Scaling and interleaving of subsystem Lyapunov exponents for spatio-temporal systems.

The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the spectrum of a subsystem by a suitable rescaling in a very cost effective way. We compute the Lyapunov spectrum for the subsystem by truncating the original Jacobian without modifying the original dynamics and thus taking into account only a portion of the information of the entire system. In doing so we notice that the Lyapunov spectra for consecutive subsystem sizes are interleaved and we discuss the possible ways in which this may arise. We also present a new rescaling method, which gives a significantly better fit to the original Lyapunov spectrum. We evaluate the performance of our rescaling method by comparing it to the conventional rescaling (dividing by the relative subsystem volume) for one- and two-dimensional lattices in spatio-temporal chaotic regimes. Finally, we use the new rescaling to approximate quantities derived from the Lyapunov spectrum (largest Lyapunov exponent, Lyapunov dimension, and Kolmogorov-Sinai entropy), finding better convergence as the subsystem size is increased than with conventional rescaling. (c) 1999 American Institute of Physics.

Number, shape, and topography of leakage points in acute type I central serous retinopathy.

The evaluation of 430 consecutive eyes (87.5% from male, 12.5% from female patients) showed a leakage point with uniform dye spread in 93%. In 7%, a smoke-stack phenomenon was observed. The number of leakage points reached from 1 (71.6%) to 7 (0.2%). Most leakage points were found in a 1-mm-wide ring-shaped zone starting 0.5 mm from the center of the fovea. Beyond this zone the incidence dropped rapidly with the exception of the upper nasal quadrant. Of the leakage points, 33.2% were located in the upper nasal, 21.2% in the lower nasal, 19.0% in the upper temporal, and 14.8% in the lower temporal quadrant. Leakage points occurred more than 3 mm away from the center of the fovea in 11.8%. The papillomacular bundle contained 25.4% of the leakage points. Leakage points in recurrences were located within 1 mm of the primary leakage point in 80% of the cases.