Execute (Setup): set textwidth=79 set nojoinspaces set shiftwidth=2 let g:vimtex_format_enabled = 1 silent! VimtexReload Given tex (Format: Inline comment): Lorem ipsum dolor sit amet, consetetur sadipscing % a comment elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Do (Format text): gqG Expect tex (Verify): Lorem ipsum dolor sit amet, consetetur sadipscing % a comment elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Given tex (Format: Line breaking): start a new paragraph \\ start a new line but not a new paragraph \\* flush all, start a new (odd numbered) page \cleardoublepage flush all, start a new page \clearpage allow to break the line here \linebreak request a new line \newline request a new page \newpage encourage page break \pagebreak Do (Format text): gqG Expect tex (Verify): start a new paragraph \\ start a new line but not a new paragraph \\* flush all, start a new (odd numbered) page \cleardoublepage flush all, start a new page \clearpage allow to break the line here \linebreak request a new line \newline request a new page \newpage encourage page break \pagebreak Given tex (Format: Advanced example): Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. \begin{itemize} \item Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea \\ rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem \item ipsum dolor sit amet. start a new paragraph % test Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. \end{itemize} Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Do (Format text): gqG Expect tex (Verify): Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. \begin{itemize} \item Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea \\ rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem \item ipsum dolor sit amet. start a new paragraph % test Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. \end{itemize} Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Given tex (Format: With math): Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt asd asdj klkut \( g(x) = 4\) labore et dolore magna aliquyam erat, sed diam volu. $f(x) = 3$ vero eos et accusam et justo duo dolores et ea \begin{align} f(x) &= 1 \\ g(x) &= 2 \end{align} rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. \[ e^{2\pi i} = 1 \] Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt asd asdj klkut labore et Do (Format text): gqG Expect tex (Verify): Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt asd asdj klkut \( g(x) = 4\) labore et dolore magna aliquyam erat, sed diam volu. $f(x) = 3$ vero eos et accusam et justo duo dolores et ea \begin{align} f(x) &= 1 \\ g(x) &= 2 \end{align} rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. \[ e^{2\pi i} = 1 \] 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}.