Molecular studies suggest an earlier origin for butterflies, around 80 million years ago, but this still represents a clear 40 million year gap between the two insect groups.
Elginerpeton gives the latest date for the origin of limbs, around 380 million years ago.
This solution makes ( t + − t − ) / τ ℓ ∗ turns around the origin for t ∈ [ t −, t + ].
Data for three different line-scans is scattered around the origin for the OFF-ring and along the strain-free (p-doping) vector for the ON-ring with the average ON-ring coordinate value (purple dot) being (1584.9, 2642.4).
This solution makes 2 ( t + − t − ) / τ ℓ ∗ half-turns around the origin for t ∈ [ t −, t + ]. Figure 4, although not exhaustive of all the conceivable cases, summarizes several different possibilities.
Remarkably, we observed the transition from large scatter in expression distributions around the origin for single ORFs to smooth lines for group of 50 ORFs onwards for all genotypes.
We observed i) large scatter in expression distributions around the origin for ORFs in the collective mode and ii) linear expression distribution of ORFs in the acute-stochastic mode (Figure 6A F, left panels).
Asymptotic formulae for circularity are known, but to compare actual ant raft shapes to the random walk growth model around an origin for moderate values of N, it is necessary to run our own simulation.
The findings provide support for a Hunan origin for the Triculinae, no later than around 8 Ma.
Ideas of an endosymbiotic origin for plastids and mitochondria have been around since the early times of cellular microscopy [7], [8], but these were only broadly discussed later, when Lynn Margulis proposed the serial endosymbiotic theory [9].
