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Table 2 Notation adopted for modeling chemical compounds

From: A novel method for inference of acyclic chemical compounds with bounded branch-height based on artificial neural networks and integer programming

Symbol Designation
\(\Lambda \) A set of labels representing chemical elements
\(\text {mass}({\mathtt{a}})\) Atomic mass of chemical element \({\mathtt{a}}\in \Lambda \)
\({\text {val}}({\mathtt{a}})\) Valence of chemical element \({\mathtt{a}}\in \Lambda \)
\(\text {mass}^*({\mathtt{a}})\) \(\lfloor 10\cdot \text {mass}({\mathtt{a}})\rfloor \), \({\mathtt{a}}\in \Lambda \)
\({\mathtt{a}}< \mathtt{b}\) A total order over labels in the set \(\Lambda \), indicating \(\text {mass}({\mathtt{a}}) < \text {mass}(\mathtt{b})\)
\(\gamma = ({\mathtt{a}}, \mathtt{b}, m)\) Adjacency configuration for an atom pair, \({\mathtt{a}}, \mathtt{b}\in \Lambda \), \(m \in [1, 3]\)
\(\overline{\gamma }\) For an adjacency configuration \(\gamma = ({\mathtt{a}}, \mathtt{b}, m)\), \(\overline{\gamma } = (\mathtt{b}, {\mathtt{a}}, m)\)
\(\Gamma _<\) Set of adjacency configurations \(\gamma = ({\mathtt{a}}, \mathtt{b}, m) \in \Lambda \times \Lambda \times [1, 3]\) with \({\mathtt{a}}< \mathtt{b}\)
\(\Gamma _>\) Set of adjacency configurations \(\Gamma _> = \{ \overline{\gamma } \mid \gamma \in \Gamma _< \}\)
\(\Gamma _=\) Set of adjacency configurations, \(\Gamma _= = \{ ({\mathtt{a}}, {\mathtt{a}}, m) \mid {\mathtt{a}}\in \Lambda , m = [1, 3] \}\)
\(\Gamma \) \(\Gamma = \Gamma _< \cup \Gamma _=\)
\(\alpha \) A mapping of atom labels in \(\Lambda \) to graph vertices
\(\beta \) A mapping of integers in [1, 3] to graph edges, overloaded as \(\beta (u) = \sum _{uv \in E(H)} \beta (uv)\) for vertices \(u \in V(H)\) in a graph H
\(\text {Bc}\) Set of bond-configurations \(\mu \in [1, 4] \times [1, 4] \times [1, 3]\)