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\section{Relative Formulation}  \subsection{Rate}  To use the framework we have previosly developed we need to generalize the theory to handle multiple S(t) functions all contributing to the model. To do this we need to make some useful definitions and see how the connect to both the formulation analyzing chemical kinetics by Ross, and to the work proposed by Fisher himself. First we can define three different forms of rates. The first we will call the relative rate, the all $\gamma$ formulation.  \begin{equation}  k_{rel}\equiv \frac{d}{dt}[\ln\gamma_i]=\frac{d}{dt}\left[\ln S_i-\ln\sum_i S_i\right]  \end{equation}  \subsection{Fisher Information}  Using these definitions we can then formulate the associated Fisher Information for each of these rates. The relative Fisher Information $I_r$, and the absolute Fisher Information $I_a$.  \begin{equation}  I_r=\sum_i \gamma_i k_{rel}=\sum_i \gamma_i \frac{d}{dt}[\ln\gamma_i]  \end{equation}  This is where the "all $\gamma$" formulation derives its name.  \subsection{GFE to FE}  \subsection{Fisher equations}  We can now define the assoicated Fisher Equation for the previously defined Fisher Information.  \begin{equation}  GFE_r\equiv \frac{d}{dt}\left[\sum_i \gamma_i k_{rel}\right]  \end{equation}  \subsection{Inequality}  diff --git a/layout.md b/layout.md  index 835b6c4..20480cc 100644  --- a/layout.md  +++ b/layout.md 
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abstract.tex  Introduction.tex  Pre-theory background.tex  Relative Formulation.tex  Absolute Formulation1.tex  The Relative Formulation.tex  All S Formulation.tex