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\subsection{Simulations}  To infer measure  the virial-infall times of satellite dwarf galaxies satellites  in afully hierarchical  cosmological context, we use ELVIS (Exploring the Local Volume in Simulations), a suite of cosmological zoom-in $N$-body simulations that are targeted to modeling the LG \citep{GarrisonKimmel2014}. ELVIS was run using \textsc{GADGET-3} and \textsc{GADGET-2} \citep{Springel2005e}, with initial conditions generated using \textsc{MUSIC} \citep{HahnAbel2011}, all with $\Lambda$CDM cosmology based on WMAP7 \citep{Larson2011}: $\sigma_8 = 0.801$, $\omegamatter = 0.266$, $\omegalambda = 0.734$, $n_s = 0.963$ $\sigma_8=0.801$, $\omegamatter=0.266$, $\omegalambda=0.734$, $n_s=0.963$  and $h = 0.71$. $h=0.71$.  Within the zoom-in regions, the particle mass is $1.9 \times 10 ^ 5 M_\odot$ $1.9\times10^5\msun$  and the Plummer-equivalent force softening is $140 \pc$ $140\pc$  (comoving at $z > 9$, physical at $z < 9$). ELVIS contains 48 dark-matter halos of masses similar to the MW or M31 ($\mvir = 1.0 - 2.8 \times 10 ^ {12} \msun$), with a median virial radius of $\rvir \approx 300 \kpc$.   Half of these halos are located in zoom-in regions that were selected to contain a pair of halos that resemble the masses, distance, and relative velocity of the MW-M31 pair, while the other half are single isolated halos matched in masses to the paired ones.