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:
“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 (1857–1930)
“The source of our actions resides in an unconscious propensity to regard ourselves as the center, the cause, and the conclusion of time. Our reflexes and our pride transform into a planet the parcel of flesh and consciousness we are.”
—E.M. Cioran (b. 1911)
“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 (1825–95)