Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework which is presented step-by-step with examples throughout. In this second part of two papers, we give the general categorical formulation

Variations and trends in state nursing facility capacity: 1978-93.

The demand for nursing facility (NF) beds has been growing with the aging of the population and many other factors. As the need for nursing home care grows, the Nation's capacity to provide such care is the subject of increasing concern. This article examines licensed NFs and beds, presenting data on trends from 1978-93. Measures of the adequacy of NF beds in States are examined over time, including the ratio of beds per aged population, occupancy rates, and State official's opinions of the adequacy of supply. State and regional variations are shown over time, and we speculate on the factors which may be associated with the variation