From 9f65785327318265632f7d1a27d0cc9ac7b7ebcc Mon Sep 17 00:00:00 2001
From: youainti <youainti@protonmail.com>
Date: Tue, 24 Aug 2021 10:16:49 -0700
Subject: [PATCH] Began incorporating Tom Marsh's suggestions

---
 CurrentWriting/Main.tex                       | 43 +++++++++++++------
 .../sections/07_ComputationalApproach.tex     | 10 +++--
 2 files changed, 36 insertions(+), 17 deletions(-)

diff --git a/CurrentWriting/Main.tex b/CurrentWriting/Main.tex
index ccbaff7..d9a3dac 100644
--- a/CurrentWriting/Main.tex
+++ b/CurrentWriting/Main.tex
@@ -21,12 +21,25 @@
 \subfile{sections/00_Introduction} %Currently from past semesters.
 %roughly done 2021-07-15
 
-
-\section{Modeling the Environment}
-\subsection{Laws of Motion}\label{SEC:Laws}
+%Describe sections
+The paper is organized as follows.
+\cref{SEC:Environment}, describes the laws of motion 
+governing satellites and debris(\ref{SEC:Laws}), 
+%discusses the laws of motion that govern satellite constellations and debris.
+places limits on various measures of risk (\ref{SEC:Survival}),
+%uses the laws of motion to put upper bounds on average, fleetwide marginal survival rates.
+and reviews various definitions of kessler syndrome in 
+the context of dynamic modeling, their advantages, and their disadvanteges (\ref{SEC:Kessler}).
+In \cref{SEC:Models} the dynamic problem faced by constellation operators and 
+social planners is first described.
+Finally \cref{SEC:Computation} describes the computational approach and results.
+
+
+\section{Modeling the Environment}\label{SEC:Environment}
+\subsection{Laws of motion}\label{SEC:Laws}
 \subfile{sections/01_LawsOfMotion} %Roughly done 2021-07-15
 
-\subsubsection{Survival Analysis}\label{SEC:Survival}
+\subsection{Marginal survival rates}\label{SEC:Survival}
 \subfile{sections/03_SurvivalAnalysis} %roughly done 2021-07-14
 
 \subsection{Kessler Syndrome}\label{SEC:Kessler}
@@ -36,7 +49,7 @@
 
 
 
-\section{Model}
+\section{Model}\label{SEC:Models}
 \subsection{Constellation Operator's Program}\label{SEC:Operator}
 \subfile{sections/04_ConstellationOperator} %TODO
 
@@ -46,12 +59,6 @@
 \section{Computation}\label{SEC:Computation}
 \subfile{sections/07_ComputationalApproach} %TODO
 
-\section{Assumptions and Caveats}
-I hope to write a section clearly explaining assumptions, caveats, and shortcomings here.
-%time periods are long enough for debris to disperse after collisions.
-%Only a single type of debris
-%With my current computational idea; each constellation provides the same risk to each other constellation
-%   That can be easily adjusted in the computational models.
 
 \newpage
 \section{References}
@@ -67,12 +74,22 @@ Needs completed.
 \subfile{sections/apx_02_GeneralizedEuEqSteps} 
 
 
+\subsection{Collected Assumptions and Caveats}\label{APX:CollectedAssumptions}
+I hope to write a section clearly explaining assumptions, caveats, and shortcomings here.
+These will later get written back into the other sections, but I want to collect them 
+in a single place first.
+%time periods are long enough for debris to disperse after collisions.
+%Only a single type of debris
+%With my current computational idea; each constellation provides the same risk to each other constellation
+% That can be easily adjusted in the computational models.
+
 \end{document}
 
 %%% Notes to keep track of
 % Possible other things to investigate
-%   - Free-entry conditions: When for every type of operator, a stock of zero
-%       implies no entry (x = 0).
+%   - Free-entry conditions: which of the following?
+%       - When for every operator, the current stocks imply no more launches(x = 0).
+%       - When for every type of operator, the current stocks plus an own stock of 0 imply no more launches(x = 0).
 % 
 % 
 % 
diff --git a/CurrentWriting/sections/07_ComputationalApproach.tex b/CurrentWriting/sections/07_ComputationalApproach.tex
index 52e1990..63568d2 100644
--- a/CurrentWriting/sections/07_ComputationalApproach.tex
+++ b/CurrentWriting/sections/07_ComputationalApproach.tex
@@ -127,13 +127,15 @@ examine the necessary Inada conditions.
 \subsection{Computational Results}
 Cases to consider
 \begin{itemize}
-    \item Reproduce Rao Rondina model
+    \item Reproduce Rao-Rondina single satellite model.
     \item Reproduce Adilov, perfect competition, cornot-like market.
     \item Add military operators to Adilov's model. 
-        This will involve some sort of complementarities.
+        This will involve some sort of competitive complementarity 
+        with diminishing marginal returns.
     \item Competitive market where the number of satellites improves quality, i.e. allows 
-        for pricing differences (Orbital Internet and comms).
-    \item Interacting orbital shells, using a vector of debris.
+        for pricing differences (Orbital Internet, e.g. Starlink).
+    \item Interacting orbital shells, using a vector representation of heterogeneous risk
+        imposed by constellations and debris.
 \end{itemize}
 
 \end{document}