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Analysis of the trained networks elucidates that robust transient trajectories of the neural population are the key driver of sequential categorical decisions.
While, small values of ϵ are enough to account for the almost horizontal transient trajectories in autonomous systems (Fig. 4), they are not enough to account for the almost horizontal directions of motion for limit cycles trajectories in forced systems such as in Fig. 8.
During the first freezing epoch (∼23 seconds), eight transient trajectories were detected (see triangles at the bottom of Fig. 4A).
These spontaneous, transient trajectories also took place on a similar time-scale and exhibited the same directional specificity.
We further examined the effect of random changes of activity by shuffling the data specifically duration reactivations and then plotting the transient trajectories using sliding-window technique.
Interestingly, as the conditioned tone trace emerged, US-triggered ensemble responses which originally evoked only US-specific transient trajectories began to turn into the US-to-CS association trajectories.
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Although the analytical formulations are distinct for the two dynamic regimes, it is found that directly splicing the inter- and intrawell predictions facilitates good agreement with the exact dynamics of the full reconstructed, transient trajectory.
The objective of this paper is to design and to validate a nonlinear multivariable controller, based on the exact feedback linearization technique, which has the capacity to stabilize the photoautotrophic microalgae growth in photobioreactor regardless of the operation point or the transient trajectory.
In this particular example, the shape of the observed transient trajectory does not differ much from its equivalent in an autonomous monostable system.
In summary, we have illustrated how pursuit mechanisms in non-autonomous systems can either lead to the stable maintenance of a transient trajectory (as in Figure 5), or to a drastic change in its direction (as in Figure 6) depending on the geometric arrangement of the attractor with regard to the converging trajectory.
For exchange of three counter-ions, the transient adsorption/desorption trajectories follow completely different equilibration trajectories in composition space.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com