The method is based on replacement of the non-linear vector field by a set of linear ones, each valid over a short segment of the evolving trajectory or over sufficiently small interval of time.
Thorne and Patterson [ 30] explored how understanding the emotional needs of a patient can be an important element of ensuring that health professionals provide appropriate support to patients over the evolving trajectory of living with an illness such as diabetes.
The change in the quasi-potential, Δ V q, can be rewritten from Eq. 4 as: (5) For positive increments in time Δ t, Δ V q is thus always negative along an evolving trajectory, ensuring that trajectories flow "downhill" along a putative "quasi-potential surface".
Hence, it is generally not possible to exactly represent a non-linear dynamical system by a linear one over finite segments of the evolving trajectories in the phase space.
To increase the chance of success in sustainable transformations, it is important to examine past evolving trajectories, identify key variables and their interactions, and understand how they result in fundamental structural changes (Chapin et al. 2006; Olsson et al. 2014; Reid et al. 2010; Scheffer and Westley 2007).
Consider the propagator, \ \bJ \bx t))\), a function that evolves trajectories \ \bx t)\) in time (an example of a propagator is given in the Appendix).
Written in the wake of Stalin's death, it charts a trajectory evolving from pain and terror to giddy release.
In the case of E + I − 2 E I ≥ 0, the monotonicity of δ ( g ) suggests that for a trajectory evolving from an initial condition of ( v, g ) = ( 0, g ( 0 ) ) to a final condition ( v, g ) = ( 1, g ( t ) ), the drop g ( 0 ) − g ( t ) should be smaller for larger g ( 0 ).
Dynamicists seek neural correlates of stimuli and associated behaviors in spatial patterns of oscillatory fields of dendritic activity that self-organize and evolve as trajectories through high-dimensional brain state space; the codes are landscapes of chaotic attractors.
For instance, the HOT-ALOHA, Guerrero Negro, and YNP datasets all include metagenomes dominated by cyanobacteria whose metabolism is driven by oxygenic photosynthesis, yet clustering of these photosynthetic communities by inorganic factors suggests they have evolved on trajectories optimizing their genomes for conditions specific to each of these environments.
But marking yet another career about-face in an ever-evolving trajectory that promises plenty of surprises still, Ms. Smith gives us Hedda's withering public persona alongside access to her private ache.
