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This paper examines the most probable route to chaos in high-dimensional dynami-cal systems function space (time-delay neural networks) endowed with a probability measure in a computational setting. The most probable route to chaos (relative to the measure we impose on the function space) as the dimension is increased is observed to be a sequence of(More)
This report investigates the dynamical stability conjectures of Palis and Smale and Pugh and Shub from the standpoint of numerical observation and lays the foundation for a stability conjecture. As the dimension of a dissipative dynamical system is increased, it is observed that the number of positive Lyapunov exponents increases monotonically, the Lyapunov(More)
An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter windows with periodic behavior decreases. A subset of parameter space remains where noncatastrophic topological change(More)
Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal approximators (neural networks). The eigenvalue spectrum is considered both numerically and analytically(More)
The Annals is reprinting this interview, more a monologue than a conversation, because Donald E. Knuth is one of the giants of computing. We would like to understand how he developed, what he thought, and how he came by this idea or that as he created his many contributions, not the least of which is the brilliant clarity and comprehensiveness with which he(More)
—A methodology for understanding and detecting nonconvulsive seizures in individuals with sub-arachnoid hemorrhage is introduced. Specifically, beginning with an EEG signal, the power spectrum is estimated yielding a multivariate time series which is then analyzed using empirical orthogonal functional analysis. This methodology allows for easy(More)
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