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Real networks comprise from hundreds to millions of interacting elements and permeate all contexts, from technology to biology to society. All of them display non-trivial connectivity patterns, including the small-world phenomenon, making nodes to be separated by a small number of intermediate links. As a consequence, networks present an apparent lack of metric structure and are difficult to map. Yet, many networks have a hidden geometry that enables meaningful maps in the two-dimensional hyperbolic plane. The discovery of such hidden geometry and the understanding of its role have become fundamental questions in network science giving rise to the field of network geometry. This Element reviews fundamental models and methods for the geometric description of real networks with a focus on applications of real network maps, including decentralized routing protocols, geometric community detection, and the self-similar multiscale unfolding of networks by geometric renormalization.
(1) To develop a useful tool to measure food, alcohol and tobacco items; (2) to document the availability of these items in Almaty, Kazakstan; (3) to describe the relationship between consumption and availability; and (4) to identify possible relationships between availability and health outcomes in the city and region.
Design:
A survey of 648 vendors in Almaty, Kazakstan was conducted over one month from December 1999 to January 2000. Vendors identified which items they sold from a list of 61 food, alcohol and tobacco items.
Setting:
Vendors were approached in three of the six regions of Almaty, Kazakstan. Regions canvassed included Auzov, one of the three ‘sleeping regions’; Medeo, one of the two downtown regions; and Turksib, a more suburban/rural area of the city.
Results:
There was a significant correlation between alcohol and cigarette consumption and availability. The relative availability of items was numerically and spatially consistent throughout the city. Fruits and vegetables occurred infrequently (<20% of sites) and in relative isolation from the rest of the system, while candy and cigarettes occurred with a higher relative frequency (75–80% of sites). Maps of vendors showed clusters around geographical features such as major roads and intersections.
Conclusions:
Combining a checklist and mapping tools provides a model of consumer item availability that can help identify priorities for public health and urban planning professionals. The wide availability of cigarettes, alcohol, candy, coffee and tea, and limited availability of fruits, vegetables and whole grains, is likely to support increasing rates of chronic disease in Almaty.
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