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 24
... space are the byproduct of a universal structure: they are representable by ... Hilbert who unveiled the central role of sums of squares decomposi- tions ... Hilbert's footprint was cast in the spectral theorem for self-adjoint linear ...
... Hilbert space techniques and real algebraic geometry . We specialize to basic semi- algebraic sets KC S2d - 1 CR2d of an odd - dimensional sphere , and prove that the expected Positivstellensatz ( i.e. the structure theorem of a ...
... Hilbert space operators known as spherical isometries , and separately from the works of geometers and complex analysts dealing with Cauchy - Riemann manifolds and proper holomorphic maps between Euclidean balls . The following pages ...
... Hilbert space will be denoted 2.1 . Linear systems . A linear system & is given by the linear differ- ential equations dx Ax + Bu , dt У Cx , with the vector • x ( t ) at each time t being in the vector space X called the state space ...
Du har nået visningsgrænsen for denne bog.
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 |