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. |
Fra bogen
Resultater 1-5 af 89
... matrix inequalities arising in engineering systems . 3. The article Algebraic statistics and contingency table prob ... matrices and optimization of polynomials is an invaluable source , as the only one of this kind , for the rapidly ...
... matrix of coef- ficients will have arbitrarily many negative eigenvalues . Suppose however that we write R as a squared norm | ƒ2 on the sphere . What can we say about N , the rank of the coefficient matrix of f2 ? This problem is diffi ...
... matrix inequalities ( MIs ) . Unfortunately , many of these MIs are badly behaved and unsuited to numerics . Thus engineers have spent considerable energy and cleverness doing non - commutative algebra to convert , on an ad hoc basis ...
... matrices which appear in the formulas in a manner which respects matrix multiplication . Dimension dependent MIs have unknowns which are tuples of numbers . The results presented here suggest the surprising conclusion that for dimension ...
... matrices Ao , A1 , ... , Ag , the func- Sa ( R ) given by tion L : R9 ← L ( x ) = ΣAjxj j = 0 is a classical linear pencil ; and the inequality L ( x ) 0 is the classical ( commutative ) linear matrix inequality . Here ( x1 ...
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 |