Fractals, chaos, power laws - minutes from an infinite paradise
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Estimation of time-delayed mutual information and bias for irregularly and sparsely sampled time-series.
A method to estimate the time-dependent correlation via an empirical bias estimate of the time-delayed mutual information for a time-series is proposed. In particular, the bias of the time-delayed mutual information is shown to often be equivalent to the mutual information between two distributions of points from the same system separated by infinite time. Thus intuitively, estimation of the bi...
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It is well known that energy spectra of particles from atmospheric family events which are observed by the emulsion chambers at mountain altitudes are essentially following power-like dependence. On the other hand the occurence of power-law distributions is a very common feature in nature and it is usually connected with such notions as criticality, fractals and chaotic dynamics and studied usi...
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The basic rules of central place networks are abstracted and formulated as three geometric series scaling laws, which can be transformed into several power laws associated with fractal structure. The scaling laws might be the Rosetta Stone to understand the complexity of human geographical systems because they take the form of Horton and Strahler's laws in geomorphology and Gutenberg and Richte...
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Since Newton, the temporal evolution of natural systems has been described by mathematical laws expressed in terms of differential equations. The equations uniquely determine the system state at time t+ dt as a function of its previous state at time t. The state of the system is defined by a set of coordinatesX taking their values in the so-called phase space [1]. These coordinates are for inst...
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