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Classical antibacterial drugs were designed to target specific bacterial properties distinct from host human cells to maximize potency and selectivity. These designs were quite effective as they could be easily derivatized to bear next-generation drugs. However, the rapid mutation of bacteria and their associated acquired drug resistance have led to the rise of highly pathogenic superbug bacterial strains for which treatment with first line drugs is no match. More than ever, there is a dire need for antibacterial drug design that goes beyond conventional standards. Taking inspiration by the body’s innate immune response to employ its own supply of labile copper ions in a toxic attack against pathogenic bacteria, which have a very low Cu tolerance, this review article examines the feasibility of Cu-centric strategies for antibacterial preventative and therapeutic applications. Promising results are shown for the use of Cu-containing materials in the hospital setting to minimize patient bacterial infections. Studies directed at disrupting bacterial Cu regulatory pathways elucidate new drug targets that can enable toxic increase of Cu levels and perturb bacterial dependence on iron. Likewise, Cu intracellular chelation/prochelation strategies effectively induce bacterial Cu toxicity. Cu-based small molecules and nanoparticles demonstrate the importance of the Cu ions in their mechanism and display potential synergism with classical drugs. 

Classical parking functions are defined as the parking preferences for $$n$$ cars driving (from west to east) down a one-way street containing parking spaces labeled from $$1$$ to $$n$$ (from west to east). Cars drive down the street toward their preferred spot and park there if the spot is available. Otherwise, the car continues driving down the street and takes the first available parking space, if such a space exists. If all cars can park using this parking rule, we call the $$n$$-tuple containing the cars' parking preferences a parking function.   In this paper, we introduce a generalization of the parking rule allowing cars whose preferred space is taken to first proceed up to $$k$$ spaces west of their preferred spot to park before proceeding east if all of those $$k$$ spaces are occupied. We call parking preferences which allow all cars to park under this new parking rule $$k$$-Naples parking functions of length $$n$$. This generalization gives a natural interpolation between classical parking functions, the case when $k=0$, and all $$n$$-tuples of positive integers $$1$$ to $$n$$, the case when $$k\geq n-1$$. Our main result provides a recursive formula for counting $$k$$-Naples parking functions of length $$n$$. We also give a characterization for the $k=1$ case by introducing a new function that maps $$1$$-Naples parking functions to classical parking functions, i.e. $$0$$-Naples parking functions. Lastly, we present a bijection between $$k$$-Naples parking functions of length $$n$$ whose entries are in weakly decreasing order and a family of signature Dyck paths.