Emerging Applications Of Algebraic Geometry
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Emerging Applications Of Algebraic Geometry
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Author : Mihai Putinar
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
Emerging Applications Of Algebraic Geometry written by Mihai Putinar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Mathematics categories.
Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.
Emerging Applications Of Algebraic Geometry
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Author : Mihai Putinar
language : en
Publisher: Springer
Release Date : 2008-10-27
Emerging Applications Of Algebraic Geometry written by Mihai Putinar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-27 with Mathematics categories.
Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.
Emerging Applications Of Algebraic Geometry
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Author : Mihai Putinar
language : en
Publisher: Springer
Release Date : 2008-11-01
Emerging Applications Of Algebraic Geometry written by Mihai Putinar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.
Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.
Software For Algebraic Geometry
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Author : Michael E. Stillman
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-29
Software For Algebraic Geometry written by Michael E. Stillman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-29 with Mathematics categories.
Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in both theoretical advances and applications. Over the past fifteen years, several excellent general purpose packages for computations in algebraic geometry have been developed, such as, CoCoA, Singular and Macaulay 2. While these packages evolve continuously, incorporating new mathematical advances, they both motivate and demand the creation of new mathematics and smarter algorithms. This volume reflects the workshop “Software for Algebraic Geometry” held in the week from 23 to 27 October 2006, as the second workshop in the thematic year on Applications of Algebraic Geometry at the IMA. The papers in this volume describe the software packages Bertini, PHClab, Gfan, DEMiCs, SYNAPS, TrIm, Gambit, ApaTools, and the application of Risa/Asir to a conjecture on multiple zeta values. They offer the reader a broad view of current trends in computational algebraic geometry through software development and applications.
Algorithms In Algebraic Geometry
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Author : Alicia Dickenstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-10
Algorithms In Algebraic Geometry written by Alicia Dickenstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-10 with Mathematics categories.
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its Applications on September 2006 is one tangible indication of the interest. This volume of articles captures some of the spirit of the IMA workshop.
Semidefinite Optimization And Convex Algebraic Geometry
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Author : Grigoriy Blekherman
language : en
Publisher: SIAM
Release Date : 2013-03-21
Semidefinite Optimization And Convex Algebraic Geometry written by Grigoriy Blekherman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Mathematics categories.
An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
A Course In Real Algebraic Geometry
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Author : Claus Scheiderer
language : en
Publisher: Springer Nature
Release Date : 2024-09-12
A Course In Real Algebraic Geometry written by Claus Scheiderer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-12 with Mathematics categories.
This textbook is designed for a one-year graduate course in real algebraic geometry, with a particular focus on positivity and sums of squares of polynomials. The first half of the book features a thorough introduction to ordered fields and real closed fields, including the Tarski–Seidenberg projection theorem and transfer principle. Classical results such as Artin's solution to Hilbert's 17th problem and Hilbert's theorems on sums of squares of polynomials are presented in detail. Other features include careful introductions to the real spectrum and to the geometry of semialgebraic sets. The second part studies Archimedean positivstellensätze in great detail and in various settings, together with important applications. The techniques and results presented here are fundamental to contemporary approaches to polynomial optimization. Important results on sums of squares on projective varieties are covered as well. The last part highlights applications to semidefinite programming and polynomial optimization, including recent research on semidefinite representation of convex sets. Written by a leading expert and based on courses taught for several years, the book assumes familiarity with the basics of commutative algebra and algebraic varieties, as can be covered in a one-semester first course. Over 350 exercises, of all levels of difficulty, are included in the book.
Computations In Algebraic Geometry With Macaulay 2
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Author : David Eisenbud
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Computations In Algebraic Geometry With Macaulay 2 written by David Eisenbud and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re cently developed algorithms have made theoretical aspects of the subject accessible to a broad range of mathematicians and scientists. The algorith mic approach to the subject has two principal aims: developing new tools for research within mathematics, and providing new tools for modeling and solv ing problems that arise in the sciences and engineering. A healthy synergy emerges, as new theorems yield new algorithms and emerging applications lead to new theoretical questions. This book presents algorithmic tools for algebraic geometry and experi mental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. A wide range of mathematical scientists should find these expositions valuable. This includes both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all.
Moments Positive Polynomials And Their Applications
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Author : Jean Bernard Lasserre
language : en
Publisher: World Scientific
Release Date : 2009-10-02
Moments Positive Polynomials And Their Applications written by Jean Bernard Lasserre and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-02 with Mathematics categories.
Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the Generalized Moment Problem (GMP).This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones, standard duality in convex optimization nicely expresses the duality between moments and positive polynomials.In the second part, the methodology is particularized and described in detail for various applications, including global optimization, probability, optimal control, mathematical finance, multivariate integration, etc., and examples are provided for each particular application.
International Encyclopedia Of Statistical Science
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Author : Miodrag Lovric
language : en
Publisher: Springer Nature
Release Date : 2025-06-19
International Encyclopedia Of Statistical Science written by Miodrag Lovric and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Mathematics categories.
The International Encyclopedia of Statistical Science stands as a monumental effort to enrich statistics education globally, particularly in regions facing educational challenges. By amalgamating the expertise of over 700 authors from 110 countries, including Nobel Laureates and presidents of statistical societies, it offers an unparalleled resource for readers worldwide. This encyclopedia is not just a collection of entries; it is a concerted effort to revive statistics as a vibrant, critical field of study and application. Providing a comprehensive and accessible account of statistical terms, methods, and applications, it enables readers to gain a quick insight into the subject, regardless of their background. This work serves to refresh and expand the knowledge of researchers, managers, and practitioners, highlighting the relevance and applicability of statistics across various fields, from economics and business to healthcare and public policy. Furthermore, it aims to inspire students by demonstrating the significance of statistics in solving real-world problems, thus encouraging a new generation to explore and contribute to the field.