In an asynchronous system, there are usually many trajectories out of any state that visit various attractors.
Close inspection of a subset of our simulations confirmed that the most complex behavior occurs for r = 3, with many trajectories reaching periodic orbits of the fourth type, that is, of length >3, that appear to have very small basins of attraction.
But a million different dreams had to collapse into a single reality when the real-life Presidency began, in much the same way that a "probability wave" of many trajectories collapses into a single photon in physics.
Of the many trajectories found, the optimal trajectory submitted for the competition is reported.
Of the many trajectories found, three optimal trajectories are reported and compared, including the one submitted for the competition.
In the Fig. 4c one can notice that the level of the noise that is required to lead most paths to zero is relatively large and even in this figure there are still many of trajectories that reach a high level.
Judging by the trajectories of many of those passes, there were likely busloads of Vikings fans at Lambeau who thought he threw 30 too many.
Then, the trajectories of many electrons are traced under existence of monochromatic Pc5 waves for about 10 wave periods.
Sacha Kocsis of Griffith University in Brisbane, Australia, Aephraim Steinberg of the University of Toronto in Canada, and colleagues have measured the average trajectories of many photons in the experiment, as they report today in Science.
Total internal reflection and video microscopy are used to track three-dimensional trajectories of many single diffusing colloids that are analyzed to yield interaction potentials, mean-square displacements, and colloid-surface association lifetimes.
