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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
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}.