Optimal Transport Networks in Nature

Optimal Transport Networks in Nature

Author: Natalya Kizilova

Publisher: World Scientific Publishing Company

Published: 2010

Total Pages: 200

ISBN-13: 9789812838735

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This unique book presents a broad range of data on geometry and topology of long-distance liquid transport networks in nature including circulatory and respiratory systems of mammals, trophic fluid transport systems of animals, and conducting systems of higher plants. It is the very first book where evidence of the common design principles and optimal properties of the transportation networks of vascular plants and animals is provided. The book also provides a comprehensive comparative study of the recent measurement results and data analysis, including unique data obtained by the author to conduct systems of plant leaves of different shapes, sizes, venation types and evolutionary ages. It was shown that the mathematical solutions of the optimization problem for the animal and plant conducting systems lead to the same design principles, despite different physical conditions of the fluid transport.


Book Synopsis Optimal Transport Networks in Nature by : Natalya Kizilova

Download or read book Optimal Transport Networks in Nature written by Natalya Kizilova and published by World Scientific Publishing Company. This book was released on 2010 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book presents a broad range of data on geometry and topology of long-distance liquid transport networks in nature including circulatory and respiratory systems of mammals, trophic fluid transport systems of animals, and conducting systems of higher plants. It is the very first book where evidence of the common design principles and optimal properties of the transportation networks of vascular plants and animals is provided. The book also provides a comprehensive comparative study of the recent measurement results and data analysis, including unique data obtained by the author to conduct systems of plant leaves of different shapes, sizes, venation types and evolutionary ages. It was shown that the mathematical solutions of the optimization problem for the animal and plant conducting systems lead to the same design principles, despite different physical conditions of the fluid transport.

Optimal Transportation Networks

Optimal Transportation Networks

Author: Marc Bernot

Publisher: Springer Science & Business Media

Published: 2009

Total Pages: 204

ISBN-13: 3540693149

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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.


Book Synopsis Optimal Transportation Networks by : Marc Bernot

Download or read book Optimal Transportation Networks written by Marc Bernot and published by Springer Science & Business Media. This book was released on 2009 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Optimal Transport

Optimal Transport

Author: Cédric Villani

Publisher: Springer Science & Business Media

Published: 2008-10-26

Total Pages: 970

ISBN-13: 3540710507

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At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.


Book Synopsis Optimal Transport by : Cédric Villani

Download or read book Optimal Transport written by Cédric Villani and published by Springer Science & Business Media. This book was released on 2008-10-26 with total page 970 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.

Nature-Inspired Computing and Optimization

Nature-Inspired Computing and Optimization

Author: Srikanta Patnaik

Publisher: Springer

Published: 2017-03-07

Total Pages: 506

ISBN-13: 3319509209

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The book provides readers with a snapshot of the state of the art in the field of nature-inspired computing and its application in optimization. The approach is mainly practice-oriented: each bio-inspired technique or algorithm is introduced together with one of its possible applications. Applications cover a wide range of real-world optimization problems: from feature selection and image enhancement to scheduling and dynamic resource management, from wireless sensor networks and wiring network diagnosis to sports training planning and gene expression, from topology control and morphological filters to nutritional meal design and antenna array design. There are a few theoretical chapters comparing different existing techniques, exploring the advantages of nature-inspired computing over other methods, and investigating the mixing time of genetic algorithms. The book also introduces a wide range of algorithms, including the ant colony optimization, the bat algorithm, genetic algorithms, the collision-based optimization algorithm, the flower pollination algorithm, multi-agent systems and particle swarm optimization. This timely book is intended as a practice-oriented reference guide for students, researchers and professionals.


Book Synopsis Nature-Inspired Computing and Optimization by : Srikanta Patnaik

Download or read book Nature-Inspired Computing and Optimization written by Srikanta Patnaik and published by Springer. This book was released on 2017-03-07 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides readers with a snapshot of the state of the art in the field of nature-inspired computing and its application in optimization. The approach is mainly practice-oriented: each bio-inspired technique or algorithm is introduced together with one of its possible applications. Applications cover a wide range of real-world optimization problems: from feature selection and image enhancement to scheduling and dynamic resource management, from wireless sensor networks and wiring network diagnosis to sports training planning and gene expression, from topology control and morphological filters to nutritional meal design and antenna array design. There are a few theoretical chapters comparing different existing techniques, exploring the advantages of nature-inspired computing over other methods, and investigating the mixing time of genetic algorithms. The book also introduces a wide range of algorithms, including the ant colony optimization, the bat algorithm, genetic algorithms, the collision-based optimization algorithm, the flower pollination algorithm, multi-agent systems and particle swarm optimization. This timely book is intended as a practice-oriented reference guide for students, researchers and professionals.

