  The subject of the present work is the de Rham part of non-commutative Hodge
structures on the periodic cyclic homology of differential graded algebras and
categories. We discuss explicit formulas for the corresponding connection on
the periodic cyclic homology viewed as a bundle over the punctured formal disk.
Our main result says that for the category of matrix factorizations of a
polynomial the formulas reproduce, up to a certain shift, a well-known
connection on the associated twisted de Rham cohomology which plays a central
role in the geometric approach to the Hodge theory of isolated singularities.
