deletions | additions       diff --git a/Given_that_each_song.tex b/Given_that_each_song.tex  index e173a9b..afefbfc 100644  --- a/Given_that_each_song.tex  +++ b/Given_that_each_song.tex 
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The solid curved line in Figure \ref{fig:usage-plays} shows regions for which songs display a strong correlation.\footnote{Specifically, the line represents a linear regression model that predicts usage in terms of concert plays. The data were fit to a line; the line appears curved because the values on both axes are plotted on logarithmic (base-$10$) scale to preserve diagram clarity.} The two dashed lines represent the $40^{\text{th}}$-quantile and $75^{\text{th}}$-quantile of concert plays. These quantiles were subjectively chosen in order to provide a discussion of songs that are noteworthy outliers from the trend. Finally, the two closed polygons labeled {\bf A} and {\bf B} represent the interesting outlying songs. Polygon {\bf A} encapsulates songs that were heavily listened to by last.fm members, but played few times in concert by the Grateful Dead. On the other hand, {\bf B} encapsulates songs that were heavily played by the Grateful Dead, but less listened to (and possibly overlooked) by last.fm members.\footnote{A random sample of songs were removed from this diagram to preserve clarity as to ensure that song labels did not overlap. Furthermore, while {\bf A} and {\bf B} occupy regions outside of their quantile delimitations, this is to ensure that song labels were encapsulated.}  Polygon {\bf A} encapsulates those songs that were heavily listened to by last.fm users but not heavily played by the Grateful Dead in concert. Many of the songs in polygon {\bf A} are old classics that did not persist due to either changes in the band or to the band's extremely prolific period of songwriting in the early 1970s. For example, although the song \ttt{Mister Charlie} was played for the last time in concert on May 26, 1972 at the Strand Lyceum in London, England, it was featured on the \album{Europe `72} album \cite{europe:dead1972}. album.  This album reached a peak spot of 24 on the Billboard pop albums chart in 1973. Thus, while not being played much in concert during the band's lifetime, \ttt{Mister Charlie} remains a fan treasure by virtue of securing a place on a much celebrated album. Similar arguments can be made for \ttt{Sage and Spirit} and \ttt{Blues for Allah} which, while technically difficult and therefore generally avoided in concert, are songs that were released on the \album{Blues For Allah} LP\cite{allah:dead1975}  which reached spot 12 on the Billboard charts for pop album in 1975. \ttt{Good Morning Little School Girl} was primarily sung by Ron McKernan, whose untimely death in 1973 caused the song to be removed from the Grateful Dead concert play list except for a few special appearances in the late 80s and early 90s.\footnote{It is worth noting that \ttt{Mister Charlie} was also primarily sung by Ron McKernan and thus, didn't last with the Grateful Dead past his lifetime.} However, \ttt{Good Morning Little School Girl} is the opening track of the \album{Two from the Vault} album \cite{twovalut:dead1992} that contains a live recording of the August 24, 1968 Shrine Exhibit Hall performance of the Grateful Dead. Although Jerry Garcia was the primary singer of \ttt{Death Don't Have No Mercy}, the song had a similar concert fate as \ttt{Good Morning Little School Girl} and was also released on the \album{Two from the Vault} live album. \album{Two from the Vault} reached position 119 in 1992 on the Billboard charts.\footnote{\ttt{The Eleven} and \ttt{Cryptic Envelopment} are also on \album{Two from the Vault}.} Likewise, \ttt{Hard to Handle}, like \ttt{Good Morning Little School Girl} was a Ron McKernan specialty that was dropped after his death, except for being played during the New Year's Eve show of 1982 in Oakland, California. Finally, \ttt{Cryptic Envelopment} provided a medley prelude to the popular \ttt{The Other One} and only later in the bands life was \ttt{The Other One} separated from \ttt{Cryptic Envelopment} and preceded by \ttt{Drums}. It is worth noting that 28 of the 77 live albums of the Grateful Dead include \ttt{The Other One} while only 7 include \ttt{Cryptic Envelopment}. Polygon {\bf B} encapsulates those songs that were heavily played in concert throughout the Grateful Dead's career, but for various reasons, were less frequently listened to by last.fm members. \ttt{Drums} is perhaps the most salient of this collection of songs at the extreme of the boundary. \ttt{Drums} is an all-drum improvisational piece that usually appeared in the second set of a Grateful Dead concert. Usually appearing with \ttt{Drums} was the full sonic spectrum improvisation of \ttt{Space} which included all band members. Both \ttt{Drums} and \ttt{Space} found a stable home on the \album{Infrared Roses} album \cite{infrared:dead1991}, but unfortunately, due to the esoteric nature of these improvisations, Infrared Roses has been less well received by the general public and thus received no popular awards and did not make it on any music charts. Furthermore, to compound the situation, the Grateful Dead provided unique names for \album{Infrared Roses} tracks and thus, when played by last.fm users, are not associated with the typical \ttt{Drums} and \ttt{Space} songs of the concert set lists. It is interesting to note the songs \ttt{Saint of Circumstance,} \ttt{When I Paint My Masterpiece,} \ttt{Victim or the Crime,} \ttt{Lost Sailor,} and \ttt{Greatest Story} in the bottom left of polygon {\bf B}. All of these songs were created by the song writing duo of Barlow and Weir and sung in concert often by Bob Weir. While these songs were played extensively in concert, they received relatively little attention from last.fm users.  Finally, the extreme upper right of this plot is important as \ttt{Trucking} and \ttt{Sugar Magnolia} represent not only the most popular songs in terms of times played in concert, but in terms of times listened to on last.fm. \ttt{Trucking} is on 25 of the 90 released Grateful Dead albums and \ttt{Sugar Magnolia} is on 32 of those albums. Both \ttt{Trucking} and \ttt{Sugar Magnolia} were also well received publicly. \ttt{Trucking} reached position 64 in 1971 and \ttt{Sugar Magnolia} reached position 91 in 1973 on the Billboard pop singles charts. Also in this area is \ttt{Touch of Grey}. \ttt{Touch of Grey} was the only Grateful Dead song with an accompanying music video and in 1987, reached the top 10 Billboard single's chart. By comparison to produced greatest hits albums, Table \ref{tab:hits1} lists the songs that were released on the 2003 \album{Very Best of the Grateful Dead} compilation. Of these songs, 12 out of the 17 songs are in the top right quadrant (these songs are marked with an $^*$ in Table \ref{tab:hits1}), meaning that they were both played and listened to heavily by the Grateful Dead and their fans, respectively.\footnote{\ttt{Eyes of the World} and \ttt{Estimated Prophet} are not displayed as they were randomly removed to preserve diagram clarity.} A similar situation exists with the \album{Skeletons from the Closet} greatest hits album for which 8 out of 11 songs are in the top right quadrant\cite{skelcloset:dead1974}  (Table \ref{tab:hits2} presents the songs on the album).\footnote{\ttt{Mexicali Blues} is not displayed as it was randomly removed to preserve diagram clarity.} Of particular importance is \ttt{Box of Rain} (on \album{Very Best of the Grateful Dead}) by Phil Lesh and Robert Hunter. This song, written after the death of Phil Lesh's father, is not only the last song ever played by the Grateful Dead in concert\footnote{The final Grateful Dead performance took place at Soldier Field on July 9, 1995 in Chicago. Jerry Garcia died exactly one month later on August 9, 1995.}, but also unique in that it is one of the few songs for which Phil Lesh was the primary singer. In summary, the upper right hand quadrant of this diagram is ripe for creating compilation and greatest hits albums as it reflects both what the band as well as present day fans appreciate.