Nature's Fabric

Nature's Fabric

Author: David Lee

Publisher: University of Chicago Press

Published: 2017-09-28

Total Pages: 469

ISBN-13: 022618059X

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Leaves are all around us—in backyards, cascading from window boxes, even emerging from small cracks in city sidewalks given the slightest glint of sunlight. Perhaps because they are everywhere, it’s easy to overlook the humble leaf, but a close look at them provides one of the most enjoyable ways to connect with the natural world. A lush, incredibly informative tribute to the leaf, Nature’s Fabric offers an introduction to the science of leaves, weaving biology and chemistry with the history of the deep connection we feel with all things growing and green. Leaves come in a staggering variety of textures and shapes: they can be smooth or rough, their edges smooth, lobed, or with tiny teeth. They have adapted to their environments in remarkable, often stunningly beautiful ways—from the leaves of carnivorous plants, which have tiny “trigger hairs” that signal the trap to close, to the impressive defense strategies some leaves have evolved to reduce their consumption. (Recent studies suggest, for example, that some plants can detect chewing vibrations and mobilize potent chemical defenses.) In many cases, we’ve learned from the extraordinary adaptations of leaves, such as the invention of new self-cleaning surfaces inspired by the slippery coating found on leaves. But we owe much more to leaves, and Lee also calls our attention back to the fact that that our very lives—and the lives of all on the planet—depend on them. Not only is foliage is the ultimate source of food for every living thing on land, its capacity to cycle carbon dioxide and oxygen can be considered among evolution’s most important achievements—and one that is critical in mitigating global climate change. Taking readers through major topics like these while not losing sight of the small wonders of nature we see every day—if you’d like to identify a favorite leaf, Lee’s glossary of leaf characteristics means you won’t be left out on a limb—Nature’s Fabric is eminently readable and full of intriguing research, sure to enhance your appreciation for these extraordinary green machines.


Book Synopsis Nature's Fabric by : David Lee

Download or read book Nature's Fabric written by David Lee and published by University of Chicago Press. This book was released on 2017-09-28 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leaves are all around us—in backyards, cascading from window boxes, even emerging from small cracks in city sidewalks given the slightest glint of sunlight. Perhaps because they are everywhere, it’s easy to overlook the humble leaf, but a close look at them provides one of the most enjoyable ways to connect with the natural world. A lush, incredibly informative tribute to the leaf, Nature’s Fabric offers an introduction to the science of leaves, weaving biology and chemistry with the history of the deep connection we feel with all things growing and green. Leaves come in a staggering variety of textures and shapes: they can be smooth or rough, their edges smooth, lobed, or with tiny teeth. They have adapted to their environments in remarkable, often stunningly beautiful ways—from the leaves of carnivorous plants, which have tiny “trigger hairs” that signal the trap to close, to the impressive defense strategies some leaves have evolved to reduce their consumption. (Recent studies suggest, for example, that some plants can detect chewing vibrations and mobilize potent chemical defenses.) In many cases, we’ve learned from the extraordinary adaptations of leaves, such as the invention of new self-cleaning surfaces inspired by the slippery coating found on leaves. But we owe much more to leaves, and Lee also calls our attention back to the fact that that our very lives—and the lives of all on the planet—depend on them. Not only is foliage is the ultimate source of food for every living thing on land, its capacity to cycle carbon dioxide and oxygen can be considered among evolution’s most important achievements—and one that is critical in mitigating global climate change. Taking readers through major topics like these while not losing sight of the small wonders of nature we see every day—if you’d like to identify a favorite leaf, Lee’s glossary of leaf characteristics means you won’t be left out on a limb—Nature’s Fabric is eminently readable and full of intriguing research, sure to enhance your appreciation for these extraordinary green machines.

Optimal Transport Strategies

Optimal Transport Strategies

Author: Wonjung Kim (Ph. D.)

