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We explain how the spectral curve can be extracted from the ${\cal W}$-representation of a matrix model. It emerges from the part of the ${\cal W}$-operator, which is linear in time-variables. A possibility of extracting
the spectral curve in this way is important because there are models where
matrix integrals are not yet available, and still they possess all their
important features. We apply this reasoning to the family of WLZZ models and
discuss additional peculiarities which appear for the non-negative value of the
family parameter $n$, when the model depends on additional couplings (dual
times). In this case, the relation between topological and $1/N$ expansions is
broken. On the other hand, all the WLZZ partition functions are
$\tau$-functions of the Toda lattice hierarchy, and these models also celebrate
the superintegrability properties.

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