Related papers: Amorphic complexity

We review several statistical complexity measures proposed over the last decade and a half as general indicators of structure or correlation. Recently, Lopez-Ruiz, Mancini, and Calbet [Phys. Lett. A 209 (1995) 321] introduced another…

For general asymptotically sub-additive potentials (resp. asymptotically additive potentials) on general topological dynamical systems, we establish some variational relations between the topological entropy of the level sets of Lyapunov…

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…

A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis…

We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…

For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…

There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…

The article presents a new perspective on the isomorphism problem for non-ergodic measure-preserving dynamical systems with discrete spectrum which is based on the connection between ergodic theory and topological dynamics constituted by…

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…

We propose a measure of learning efficiency for non-finite state spaces. We characterize the complexity of a learning problem by the metric entropy of its state space. We then describe how learning efficiency is determined by this measure…

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…

A classical dynamical system can be viewed as a probability space equipped with a measure-preserving time evolution map, admitting a purely algebraic formulation in terms of the algebra of bounded functions on the phase space. Similarly, a…

It is known that the asymptotic invariant manifolds around an unstable periodic orbit in conservative systems can be represented by convergent series (Cherry 1926, Moser 1956, 1958, Giorgilli 2001). The unstable and stable manifolds…

The (e,n)-complexity functions describe total instability of trajectories in dynamical systems. They reflect an ability of trajectories going through a Borel set to diverge on the distance $\epsilon$ during the time interval n. Behavior of…

Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we…

Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…

The definition of complexity through Statistical Complexity Measures (SCM) has recently seen major improvements. Mostly, effort is concentrated in measures on time series. We propose a SCM definition for spatial dynamical systems. Our…

This paper characterizes the annealed, topological complexity (both of total critical points and of local minima) of the elastic manifold. This classical model of a disordered elastic system captures point configurations with…

We define a simpler notion of symmetric topological complexity more ad hoc to the motion planning problem which was the original motivation for the definition of topological complexity. This is a homotopy invariant that we call…

In this paper, we study dynamics of maps on quasi-graphs characterizing their invariant measures. In particular, we prove that every invariant measure of quasi-graph map with zero topological entropy has discrete spectrum. Additionally, we…