Tensor techniques in synmechanics

Conceptual tools are presented for Multiscale Time Series Analysis and tested on a long chronosere of plant particle counts taken from lake sediment in Eastern Beringia's dry arctic steppe tundra. The analysis identifies statistically significant directional regularities in the plant particle chronosere from which assembly rules are inferred that control the composition of the attractor (climax) state in the source vegetation. The rules facilitate construction of predictive assembly scenarios under assumed change in the global climate. The results are reinforcing the idea that regularity and scale-dependence are both part of the chaotic vegetation process, yet, random variation is dominant. Therefore, the appropriate approach to probe for regularity and scale dependence is probabilistic. Tests show increasing sharpness of regularity with increasing lag in the directional pairing of paleorelevés. This is telling us the vegetation process is indeed a multiscale phenomenon and requires a multiscale frame in vegetation study. Periodic convergence of the vegetation process onto low-velocity phases (low values of 1st derivative) coincide with low-velocity phases in the temperature process. When the temperature's process velocity increases, the vegetation's processes velocity increases too. This makes vegetation science's climax theory congruent with the attractor concept of general systems theory.