Search results for "Entropy rate"
showing 4 items of 4 documents
An integrated approach based on uniform quantization for the evaluation of complexity of short-term heart period variability: Application to 24 h Hol…
2007
We propose an integrated approach based on uniform quantization over a small number of levels for the evaluation and characterization of complexity of a process. This approach integrates information-domain analysis based on entropy rate, local nonlinear prediction, and pattern classification based on symbolic analysis. Normalized and non-normalized indexes quantifying complexity over short data sequences (â¼300 samples) are derived. This approach provides a rule for deciding the optimal length of the patterns that may be worth considering and some suggestions about possible strategies to group patterns into a smaller number of families. The approach is applied to 24 h Holter recordings of …
Explicit Upper Bound for Entropy Numbers
2004
We give an explicit upper bound for the entropy numbers of the embedding I : W r,p(Ql) → C(Ql) where Ql = (−l, l)m ⊂ Rm, r ∈ N, p ∈ (1,∞) and rp > m.
Markov extensions for multi-dimensional dynamical systems
1999
By a result of F. Hofbauer [11], piecewise monotonic maps of the interval can be identified with topological Markov chains with respect to measures with large entropy. We generalize this to arbitrary piecewise invertible dynamical systems under the following assumption: the total entropy of the system should be greater than the topological entropy of the boundary of some reasonable partition separating almost all orbits. We get a sufficient condition for these maps to have a finite number of invariant and ergodic probability measures with maximal entropy. We illustrate our results by quoting an application to a class of multi-dimensional, non-linear, non-expansive smooth dynamical systems.
Geometric Entropies of Mixing (EOM)
2005
Trigonometric and trigonometric-algebraic entropies are introduced. Regularity increases the entropy and the maximal entropy is shown to result when a regular $n$-gon is inscribed in a circle. A regular $n$-gon circumscribing a circle gives the largest entropy reduction, or the smallest change in entropy from the state of maximum entropy which occurs in the asymptotic infinite $n$ limit. EOM are shown to correspond to minimum perimeter and maximum area in the theory of convex bodies, and can be used in the prediction of new inequalities for convex sets. These expressions are shown to be related to the phase functions obtained from the WKB approximation for Bessel and Hermite functions.