177 lines
8.0 KiB
Plaintext
177 lines
8.0 KiB
Plaintext
Execute (Setup):
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set textwidth=79
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set nojoinspaces
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set shiftwidth=2
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let g:vimtex_format_enabled = 1
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silent! VimtexReload
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Given tex (Format: Inline comment):
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Lorem ipsum dolor sit amet, consetetur sadipscing % a comment
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elitr, sed diam
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nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat,
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sed diam voluptua. At vero eos et accusam et justo duo dolores et ea
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rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem
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ipsum dolor sit amet.
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Do (Format text):
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gqG
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Expect tex (Verify):
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Lorem ipsum dolor sit amet, consetetur sadipscing % a comment
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elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna
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aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores
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et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum
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dolor sit amet.
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Given tex (Format: Line breaking):
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start a new paragraph \\
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start a new line but not a new paragraph \\*
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flush all, start a new (odd numbered) page \cleardoublepage
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flush all, start a new page \clearpage
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allow to break the line here \linebreak
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request a new line \newline
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request a new page \newpage
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encourage page break \pagebreak
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Do (Format text):
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gqG
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Expect tex (Verify):
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start a new paragraph \\
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start a new line but not a new paragraph \\*
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flush all, start a new (odd numbered) page \cleardoublepage
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flush all, start a new page \clearpage
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allow to break the line here \linebreak
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request a new line \newline
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request a new page \newpage
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encourage page break \pagebreak
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Given tex (Format: Advanced example):
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Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam
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nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat,
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sed diam voluptua. At vero eos et accusam et justo duo dolores et ea
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rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem
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ipsum dolor sit amet.
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\begin{itemize}
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\item Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam
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nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat,
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sed diam voluptua. At vero eos et accusam et justo duo dolores et ea \\
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rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem
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\item ipsum dolor sit amet.
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start a new paragraph % test
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Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam
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nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat,
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sed diam voluptua. At vero eos et accusam et justo duo dolores et ea
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rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem
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ipsum dolor sit amet.
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\end{itemize}
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Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam
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nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat,
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sed diam voluptua. At vero eos et accusam et justo duo dolores et ea
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rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem
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ipsum dolor sit amet.
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Do (Format text):
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gqG
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Expect tex (Verify):
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Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod
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tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At
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vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd
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gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.
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\begin{itemize}
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\item Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam
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nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed
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diam voluptua. At vero eos et accusam et justo duo dolores et ea \\
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rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem
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\item ipsum dolor sit amet.
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start a new paragraph % test
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Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy
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eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam
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voluptua. At vero eos et accusam et justo duo dolores et ea rebum. Stet
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clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit
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amet.
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\end{itemize}
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Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod
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tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At
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vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd
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gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.
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Given tex (Format: With math):
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Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed
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diam nonumy eirmod tempor invidunt asd asdj klkut \( g(x)
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= 4\) labore et dolore magna aliquyam erat, sed diam volu.
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$f(x) = 3$ vero eos et accusam et justo duo dolores et ea
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\begin{align}
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f(x) &= 1 \\
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g(x) &= 2
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\end{align}
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rebum. Stet clita kasd gubergren, no sea takimata sanctus
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est Lorem ipsum dolor sit amet.
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\[
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e^{2\pi i} = 1
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\]
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Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed
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diam nonumy eirmod tempor invidunt asd asdj klkut labore et
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Do (Format text):
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gqG
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Expect tex (Verify):
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Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod
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tempor invidunt asd asdj klkut \( g(x) = 4\) labore et dolore magna aliquyam
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erat, sed diam volu. $f(x) = 3$ vero eos et accusam et justo duo dolores et ea
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\begin{align}
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f(x) &= 1 \\
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g(x) &= 2
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\end{align}
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rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor
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sit amet.
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\[
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e^{2\pi i} = 1
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\]
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Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod
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tempor invidunt asd asdj klkut labore et
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Given tex (Format: Strange bug):
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Therefore, in that case the observed dynamics cannot be truly
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Markovian. We can still approximately capture the observed density dynamics
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with eq.~\ref{eq:fpe}; however the local coefficients are then effectively
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averages over the co-evolving unobserved distribution. For example, $\vec
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v(\vec x,t)=\int p(\vec x^u|\vec x,t)v(\vec x,\vec x^u,t)dx^u$. This has some
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important consequences. First, the effective Markovian coefficients $\vec v,
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\lambda, D$, will generally depend on time, reflecting the time evolution of
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the hidden $p(\vec x^u)$ over the time scale of the experiment. Second, the
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effective coefficients may also depend on the initial condition: a cell
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population started concentrated around label $\vec x_0$ implies a certain
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distribution over $x^u$ when sampled at label $\vec x$ some time later; another
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population started around $\vec x_1$ carries a different history when it, too,
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visits $\vec x$ later. Therefore, for instance the effective drift $\vec v(\vec
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x)$ will be different in the two cases. We conclude that, if unobserved degrees
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of freedom have dynamics on the time scale of the experiment eq.~\ref{eq:fpe}
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is an approximation whose coefficients become \emph{non-universal} (dependent
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on intial conditions) and \emph{time-dependent}.
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Do (Format text):
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gqG
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Expect tex (Verify):
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Therefore, in that case the observed dynamics cannot be truly Markovian. We can
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still approximately capture the observed density dynamics with
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eq.~\ref{eq:fpe}; however the local coefficients are then effectively averages
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over the co-evolving unobserved distribution. For example, $\vec v(\vec
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x,t)=\int p(\vec x^u|\vec x,t)v(\vec x,\vec x^u,t)dx^u$. This has some
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important consequences. First, the effective Markovian coefficients $\vec v,
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\lambda, D$, will generally depend on time, reflecting the time evolution of
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the hidden $p(\vec x^u)$ over the time scale of the experiment. Second, the
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effective coefficients may also depend on the initial condition: a cell
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population started concentrated around label $\vec x_0$ implies a certain
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distribution over $x^u$ when sampled at label $\vec x$ some time later; another
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population started around $\vec x_1$ carries a different history when it, too,
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visits $\vec x$ later. Therefore, for instance the effective drift $\vec v(\vec
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x)$ will be different in the two cases. We conclude that, if unobserved degrees
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of freedom have dynamics on the time scale of the experiment eq.~\ref{eq:fpe}
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is an approximation whose coefficients become \emph{non-universal} (dependent
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on intial conditions) and \emph{time-dependent}.
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