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Added the strange formatting bug as Vader test (#436)

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Karl Yngve Lervåg 2016-07-26 12:41:51 +02:00
parent c56694b08e
commit 35fae13d17
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test/vader/format.vader
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@ -132,3 +132,45 @@ Expect tex (Verify):
Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod
tempor invidunt asd asdj klkut labore et tempor invidunt asd asdj klkut labore et
Given tex (Format: Strange bug):
Therefore, in that case the observed dynamics cannot be truly
Markovian. We can still approximately capture the observed density dynamics
with eq.~\ref{eq:fpe}; however the local coefficients are then effectively
averages over the co-evolving unobserved distribution. For example, $\vec
v(\vec x,t)=\int p(\vec x^u|\vec x,t)v(\vec x,\vec x^u,t)dx^u$. This has some
important consequences. First, the effective Markovian coefficients $\vec v,
\lambda, D$, will generally depend on time, reflecting the time evolution of
the hidden $p(\vec x^u)$ over the time scale of the experiment. Second, the
effective coefficients may also depend on the initial condition: a cell
population started concentrated around label $\vec x_0$ implies a certain
distribution over $x^u$ when sampled at label $\vec x$ some time later; another
population started around $\vec x_1$ carries a different history when it, too,
visits $\vec x$ later. Therefore, for instance the effective drift $\vec v(\vec
x)$ will be different in the two cases. We conclude that, if unobserved degrees
of freedom have dynamics on the time scale of the experiment eq.~\ref{eq:fpe}
is an approximation whose coefficients become \emph{non-universal} (dependent
on intial conditions) and \emph{time-dependent}.
Do (Format text):
gqG
Expect tex (Verify):
Therefore, in that case the observed dynamics cannot be truly Markovian. We can
still approximately capture the observed density dynamics with
eq.~\ref{eq:fpe}; however the local coefficients are then effectively averages
over the co-evolving unobserved distribution. For example, $\vec v(\vec
x,t)=\int p(\vec x^u|\vec x,t)v(\vec x,\vec x^u,t)dx^u$. This has some
important consequences. First, the effective Markovian coefficients $\vec v,
\lambda, D$, will generally depend on time, reflecting the time evolution of
the hidden $p(\vec x^u)$ over the time scale of the experiment. Second, the
effective coefficients may also depend on the initial condition: a cell
population started concentrated around label $\vec x_0$ implies a certain
distribution over $x^u$ when sampled at label $\vec x$ some time later; another
population started around $\vec x_1$ carries a different history when it, too,
visits $\vec x$ later. Therefore, for instance the effective drift $\vec v(\vec
x)$ will be different in the two cases. We conclude that, if unobserved
degrees of freedom have dynamics on the time scale of the experiment
eq.~\ref{eq:fpe} is an approximation whose coefficients become
\emph{non-universal} (dependent on intial conditions) and
\emph{time-dependent}.