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We are all playing an intricate part in the whole, and when and where our parts intersect, and for how long, is a much bigger story than we can imagine.
But on set, Jarrod, our VTR guy, was able to reverse the dancers' take and ghost it over Max's take to give us a rough idea of how the actions lined up, and that was really the first time any of us would see all of the moving parts intersect.
The broken-stick model is a member of this class: there are two linear parts, one before and one after the change point, and continuity is imposed such that the linear parts intersect at the change point.
It is possible to add a constraint to (3) such that the two linear parts intersect at the midpoint of the bridge between the two parts, i.e., at τ + ϵ / 2. This constraint implies β 2 = β 0 + β 1 (τ + ϵ / 2 ) − β 3 (τ + ϵ / 2 ), and the model becomes effectively a smoothed broken-stick model.
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It preserves the confounding spirit of the original, with jittery percussion parts intersecting and unwinding in a way that feels head-spinning, like a panic attack in a tangle of vines.
Most recently manufactured automobile and hydraulic parts contain intersecting holes.
Having said all that, "Awake" is a show that is visibly trying to figure out what it wants to be in its first few episodes, and there are a lot of moving parts and intersecting agendas for Killen and fellow executive producer Howard Gordon ("Homeland") to keep track of.
These sequences will be part of an intersecting larger piece of music, which would run from station to station, and cross one another as, say, the 4, 5, 6 line (one musical piece) intersects with the L, N, R, Q and W (another musical piece) at Union Square".
It also meant solving the complex problem of how to keep cloth untangled that is, how to keep it from passing through itself when parts of it intersect.
If model (3) includes the restriction on β 2 such that the two linear parts in (3) intersect at the midpoint of the bridge between the parts, then (3) will yield the same fit as (4).
Vast numbers of staff were culled according to the geometric principle of the Venn diagram - that when two or three operations are "converged", the intersecting parts must represent duplication and therefore be expendable.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com