Related papers: On the concept of complexity in random dynamical s…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
It is not obvious what fraction of all the potential information residing in the molecules and structures of living systems is significant or meaningful to the system. Sets of random sequences or identically repeated sequences, for example,…
Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…
In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum…
For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated…
The problem of defining and studying complexity of a time series has interested people for years. In the context of dynamical systems, Grassberger has suggested that a slow approach of the entropy to its extensive asymptotic limit is a sign…
We define the notion of localizable property for a dynamical system. Then we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the…
Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the KS-entropy diverges we analyse the difference between the total entropy of a noisy system and the entropy of…
This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that input signals have only a finite number k of frequency components, and systems to be identified have dimension no…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
The concept of statistical complexity is studied to characterize the classical kicked top model which plays important role in the qbit systems and the chaotic properties of the entanglement. This allows us to understand this driven…
A powerful tool is developed for the characterization of chaotic signals. The approach is based on the symbolic encoding of time series (according to their ordinal patterns) combined with the ensuing characterization of the corresponding…
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,…
We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define…
Although information content is invariant up to an additive constant, the range of possible additive constants applicable to programming languages is so large that in practice it plays a major role in the actual evaluation of K(s), the…
We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
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…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
A measure called Physical Complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organism's genome.…