Publisher:

Published: 2013

Total Pages: 112

ISBN-13:

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It is generally presupposed that the shapes and mechanisms encountered in nature have evolved in such a way as to maximize the robustness of a species. However, most such optimization problems arising in biology are sufficiently complex that it is neither clear what is being optimized, nor what are the relevant constraints. We here consider a number of natural fluid transport systems that may be framed in terms of constrained optimization problems. We first examine natural drinking strategies. We classify the drinking strategies of a broad range of creatures according to the principal forces involved, and present physical pictures for each style. Simple scaling arguments are developed and tested against existing data. While suction is the most common drinking strategy, various alternative styles have evolved among creatures whose morphological, physiological and environmental constraints preclude it. Many small creatures rely on relatively subtle capillary effects for fluid uptake. Particular attention is given to nectar drinking strategies. Nectar drinkers must feed quickly and efficiently due to the threat of predation. While the sweetest nectar offers the greatest energetic rewards, the sharp increase of viscosity with sugar concentration makes it the most difficult to transport. An optimal sugar concentration is thus expected for which the energy intake rate is maximized. An extensive data set indicates that the sugar concentration that optimizes energy transport depends exclusively on the drinking technique employed. We identify three nectar drinking techniques: active suction, capillary suction, and viscous dipping and rationalize the reported optimal concentrations for each through consideration of the appropriate constrained optimization problem. Blood flow in vertebrates and phloem flow in plants are known to be optimized for efficient transport of oxygen and sugar, respectively. Efficient transport of material is similarly advantageous in engineered transport systems such as traffic and wireless networks. We thus develop a general framework for determining the concentration that maximizes the material flow in a number of transport systems.


Book Synopsis Optimal Transport Strategies by : Wonjung Kim (Ph. D.)

Download or read book Optimal Transport Strategies written by Wonjung Kim (Ph. D.) and published by . This book was released on 2013 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is generally presupposed that the shapes and mechanisms encountered in nature have evolved in such a way as to maximize the robustness of a species. However, most such optimization problems arising in biology are sufficiently complex that it is neither clear what is being optimized, nor what are the relevant constraints. We here consider a number of natural fluid transport systems that may be framed in terms of constrained optimization problems. We first examine natural drinking strategies. We classify the drinking strategies of a broad range of creatures according to the principal forces involved, and present physical pictures for each style. Simple scaling arguments are developed and tested against existing data. While suction is the most common drinking strategy, various alternative styles have evolved among creatures whose morphological, physiological and environmental constraints preclude it. Many small creatures rely on relatively subtle capillary effects for fluid uptake. Particular attention is given to nectar drinking strategies. Nectar drinkers must feed quickly and efficiently due to the threat of predation. While the sweetest nectar offers the greatest energetic rewards, the sharp increase of viscosity with sugar concentration makes it the most difficult to transport. An optimal sugar concentration is thus expected for which the energy intake rate is maximized. An extensive data set indicates that the sugar concentration that optimizes energy transport depends exclusively on the drinking technique employed. We identify three nectar drinking techniques: active suction, capillary suction, and viscous dipping and rationalize the reported optimal concentrations for each through consideration of the appropriate constrained optimization problem. Blood flow in vertebrates and phloem flow in plants are known to be optimized for efficient transport of oxygen and sugar, respectively. Efficient transport of material is similarly advantageous in engineered transport systems such as traffic and wireless networks. We thus develop a general framework for determining the concentration that maximizes the material flow in a number of transport systems.

Topics in Optimal Transportation

Topics in Optimal Transportation

Author: Cédric Villani

Publisher: American Mathematical Soc.

Published: 2021-08-25

Total Pages: 370

ISBN-13: 1470467267

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This is the first comprehensive introduction to the theory of mass transportation with its many—and sometimes unexpected—applications. In a novel approach to the subject, the book both surveys the topic and includes a chapter of problems, making it a particularly useful graduate textbook. In 1781, Gaspard Monge defined the problem of “optimal transportation” (or the transferring of mass with the least possible amount of work), with applications to engineering in mind. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind. Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology. Originating from a graduate course, the present volume is intended for graduate students and researchers, covering both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis.


Book Synopsis Topics in Optimal Transportation by : Cédric Villani

Download or read book Topics in Optimal Transportation written by Cédric Villani and published by American Mathematical Soc.. This book was released on 2021-08-25 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive introduction to the theory of mass transportation with its many—and sometimes unexpected—applications. In a novel approach to the subject, the book both surveys the topic and includes a chapter of problems, making it a particularly useful graduate textbook. In 1781, Gaspard Monge defined the problem of “optimal transportation” (or the transferring of mass with the least possible amount of work), with applications to engineering in mind. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind. Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology. Originating from a graduate course, the present volume is intended for graduate students and researchers, covering both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis.

