Monotone measures of statistical complexity

Piecewise monotone maps without periodic points: Rigidity, measures and complexity.

Piecewise monotone maps without periodic points : Rigidity , measures and complexity

We consider piecewise monotone maps of the interval with zero entropy or no periodic points. First, we give a rigid model for these maps: the interval translations mappings, possibly with ips. It follows, e.g., that the complexity of a piecewise monotone map of the interval is at most polynomial if and only if this map has a nite number of periodic points up to monotone equivalence. Second, we ...

Identification of Monotone Measures

Identification of monotone measures is a very challenge process. Based on an existing data set of a set function (or, set functions) defined on the power set of a given finite universal set, to determine a monotone measure, simply switching the values of the given set function that violate the monotonicity is not the optimal way and it also causes some side effects. The paper proposes an algori...

Degrees of monotone complexity

Levin and Schnorr (independently) introduced the monotone complexity, Km(α), of a binary string α. We use monotone complexity to define the relative complexity (or relative randomness) of reals. We define a partial ordering ≤Km on 2 by α ≤Km β iff there is a constant c such that Km(α n) ≤ Km(β n) + c for all n. The monotone degree of α is the set of all β such that α ≤Km β and β ≤Km α. We show ...

Statistical Measures of Complexity for Strongly Interacting Systems

In recent studies, new measures of complexity for nonlinear systems have been proposed based on probabilistic grounds, as the LMC measure (Phys. Lett. A 209 (1995) 321). All these measures share an intuitive consideration: complexity seems to emerge in nature close to instability points, as for example the phase transition points characteristic of critical phenomena. Here we discuss these measu...