Remove volatility factor from SP rewards

main.tex

@@ -72,7 +72,7 @@
 {\Huge Synthetic Assets on Cardano}\\[2\baselineskip]
 {\Large Indigo Laboratories, Inc.}\\[0.5\baselineskip]
 {\large info@indigo-labs.io}\\[3\baselineskip]
-{\large November 2022, v1.0.1}
+{\large November 2022, v1.1.0}
 }
 \end{titlepage}
 
@@ -1101,43 +1101,12 @@ \subsubsection{Stability Pool Staking
 is based on three variables:
 
 \begin{enumerate}
-\item
-  Volatility of the SP's iAsset's underlying asset (\(\sigma\))
 \item
   Stability Pool Saturation (\(\varphi\))
 \item
   Market cap of the SP's iAsset (\(\omega\))
 \end{enumerate}
 
-\hypertarget{volatility-for-a-sp-sigma}{%
-\paragraph{\texorpdfstring{Volatility for a SP
-(\(\sigma\))}{Volatility for a SP (\textbackslash sigma)}}\label{volatility-for-a-sp-sigma}}
-
-can be calculated using the formula:
-
-\[\sigma = \left\{ \begin{matrix}
-\begin{pmatrix}
-\text{let}\text{\ y\ }\text{equal}\ \left\langle \frac{x_{j}}{x_{j - 1}} - 1\ :j\  \in \ \left\langle 2,\ldots,\left| x \right| \right\rangle \right\rangle \\
-\  \\
-\sqrt{\frac{\sum_{i = 1}^{\left| y \right|}\left( y_{i} - \overline{y} \right)^{2}}{\left| y \right|}} \\
-\end{pmatrix} & \text{if}\ \left| x \right| > 30 \\
-\  & \  \\
-0 & \text{if}\ \left| x \right| \leq 30 \\
-\end{matrix} \right.\ \]
-
-Where:
-
-\begin{itemize}
-\item
-  \(\sigma\) is the volatility of the iAsset
-\item
-  \(x\) is the sequence of the iAsset's tracked asset's historical daily
-  close price for the past year (or maximum amount of time that data
-  exists for) denominated in iAsset's collateral (i.e., ADA)
-\end{itemize}
-
-\filbreak
-
 \hypertarget{stability-pool-saturation-varphi}{%
 \paragraph{\texorpdfstring{Stability Pool Saturation
 (\(\varphi\))}{Stability Pool Saturation (\textbackslash varphi)}}\label{stability-pool-saturation-varphi}}
@@ -1204,12 +1173,6 @@ \subsubsection{Stability Pool Staking
 \(\sigma\), \(\varphi\), and \(\omega\), and is calculated daily using:
 
 \[\rho = \begin{pmatrix}
-\text{let}\ \sigma_{s}\ \text{equal}\ \sum_{i = 1}^{\left| \sigma \right|}\left\{ \begin{matrix}
-\frac{1}{\sigma_{i}} & \text{if}\ \sigma_{i} > 0\ \text{and}\ t_{i} > 0 \\
-\  & \  \\
-0 & \text{otherwise} \\
-\end{matrix} \right.\  \\
-\  \\
 \text{let}\ \varphi_{s}\ \text{equal}\ \sum_{i = 1}^{\left| \varphi \right|}\left\{ \begin{matrix}
 \frac{1}{\varphi_{i}} & \text{if}\ \varphi_{i} > 0\ \text{and}\ t_{i} > 0 \\
 \  & \  \\
@@ -1226,12 +1189,6 @@ \subsubsection{Stability Pool Staking
 0 & \text{if}\ t_{a} \leq 0 \\
 \  & \  \\
 \begin{pmatrix}
-\text{let}\ \sigma_{v}\ \text{equal}\ \left\{ \begin{matrix}
-\frac{1}{\sigma_{a}}/\sigma_{s} & \text{if}\ \sigma_{a} > 0\ \text{and}\ \sigma_{s} > 0 \\
-\  & \  \\
-0 & \text{otherwise} \\
-\end{matrix} \right.\  \\
-\  \\
 \text{let}\ \varphi_{v}\ \text{equal}\ \left\{ \begin{matrix}
 \frac{1}{\varphi_{a}}/\varphi_{s} & \text{if}\ \varphi_{a} > 0\ \text{and}\ \varphi_{s} > 0 \\
 \  & \  \\
@@ -1245,9 +1202,9 @@ \subsubsection{Stability Pool Staking
 \end{matrix} \right.\  \\
 \  \\
 \left\{ \begin{matrix}
-\frac{\sigma_{v} + \varphi_{v} + \omega_{v}}{3} & \text{if}\ \varphi_{s} > 0\ \text{and}\ \omega_{s} > 0 \\
+\frac{\varphi_{v} + \omega_{v}}{2} & \text{if}\ \varphi_{s} > 0\ \text{and}\ \omega_{s} > 0 \\
 \  & \  \\
-\sigma_{v} & \text{otherwise} \\
+0 & \text{otherwise} \\
 \end{matrix} \right.\  \\
 \end{pmatrix} & \text{otherwise} \\
 \end{matrix} \right.\  \\
@@ -1258,8 +1215,6 @@ \subsubsection{Stability Pool Staking
 \begin{itemize}
 \item
   \(\rho\) is the distribution coefficient for the iAsset
-\item
-  \(\sigma\) is the sequence of volatility values of each iAsset
 \item
   \(\varphi\) is the sequence of Stability Pool saturation values of
   each iAsset

