Network Theory
John Baez
March 4, 2011
Scientists use diagrams of networks in many different ways. To make
sense of this, I'm writing a series of articles on network theory.
You can navigate forwards and back through these using the blue
arrows. And by clicking the links that say "on Azimuth", you can see
blog entries containing these articles. Those let you read comments
about my articles—and also make comments or ask questions of
your own!
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Part 1 - toward a general theory of networks.
Also available on Azimuth.
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Part 2 - stochastic Petri nets; the master equation versus the rate equation. Also available on Azimuth.
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Part 3 - the rate equation of a stochastic Petri net, and applications to chemistry and infectious disease. Also available on Azimuth.
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Part 4 - the master equation of a stochastic Petri net, and analogies to quantum field theory. Also available on Azimuth.
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Part 5 - the stochastic Petri net for a Poisson process; analogies between quantum theory and probability theory. Also available on Azimuth.
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Part 6 - the master equation in terms of annihilation and creation operators. Also available on Azimuth.
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Part 7 - a stochastic Petri net from population biology whose rate equation is the logistic equation; an equilibrium solution of the corresponding master equation. Also available on Azimuth.
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Part 8 - the rate equation and master equation of a stochastic Petri net; the role of Feynman diagrams. Also available on Azimuth.
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Part 9 - the Anderson-Craciun-Kurtz theorem, which gives equilibrium solutions of the master equation from complex balanced equilibrium solutions of the rate equation; coherent states. Also available on Azimuth.
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Part 10 - an example of the Anderson-Craciun-Kurtz theorem. Also available on Azimuth.
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Part 11 - a stochastic version of Noether's theorem. Also available on Azimuth.
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Part 12 - comparing quantum mechanics and stochastic mechanics. Also available on Azimuth.
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Part 13 - comparing the quantum and stochastic versions of Noether's theorem. Also available on Azimuth.
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Part 14 - an example: chemistry and the Desargues graph. Also available on Azimuth, together with a special post on answers to the puzzle.
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Part 15 - Markov processes and quantum processes coming from graph Laplacians, illustrated using the Desargues graph. Also available on Azimuth.
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Part 16 - Dirichlet operators and electrical circuits made of resistors. Also available on Azimuth.
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Part 17 - Reaction networks versus Petri nets; Feinberg's deficiency zero theorem. Also available on Azimuth.
To understand ecosystems, ultimately will be to understand networks. -
B. C. Patten and M. Witkamp
© 2011 John Baez
baez@math.removethis.ucr.andthis.edu
