deletions | additions       diff --git a/Data Section.tex b/Data Section.tex  index 8111d2d..91dba97 100644  --- a/Data Section.tex  +++ b/Data Section.tex 
...
We draw our obseravational data from Data Release 7 (DR7) of the Sloan Digital Sky Survay (SDSS), making use of derived data products from the NYU Value-Added Galactic Catalog (VAGC). The magnitudes from the NYU VAGC that we use have been k-corrected to z = 0.1 using the code Kcorrect. Additionally, we restrict ourselves to regions of SDSS where the spectroscopic completeness parameter FGOTMAIN exceeds 0.7. We also reject all galaxies with velocity errors greater than 25 km/s.  In selecting our sample, we initially adhere closely to the procudure of I14. We select a sample of hosts in the magnitude range $-23 \lt r \lt -20$ and within a redshift range of $0.002 \lt z \lt 0.05$. A host is considered isolated if there are no brighter objects within 500 kpc on the sky in projection and within 1500 km/s in velocity space. Only isolated hosts are retained, reducing the number of sources to 22780 isolated hosts. From there we identified satellites around each host. Galaxies meet the criteria for being counted as satellites if their magnitudes lie in the range $r_{host} + 1 < r_{sat} < -16$, their projected distance from the host lies between 20 kpc and 150 kpc, and their velocity offset from the host lies in the range $\rm 25 \, km/s < |v_{sat} - v{host}| v_{host}|  < 300 \,km/s \times exp(-(d_{proj}/300 \, kpc)^{0.8})$ This velocity bound is taken from I14, and is designed to reduce the contamination from interlopers in the satellite sample. Since our interest is on pairs of satellites, we focus on hosts with two or more satellites. Our sample contains 427 such hosts, with 965 assosiated satellites. \subsection{Corotation signal}  In this subsection, we investigate pairs of satellite pairs located diametrically opposite their host for signals of corotation. To facilitate this, we will introduce the parameter $\alpha$, defined as the angle between the line extending from one satellite through the host and the position vector of the second satellite. This definition is sketched in Figure \ref{fig:corot}.