title: A computational method for the detection of activation/deactivation patterns in biological signals with three levels of electric intensity.
abstract: In the present work, we develop a computational technique to approximate the changes of phase in temporal series associated to electric signals of muscles which perform activities at three different levels of intensity. We suppose that the temporal series are samples of independent, normally distributed random variables with mean equal to zero, and variance equal to one of three possible values, each of them associated to a certain degree of electric intensity. For example, these intensity levels may represent a leg muscle at rest, or active during a light activity (walking), or active during a highly demanding performance (jogging). The model is presented as a maximum likelihood problem involving discrete variables. In turn, this problem is transformed into a continuous one via the introduction of continuous variables with penalization parameters, and it is solved recursively through an iterative numerical method. An a posteriori treatment of the results is used in order to avoid the detection of relatively short periods of silence or activity. We perform simulations with synthetic data in order to assess the validity of our technique. Our computational results show that the method approximates well the occurrence of the change points in synthetic temporal series, even in the presence of autocorrelated sequences. In the way, we show that a generalization of a computational technique for the change-point detection of electric signals with two phases of activity (Esquivel-Frausto et al., 2010 [40]), may be inapplicable in cases of temporal series with three levels of intensity. In this sense, the method proposed in the present manuscript improves previous efforts of the authors.
authors.affiliation: Departamento de Estadística, Universidad Autónoma de Aguascalientes, Aguascalientes 20131, Mexico. Electronic address: jaguerrero@correo.uaa.mx.
authors.forename: J A
authors.initials: JA
authors.lastname: Guerrero
authors.affiliation: Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Aguascalientes 20131, Mexico. Electronic address: jemacias@correo.uaa.mx.
authors.forename: J E
authors.initials: JE
authors.lastname: Macías-Díaz
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D055724:Electrophysiological Phenomena; D006801:Humans; D016013:Likelihood Functions; D055641:Mathematical Concepts; D008954:Models, Biological; D009132:Muscles / Q000502:physiology*; D015398:Signal Transduction / Q000502:physiology; D059629:Signal-To-Noise Ratio
keywords: Biological electric signals; Change-point estimation; Heteroscedastic temporal series; Maximum likelihood methods; Multiple activity levels; Penalized optimization