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Because intentionality is hierarchical, there are equivalent mappings between actions and intentions.
A given set of bit-wise distance spectra [W 0,W 1 ] characterizes an entire class of equivalent mappings, where W 0 is the bit-wise distance spectrum given no a priori information and W 1 is the bit-wise distance spectrum given full a priori information.
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However, the pattern does not have an influence on the global color mapping, since both cases, T (n1) and T (n2), show equivalent color mappings of their morphology and their MCEP patterns.
For instance, all reactions involving molecular oxygen (Fig. 7a) have at least two chemically equivalent atom mappings.
Otherwise, a discrepancy between two equivalent atom mappings would be indistinguishable from a discrepancy due to an incorrect prediction.
A single chemical reaction can admit multiple chemically equivalent atom mappings when chemically equivalent atoms are present in a substrate, a product, or both.
A compact representation of all chemically equivalent atom mappings for a single reaction can be achieved by assigning the same atom mapping number to chemically equivalent atoms (Fig. 7).
Since oxygen atoms 5, and 6 and 9, 10, and 11 are chemically equivalent twelve accurate atom mappings could be predicted for this reaction.
Therefore, each chemical reaction can be represented by one set, or multiple chemically equivalent sets, of atom mappings, each of which may be interpreted as a graph with a set of disconnected edges, each of which establishes a bijective relation between a substrate and product atom (Fig. 1).
We deal with the stability of the orthogonality preserving property in the class of mappings phase-equivalent to linear or conjugate-linear ones.
CLCA can be used to enumerate alternative atom mappings by identifying equivalent atoms.
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