- spatial attraction model (SAM) --- quality assessment --- Fuzzy-GA decision making system --- land cover change --- multi-view canonical correlation analysis ensemble --- land cover --- semantic labeling --- sparse representation --- dimensionality expansion --- speckle filters --- hyperspectral imagery --- fully convolutional network --- infrared image --- Siamese neural network --- Random Forests (RF) --- feature matching --- color matching --- geostationary satellite remote sensing image --- change feature analysis --- road detection --- deep learning --- aerial images --- image segmentation --- aerial image --- multi-sensor image matching --- HJ-1A/B CCD --- endmember extraction --- high resolution --- multi-scale clustering --- heterogeneous domain adaptation --- hard classification --- regional land cover --- hypergraph learning --- automatic cluster number determination --- dilated convolution --- MSER --- semi-supervised learning --- gate --- Synthetic Aperture Radar (SAR) --- downscaling --- conditional random fields --- urban heat island --- hyperspectral image --- remote sensing image correction --- skip connection --- ISPRS --- spatial distribution --- geo-referencing --- Support Vector Machine (SVM) --- very high resolution (VHR) satellite image --- classification --- ensemble learning --- synthetic aperture radar --- conservation --- convolutional neural network (CNN) --- THEOS --- visible light and infrared integrated camera --- vehicle localization --- structured sparsity --- texture analysis --- DSFATN --- CNN --- image registration --- UAV --- unsupervised classification --- SVMs --- SAR image --- fuzzy neural network --- dimensionality reduction --- GeoEye-1 --- feature extraction --- sub-pixel --- energy distribution optimizing --- saliency analysis --- deep convolutional neural networks --- sparse and low-rank graph --- hyperspectral remote sensing --- tensor low-rank approximation --- optimal transport --- SELF --- spatiotemporal context learning --- Modest AdaBoost --- topic modelling --- multi-seasonal --- Segment-Tree Filtering --- locality information --- GF-4 PMS --- image fusion --- wavelet transform --- hashing --- machine learning techniques --- satellite images --- climate change --- road segmentation --- remote sensing --- tensor sparse decomposition --- Convolutional Neural Network (CNN) --- multi-task learning --- deep salient feature --- speckle --- canonical correlation weighted voting --- fully convolutional network (FCN) --- despeckling --- multispectral imagery --- ratio images --- linear spectral unmixing --- hyperspectral image classification --- multispectral images --- high resolution image --- multi-objective --- convolution neural network --- transfer learning --- 1-dimensional (1-D) --- threshold stability --- Landsat --- kernel method --- phase congruency --- subpixel mapping (SPM) --- tensor --- MODIS --- GSHHG database --- compressive sensing


Book
Learning to Understand Remote Sensing Images,
Author:
ISBN: 3038976857 3038976849 Year: 2019 Publisher: MDPI - Multidisciplinary Digital Publishing Institute

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Abstract

With the recent advances in remote sensing technologies for Earth observation, many different remote sensors are collecting data with distinctive properties. The obtained data are so large and complex that analyzing them manually becomes impractical or even impossible. Therefore, understanding remote sensing images effectively, in connection with physics, has been the primary concern of the remote sensing research community in recent years. For this purpose, machine learning is thought to be a promising technique because it can make the system learn to improve itself. With this distinctive characteristic, the algorithms will be more adaptive, automatic, and intelligent. This book introduces some of the most challenging issues of machine learning in the field of remote sensing, and the latest advanced technologies developed for different applications. It integrates with multi-source/multi-temporal/multi-scale data, and mainly focuses on learning to understand remote sensing images. Particularly, it presents many more effective techniques based on the popular concepts of deep learning and big data to reach new heights of data understanding. Through reporting recent advances in the machine learning approaches towards analyzing and understanding remote sensing images, this book can help readers become more familiar with knowledge frontier and foster an increased interest in this field.

Keywords

metadata --- image classification --- sensitivity analysis --- ROI detection --- residual learning --- image alignment --- adaptive convolutional kernels --- Hough transform --- class imbalance --- land surface temperature --- inundation mapping --- multiscale representation --- object-based --- convolutional neural networks --- scene classification --- morphological profiles --- hyperedge weight estimation --- hyperparameter sparse representation --- semantic segmentation --- vehicle classification --- flood --- Landsat imagery --- target detection --- multi-sensor --- building damage detection --- optimized kernel minimum noise fraction (OKMNF) --- sea-land segmentation --- nonlinear classification --- land use --- SAR imagery --- anti-noise transfer network --- sub-pixel change detection --- Radon transform --- segmentation --- remote sensing image retrieval --- TensorFlow --- convolutional neural network --- particle swarm optimization --- optical sensors --- machine learning --- mixed pixel --- optical remotely sensed images --- object-based image analysis --- very high resolution images --- single stream optimization --- ship detection --- ice concentration --- online learning --- manifold ranking --- dictionary learning --- urban surface water extraction --- saliency detection --- spatial attraction model (SAM) --- quality assessment --- Fuzzy-GA decision making system --- land cover change --- multi-view canonical correlation analysis ensemble --- land cover --- semantic labeling --- sparse representation --- dimensionality expansion --- speckle filters --- hyperspectral imagery --- fully convolutional network --- infrared image --- Siamese neural network --- Random Forests (RF) --- feature matching --- color matching --- geostationary satellite remote sensing image --- change feature analysis --- road detection --- deep learning --- aerial images --- image segmentation --- aerial image --- multi-sensor image matching --- HJ-1A/B CCD --- endmember extraction --- high resolution --- multi-scale clustering --- heterogeneous domain adaptation --- hard classification --- regional land cover --- hypergraph learning --- automatic cluster number determination --- dilated convolution --- MSER --- semi-supervised learning --- gate --- Synthetic Aperture Radar (SAR) --- downscaling --- conditional random fields --- urban heat island --- hyperspectral image --- remote sensing image correction --- skip connection --- ISPRS --- spatial distribution --- geo-referencing --- Support Vector Machine (SVM) --- very high resolution (VHR) satellite image --- classification --- ensemble learning --- synthetic aperture radar --- conservation --- convolutional neural network (CNN) --- THEOS --- visible light and infrared integrated camera --- vehicle localization --- structured sparsity --- texture analysis --- DSFATN --- CNN --- image registration --- UAV --- unsupervised classification --- SVMs --- SAR image --- fuzzy neural network --- dimensionality reduction --- GeoEye-1 --- feature extraction --- sub-pixel --- energy distribution optimizing --- saliency analysis --- deep convolutional neural networks --- sparse and low-rank graph --- hyperspectral remote sensing --- tensor low-rank approximation --- optimal transport --- SELF --- spatiotemporal context learning --- Modest AdaBoost --- topic modelling --- multi-seasonal --- Segment-Tree Filtering --- locality information --- GF-4 PMS --- image fusion --- wavelet transform --- hashing --- machine learning techniques --- satellite images --- climate change --- road segmentation --- remote sensing --- tensor sparse decomposition --- Convolutional Neural Network (CNN) --- multi-task learning --- deep salient feature --- speckle --- canonical correlation weighted voting --- fully convolutional network (FCN) --- despeckling --- multispectral imagery --- ratio images --- linear spectral unmixing --- hyperspectral image classification --- multispectral images --- high resolution image --- multi-objective --- convolution neural network --- transfer learning --- 1-dimensional (1-D) --- threshold stability --- Landsat --- kernel method --- phase congruency --- subpixel mapping (SPM) --- tensor --- MODIS --- GSHHG database --- compressive sensing

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