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\section{Population Synthesis}   \label{sec:population_synthesis_parameters} \section{Eclipse Statistics}  \paragraph{SFR, IMF and z}  \label{par:sfr_imf_and_z}   The authors assume a constant Star Formation Rate (0-12Gyr) and a time independent IMF \cite{kroupa_variation_2001} . The metallicity parameter [Fe/H] is constant for the duration of a BSE code run (i.e. it is age-independent and uniform) so the authors combined several runs with different upper and lower IMF limits in order to mimic the observed [Fe/H] distributions.   % paragraph sfr_imf_and_z (end)   \paragraph{Binary parameters $f(a, q, e)$}  \label{par:_f_a_q_e_}  For the binary runs the authors make simplifying first assumption that the function $f(a,q,e)$ is separable and assign 3 independent functions to $f(a)$, $f(q)$ and $f(e)$ respectively.  % paragraph _f_a_q_e_ (end)     % section population_synthesis_parameters (end)   diff --git a/section3.tex b/section3.tex  new file mode 100644  index 0000000..a95b584  --- /dev/null  +++ b/section3.tex 
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\section{Population Synthesis}     \paragraph{}     It is straightforward to show the probability of an eclipse at any depth is $P_eo = r_s + r_g$ but the authors wish to study the probability of an eclipse of \textbf{any specified} magnitude depth.     In order to calculate this probability, the function $i(\Delta m)$ must be derived. Although the maximum primary eclipse depth $\Delta m$ is a well defined function of the inclination angle i, iteration is needed to find this inverse function $i(\Delta m)$     With a random distribution of inclinations the probability of a primary eclipse deeper than $\Delta m$ is $cos(i(\Delta m))$     \paragraph{}     For the binary runs the authors make simplifying first assumption that the function $f(a,q,e)$ is separable and assign 3 independent functions to $f(a)$, $f(q)$ and $f(e)$ respectively.