Shortcut Model - Conclusion

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:

    A certain kind of rich man afflicted with the symptoms of moral dandyism sooner or later comes to the conclusion that it isn’t enough merely to make money. He feels obliged to hold views, to espouse causes and elect Presidents, to explain to a trembling world how and why the world went wrong. The spectacle is nearly always comic.
    Lewis H. Lapham (b. 1935)

    I have come to the conclusion that the closer people are to what may be called the front lines of government ... the easier it is to see the immediate underbrush, the individual tree trunks of the moment, and to forget the nobility the usefulness and the wide extent of the forest itself.... They forget that politics after all is only an instrument through which to achieve Government.
    Franklin D. Roosevelt (1882–1945)

    I’ve 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 wolf’s....
    Allen Tate (1899–1979)