Conclusion
The shortcut model is useful for studying the dimension dependence of different processes. The processes studied include the behaviour of the power law potential as a function of the dimension, the behaviour of self-avoiding random walks, and the scaling of the mean path length. It may be useful to compare the shortcut model with the small-world network, since the definitions have a lot of similarity. In the small-world network also one starts with a regular lattice and adds shortcuts with probability . However, the shortcuts are not constrained to connect to a node a fixed distance ahead. Instead, the other end of the shortcut can connect to any randomly chosen node. As a result, the small world model tends to a random graph rather than a two-dimensional graph as the shortcut probability is increased.
Read more about this topic: Shortcut Model
Famous quotes containing the word conclusion:
“of making many books there is no end; and much study is a weariness
of the flesh.
Let us hear the conclusion of the whole matter: Fear God, and keep
his commandments: for this is the whole duty of man.”
—Bible: Hebrew Ecclesiastes (l. XII, 13)
“Ive heard the wolves scuffle, and said: So this
Is man; so what better conclusion is there
The day will not follow night, and the heart
Of man has a little dignity, but less patience
Than a wolfs....”
—Allen Tate (18991979)
“So this
Is man; sowhat better conclusion is there
The day will not follow night, and the heart
Of man has a little dignity, but less patience
Than a wolfs,”
—Allen Tate (18991979)