Which preposition to use with correlation

of Occurrences 15%

The mastery of one fact may lead to the correlation of a psychic law.

with Occurrences 3%

"Under the life-conditions prevailing in this part of the Andes, and possibly in correlation with the increased action of the respiratory muscles in a rarefied air, domestic cattle occasionally develop first ribs, closely approaching the form observed in bison."

between Occurrences 1%

There are intricate correlations between department and department.

for Occurrences 1%

Even this inverted correspondence, however, is for the most part lacking in the subsequent eclogues, and it must be admitted that in so far as Spenser depended on a cyclic correlation for the unifying of his design, he achieved at best but partial effect.

to Occurrences 1%

So that nothing in nature should be counted mean, which can thus be exalted; but rather be honored, since no object can become so assimilated except by its predetermined correlation to our better nature.

Which preposition to use with  correlation