9 F eb 2 00 5 Recurrence plot statistics and the effect of embedding
نویسنده
چکیده
Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably determinism and entropy of line length distribution, to the correlation sum as a function of embedding dimension. These expressions are obtained by deriving the transformation which generates an embedded recurrence plot from an unembedded plot. A single unembedded recurrence plot thus provides the statistics of all possible embedded recurrence plots. If the correlation sum scales exponentially with embedding dimension, we show that these statistics are determined entirely by the exponent of the exponential. This explains the results of Iwanski and Bradley (Chaos 8 [1998] 861-871) who found that certain recurrence plot statistics are apparently invariant to embedding dimension for certain low-dimensional systems. We also examine the relationship between the mutual information content of two timeseries and the common recurrent structure seen in their recurrence plots. This allows time-localized contributions to mutual information to be visualized. This technique is demonstrated using geomagnetic index data; we show that the AU and AL geomagnetic indices share half their information, and find the timescale on which mutual features appear.
منابع مشابه
X iv : h ep - t h / 05 02 09 1 v 1 9 F eb 2 00 5 SHEP - 05 - 05 D 7 Brane Embeddings and Chiral Symmetry Breaking
We study the embedding of D7 brane probes in five geometries that are deformations of AdS 5 × S 5. Each case corresponds to the inclusion of quark fields in a dual gauge theory where we are interested in investigating whether chiral symmetry breaking occurs. We use a supersymmetric geometry describing an N = 2 theory on its moduli space and a dilaton driven non-supersymmetric flow to establish ...
متن کاملMagnetism Division Fachverband Magnetismus (MA)
MA 1.1 Mon 9:30–10:00 EB 301 Composite nanoparticles and nanopatterns for ultrahigh density magnetic recording — •Dagmar Goll MA 6.1 Mon 14:00–14:30 EB 301 Genuine bulk electronic structures of strongly correlated transition metal oxides revealed by high energy photoelectron spectroscopy — •Shigemasa Suga MA 6.2 Mon 14:30–15:00 EB 301 Probing spin excitations in magnetic nanostructures and half...
متن کاملRecovering smooth dynamics from time series with the aid of recurrence plots.
A graphical method based on recurrence plots is used in the reconstruction of the phase space from a time series of measurements. It is demonstrated that if the embedding delay and dimension are correctly chosen, the recurrence plot of a smooth dynamical system has a particularly simple form. It is shown how to use recurrence plots to determine the correct embedding parameters so that reliable ...
متن کاملeb 2 00 1 N = 1 M 5 - brane geometries
We find new solutions to 11-dimensional supergravity describing M5-branes wrapped on holomorphic 2-cycles embedded in C. These solutions preserve N = 1 supersymmetry in four dimensions. They are dual to N = 1 gauge theories in four dimensions by Maldacena’s duality. USITP-00-19 DTP/00/111 hep-th/0012194 email: [email protected] email: [email protected] email: [email protected] email: Douglas.Smith...
متن کامل