Sentence examples for evolving trajectories from inspiring English sources

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).

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".

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).

The approach is tested on ammonia by evolving eight trajectories on a full-dimensional PES.

In many ways, the history of modern Singapore – which celebrates its 50th anniversary this year as an independent nation-state – can be seen as a constantly evolving innovation trajectory, as Singapore constantly finds new ways to insert itself into the world's economic growth cycles.

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.

Other industries evolving on creative trajectories include pharmaceuticals, oil and gas exploration, and prepackaged software.