Long-time Behavior of Surface Electromyography Time Series

POSTER

Abstract

We have previously reported that the mean-square displacement from the sEMG time series $x_{i}$ with $i=1,2,..., 2^{16}$ exhibits diffusive behavior for short times, $t \stackrel{<}{\sim} 50 \, \mbox{ms}$, which is followed by a plateau-like behavior for intermediate times, $50 \, \mbox{ms} \stackrel{<}{\sim} t \stackrel{<}{\sim} 500 \, \mbox{ms}$. For long times, $t \stackrel{>}{\sim} 500 \, \mbox{ms}$, the msd increases as time $t$ increases. We show that the long-time behavior reflects non-stationarity of the signal; we find that for a fixed time interval $t=\mbox{const}$, the displacement $X_{s,t} = \sum_{i=0}^{t-1} x_{s+i} \simeq \mu_{1} $ for $s \in [s_{0}, s_{1}]$ and $X_{s,t} = - \mu_{2}$ for $s \notin [s_{0}, s_{1}]$. This property explains the fit of the probability distribution $p_{t} ( X) = \left< \delta ( X - X_{s,t} )\right>_{s}$ as a superposition of two Gaussians that we reported in Physica A {\bf 386}, 698-709 (2007). Supported by a grant from the Research Corporation [UZ].

Authors

  • Doug Petkie

    AFRL/RX, AFRL/RX, Systran Systems Inc, UCSD, Los Alamos National Laboratory, Ohio Northern University, BFS, Germany, Florida State University, Monmouth College, Ohio Wesleyan University, Department of Chemical and Biomolecular Engineering, The University of Akron, Physics Department, John Carroll University, Department of Chemistry, Knight Chemical Laboratories, The University of Akron, Australian National University, Miami University, Oxford, OH, University of Cincinnati, University of Findlay, Naval Research Laboratory, Washington, DC 20375, Cleveland State University, Health Sciences Dept, Cleveland State University, Physics Dept, Cleveland State University, Bucknell University, Wright State University, Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson AFB, Wright State University, Department of Physics, University of Puerto Rico, Department of Mechanical Engineer, Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson AFB and UES, Inc., Department of Environmental Science and Policy, School of Science, Marist College, Poughkeepsie, NY 12601, USA, AFRL/711 HPW, EPA Sustainable Technology Division, University of Akron, Rose-Hulman Institute of Technology, Harvard University, LSU, Ohio University, Wittenberg University, Student

  • Ulrich Zurcher

    Physics Dept, Cleveland State University

  • Miron Kaufman

    Physics Dept, Cleveland State University, Cleveland State University

  • Doug Petkie

    AFRL/RX, AFRL/RX, Systran Systems Inc, UCSD, Los Alamos National Laboratory, Ohio Northern University, BFS, Germany, Florida State University, Monmouth College, Ohio Wesleyan University, Department of Chemical and Biomolecular Engineering, The University of Akron, Physics Department, John Carroll University, Department of Chemistry, Knight Chemical Laboratories, The University of Akron, Australian National University, Miami University, Oxford, OH, University of Cincinnati, University of Findlay, Naval Research Laboratory, Washington, DC 20375, Cleveland State University, Health Sciences Dept, Cleveland State University, Physics Dept, Cleveland State University, Bucknell University, Wright State University, Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson AFB, Wright State University, Department of Physics, University of Puerto Rico, Department of Mechanical Engineer, Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson AFB and UES, Inc., Department of Environmental Science and Policy, School of Science, Marist College, Poughkeepsie, NY 12601, USA, AFRL/711 HPW, EPA Sustainable Technology Division, University of Akron, Rose-Hulman Institute of Technology, Harvard University, LSU, Ohio University, Wittenberg University, Student