Little notebook | Of my exploration

On convex crossing number of lattice graphs

\[\newcommand{\crn}[1]{\text{cr}(#1)} \newcommand{\ccrn}[1]{\text{ccr}(#1)} \newcommand{\id}{\text{id}} \newcommand{\var}[1]{\text{var}(#1)}\] This was a study during my Bachelor thesis in my first year at ENS Ulm, carried out at Hamilton Institute, Maynooth University, under supervision of Prof. Damien Woods. For the context, it was an attemp...

An Ising model in RNA folding (part 3)

\[\newcommand{\NP}{\textsf{NP}} \newcommand{\APX}{\textsf{APX}} \newcommand{\sP}{\textsf{#P}} \newcommand{\A}{\textsf{A}} \newcommand{\T}{\textsf{T}} \newcommand{\G}{\textsf{G}} \newcommand{\C}{\textsf{C}}\] This is part 3/3 of my Bachelor thesis during my first year at Ulm, carried out at Hamilton Institute, Maynooth University and under super...

An Ising model in RNA folding (part 2)

\[\newcommand{\APX}{\textsf{APX}} \newcommand{\sP}{\textsf{#P}}\] This is part 2/3 of my Bachelor thesis during my first year at Ulm, carried out at Hamilton Institute, Maynooth University and under supervision of Prof. Damien Woods, titled “Computational complexity of an Ising model in pseudoknotted nucleic acid folding”, to be published. 5. ...

An Ising model in RNA folding (part 1)

\[\newcommand{\NP}{\textsf{NP}} \newcommand{\APX}{\textsf{APX}} \newcommand{\sP}{\textsf{#P}} \newcommand{\A}{\textsf{A}} \newcommand{\T}{\textsf{T}} \newcommand{\G}{\textsf{G}} \newcommand{\C}{\textsf{C}} \newcommand{\U}{\textsf{U}}\] This is part 1/3 of my Bachelor thesis during my first year at Ulm, carried out at Hamilton Institute, Maynoot...

A slightly modified proof of $\textsf{NP}$-hardness of RNA interaction problem

\[\newcommand{\NP}{\textsf{NP}} \newcommand{\A}{\textsf{A}} \newcommand{\T}{\textsf{T}} \newcommand{\G}{\textsf{G}} \newcommand{\C}{\textsf{C}} \newcommand{\U}{\textsf{U}}\] Abstract. This note is devoted to a slightly modified proof of \(\NP\)-hardness for \(\textsf{RNA-RNAi}\) under Nussinov counting model, along the lines of that by Alkan et...