The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion

Fractional Brownian motion (fBm) has been used as a theoretical framework to study real time series appearing in diverse scientific fields. Because its intrinsic non-stationarity and long range dependence, its characterization via the Hurst parameter H requires sophisticated techniques that often yield ambiguous results. In this work we show that fBm series map into a scale free visibility graph whose degree distribution is a function of H. Concretely, it is shown that the exponent of the power law degree distribution depends linearly on H. This also applies to fractional Gaussian noises (fGn) and generic f^(-b) noises. Taking advantage of these facts, we propose a brand new methodology to quantify long range dependence in these series. Its reliability is confirmed with extensive numerical simulations and analytical developments. Finally, we illustrate this method quantifying the persistent behavior of human gait dynamics.Comment: 5 pages, submitted for publicatio

Porous substrates for label-free molecular level detection of nonresonant organic molecules

We report on the design of practical surface enhanced Raman scattering (SERS) substrate based upon 3D alumina membranes with cylindrical nanopores chemically modified with polyelectrolyte coating and loaded with gold nanoparticle clusters. These substrates allow for a molecular-level, label-free detection of common plastic explosive materials (TNT, DNT) down to 5-10 zeptograms or 15-30 molecules and a common liquid explosive (HMTD) down to 1 picogram. Such a sensitive detection of organic molecules by utilizing efficient SERS substrates opens the path for affordable and label-free detection of trace amount of practically important chemical compounds.close818