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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... Positivstellensätze over the real field, elimination the- ory, and invariant theory, all with a computational/numerical component predominant in the background. In order to explain why optimization and control theory appear nat- urally ...
... Positivstellensätze, that is theorems which quantify in algebraic certificates the existence of solutions of polynomial inequalities (e.g.: b2−c ≥ 0 implies that there exists a real x satisfying x2 − 2bx + c = 0). It comes then as no ...
... Positivstellensatz ( i.e. the structure theorem of a positive polynomial on such a set ) can further be simplified by means of the induced complex variables R2d Cd . To this aim we greatly benefit from the = * Department of Mathematics ...
... Positivstellensatz cannot provide effective information on NA based upon only dimension and degree . One must take into account precise information about the size of R , and even then things are delicate . Example 4.1 relies on Faran's ...
... ( Positivstellensätze ) and the other has a new flavor focusing on how noncommutative convexity ( similarly , a variety with positive curvature ) is very constrained , so few actually exist . 1. Introduction . This article sketches a few ...
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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 |