Computational Optimal Transport

Computational Optimal Transport

Author: Gabriel Peyre

Publisher: Foundations and Trends(r) in M

Published: 2019-02-12

Total Pages: 272

ISBN-13: 9781680835502

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The goal of Optimal Transport (OT) is to define geometric tools that are useful to compare probability distributions. Their use dates back to 1781. Recent years have witnessed a new revolution in the spread of OT, thanks to the emergence of approximate solvers that can scale to sizes and dimensions that are relevant to data sciences. Thanks to this newfound scalability, OT is being increasingly used to unlock various problems in imaging sciences (such as color or texture processing), computer vision and graphics (for shape manipulation) or machine learning (for regression, classification and density fitting). This monograph reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications. Computational Optimal Transport presents an overview of the main theoretical insights that support the practical effectiveness of OT before explaining how to turn these insights into fast computational schemes. Written for readers at all levels, the authors provide descriptions of foundational theory at two-levels. Generally accessible to all readers, more advanced readers can read the specially identified more general mathematical expositions of optimal transport tailored for discrete measures. Furthermore, several chapters deal with the interplay between continuous and discrete measures, and are thus targeting a more mathematically-inclined audience. This monograph will be a valuable reference for researchers and students wishing to get a thorough understanding of Computational Optimal Transport, a mathematical gem at the interface of probability, analysis and optimization.


Book Synopsis Computational Optimal Transport by : Gabriel Peyre

Download or read book Computational Optimal Transport written by Gabriel Peyre and published by Foundations and Trends(r) in M. This book was released on 2019-02-12 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of Optimal Transport (OT) is to define geometric tools that are useful to compare probability distributions. Their use dates back to 1781. Recent years have witnessed a new revolution in the spread of OT, thanks to the emergence of approximate solvers that can scale to sizes and dimensions that are relevant to data sciences. Thanks to this newfound scalability, OT is being increasingly used to unlock various problems in imaging sciences (such as color or texture processing), computer vision and graphics (for shape manipulation) or machine learning (for regression, classification and density fitting). This monograph reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications. Computational Optimal Transport presents an overview of the main theoretical insights that support the practical effectiveness of OT before explaining how to turn these insights into fast computational schemes. Written for readers at all levels, the authors provide descriptions of foundational theory at two-levels. Generally accessible to all readers, more advanced readers can read the specially identified more general mathematical expositions of optimal transport tailored for discrete measures. Furthermore, several chapters deal with the interplay between continuous and discrete measures, and are thus targeting a more mathematically-inclined audience. This monograph will be a valuable reference for researchers and students wishing to get a thorough understanding of Computational Optimal Transport, a mathematical gem at the interface of probability, analysis and optimization.

Lectures on Optimal Transport

Lectures on Optimal Transport

Author: Luigi Ambrosio

Publisher: Springer Nature

Published: 2021-07-22

Total Pages: 250

ISBN-13: 3030721620

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This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations.


Book Synopsis Lectures on Optimal Transport by : Luigi Ambrosio

Download or read book Lectures on Optimal Transport written by Luigi Ambrosio and published by Springer Nature. This book was released on 2021-07-22 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations.

Credible Asset Allocation, Optimal Transport Methods, and Related Topics

Credible Asset Allocation, Optimal Transport Methods, and Related Topics

Author: Songsak Sriboonchitta

Publisher: Springer Nature

Published: 2022-07-29

Total Pages: 762

ISBN-13: 3030972739

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This book describes state-of-the-art economic ideas and how these ideas can be (and are) used to make economic decision (in particular, to optimally allocate assets) and to gauge the results of different economic decisions (in particular, by using optimal transport methods). Special emphasis is paid to machine learning techniques (including deep learning) and to different aspects of quantum econometrics—when quantum physics and quantum computing models are techniques are applied to study economic phenomena. Applications range from more traditional economic areas to more non-traditional topics such as economic aspects of tourism, cryptocurrencies, telecommunication infrastructure, and pandemic. This book helps student to learn new techniques, practitioners to become better knowledgeable of the state-of-the-art econometric techniques, and researchers to further develop these important research directions


Book Synopsis Credible Asset Allocation, Optimal Transport Methods, and Related Topics by : Songsak Sriboonchitta

Download or read book Credible Asset Allocation, Optimal Transport Methods, and Related Topics written by Songsak Sriboonchitta and published by Springer Nature. This book was released on 2022-07-29 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes state-of-the-art economic ideas and how these ideas can be (and are) used to make economic decision (in particular, to optimally allocate assets) and to gauge the results of different economic decisions (in particular, by using optimal transport methods). Special emphasis is paid to machine learning techniques (including deep learning) and to different aspects of quantum econometrics—when quantum physics and quantum computing models are techniques are applied to study economic phenomena. Applications range from more traditional economic areas to more non-traditional topics such as economic aspects of tourism, cryptocurrencies, telecommunication infrastructure, and pandemic. This book helps student to learn new techniques, practitioners to become better knowledgeable of the state-of-the-art econometric techniques, and researchers to further develop these important research directions