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:
“The conclusion suggested by these arguments might be called the paradox of theorizing. It asserts that if the terms and the general principles of a scientific theory serve their purpose, i. e., if they establish the definite connections among observable phenomena, then they can be dispensed with since any chain of laws and interpretive statements establishing such a connection should then be replaceable by a law which directly links observational antecedents to observational consequents.”
—C.G. (Carl Gustav)
“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)
“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)