We show how to twist the C⁎-algebra of a k-graph by a T-valued 2-cocycle and demonstrate that examples include all noncommutative tori.
Other examples include all the structures for moving people or freight, like railroads, or underground systems.
Some of the bad examples include all-male committees, usually comprised of men aged over 50, as well as women's spaces that are cramped and lacking appropriate sanitary facilities.
The Omidyar organization's efforts to bring financial services to underserved populations, for example, include all three types of contributions.
Some confer additional benefits: the Swiss Pass, for example, includes all public transport in 38 cities and towns and free admission to most museums.
In general, these segments were defined by applications commonality: the distribution segment, for example, included all companies for which inventory and physical distribution costs represented a major component of controllable expense.
Some indexes are, of course, broader in coverage; the Japanese index, for example, includes all households, urban or rural, except one-person households and those headed by farmers or fishermen.
This example includes all trees within the woodland species group of Jenkins (black) and their mapping to Chojnacky species groups (not identified) in the East (red, North and South) and the West (blue, Pacific Coast and Rocky Mountain).
Facebook by comparison, is at 4 billion public items shared but of course it all depends on what your definition of share or a delivery is (Facebook's for example includes all public status updates, photos, etc that users are sharing. Twitter and Google are counting how many times an update must be served to cover everyone's follower streams).
