Nonextensive Statistical Mechanics

7.4 Computer Sciences 271Fig. 7.67 Cumulative distribution of the daily net exchange of shares (between all pairs of twoinstitutions), at the London Stock Exchange (Block market). Data from I.I. Zovko; fitting byE.P. Borges [using the analytic form (in red) emerging within crossover statistics; see Eq. (6.4)];unpublished (2005).1Probability density0.10.01P(x) = ⎯⎯⎯⎯⎯⎯⎯10.001 [1+(q–1)β qx 2 ⎯⎯] 1 q–1q = 2.136, √ ⎯⎯ 1/β q= 188,982 ¥0.000110 100 1000 10000 100000Price [1000 Yen]Fig. 7.68 Cumulative distribution of the land prices in Japan. Data from [586]; fitting byE.P. Borges (2003).algorithm. The visiting algorithm is based on an exploration of phase-space usinga q V -Gaussian (instead of using either a Gaussian or a Cauchy distribution), andthe acceptance algorithm is based on a q A -exponential weight (instead of the MonteCarlo Boltzmann weight). Therefore, a GSA machine is characterized by the pair(q V , q A ). The choice (1, 1) is the Boltzmann machine, and the choice (2, 1) is theCauchy machine. In practice, the most performant values have been shown to beq V > 1, slightly below the maximal admissible value for the D-dimensional problem(for D = 1 the maximal admissible value is q V = 3, and a performant value isq V ≃ 2.7); for D dimensions, the maximal admissible value is q V = (D + 2)/D),