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Analysis of chemical graphs is becoming a major research topic incomputational molecular biology due to its potential applications to drugdesign. One of the major approaches in such a study is inverse quantitativestructure activity/property relationships (inverse QSAR/QSPR) analysis, whichis to infer chemical structures from given chemical activities/properties.Recently, a novel framework has been proposed for inverse QSAR/QSPR using bothartificial neural networks (ANN) and mixed integer linear programming (MILP).This method consists of a prediction phase and an inverse prediction phase. Inthe first phase, a feature vector $f(G)$ of a chemical graph $G$ is introducedand a prediction function $\psi_{\mathcal{N}}$ on a chemical property $\pi$ isconstructed with an ANN $\mathcal{N}$. In the second phase, given a targetvalue $y^*$ of the chemical property $\pi$, a feature vector $x^*$ is inferredby solving an MILP formulated from the trained ANN $\mathcal{N}$ so that$\psi_{\mathcal{N}}(x^*)$ is equal to $y^*$ and then a set of chemicalstructures $G^*$ such that $f(G^*)= x^*$ is enumerated by a graph enumerationalgorithm. The framework has been applied to chemical compounds with a ratherabstract topological structure such as acyclic or monocyclic graphs and graphswith a specified polymer topology with cycle index up to 2.  In this paper, we propose a new flexible modeling method to the framework sothat we can specify a topological substructure of graphs and a partialassignment of chemical elements and bond-multiplicity to a target graph.

A novel method for inference of chemical compounds with prescribed topological substructures based on integer programming