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We consider the problem of defining an appropriate local descriptor corresponding to an arbitrary global descriptor. Although it does not seem easy to rigorously and uniquely define local analogues of derived global descriptors (e.g., the electrophilicity) or the fundamental global descriptors associated with the canonical ensemble (e.g., the hardness), the local response of these global descriptors can be defined unambiguously. We look at the local response of the global electrophilicity and compare it to the conventional, ad hoc, definition of the local electrophilicity. The local response of global nucleofugality and electrofugality is also discussed. [ABSTRACT FROM AUTHOR]