In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex. The main motivation for considering path complexes comes from directed graphs (digraphs). We obtain a new notion of the path homology and cohomology of a digraph.

We discuss a method for deriving differential equations for the prepotential and the mirror map arising from a pair of Calabi-Yau manifold. Examples with one Kahler modulus are given. Here we nd that the differential equations we derive almost entirely characterize the prepotential and the mirror map in question. Some of the results here have been announced previously in

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An n dimensional minimal submanifold $\sum$  of $R^{n+m}$ is called nonparametric if $\sum$  can be represented as the graph of a vector-valued function $f : D \subset \mathbb{ R}^n \to \mathbb{R}^n$. This note provides a sufficient condition for the stability of such $\sum$ in terms of the norm of the differential $df$.