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In Discovering Complexity, William Bechtel and Robert Richardson examine two heuristics that guided the development of mechanistic models in the life sciences: decomposition and localization. Drawing on historical cases from disciplines including cell biology, cognitive neuroscience, and genetics, they identify a number of "choice points" that life scientists confront in developing mechanistic explanations and show how different choices result in divergent explanatory models. Describing decomposition as the attempt to differentiate functional and structural components of a system and localization as the assignment of responsibility for specific functions to specific structures, Bechtel and Richardson examine the usefulness of these heuristics as well as their fallibility--the sometimes false assumption underlying them that nature is significantly decomposable and hierarchically organized. When Discovering Complexity was originally published in 1993, few philosophers of science perceived the centrality of seeking mechanisms to explain phenomena in biology, relying instead on the model of nomological explanation advanced by the logical positivists (a model Bechtel and Richardson found to be utterly inapplicable to the examples from the life sciences in their study). Since then, mechanism and mechanistic explanation have become widely discussed. In a substantive new introduction to this MIT Press edition of their book, Bechtel and Richardson examine both philosophical and scientific developments in research on mechanistic models since 1993.

Research --- Decomposition method --- Localization theory --- Complexity (Philosophy) --- Methodology --- Decomposition method. --- Localization theory. --- Methodology. --- 168.5 --- Multidisciplinair karakter der wetenschappen --- Categories (Mathematics) --- Homotopy theory --- Nilpotent groups --- Method, Decomposition --- Operations research --- Programming (Mathematics) --- System analysis --- Philosophy --- Emergence (Philosophy) --- Recherche --- Décomposition (méthode mathématique) --- Localisation, Théorie de la --- Complexité (philosophie) --- methodologie

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Domain decomposition is an active, interdisciplinary research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models of natural and engineered systems. Since the advent of hierarchical distributed memory computers, it has been motivated by considerations of concurrency and locality in a wide variety of large-scale problems, continuous and discrete. Historically, it emerged from the analysis of partial differential equations, beginning with the work of Schwarz in 1870. The present volume sets forth new contributions in areas of numerical analysis, computer science, scientific and industrial applications, and software development.

Decomposition method --- Differential equations, Partial --- Method, Decomposition --- Operations research --- Programming (Mathematics) --- System analysis --- Engineering. --- Computer science --- Computer science. --- Engineering, general. --- Computational Mathematics and Numerical Analysis. --- Computational Science and Engineering. --- Numerical and Computational Physics, Simulation. --- Mathematics of Computing. --- Mathematics. --- Informatics --- Science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Construction --- Industrial arts --- Technology --- Mathematics --- Computer mathematics. --- Physics. --- Computer science—Mathematics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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This monograph has two main objectives. The first one is to give a self-contained exposition of the relevant facts about set operads, in the context of combinatorial species and its operations. This approach has various advantages: one of them is that the definition of combinatorial operations on species, product, sum, substitution and derivative, are simple and natural. They were designed as the set theoretical counterparts of the homonym operations on exponential generating functions, giving an immediate insight on the combinatorial meaning of them. The second objective is more ambitious. Before formulating it, authors present a brief historic account on the sources of decomposition theory. For more than forty years decompositions of discrete structures have been studied in different branches of discrete mathematics: combinatorial optimization, network and graph theory, switching design or boolean functions, simple multi-person games and clutters, etc.

Mathematics. --- Special Functions. --- Complex Systems. --- Operator Theory. --- Operator theory. --- Functions, special. --- Mathématiques --- Théorie des opérateurs --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Operads. --- Decomposition method. --- Computer science --- Categories (Mathematics) --- Category theory (Mathematics) --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Method, Decomposition --- Special functions. --- System theory. --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Operations research --- Programming (Mathematics) --- System analysis --- Functional analysis --- Special functions --- Mathematical analysis --- Systems, Theory of --- Systems science --- Science --- Philosophy

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Decomposition method --- Differential equations, Partial --- Décomposition (Méthode mathématique) --- Equations aux dérivées partielles --- Congresses --- Congrès --- Congresses. --- -Differential equations, Partial --- -519.6 --- 681.3 *G18 --- Partial differential equations --- Method, Decomposition --- Operations research --- Programming (Mathematics) --- System analysis --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Décomposition (Méthode mathématique) --- Equations aux dérivées partielles --- Congrès --- 519.6 --- Decomposition method - Congresses. --- Differential equations, Partial - Congresses.

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th This volume contains a selection of 41 refereed papers presented at the 18 International Conference of Domain Decomposition Methods hosted by the School of Computer Science and Engineering(CSE) of the Hebrew University of Jerusalem, Israel, January 12–17, 2008. 1 Background of the Conference Series The International Conference on Domain Decomposition Methods has been held in twelve countries throughout Asia, Europe, the Middle East, and North America, beginning in Paris in 1987. Originally held annually, it is now spaced at roughly 18-month intervals. A complete list of past meetings appears below. The principal technical content of the conference has always been mathematical, but the principal motivation has been to make efficient use of distributed memory computers for complex applications arising in science and engineering. The leading 15 such computers, at the “petascale” characterized by 10 oating point operations per second of processing power and as many Bytes of application-addressablem- ory, now marshal more than 200,000 independent processor cores, and systems with many millions of cores are expected soon. There is essentially no alternative to - main decomposition as a stratagem for parallelization at such scales. Contributions from mathematicians, computer scientists, engineers, and scientists are together necessary in addressing the challenge of scale, and all are important to this conference.

Decomposition method -- Congresses. --- Differential equations, Partial -- Congresses. --- Decomposition method --- Differential equations, Partial --- Mathematics --- Civil & Environmental Engineering --- Mathematics - General --- Operations Research --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Decomposition method. --- Mathematics. --- Math --- Method, Decomposition --- Computer science --- Computer mathematics. --- Mathematical models. --- Physics. --- Computational Mathematics and Numerical Analysis. --- Mathematical Modeling and Industrial Mathematics. --- Computational Science and Engineering. --- Numerical and Computational Physics. --- Mathematics of Computing. --- Science --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Models, Mathematical --- Simulation methods --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Operations research --- Programming (Mathematics) --- System analysis --- Computer science. --- Numerical and Computational Physics, Simulation. --- Informatics --- Computer science—Mathematics.