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This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.

Mathematics. --- Algebraic geometry. --- Probabilities. --- History. --- Algebraic topology. --- Differential equations. --- General Mathematics and Education. --- Algebraic Geometry. --- Probability Theory. --- History of Mathematical Sciences. --- Algebraic Topology. --- Differential Equations. --- 517.91 Differential equations --- Differential equations --- Topology --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Algebraic geometry --- Geometry --- Math --- Science --- Matemàtica

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The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.

Transportation --- Traffic engineering --- Business & Economics --- Civil & Environmental Engineering --- Mathematics --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Calculus --- Operations Research --- Transportation Economics --- Mathematical models --- Transportation engineering --- Mathematical models. --- Public transportation --- Transport --- Transportation, Primitive --- Transportation companies --- Transportation industry --- Economic aspects --- Mathematics. --- Operations research. --- Decision making. --- Applied mathematics. --- Engineering mathematics. --- Calculus of variations. --- Management science. --- Engineering economics. --- Engineering economy. --- Calculus of Variations and Optimal Control; Optimization. --- Operations Research, Management Science. --- Engineering Economics, Organization, Logistics, Marketing. --- Operation Research/Decision Theory. --- Applications of Mathematics. --- Economy, Engineering --- Engineering economics --- Industrial engineering --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Engineering --- Engineering analysis --- Mathematical analysis --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Operational analysis --- Operational research --- Management science --- Research --- System theory --- Math --- Science --- Decision making --- Civil engineering --- Locomotion --- Commerce --- Communication and traffic --- Storage and moving trade --- Mathematical optimization. --- Operations Research/Decision Theory. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Simulation methods --- System analysis

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Recent years have seen dramatic progress in shape recognition algorithms applied to ever-growing image databases. They have been applied to image stitching, stereo vision, image mosaics, solid object recognition and video or web image retrieval. More fundamentally, the ability of humans and animals to detect and recognize shapes is one of the enigmas of perception. The book describes a complete method that starts from a query image and an image database and yields a list of the images in the database containing shapes present in the query image. A false alarm number is associated to each detection. Many experiments will show that familiar simple shapes or images can reliably be identified with false alarm numbers ranging from 10-5 to less than 10-300. Technically speaking, there are two main issues. The first is extracting invariant shape descriptors from digital images. The second is deciding whether two shape descriptors are identifiable as the same shape or not. A perceptual principle, the Helmholtz principle, is the cornerstone of this decision. These decisions rely on elementary stochastic geometry and compute a false alarm number. The lower this number, the more secure the identification. The description of the processes, the many experiments on digital images and the simple proofs of mathematical correctness are interlaced so as to make a reading accessible to various audiences, such as students, engineers, and researchers.

Image processing. --- Pattern recognition systems. --- Shapes. --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Pattern classification systems --- Pattern recognition computers --- Pattern perception --- Computer vision --- Forms (Shapes) --- Shape --- Geometry --- Surfaces --- Geometry. --- Visualization. --- Computer vision. --- Artificial intelligence. --- Mathematics. --- Image Processing and Computer Vision. --- Artificial Intelligence. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Game Theory, Economics, Social and Behav. Sciences. --- Math --- Science --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Mathematics --- Euclid's Elements --- Optical data processing. --- Game theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Optical computing --- Visual data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment

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This proceedings volume focuses on different aspects of environmental assessment, monitoring, and management of urban and technogenic soils. Soils of Urban, Industrial, Traffic, Mining and Military Areas (SUITMAs) differ substantially from their natural zonal counterparts in their physical, chemical and biological features, their performed functions, and supported services. This book discusses the monitoring, analysis and assessment of the effects of urbanization on soil functions and services. Further, it helps to find solutions to the environmental consequences of urbanization and discusses best management practices such as management and design of urban green infrastructure, waste management, water purification, and reclamation and remediation of contaminated soils in the context of sustainable urban development. The book includes thematic sections corresponding to 14 sessions of the SUITMA 9 congress, covering broad topics that highlight the importance of urban soils for society and environment and summarizing the lessons learned and existing methodologies in analyses, assessments, and modeling of anthropogenic effects on soils and the related ecological risks. This proceedings book appeals to scientists and students as well as practitioners in soil and environmental science, urban planning, geography and related disciplines, and provides useful information for policy makers and other stakeholders working in urban management and greenery.