preprocess.sh

@@ -6,11 +6,11 @@ set -e
 
 # Convert tabularx tables to longtables so pandoc can understand
 sed 's/\\end{tabularx}/\\end{longtable}/g' "${1:-main.tex}" > main.tex.tmp.pandoc
-sed -i 's/\\begin{tabularx}{\\linewidth}{/\\begin{longtable}[]{/g' main.tex.tmp.pandoc
-sed -i 's/\\begin{longtable}.*/\L&/g' main.tex.tmp.pandoc
+sed -i '' -e 's/\\begin{tabularx}{\\linewidth}{/\\begin{longtable}[]{/g' main.tex.tmp.pandoc
+sed -i '' -e 's/\\begin{longtable}.*/\L&/g' main.tex.tmp.pandoc
 
 # Fix texttt
-sed -i 's/}\\texttt{//g' main.tex.tmp.pandoc
+sed -i '' -e 's/}\\texttt{//g' main.tex.tmp.pandoc
 
 # Process with pandoc
 pandoc main.tex.tmp.pandoc -f latex -t latex -o main.tex.tmp.pandoc
@@ -29,7 +29,7 @@ start=$(grep -n '\tableofcontents' main.tex.tmp | head -1 | cut -d ':' -f 1)
 end=$(grep -n '\hypertarget' main.tex.tmp | head -1 | cut -d ':' -f 1)
 start=$((start + 1))
 end=$((end - 2))
-sed -i "${start},${end}d" main.tex.tmp
+sed -i '' -e "${start},${end}d" main.tex.tmp
 
 # Copy over end of main.tex
 total_lines=$(wc -l main.tex | cut -d ' ' -f 1)
@@ -39,20 +39,20 @@ echo "" >> main.tex.tmp
 tail -n "$end" main.tex >> main.tex.tmp
 
