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In patients with β-lactam allergies, administration of non–β-lactam surgical prophylaxis is associated with increased risk of infection. Although many patients self-report β-lactam allergies, most are unconfirmed or mislabeled. A quality improvement process, utilizing a structured β-lactam allergy tool, was implemented to improve the utilization of preferred β-lactam surgical prophylaxis.
We introduce the safe recursive set functions based on a Bellantoni–Cook style subclass of the primitive recursive set functions. We show that the functions computed by safe recursive set functions under a list encoding of finite strings by hereditarily finite sets are exactly the polynomial growth rate functions computed by alternating exponential time Turing machines with polynomially many alternations. We also show that the functions computed by safe recursive set functions under a more efficient binary tree encoding of finite strings by hereditarily finite sets are exactly the quasipolynomial growth rate functions computed by alternating quasipolynomial time Turing machines with polylogarithmic many alternations.
We characterize the safe recursive set functions on arbitrary sets in definability-theoretic terms. In its strongest form, we show that a function on arbitrary sets is safe recursive if and only if it is uniformly definable in some polynomial level of a refinement of Jensen's J-hierarchy, relativized to the transitive closure of the function's arguments.
We observe that safe recursive set functions on infinite binary strings are equivalent to functions computed by infinite-time Turing machines in time less than ωω. We also give a machine model for safe recursive set functions which is based on set-indexed parallel processors and the natural bound on running times.
Eighteen analyses are presented for 12 different Moche copper pedestal cups. Eight of the cups were made from naturally-occurring copper metal ore; the remaining 4 from copper obtained by smelting of complex oxidized ores. The use of both ore types suggests either a matter of convenience or technology in transition. In general, these people possessed a more advanced level of metallurgical technology than their utilization of primitive naturally-occurring copper metal implies.
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