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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Mihai Putinar, Seth Sullivant. THE IMA VOLUMES IN MATHEMATICS AND ITS APPLICATIONS EDITORS Mihfli Putinar Seth Sullivant ergmg j Applicatio of Algera _ f' in Mathematics and its Applications Volume 149 Series Editors Douglas. Front Cover.
Mihai Putinar, Seth Sullivant. Editors Mihai Putinar Department of Mathematics University of California Santa Barbara, CA 93106 USA http://www.math.ucsb.edu/~mputinar/ Series Editors Douglas N. Arnold Arnd Scheel Institute for ...
Mihai Putinar, Seth Sullivant. A short description of the articles that appear in the volume follows. For a general perspective, more details and a better description we recommend the reader to consult the introductions to any one of the ...
Mihai Putinar, Seth Sullivant. POLYNOMIAL OPTIMIZATION ON ODD-DIMENSIONAL SPHERES JOHN P. D'ANGELO" AND MIHAI PUTINARl Abstract. The sphere S2d_1 naturally embeds into the complex afiine space (Cd. We show how the complex variables in ...
Mihai Putinar, Seth Sullivant. This polynomial p is nonnegative for all z, and its zero set is the complex plane given by 21 = Z3 = 0 with Z2 arbitrary. Yet p is not a sum of squared moduli; even more striking is that p cannot be written ...
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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 |