 # Format tables
-sed -i 's/\\tabularnewline/\n\\tabularnewline\n\\midrule/g' main.tex.tmp
-sed -i -e '1h;2,$H;$!d;g' -e 's/\\midrule\n\\midrule/\\midrule/g' main.tex.tmp
-sed -i -e '1h;2,$H;$!d;g' -e 's/\\midrule\n\\toprule/\\toprule/g' main.tex.tmp
-sed -i -e '1h;2,$H;$!d;g' -e 's/\\midrule\n\\bottomrule/\\bottomrule/g' main.tex.tmp
-sed -i 's/\\strut//g' main.tex.tmp
-sed -i '/^\\begin{minipage}/d' main.tex.tmp
-sed -i 's/^\\end{minipage}.*/\&/g' main.tex.tmp
-sed -i -e '1h;2,$H;$!d;g' -e 's/\&\n\\tabularnewline/\\tabularnewline/g' main.tex.tmp
-sed -i '/\\endfirsthead/,/\\midrule/d' main.tex.tmp
-sed -i -e '1h;2,$H;$!d;g' -e 's/\\\midrule\n\\midrule/\\midrule/g' main.tex.tmp
-sed -i 's/\\ldots{}/\\ldots/g' main.tex.tmp
+sed -i '' -e 's/\\tabularnewline/\n\\tabularnewline\n\\midrule/g' main.tex.tmp
+sed -i '' -e '1h;2,$H;$!d;g' -e 's/\\midrule\n\\midrule/\\midrule/g' main.tex.tmp
+sed -i '' -e '1h;2,$H;$!d;g' -e 's/\\midrule\n\\toprule/\\toprule/g' main.tex.tmp
+sed -i '' -e '1h;2,$H;$!d;g' -e 's/\\midrule\n\\bottomrule/\\bottomrule/g' main.tex.tmp
+sed -i '' -e 's/\\strut//g' main.tex.tmp
+sed -i '' -e '/^\\begin{minipage}/d' main.tex.tmp
+sed -i '' -e 's/^\\end{minipage}.*/\&/g' main.tex.tmp
+sed -i '' -e '1h;2,$H;$!d;g' -e 's/\&\n\\tabularnewline/\\tabularnewline/g' main.tex.tmp
+sed -i '' -e '/\\endfirsthead/,/\\midrule/d' main.tex.tmp
+sed -i '' -e '1h;2,$H;$!d;g' -e 's/\\\midrule\n\\midrule/\\midrule/g' main.tex.tmp
+sed -i '' -e 's/\\ldots{}/\\ldots/g' main.tex.tmp
 
 # Convert longtables back to tabularx
-sed -i 's/\\end{longtable}/\\end{tabularx}/g' main.tex.tmp
+sed -i '' -e 's/\\end{longtable}/\\end{tabularx}/g' main.tex.tmp
 tabularx_headers=($(grep '\\begin{tabularx}' main.tex))
 longtable_headers=($(grep -n '\\begin{longtable}' main.tex.tmp | cut -d ':' -f 1))
 
@@ -67,7 +67,7 @@ script_dir=$(cd -- "$(dirname -- "${BASH_SOURCE[0]}")" &> /dev/null && pwd)
 python3 $script_dir/figures.py
 
 # Remove height from images
-sed -i 's/\,height=\\textheight//g' main.tex.tmp
+sed -i '' -e 's/\,height=\\textheight//g' main.tex.tmp
 
 # Done
 mv main.tex.tmp main.tex

to-docx.sh

@@ -6,15 +6,15 @@ set -e
 
 # Convert tabularx tables to longtables so pandoc can understand
 sed 's/\\end{tabularx}/\\end{longtable}/g' "${1:-main.tex}" > main.tex.tmp.pandoc
-sed -i 's/\\begin{tabularx}{\\linewidth}{/\\begin{longtable}[]{/g' main.tex.tmp.pandoc
-sed -i 's/\\begin{longtable}.*/\L&/g' main.tex.tmp.pandoc
+sed -i '' -e 's/\\begin{tabularx}{\\linewidth}{/\\begin{longtable}[]{/g' main.tex.tmp.pandoc
+sed -i '' -e 's/\\begin{longtable}.*/\L&/g' main.tex.tmp.pandoc
 
 # Convert formulas
-sed -i 's/\\genfrac{}{}{}{}/\\frac/g' main.tex.tmp.pandoc
-sed -i 's/\\cfrac/\\frac/g' main.tex.tmp.pandoc
-sed -i 's/\\raisebox//g' main.tex.tmp.pandoc
-sed -i 's/{\$/{/g' main.tex.tmp.pandoc
-sed -i 's/\$}/}/g' main.tex.tmp.pandoc
+sed -i '' -e 's/\\genfrac{}{}{}{}/\\frac/g' main.tex.tmp.pandoc
+sed -i '' -e 's/\\cfrac/\\frac/g' main.tex.tmp.pandoc
+sed -i '' -e 's/\\raisebox//g' main.tex.tmp.pandoc
+sed -i '' -e 's/{\$/{/g' main.tex.tmp.pandoc
+sed -i '' -e 's/\$}/}/g' main.tex.tmp.pandoc
 
 # Process with pandoc
 pandoc main.tex.tmp.pandoc -f latex -t docx -o main.docx