Two Universality Properties Associated with the Monkey Model of Zipf's Law

The distribution of word probabilities in the monkey model of Zipf's law is associated with two universality properties: (1) the power law exponent converges strongly to $-1$ as the alphabet size increases and the letter probabilities are specified as the spacings from a random division of the unit interval for any distribution with a bounded density function on $[0,1]$; and (2), on a logarithmic scale the version of the model with a finite word length cutoff and unequal letter probabilities is approximately normally distributed in the part of the distribution away from the tails. The first property is proved using a remarkably general limit theorem for the logarithm of sample spacings from Shao and Hahn, and the second property follows from Anscombe's central limit theorem for a random number of i.i.d. random variables. The finite word length model leads to a hybrid Zipf-lognormal mixture distribution closely related to work in other areas.Comment: 14 pages, 3 figure

Perceptions of local hospitals and food producers on opportunities and barriers to implementing a farm-to-hospital program

The purpose of this study was to explore current perceptions and attitudes of local food producers and hospital staff towards incorporating locally-sourced foods into hospital food service programs. Perceived opportunities and challenges to procuring and using local products in the hospital setting were identified. Additionally, perceived enablers and barriers of local producers were identified around working directly with institutions. The goal of this study was to integrate perceptions of producers and hospital staff to develop locally relevant suggestions for strengthening producer-hospital relationships and increase the amounts of local foods in hospital food service programs. Qualitative data was collected by conducting interviews with hospital staff involved with food procurement and management, as well as with local producers and food distributors. Demographic data was also collected from participants. Findings resulted in the identification of opportunities and challenges associated with direct working relationships between local food producers and hospitals and the increase of locally-sourced foods in food services. Barriers included price, product availability and quantity while opportunities included positive relationships, product quality, and champion leaders. The integration of results allowed for the development of capacity building suggestions. Such suggestions included the development of aggregated food systems, hospital staff wellness programs and collaborative problem solving processes. Most significantly, this study suggested that efforts to connect producers and hospitals in collaborative dialogue to identify and resolve misconceptions and misinformation may serve to most successfully strengthen Montana’s farm-to-institution system and increase the amounts of locally-sourced foods being used in hospital food service programs