Little notebook | Of my exploration

Relative position problem: simplex method

\[\newcommand{\vertex}[1]{\text{vert}\left(#1\right)} \newcommand{\conv}[1]{\text{conv}\left(#1\right)}\] This is mainly taken from Chapter 7 of my Bachelor thesis at École Polytechnique under supervision of Prof. Sarah J. Berkemer and Prof. Yann Ponty, titled “Polynomial-time parametric optimisation” 1. Introduction We have seen review on GJ...

Relative position problem: motivation

\[\newcommand{\proj}[1]{\text{proj }(#1)} \newcommand{\vol}[1]{\text{vol}(#1)}\] This is mainly taken from Chapter 4 and 5 of my Bachelor thesis at École Polytechnique under supervision of Prof. Sarah J. Berkemer and Prof. Yann Ponty, titled “Polynomial-time parametric optimisation” 1. Introduction We have seen the motivation and the mathemat...

Relative position problem: ellipsoid method

\[\newcommand{\vol}[1]{\text{vol}\left(#1\right)} \newcommand{\conv}[1]{\text{conv}\left(#1\right)} \newcommand{\sgn}[1]{\text{sgn}\left(#1\right)}\] This is mainly taken from Chapter 8 of my Bachelor thesis at École Polytechnique under supervision of Prof. Sarah J. Berkemer and Prof. Yann Ponty, titled “Polynomial-time parametric optimisation”...

Introduction to RNA polytopes

\[\newcommand{\conv}{\text{conv}} \newcommand{\vertex}{\text{vert}}\] This is mainly taken from Chapter 1, 2, and 3 of my Bachelor thesis at École Polytechnique under supervision of Prof. Sarah J. Berkemer and Prof. Yann Ponty, titled “Polynomial-time parametric optimisation” 1. Introduction 1.1. Importance of RNA Since the discovery of ribos...

Robustness problem in RNA folding: telescoping method

\[\newcommand{\vertex}{\text{vert}}\] This is mainly taken from Chapter 6 of my Bachelor thesis at École Polytechnique under supervision of Prof. Sarah J. Berkemer and Prof. Yann Ponty, titled “Polynomial-time parametric optimisation” 1. Introduction Along side with the problem of parameter learnability (and more generally relative position p...