After decades of urban growth, mass transport, including buses, will play a significant role in our daily life. Therefore the requirements for buses and their bus door system are increasing. Ventura Systems is a company that is specialized in bus door systems and wishes to gain knowledge on their bus door system using mathematical modeling. This bachelor thesis provides the base for the mathematical models for modeling a bus door system. Multiple models are presented and one model is analyzed in more depth.

About three quarters of our DNA is wrapped into nucleosomes: DNA spools with a protein core. It is well known that the affinity of a given DNA stretch to be incorporated into a nucleosome depends on the geometry and elasticity of the basepair sequence involved, causing the positioning of nucleosomes. Here we show that DNA elasticity can have a much deeper effect on nucleosomes than just their positioning: it affects their "identities". Employing a recently developed computational algorithm, the mutation Monte Carlo method, we design nucleosomes with surprising physical characteristics. Unlike any other nucleosomes studied so far, these nucleosomes are short-lived when put under mechanical tension whereas other physical properties are largely unaffected. This suggests that the nucleosome, the most abundant DNA-protein complex in our cells, might more properly be considered a class of complexes with a wide array of physical properties, and raises the possibility that evolution has shaped various nucleosome species according to their genomic context.@en