We introduce generalized trajectories where the individual symbols are interpreted as operations performed on the operand words. The various previously considered trajectory-based operations can all be expressed in this formalism. It is shown that the generalized operations can simulate Turing machine computations. We consider the equivalence problem and a notion of unambiguity that is sufficie...

It is proven that an initial value problem of an autonomous system verifying some conditions has exactly one open continuously di€erentiable trajectory on R, whose limit set is not one point. The proof of the result is based upon continuation methods. 1. Preliminaries Di€erential equations play a key role in nature and technology because they control their processes. In time-dependent processes...

In this paper, we present a simple algorithm for selecting and linking interesting ow vectors across a sequence of frames for computing motion trajectories. We track tokens which have both interesting pixel gray values in the spatial domain and in the optical ow eld in the temporal domain. This and operation eeectively remove some redundant trajectories. Due to errors introduced during the comp...