We consider the problem of constructing public facilities, such as hospitals,
airports, or malls, in a country with a non-uniform population density, such
that the average distance from a person's home to the nearest facility is
minimized. Approximate analytic arguments suggest that the optimal distribution
of facilities should have a density that increases with population density, but
does so slower than linearly, as the two-thirds power. This result is confirmed
numerically for the particular case of the United States with recent population
data using two independent methods, one a straightforward regression analysis,
the other based on density dependent map projections. We also consider
strategies for linking the facilities to form a spatial network, such as a
network of flights between airports, so that the combined cost of maintenance
of and travel on the network is minimized. We show specific examples of such
optimal networks for the case of the United States.
We illustrate the differences between cultures that are tight (have many strong norms and a low tolerance of deviant behavior) versus loose (have weak social norms and a high tolerance of deviant behavior). Tightness-looseness is part of a complex, loosely integrated multilevel system that comprises...
We sought to break down such networks into basic building blocks. We generalize the notion of motifs, widely used for sequence analysis, to the level of networks. We define 'network motifs' as patterns of interconnections that recur in many different parts of a network at frequencies much higher tha...
This detailed longitudinal study reveals different social dynamics at different levels of organization. Taken together, these results demonstrate that low association rates, seemingly small group sizes, and fission-fusion grouping behavior mask hidden stability in the extensive and fluid social affi...
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