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We start with the initial condition that was given by Eq. (4.2).
The measure was taken over a signal window of 20 beats, sufficiently far from the initial condition that the signal had settled down.
Ergodicity in a classical statistical physics setting accounts for the independence of the asymptotic state distribution from the initial condition: that is, at large times thermal equilibrium is approached.
Remark 2.2 Similar to Lemma A.1 on p.535 of [5], we mean the initial condition that for any u ∈ Y, u admits trace value u ( x, v, 0 ) ∈ L v 2 for a.e.
Every point composing the snake reaches a local energy minimum; this means that the active contour does not find a global optimum position; rather, since it is based on local minimization, the final position strongly depends on the initial condition, that is, the initial snake position.
The initial condition that all receptors begin in the free state (subscript n refers to the neurotransmitter), and in general, K d n = K o f f n / k o n n.
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On the other, we identify the initial conditions that must be met for R&D activity to be observed under profit-seeking behaviour.
The first is to state that this fine-tuning is simply a result of the initial conditions that are needed to give us the result we have today.
In case of α = 2 in Eq. (4.10), we start with the initial conditions that were given by Eq. (4.11).
In the case of α = 2 in Eq. (4.8), we start with the initial conditions that were given by Eq. (4.9).
The sea surface height and depth-averaged horizontal velocity fields at this time are identified as (eta _0 x)) and (v_0 x)), the initial conditions that are most consistent with the full-physics simulations.
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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