Emerging Applications of Algebraic GeometryMihai Putinar, Seth Sullivant Springer Science & Business Media, 10. dec. 2008 - 376 sider 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. |
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... represented by a positive Borel measure supported on the sphere . The proof has implicitly appeared in the works of Ito [ 17 ] , Yoshino [ 33 ] , Lubin [ 22 ] and Athavale [ 3 ] , all dealing with subnormality criteria for commuting ...
... represented by a positive Borel measure , sup- ported on the sphere . The representing measure is unique by the Stone - Weierstrass Theorem . Proof of Theorem 1. Suppose first that no qi's are. POLYNOMIAL OPTIMIZATION ON ODD ...
... measure μ , supported on the unit sphere , which represents L. Therefore > 0 ≥ L ( p ) = √ pdμ ράμ > 0 , a contradiction . The proof of the general case is similar , with the difference that we have to prove that the support of the ...
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Indhold
1 | |
17 | |
ALGEBRAIC STATISTICS AND CONTINGENCY TABLE PROBLEMS LOGLINEAR MODELS LIKELIHOOD ESTIMATION AND DISCLOSUR... | 63 |
USING INVARIANTS FOR PHYLOGENETIC TREE CONSTRUCTION | 89 |
ON THE ALGEBRAIC GEOMETRY OF POLYNOMIAL DYNAMICAL SYSTEMS | 109 |
SUMS OF SQUARES MOMENT MATRICES AND OPTIMIZATION OVER POLYNOMIALS | 157 |
POSITIVITY AND SUMS OF SQUARESA GUIDE TO RECENT RESULTS | 271 |
NONCOMMUTATIVE REAL ALGEBRAIC GEOMETRY SOMEBASIC CONCEPTS AND FIRST IDEAS | 325 |
OPEN PROBLEMS IN ALGEBRAIC STATISTICS | 351 |
LIST OF WORKSHOP PARTICIPANTS | 365 |