Soil science --- Soil conservation. --- Urban Ecology. --- Sustainable architecture. --- Sustainable development. --- Endangered ecosystems. --- Soil Science & Conservation. --- Urban Geography / Urbanism (inc. megacities, cities, towns). --- Sustainable Architecture/Green Buildings. --- Sustainable Development. --- Ecosystems. --- Threatened ecosystems --- Biotic communities --- Nature conservation --- Development, Sustainable --- Ecologically sustainable development --- Economic development, Sustainable --- Economic sustainability --- ESD (Ecologically sustainable development) --- Smart growth --- Sustainable development --- Sustainable economic development --- Economic development --- Eco-architecture --- Environmentally conscious architecture --- Environmentally friendly architecture --- Green architecture --- Green building design --- Green design (Buildings) --- Sustainable design (Buildings) --- Architecture --- Sustainable design --- Cities and towns --- Urban ecology --- Urban environment --- Social ecology --- Sociology, Urban --- Conservation of soil --- Erosion control, Soil --- Soil erosion --- Soil erosion control --- Soils --- Agricultural conservation --- Soil management --- Environmental aspects --- Control --- Prevention --- Conservation --- Soil science. --- Urban geography. --- Urban ecology (Biology). --- Biocenoses --- Biocoenoses --- Biogeoecology --- Biological communities --- Biomes --- Biotic community ecology --- Communities, Biotic --- Community ecology, Biotic --- Ecological communities --- Ecosystems --- Natural communities --- Ecology --- Population biology --- City ecology (Biology) --- Geography --- Pedology (Soil science) --- Agriculture --- Earth sciences

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Phytoremediation, the use of plants to remediate environmental media, is being pursued as a new approach for the cleanup of contaminated soils and waters, including groundwater. Plant-assisted bioremediation, sometimes referred to as a type of phytoremediation, involves the interaction of plant roots and the microorganisms associated with these root systems to re- diate soils containing elevated concentrations of organic compounds. These techniques could provide cost-effective methods of remediating soils and groundwater contaminated with metals, radionuclides, and various types of organics, with fewer secondary wastes and less environmental impact than would be generated using traditional remediation methods. All plants extract necessary nutrients, including metals, from their soil and water environments. Some plants, called hyperaccumulators, have the ability to store large amounts of metals, even some metals that do not appear to be required for plant functioning. In addition, plants can take up various organic chemicals from environmental media and degrade or otherwise process them for use in their physiological processes. Phytoremediation technologies are in the early stages of development, with laboratory research and limited field trials being conducted to determine processes and refine methods. Additional research, including genetic engineering, is being conducted to improve the natural capabilities of plants to perform remediation functions and to investigate other plants with potential phytoremediation applications. Large areas in Western and Eastern countries are polluted with heavy metals and radionuclides in natural, rural, urban or industrial areas.

milieutechnologie --- milieuanalyse --- bodembescherming --- Science --- Pedology --- biotechnologie --- wetenschappen --- milieubeheer --- stralingshygiëne --- Biotechnology --- Radiotherapy. Isotope therapy --- bodemkunde --- Hygiene. Public health. Protection --- milieuzorg --- Environmental protection. Environmental technology --- wetenschap --- Soil remediation --- Soil pollution --- Phytoremediation --- Sols --- Phytorestauration --- Congresses. --- Congresses --- Décontamination --- Congrès --- Pollution --- EPUB-LIV-FT LIVCHIMI SPRINGER-B --- Biotechnology. --- Environmental protection. --- Environmental toxicology. --- Soil conservation. --- Effects of Radiation/Radiation Protection. --- Ecotoxicology. --- Soil Science & Conservation. --- Environmental Engineering/Biotechnology. --- Science, Humanities and Social Sciences, multidisciplinary. --- Conservation of soil --- Erosion control, Soil --- Soil erosion --- Soil erosion control --- Soils --- Agricultural conservation --- Soil management --- Ecotoxicology --- Pollutants --- Environmental health --- Toxicology --- Environmental quality management --- Protection of environment --- Environmental sciences --- Applied ecology --- Environmental engineering --- Environmental policy --- Environmental quality --- Chemical engineering --- Genetic engineering --- Control --- Prevention --- Conservation --- Radiation protection. --- Radiation—Safety measures. --- Soil science. --- Environmental engineering. --- Radiation monitoring --- Radiation protection --- Environmental control --- Environmental effects --- Environmental stresses --- Engineering --- Environmental protection --- Sustainable engineering --- Pedology (Soil science) --- Agriculture --- Earth sciences --- Metal contaminated soils --- NATO