Non-exponential return time distributions for vorticity extremes explained by fractional Poisson processes

Serial correlation of extreme midlatitude cyclones observed at the storm track exits is explained by deviations from a Poisson process. To model these deviations, we apply fractional Poisson processes (FPPs) to extreme midlatitude cyclones, which are defined by the 850 hPa relative vorticity of the ERA interim reanalysis during boreal winter (DJF) and summer (JJA) seasons. Extremes are defined by a 99% quantile threshold in the grid-point time series. In general, FPPs are based on long-term memory and lead to non-exponential return time distributions. The return times are described by a Weibull distribution to approximate the Mittag–Leffler function in the FPPs. The Weibull shape parameter yields a dispersion parameter that agrees with results found for midlatitude cyclones. The memory of the FPP, which is determined by detrended fluctuation analysis, provides an independent estimate for the shape parameter. Thus, the analysis exhibits a concise framework of the deviation from Poisson statistics (by a dispersion parameter), non-exponential return times and memory (correlation) on the basis of a single parameter. The results have potential implications for the predictability of extreme cyclones.

The latency distribution of motor evoked potentials in patients with multiple sclerosis

OBJECTIVE: To compare the individual latency distributions of motor evoked potentials (MEP) in patients with multiple sclerosis (MS) to the previously reported results in healthy subjects (Firmin et al., 2011). METHODS: We applied the previously reported method to measure the distribution of MEP latencies to 16 patients with MS. The method is based on transcranial magnetic stimulation and consists of a combination of the triple stimulation technique with a method originally developed to measure conduction velocity distributions in peripheral nerves. RESULTS: MEP latency distributions in MS typically showed two peaks. The individual MEP latency distributions were significantly wider in patients with MS than in healthy subjects. The mean triple stimulation delay extension at the 75% quantile, a proxy for MEP latency distribution width, was 7.3ms in healthy subjects and 10.7ms in patients with MS. CONCLUSIONS: In patients with MS, slow portions of the central motor pathway contribute more to the MEP than in healthy subjects. The bimodal distribution found in healthy subjects is preserved in MS. SIGNIFICANCE: Our method to measure the distribution of MEP latencies is suitable to detect alterations in the relative contribution of corticospinal tract portions with long MEP latencies to motor conduction.