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We next look at the limit cycles that emerge from Hopf bifurcations on each branch from the origin.
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The body of the pancreas is supplied by one to three very small branches from the origin of the right gastric artery (which is the right branch of the coeliac artery) and from the gastroduodenal artery [ 27] or one of its terminal branches, the right gastroepiploic artery [ 26].
The inner product, Si, j o), of two vectors, Ro, i and Ro, j, gives the branch length from the origin o to the most recent common ancestor c of sequences i and j, if the branch vectors are orthogonal (Fig. 9a).
Both have a branch that originates from the branch point on the origin (g^{ast} = sqrt {N}/alphamu_{E}) (in Fig. 1B, these are labeled as "3-1" and "2-2*", respectively).
Returning to the full system, we now consider the limit cycles that emerge from the three Hopf bifurcations we identified (on the 3-1 branch, 2-2 brandh, and the origin).
Everything "originates" from the origin.
If (n_{I1} = n_{I2}), then the excitatory activity along this branch is zero: there may be a further branch point in which (x_{E}) moves away from the origin, whereas I cells remain in their distinct clusters.
We estimated ω in the branches preceding the origin and subsequent duplications of DEF- and GLO-like genes from Orchidaceae and Poales by employing the branch-site models MA and MA1.
In reptiles coronary arteries branch from the systemic arch, but their position of origin varies.
Since auguritids and pinacitids branched off from the same origin, the characters displaying directed trends shared by both lineages and supported by the statistical analysis can potentially participate to a case of parallel evolution.
Therefore, the origin of the Paulinella chromatophore is believed to differ from the origin of plastids in plants and algae, which are believed to have branched from an ancestral cyanobacterium near the root of cyanobacteria (9, 16).
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