  One-dimensional quasilattices, namely, the geometrical objects to represent
quasicrystals, are classified into mutual local-derivability (MLD) classes.
Besides the familiar class, there exist an infinite number of new MLD classes,
and different MLD classes are distinguished by the inflation rules of their
representatives. It has been found that electronic properties of a new MLD
class are characterized by the presence of marginal critical states, which are
considered to be nearly localized states.
