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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... find detailed and informative answers to all of the above questions, presented in a self-contained form by experts working on the boundary of algebraic geometry and one specific area of its applications. Two major conferences organized ...
... find a polynomial ƒ with nonnegative coefficients and which agrees with p 、 on this line . We also want to know the minimum number N 、 of terms ƒ must have . For > 2 , the polynomial has negative values , and hence cannot be a sum of ...
... find an integer d such that , after multiplication by ( | z | 2 + | t | 2 ) d , the underly- ing form is positive definite . We then dehomogenize and evaluate on the sphere . Thus the isolated values of || for which we can solve the ...
... Find numerics which will solve large convex problems . How do you use special structure , such as most unknowns are matrices and the formulas are all built of noncommutative rational functions ? THEOREM 3.2 ( [ HM03 ] ) . Suppose P. 24 ...
... designing a feedback law . To be more specific , we are given a signal flow diagram : พ Given out A , B1 , B2 , C1 , C2 น У D12 , D21 Find a , b , c where the given system is ds = dt out As. SYSTEMS AND FREE SEMI - ALGEBRAIC GEOMETRY 31.
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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 |