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.

[1] The determination of delay times of solar wind conditions at the sunward libration point to effects on Earth is investigated using mutual information. This measures the amount of information shared between two timeseries. We consider the mutual information content of solar wind observations, from WIND, and the geomagnetic indices. The success of five commonly used schemes for estimating interplanetary propagation times is examined. Propagation assuming a fixed plane normal at 45 degrees to the GSE x-axis (i.e. the Parker Spiral estimate) is found to give optimal mutual information. The mutual information depends on the point in space chosen as the target for the propagation estimate, and we find that it is maximized by choosing a point in the nightside rather than dayside magnetosphere. In addition, we employ recurrence plot analysis to visualize contributions to the mutual information, this suggests that it appears on timescales of hours rather than minutes. Citation: March, T. K., S. C. Chapman, and R. O. Dendy (2005), Mutual information between geomagnetic indices and the solar wind as seen by WIND: Implications for propagation time estimates, Geophys. Res. Lett., 32, L04101,

Previous observations that suggest a substantial role for nondiffusive energy transport in tokamaks subjected to off-axis electron cyclotron heating ͑ECH͒ are compared to the output from a sandpile model. The observations considered include local and global aspects of temperature profile evolution in the DIII-D ͓for example, C. C. Petty and T. C. Luce, Nucl. Fusion 34, 121 ͑1994͔͒ and RTP ͑Rijnhuizen Tokamak Project͒ ͓for example, M.

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