In the first two chapters we review the theory developped by Cartan, Whitney and Tognoli. Then Nullstellensatz is proved both for Stein algebras and for the algebra of real analytic functions on a C-analytic space. Here we find a relation between real Nullstellensatz and seventeenth Hilbert’s problem for positive semidefinite analytic functions. Namely, a positive answer to Hilbert’s problem implies a solution for the real Nullstellensatz more similar to the one for real polinomials. A chapter is devoted to the state of the art on this problem that is far from a complete answer. In the last chapter we deal with inequalities. We describe a class of semianalytic sets defined by countably many global real analytic functions that is stable under topological properties and under proper holomorphic maps between Stein spaces, that is, verifies a direct image theorem. A smaller class admits also a decomposition into irreducible components as it happens for semialgebraic sets. During the redaction some proofs have been simplified with respect to the original ones.
This book constitutes the refereed proceedings of the 28th International Colloquium on Automata, Languages and Programming, ICALP 2001, held in Crete, Greece in July 2001. The 80 revised papers presented together with two keynote contributions and four invited papers were carefully reviewed and selected from a total of 208 submissions. The papers are organized in topical sections on algebraic and circuit complexity, algorithm analysis, approximation and optimization, complexity, concurrency, efficient data structures, graph algorithms, language theory, codes and automata, model checking and protocol analysis, networks and routing, reasoning and verification, scheduling, secure computation, specification and deduction, and structural complexity.
Cancer is a multifaceted disease in which genetic changes induce uncontrolled tumor growth. Genomic characterization of cancer is now leading to better diagnostic, prognostic and predictive biomarkers, and effective individualized management. 'Fast Facts: Comprehensive Genomic Profiling' provides a crash course in the science, methods and application of genomic profiling. Assuming only the most basic knowledge – or memory – of cell biology, the authors provide an overview of DNA and RNA biology and next-generation sequencing. This sets in context the descriptions of prognostic and predictive biomarkers for different cancer types and genomic-based treatments. Finally, but importantly, some of the practicalities of gaining and interpreting genomic information are described. Whether you need a primer or a refresher, this short colorful book demystifies this complex subject. Contents: • Genetic mutations and biomarkers • Understanding next-generation sequencing • Elements of comprehensive genomic profiles • Role in precision oncology • Predictive and prognostic biomarkers • Overcoming barriers to genotype-directed therapy
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