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For example, in neuron models, the action potential changes on a much faster time scale than ionic gating variables.
Most of the current understanding of synchronization in switching networks relies on the fast switching hypothesis, where the network dynamics evolves at a much faster time scale than the individual units.
Under the aforementioned two conditions, the enzyme-substrate complexes evolve in a much faster time scale compared with the free substrates and can be assumed to operate at quasi steady states.
Furthermore, recent increases in the sensitivity of NMR detection with a dynamic nuclear polarization technique combined with in vivo 13C labeling have allowed metabolic imaging assays to be completed on a much faster time scale and with finer spatial resolution [27], [28].
These changes in concentration occurred on a much faster time scale than those observed for PCT or CRP [ 22].
By contrast, the dendritic remodeling induced by leptin occurs over a much faster time scale as it is evident within a matter of minutes.
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We reduce the complexity of the dynamical system by taking some of its subprocesses as occurring on a much faster time-scale than others.
A basic criteria for lumping a group of states is that the reactions between states in the group occur on a much faster time-scale than that of interest to the modeller.
On the other hand, the nonprehensile manipulations mentioned above often involve much faster time scale associated with the object motion.
Given that elevations in intracellular Ca2+ following a 5 AP burst decays on much faster time scales (<1 s) these data imply that Ca2+ is likely acting through a second messenger system to control endocytosis in the acceleration phase.
The resulting output, a movie comprised of a series of 2D images can be obtained at much faster time scales (∼10 Hz) than scanning confocal images and can resolve the dynamics of many molecules simultaneously.
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