Papers:

1.) In my first paper I explain how various versions of the Loday-Quillen-Tsygan map, respectively a generalization that applies to (cyclic) A-infinity categories, various graph complexes, additionally equiped with shifted Poisson or BV-algebra structure, and Kontsevich's cocycle construction are linked together. 

This should be related to what is called open (topological) String Field Theory (SFT). Its cousin is closed SFT, as described by Sen-Zwiebach, Costello, Căldăraru-Tu, which lead to the definition of Categorical Enumerative Invariants. In a physical context instances of closed respectively open topological SFT are BCOV theory respectively holomorphic Chern-Simons. 

2.) A crucial ingredient in the theory of Categorical Enumerative Invariants is a splitting of the non-commutative Hodge filtration (related to a trivialization of the circle action on hochschild chains of a Calabi-Yau category), from which a formality morphism is constructed. In my second paper I explain how to construct a formality morphism in the open-closed theory, again depending on a splitting. Physically, an instance of the open-closed theory is  BCOV theory coupled to holomorphic Chern-Simons.