Synchrony, aggregation, and multi-area eigenanalysis

Extensions, simplifications, and tests of synchronic modal equivalencing (SME)

“…In other words, the slow modes constitute the inter-group dynamics, while the fast modes constitute the intra-group dynamics. [12]. A criterion for picking the size of the chord is noted later in this paper.…”

“…Note that basis generators for one-dimensional synchronic groups were referred to as reference generators in [12]; our present terminology seems preferable, in view of the extended (multi-dimensional) notion of synchrony that we are using now.…”

“…Approximate synchrony involves approximate alignment of these chordal rows, and measures of synchrony aim to quantify the degree of alignment. The degree of synchrony between two generators is defined in [12] as the cosine of the angle between the corresponding chordal rows. The synchronic distance of a given generator from a basis generator is defined in [lo] as the distance between its chordal row and the projection of this row on the chordal row of the basis generator.…”

“…The synchronic distance of a given generator from a basis generator is defined in [lo] as the distance between its chordal row and the projection of this row on the chordal row of the basis generator. For both these measures, it can be advantageous to work with weighted versions of the chordal rows, as noted in [IO], [12].…”

“…To pick the basis generators for a given chord, the thesis [lo] presents an algorithm that is considerably simpler than the fuzzy clustering procedure originally prescribed in [12]. In this simplified algorithm, the first basis generator picked is the one with the largest total participation, [13], in the chosen chord, where this total is measured in some convenient way.…”