Parametric ordering of complex systems

Parametric ordering of complex systems.

Cellular automata (CA) dynamics are ordered in terms of two global parameters, computable a priori from the description of rules. While one of them (activity) has been used before, the second one is new; it estimates the average sensitivity of rules to small configurational changes. For two well-known families of rules, the Wolfram complexity Classes cluster satisfactorily. The observed simulta...

Oligo-parametric Hierarchical Structure of Complex Systems

We investigate the possible origin of hierarchical structures in complex systems describable in terms of a finite and small number of parameters which control the behavioral pattern at each level of organization. We argue that the limitation on the number of important parameters at each stage is a reflection of the fact that Thom’s classification of catastrophes, i.e., qualitative changes, invo...

Dispersive Ordering and k-out-of-n Systems

Extended Abstract. The simplest and the most common way of comparing two random variables is through their means and variances. It may happen that in some cases the median of X is larger than that of Y, while the mean of X is smaller than the mean of Y. However, this confusion will not arise if the random variables are stochastically ordered. Similarly, the same may happen if one would like to ...

Complex fuzzy linear systems

Eigenfunction Statistics of Complex Systems: A Single Parametric Formulation

We derive a common mathematical formulation for the eigenvector statistics of Hermitian operators, represented by a multi-parametric probability density. The system-information in the formulation enters through a single function of all system parameter, thus indicating a single parameter scaling of the statistics. This in turn reveals a deep rooted universality hidden underneath the world of co...