Applications of computational knot theory and combinatorics to the inference of the three dimensional structure of chromosomes

This work includes both asymptotic results on the inevitability of random knotting and linking and important proprieties of reconfigurable systems. The properties of knots confined to tubes is studied numerically on the 3-dimensional simple cubic lattice, Z³. It is showed that the minimum step number needed to make a knot inside a tube decreases sharply with the size of the tube. The second third of this volume investigates a statical approach based on linking data that helps access the reproducibility of candidates reconstructions of three dimensional of yeast genome. Based on our results we concluded that the topological based approach improves current methods for assessing reproducibility. The last topic deals with the properties of cubical complex. Here we develop a computational combinatoric algorithm to generate all the states of a robot which changes according to local moves and find the minimum steps to move the system from one state to another thereof.