2. Contraction of acyclic subcomplex as BV integral. Induction of higher operations.
3. Loop action and BCOV theory
4. Tropical particle and BCOV theory
5. Tropical mirror for toric varieties
6.Higher operations from the moduli spaces, metric graphs as a first example, Losev-Manin, Deligne-Mumford and Kimura-Stasheff-Voronov as 2-dim examples. Another look on 1-4 and string theory.