Power-law Portfolios

Law and Power

Power-law random walks.

In this paper, random walks with independent steps distributed according to a Q-power-law probability distribution function with Q=1/(1-q) are studied. In the case q>1, we show that (i) a stochastic representation of the location of the walk after n steps can be explicitly given (for both finite and infinite variance) and (ii) a clear connection with the superstatistics framework can be establi...

Power-Law Graph Cuts

Algorithms based on spectral graph cut objectives such as normalized cuts, ratio cuts and ratio association have become popular in recent years because they are widely applicable and simple to implement via standard eigenvector computations. Despite strong performance for a number of clustering tasks, spectral graph cut algorithms still suffer from several limitations: first, they require the n...

Power Law and Entropy

Shannon[1] and Yavuz[2] estimated the entropy of real documents. This note drives an upper bound of entropy from the power law. Let D be a set of documents and f r(w) be the number of occurrences of a word w in the document. Given an interger k, we denote by F (k) the number of words whose frequency is k, i.e., F (k) = ♯{w ∈ D | f r(w) = k}. The entropy of the document set D is defined by E(D) ...

Law and State Power:

The struggle for power has been a persistent phenomenon throughout history, involving the rulers, general public, and various other interest groups. As one of these groups, the legal community has been in a unique position to regulate the relationship between the ruler and the public because of its dual responsibilities to provide services to the public and to impose constraints on the rulers. ...