54 lines
2.2 KiB
TeX
54 lines
2.2 KiB
TeX
%% Vol III, Chapter 2 — Mathematical Companion
|
|
%% SOURCE: docs/working/papers/SSRN_companion/Math_Companion_SSRN.tex (full LaTeX source)
|
|
%% docs/working/papers/SSRN_companion/figures/ (7 figure PDFs)
|
|
|
|
\chapter{Mathematical Companion}
|
|
\label{vol3:chap:math}
|
|
|
|
%% TODO(bob): this chapter is a formal reference for the mathematical and
|
|
%% engineering structures described in Math_Companion_SSRN.tex.
|
|
%% The full source is available at:
|
|
%% docs/working/papers/SSRN_companion/Math_Companion_SSRN.tex
|
|
%%
|
|
%% Option A: include it directly:
|
|
%% \input{../../working/papers/SSRN_companion/Math_Companion_SSRN.tex}
|
|
%% (note: preamble collision likely — requires refactoring the companion source)
|
|
%%
|
|
%% Option B: promote key sections by hand.
|
|
%%
|
|
%% Recommend Option B for maintainability. Dictate which sections to promote.
|
|
|
|
\section{Q48.16 Fixed-Point Arithmetic}
|
|
\label{vol3:sec:math:q4816}
|
|
|
|
%% SOURCE: Math_Companion_SSRN.tex (Q48.16 section)
|
|
%% TODO(bob): promote the Q48.16 definition, operations, and precision analysis.
|
|
|
|
\section{Feedback Loop Equations}
|
|
\label{vol3:sec:math:loops}
|
|
|
|
%% SOURCE: Math_Companion_SSRN.tex (feedback loop mathematical formulations)
|
|
%% TODO(bob): promote the equations for all 7 loops.
|
|
|
|
\section{Figures}
|
|
\label{vol3:sec:math:figures}
|
|
|
|
%% SOURCE: docs/working/papers/SSRN_companion/figures/ (7 PDFs)
|
|
%% TODO(bob): decide which figures to include in this volume.
|
|
%% Available figures:
|
|
%% fig1_snake_trajectory.pdf — phase-space snake trajectory
|
|
%% fig2_K_vs_window.pdf — K parameter vs window width
|
|
%% fig3_FFT_spectrum.pdf — FFT spectrum of adaptation signal
|
|
%% fig4_golden_ratio_penalties.pdf — penalty function shape
|
|
%% fig5_bimodal_distributions.pdf — heat distribution bimodality
|
|
%% fig6_performance_vs_k.pdf — performance vs K sweep
|
|
%% fig7_performance_by_regime.pdf — performance by operating regime
|
|
|
|
\begin{figure}[ht]
|
|
\centering
|
|
%% TODO(bob): uncomment and adjust path when figures are accessible from build:
|
|
%% \includegraphics[width=0.8\linewidth]{../../working/papers/SSRN_companion/figures/fig1_snake_trajectory.pdf}
|
|
\caption{Phase-space trajectory (snake plot).}
|
|
\label{fig:snake}
|
|
\end{figure}
|