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From now on, without loss of generality we assume that the initial time is zero, because otherwise we just need to perform a change of variables first to transfer the initial state to zero.
With this aim, it is convenient to perform a change of variables, and use new notations z = v − V 0 a, u = w − V 0 a, w F = V F − V 0 a, w R = V R − V 0 a, (3.5).
In order to obtain an equation in the form of Mathieu equation, we first perform a change of variables in system (1) V E = tan θ E 2, going from θ-variable to membrane voltage V E. As it is known [40], θ-neuron is formally equivalent to the Quadratic Integrate and Fire (QIF) neuron: d V E ( t ) d t = V E 2 ( t ) + I E + λ ( 1 + cos , d Θ d t = ε Θ ω. (2).
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Such support was only effective when participants performed a change detection task without concurrent subtasks.
The orthogonality of the basis is preserved by performing a change of reference in the time.
Performing the average in the above equation and performing a change of integration variables, we can write.
By performing a change of variable, it can be shown that (14) is equivalent to a second-order Bessel equation.
Participants performed a change perception task followed by a cued recall task in three blocks of 333 trials (999 total).
end{aligned} (126) In the last line we have performed a change of variables using (t' = t-t_{l-1}), (forall lin{1,ldots, n}).
Every time the script performs a change, the original string and the modified one are displayed on the screen and a human editor quickly decides if the change is correct or not.
Apart from the detected road lanes additional virtual lanes have been considered so as to cope with situations in which a vehicle is located between two lanes (e.g., if it is performing a change lane manoeuvre).
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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