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:
“Human affairs are so obscure and various that nothing can be clearly known. This was the sound conclusion of the Academic sceptics, who were the least surly of philosophers.”
—Desiderius Erasmus (1469–1536)
“We must not leap to the fatalistic conclusion that we are stuck with the conceptual scheme that we grew up in. We can change it, bit by bit, plank by plank, though meanwhile there is nothing to carry us along but the evolving conceptual scheme itself. The philosopher’s task was well compared by Neurath to that of a mariner who must rebuild his ship on the open sea.”
—Willard Van Orman Quine (b. 1908)
“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)