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:

    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)

    No one can write a best seller by trying to. He must write with complete sincerity; the clichés that make you laugh, the hackneyed characters, the well-worn situations, the commonplace story that excites your derision, seem neither hackneyed, well worn nor commonplace to him.... The conclusion is obvious: you cannot write anything that will convince unless you are yourself convinced. The best seller sells because he writes with his heart’s blood.
    W. Somerset Maugham (1874–1966)

    The conclusion has never changed: the worst sort of people come here for the worst sort of reasons and put upon those of us who have conveniently forgotten where we came from and how we got here.
    Anna Quindlen (b. 1952)