Tendency towards maximum complexity in a nonequilibrium isolated system.

The time evolution equations of a simplified isolated ideal gas, the "tetrahedral" gas, are derived. The dynamical behavior of the López-Ruiz-Mancini-Calbet complexity [R. López-Ruiz, H. L. Mancini, and X. Calbet, Phys. Lett. A 209, 321 (1995)] is studied in this system. In general, it is shown that the complexity remains within the bounds of minimum and maximum complexity. We find that there are certain restrictions when the isolated "tetrahedral" gas evolves towards equilibrium. In addition to the well-known increase in entropy, the quantity called disequilibrium decreases monotonically with time. Furthermore, the trajectories of the system in phase space approach the maximum complexity path as it evolves toward equilibrium.

Use of multilayer feedforward neural nets as a display method for multidimensional distributions.

We present a new method based on multilayer feedforward neural nets for displaying an n-dimensional distribution in a projected space of 1, 2 or 3 dimensions. A fully nonlinear net with several hidden layers is used. Efficient learning is achieved using multi-seed backpropagation. As a principal component analysis (PCA), the proposed method is useful for extracting information on the structure of the data set, but unlike the PCA, the transformation between the original distribution and the projected one is not restricted to be linear. Artificial examples and a real application are presented in order to show the reliability and potential of the method.