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:
“It is a great many years since at the outset of my career I had to think seriously what life had to offer that was worth having. I came to the conclusion that the chief good for me was freedom to learn, think, and say what I pleased, when I pleased. I have acted on that conviction... and though strongly, and perhaps wisely, warned that I should probably come to grief, I am entirely satisfied with the results of the line of action I have adopted.”
—Thomas Henry Huxley (182595)
“I have come to the conclusion that the major part of the work of a President is to increase the gate receipts of expositions and fairs and by tourists into town.”
—William Howard Taft (18571930)
“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)