  We show how the recently proposed effective theory for a Quantum Hall system
at "paired states" filling v=1 (Mod. Phys. Lett. A 15 (2000) 1679; Nucl. Phys.
B641 (2002) 547), the twisted model (TM), well adapts to describe the
phenomenology of Josephson Junction ladders (JJL) in the presence of defects.
In particular it is shown how naturally the phenomenon of flux
fractionalization takes place in such a description and its relation with the
discrete symmetries present in the TM. Furthermore we focus on closed
geometries, which enable us to analyze the topological properties of the ground
state of the system in relation to the presence of half flux quanta.
