Overview
- Authors:
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Bernard Prum
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Université Paris V, Paris, France
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Jean Claude Fort
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Université Paris V, Paris, France
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Table of contents (10 chapters)
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- Bernard Prum, Jean Claude Fort
Pages 1-18
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- Bernard Prum, Jean Claude Fort
Pages 19-39
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- Bernard Prum, Jean Claude Fort
Pages 40-57
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- Bernard Prum, Jean Claude Fort
Pages 58-81
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- Bernard Prum, Jean Claude Fort
Pages 82-98
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- Bernard Prum, Jean Claude Fort
Pages 99-119
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- Bernard Prum, Jean Claude Fort
Pages 120-135
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- Bernard Prum, Jean Claude Fort
Pages 136-160
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- Bernard Prum, Jean Claude Fort
Pages 161-173
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- Bernard Prum, Jean Claude Fort
Pages 174-204
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Back Matter
Pages 205-220
About this book
In many domains one encounters "systems" of interacting elements, elements that interact more forcefully the closer they may be. The historical example upon which the theory offered in this book is based is that of magnetization as it is described by the Ising model. At the vertices of a regular lattice of sites, atoms "choos e" an orientation under the influence of the orientations of the neighboring atoms. But other examples are known, in physics (the theories of gasses, fluids, .. J, in biology (cells are increasingly likely to become malignant when their neighboring cells are malignant), or in medecine (the spread of contagious deseases, geogenetics, .. .), even in the social sciences (spread of behavioral traits within a population). Beyond the spacial aspect that is related to the idea of "neighboring" sites, the models for all these phenomena exhibit three common features: - The unavoidable ignorance about the totality of the phenomenon that is being studied and the presence ofa great number of often unsuspected factors that are always unquantified lead inevitably to stochastic models. The concept of accident is very often inherent to the very nature of the phenomena considered, so, to justify this procedure, one has recourse to the physicist's principle of indeterminacy, or, for example, to the factor of chance in the Mendelian genetics of phenotypes.