theory.tex
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\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
\title{Source Code Volatility (SCV)\\to Spot Dead Code}
\author{Yegor Bugayenko}
\maketitle
\section{Introduction}
Volatility of source code is an experimental metric that
shows how big is the difference between actively and rarely changed (possibly dead)
code. It is assumed that a big percentage of dead code is
an indicator of maintainability problems in the project.
\section{Details}
First, by looking at Git history,
it is observed how many times every source code file out of $N$ was touched
during the lifetime of the repository (excluding the files that don't exist
in the repository anymore):
\begin{eqnarray}
T = [t_1, t_2, \dots, t_N]
\end{eqnarray}
Then, the entire interval between $\check{T}$ (the maximum value)
and $\hat{T}$ (the minimum value) is divided to $Z$ equivalent groups:
\begin{align}
G &= [g_1, g_2, \dots, g_{Z}] \\
\delta &= ( \check{T} - \hat{T} ) / Z \\
g_j &= \sum_{i=1}^N [ j(\delta-1) < t_i < j\delta ]
\end{align}
Then, the mean $\mu$ is calculated as:
\begin{eqnarray}
\mu = \frac{1}{Z}\sum_{j=1}^{Z}{g_j}
\end{eqnarray}
Finally, the variance is calculated as:
\begin{eqnarray}
Var(g) = \frac{1}{Z}\sum_{j=1}^{Z}{|g_j - \mu|^2}
\end{eqnarray}
The variance $Var(g)$ is the volatility of the source code. The smaller
the volatility the more cohesive is the repository and the smaller
the amount of the dead code inside it.
\end{document}