871 research outputs found
How to avoid potential pitfalls in recurrence plot based data analysis
Recurrence plots and recurrence quantification analysis have become popular
in the last two decades. Recurrence based methods have on the one hand a deep
foundation in the theory of dynamical systems and are on the other hand
powerful tools for the investigation of a variety of problems. The increasing
interest encompasses the growing risk of misuse and uncritical application of
these methods. Therefore, we point out potential problems and pitfalls related
to different aspects of the application of recurrence plots and recurrence
quantification analysis
Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data
The knowledge of transitions between regular, laminar or chaotic behavior is
essential to understand the underlying mechanisms behind complex systems. While
several linear approaches are often insufficient to describe such processes,
there are several nonlinear methods which however require rather long time
observations. To overcome these difficulties, we propose measures of complexity
based on vertical structures in recurrence plots and apply them to the logistic
map as well as to heart rate variability data. For the logistic map these
measures enable us not only to detect transitions between chaotic and periodic
states, but also to identify laminar states, i.e. chaos-chaos transitions. The
traditional recurrence quantification analysis fails to detect the latter
transitions. Applying our new measures to the heart rate variability data, we
are able to detect and quantify the laminar phases before a life-threatening
cardiac arrhythmia occurs thereby facilitating a prediction of such an event.
Our findings could be of importance for the therapy of malignant cardiac
arrhythmias
Non-Markov stochastic dynamics of real epidemic process of respiratory infections
The study of social networks and especially of the stochastic dynamics of the
diseases spread in human population has recently attracted considerable
attention in statistical physics. In this work we present a new statistical
method of analyzing the spread of epidemic processes of grippe and acute
respiratory track infections (ARTI) by means of the theory of discrete
non-Markov stochastic processes. We use the results of our last theory (Phys.
Rev. E 65, 046107 (2002)) to study statistical memory effects, long - range
correlation and discreteness in real data series, describing the epidemic
dynamics of human ARTI infections and grippe. We have carried out the
comparative analysis of the data of the two infections (grippe and ARTI) in one
of the industrial districts of Kazan, one of the largest cities of Russia. The
experimental data are analyzed by the power spectra of the initial time
correlation function and the memory functions of junior orders, the phase
portraits of the four first dynamic variables, the three first points of the
statistical non-Markov parameter and the locally averaged kinetic and
relaxation parameters. The received results give an opportunity to provide
strict quantitative description of the regular and stochastic components in
epidemic dynamics of social networks taking into account their time
discreteness and effects of statistical memory. They also allow to reveal the
degree of randomness and predictability of the real epidemic process in the
specific social network.Comment: 18 pages, 8figs, 1 table
Extended Recurrence Plot Analysis and its Application to ERP Data
We present new measures of complexity and their application to event related
potential data. The new measures base on structures of recurrence plots and
makes the identification of chaos-chaos transitions possible. The application
of these measures to data from single-trials of the Oddball experiment can
identify laminar states therein. This offers a new way of analyzing
event-related activity on a single-trial basis.Comment: 21 pages, 8 figures; article for the workshop ''Analyzing and
Modelling Event-Related Brain Potentials: Cognitive and Neural Approaches``
at November 29 - December 01, 2001 in Potsdam, German
Wavelet analysis of epileptic spikes
Interictal spikes and sharp waves in human EEG are characteristic signatures
of epilepsy. These potentials originate as a result of synchronous,
pathological discharge of many neurons. The reliable detection of such
potentials has been the long standing problem in EEG analysis, especially after
long-term monitoring became common in investigation of epileptic patients. The
traditional definition of a spike is based on its amplitude, duration,
sharpness, and emergence from its background. However, spike detection systems
built solely around this definition are not reliable due to the presence of
numerous transients and artifacts. We use wavelet transform to analyze the
properties of EEG manifestations of epilepsy. We demonstrate that the behavior
of wavelet transform of epileptic spikes across scales can constitute the
foundation of a relatively simple yet effective detection algorithm.Comment: 4 pages, 3 figure
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