123,981 research outputs found
Truncated horseshoes and formal languages in chaotic scattering
In this paper we study parameter families of truncated horseshoes as models
of multiscattering systems which show a transition to chaos without losing
hyperbolicity, so that the topological features of the transition are
completely describable by a parameterized family of symbolic dynamics. At a
fixed parameter value the corresponding horseshoe represents the set of orbits
trapped in the scattering region. The bifurcations are a pure boundary effect
and no other bifurcations such as saddle center bifurcations occur in this
transition scenario. Truncated horseshoes actually arise in concrete potential
scattering under suitable conditions. It is shown that a simple scattering
model introduced earlier can realize this scenario in a certain parameter range
(the "truncated sawshoe") . For this purpose, we solve the inverse scattering
problem of finding the central potential associated to the sawshoe model.
Furthermore, we review classification schemes for the transition to chaos of
truncated horseshoes originating from symbolic dynamics and formal language
theory and apply them to the truncated double horseshoe and the truncated
sawshoe.Comment: 39 pages postscript; use uudecode and uncompress ! 4 figures
available as hardcopies on reques
Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective
Neural-symbolic computing has now become the subject of interest of both
academic and industry research laboratories. Graph Neural Networks (GNN) have
been widely used in relational and symbolic domains, with widespread
application of GNNs in combinatorial optimization, constraint satisfaction,
relational reasoning and other scientific domains. The need for improved
explainability, interpretability and trust of AI systems in general demands
principled methodologies, as suggested by neural-symbolic computing. In this
paper, we review the state-of-the-art on the use of GNNs as a model of
neural-symbolic computing. This includes the application of GNNs in several
domains as well as its relationship to current developments in neural-symbolic
computing.Comment: Updated version, draft of accepted IJCAI2020 Survey Pape
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