There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The discovery that mammalian cells generate nitric oxide, a gas previously considered to be merely an atmospheric pollutant, is providing important information about many biologic processes. Nitric oxide is synthesized from the amino acid L-arginine by a family of enzymes, the nitric oxide synthases, through a hitherto unrecognized metabolic route -- namely, the L-arginine-nitric oxide pathway1–8. The synthesis of nitric oxide by vascular endothelium is responsible for the vasodilator tone that is essential for the regulation of blood pressure. In the central nervous system nitric oxide is a neurotransmitter that underpins several functions, including the formation of memory. . . .

The L-Arginine-Nitric Oxide Pathway

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Convex Analysisの二,三の進展について

Our growing dependence on increasingly complex computer and software systems necessitates the development of formalisms, techniques, and tools for assessing functional properties of these systems. One such technique that has emerged in the last twenty years is model checking, which systematically (and automatically) checks whether a model of a given system satisfies a desired property such as deadlock freedom, invariants, and request-response properties. This automated technique for verification and debugging has developed into a mature and widely used approach with many applications. Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field. The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics LTL and CTL, compares them, and covers algorithms for verifying these logics, discussing real-time systems as well as systems subject to random phenomena. Separate chapters treat such efficiency-improving techniques as abstraction and symbolic manipulation. The book includes an extensive set of examples (most of which run through several chapters) and a complete set of basic results accompanied by detailed proofs. Each chapter concludes with a summary, bibliographic notes, and an extensive list of exercises of both practical and theoretical nature.

/pdf/principles-of-model-checking-249iimickz.pdf

Principles of Model Checking

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Finite model theory and its applications. Texts in Theoretical Computer Science

We present Ehrenfeucht-Fraisse games for transitive closure logic (FO + TC) and for quantifier classes in (FO + TC). With this method we investigate the fine structure of positive transitive closure logic (FO + pos TC), and identify an infinite quantifier hierarchy inside (FO + pos TC), formed by interleaving universal quantifiers and TC-operators.

On Transitive Closure Logic

http://www.logic.rwth-aachen.de/pub/graedel/mcgames.pdf

Model-checking games for logics of imperfect information

Subclasses of Presburger arithmetic and the polynomial-time hierarchy

We investigate quantitative extensions of modal logic and the modal μ-calculus, and study the question whether the tight connection between logic and games can be lifted from the qualitative logics to their quantitative counterparts. It turns out that, if the quantitative μ-calculus is defined in an appropriate way respecting the duality properties between the logical operators, then its model checking problem can indeed be characterised by a quantitative variant of parity games. However, these quantitative games have quite different properties than their classical counterparts, in particular they are, in general, not positionally determined. The correspondence between the logic and the games goes both ways: the value of a formula on a quantitative transition system coincides with the value of the associated quantitative game, and conversely, the values of quantitative parity games are definable in the quantitative μ-calculus.

/pdf/model-checking-games-for-the-quantitative-m-calculus-4nmc8u1vc1.pdf

Erich Grädel

Papers

Finite model theory and its applications. Texts in Theoretical Computer Science

On Transitive Closure Logic

Model-checking games for logics of imperfect information

Subclasses of Presburger arithmetic and the polynomial-time hierarchy

Model Checking Games for the Quantitative μ -Calculus