56,363 research outputs found
Dynamic message-passing equations for models with unidirectional dynamics
Understanding and quantifying the dynamics of disordered out-of-equilibrium
models is an important problem in many branches of science. Using the dynamic
cavity method on time trajectories, we construct a general procedure for
deriving the dynamic message-passing equations for a large class of models with
unidirectional dynamics, which includes the zero-temperature random field Ising
model, the susceptible-infected-recovered model, and rumor spreading models. We
show that unidirectionality of the dynamics is the key ingredient that makes
the problem solvable. These equations are applicable to single instances of the
corresponding problems with arbitrary initial conditions, and are
asymptotically exact for problems defined on locally tree-like graphs. When
applied to real-world networks, they generically provide a good analytic
approximation of the real dynamics.Comment: Final versio
Opinion Exchange Dynamics
We survey a range of models of opinion exchange. From the introduction: "The
exchange of opinions between individuals is a fundamental social interaction...
Moreover, many models in this field are an excellent playground for
mathematicians, especially those working in probability, algorithms and
combinatorics. The goal of this survey is to introduce such models to
mathematicians, and especially to those working in discrete mathematics,
information theory, optimization, probability and statistics."Comment: 62 pages. arXiv admin note: substantial text overlap with
arXiv:1207.589
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