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- W1486276683 abstract "The continuous general linear group in n dimensions can be decomposed into two Lie groups: (1) an n(n-1) dimensional ‘Markov type' Lie group that is defined by preserving the sum of the components of a vector, and (2) the n dimensional Abelian Lie group, A(n), of scaling transformations of the coordinates. With the restriction of the first Lie algebra parameters to nonnegative values, one obtains exactly all Markov transformations in n dimensions that are continuously connected to the identity. In this work we show that every network, as defined by its C matrix, is in one to one correspondence to one element of the Markov monoid of the same dimensionality. It follows that any network matrix, C, is the generator of a continuous Markov transformation that can be interpreted as producing an irreversible flow among the nodes of the corresponding network." @default.
- W1486276683 created "2016-06-24" @default.
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- W1486276683 date "2005-01-01" @default.
- W1486276683 modified "2023-09-23" @default.
- W1486276683 title "Networks, Markov Lie Monoids, and Generalized Entropy" @default.
- W1486276683 cites W2042812053 @default.
- W1486276683 doi "https://doi.org/10.1007/11560326_10" @default.
- W1486276683 hasPublicationYear "2005" @default.
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