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The goal of this chapter is to describe different techniques used to measure knotting in open curves. Note that there is no "agreed upon" definition for describing knotting in open curves. As a result, we describe the context motivating each definition and then describe some advantages and disadvantages of the different approaches. 

Abstract Vertebrate genomes are partitioned into contact domains defined by enhanced internal contact frequency and formed by two principal mechanisms: compartmentalization of transcriptionally active and inactive domains, and stalling of chromosomal loop-extruding cohesin by CTCF bound at domain boundaries. While Drosophila has widespread contact domains and CTCF, it is currently unclear whether CTCF-dependent domains exist in flies. We genetically ablate CTCF in Drosophila and examine impacts on genome folding and transcriptional regulation in the central nervous system. We find that CTCF is required to form a small fraction of all domain boundaries, while critically controlling expression patterns of certain genes and supporting nervous system function. We also find that CTCF recruits the pervasive boundary-associated factor Cp190 to CTCF-occupied boundaries and co-regulates a subset of genes near boundaries together with Cp190. These results highlight a profound difference in CTCF-requirement for genome folding in flies and vertebrates, in which a large fraction of boundaries are CTCF-dependent and suggest that CTCF has played mutable roles in genome architecture and direct gene expression control during metazoan evolution.