From 35fae13d17a08a7688a385644879f073a0fc8809 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Karl=20Yngve=20Lerv=C3=A5g?= <karl.yngve+git@gmail.com>
Date: Tue, 26 Jul 2016 12:41:51 +0200
Subject: [PATCH] Added the strange formatting bug as Vader test (#436)

---
 test/vader/format.vader | 42 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 42 insertions(+)

diff --git a/test/vader/format.vader b/test/vader/format.vader
index 8fcbff2..06501eb 100644
--- a/test/vader/format.vader
+++ b/test/vader/format.vader
@@ -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}.
+