Search results for "Nonlinear dynamic"
showing 10 items of 158 documents
Upport vector machines for nonlinear kernel ARMA system identification.
2006
Nonlinear system identification based on support vector machines (SVM) has been usually addressed by means of the standard SVM regression (SVR), which can be seen as an implicit nonlinear autoregressive and moving average (ARMA) model in some reproducing kernel Hilbert space (RKHS). The proposal of this letter is twofold. First, the explicit consideration of an ARMA model in an RKHS (SVM-ARMA 2k) is proposed. We show that stating the ARMA equations in an RKHS leads to solving the regularized normal equations in that RKHS, in terms of the autocorrelation and cross correlation of the (nonlinearly) transformed input and output discrete time processes. Second, a general class of SVM-based syste…
Estimation of confidence limits for descriptive indexes derived from autoregressive analysis of time series: Methods and application to heart rate va…
2017
The growing interest in personalized medicine requires making inferences from descriptive indexes estimated from individual recordings of physiological signals, with statistical analyses focused on individual differences between/within subjects, rather than comparing supposedly homogeneous cohorts. To this end, methods to compute confidence limits of individual estimates of descriptive indexes are needed. This study introduces numerical methods to compute such confidence limits and perform statistical comparisons between indexes derived from autoregressive (AR) modeling of individual time series. Analytical approaches are generally not viable, because the indexes are usually nonlinear funct…
Are nonlinear model-free conditional entropy approaches for the assessment of cardiac control complexity superior to the linear model-based one?
2016
Objective : We test the hypothesis that the linear model-based (MB) approach for the estimation of conditional entropy (CE) can be utilized to assess the complexity of the cardiac control in healthy individuals. Methods : An MB estimate of CE was tested in an experimental protocol (i.e., the graded head-up tilt) known to produce a gradual decrease of cardiac control complexity as a result of the progressive vagal withdrawal and concomitant sympathetic activation. The MB approach was compared with traditionally exploited nonlinear model-free (MF) techniques such as corrected approximate entropy, sample entropy, corrected CE, two k -nearest-neighbor CE procedures and permutation CE. Electroca…
Advanced computation in cardiovascular physiology: New challenges and opportunities
2021
Recent developments in computational physiology have successfully exploited advanced signal processing and artificial intelligence tools for predicting or uncovering characteristic features of physiological and pathological states in humans. While these advanced tools have demonstrated excellent diagnostic capabilities, the high complexity of these computational 'black boxes’ may severely limit scientific inference, especially in terms of biological insight about both physiology and pathological aberrations. This theme issue highlights current challenges and opportunities of advanced computational tools for processing dynamical data reflecting autonomic nervous system dynamics, with a speci…
Statistical geometric affinity in human brain electric activity
2007
10 pages, 9 figures.-- PACS nrs.: 87.19.La; 05.45.Tp.-- ISI Article Identifier: 000246890100105
Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique
2010
We present an approach, framed in information theory, to assess nonlinear causality between the subsystems of a whole stochastic or deterministic dynamical system. The approach follows a sequential procedure for nonuniform embedding of multivariate time series, whereby embedding vectors are built progressively on the basis of a minimization criterion applied to the entropy of the present state of the system conditioned to its past states. A corrected conditional entropy estimator compensating for the biasing effect of single points in the quantized hyperspace is used to guarantee the existence of a minimum entropy rate at which to terminate the procedure. The causal coupling is detected acc…
Spike train statistics for consonant and dissonant musical accords in a simple auditory sensory model
2010
The phenomena of dissonance and consonance in a simple auditory sensory model composed of three neurons are considered. Two of them, here so-called sensory neurons, are driven by noise and subthreshold periodic signals with different ratio of frequencies, and its outputs plus noise are applied synaptically to a third neuron, so-called interneuron. We present a theoretical analysis with a probabilistic approach to investigate the interspike intervals statistics of the spike train generated by the interneuron. We find that tones with frequency ratios that are considered consonant by musicians produce at the third neuron inter-firing intervals statistics densities that are very distinctive fro…
Stochastic linearization critically re-examined
1997
Abstract The stochastic linearization technique, widely used for the analysis of nonlinear dynamic systems subjected to random excitations, is revisited. It is shown that the standard procedure universally adopted for determining the so-called effective stiffness of the equivalent linear system is erroneous in all previous publications. Two error-free stochastic linearization techniques are elucidated, namely those based on (1) the force linearization and (2) energy linearization.
Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model a…
2019
Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a compr…
Non-linear dynamics of alpha and theta rhythm: correlation dimensions and Lyapunov exponents from healthy subject's spontaneous EEG.
1997
The aim of the present paper was to analyze some non-linear dynamic properties of the resting EEG from healthy subjects under eyes closed conditions. For this purpose we digitally filtered the spontaneous EEG in the theta (3-8 Hz) and alpha frequency range (8-13 Hz) and considered these independent rhythms as signals from a deterministic system. Under certain conditions non-linear dynamic systems are able to generate deterministic chaos, which means that similar causes do not produce similar effects. This phenomenon is called sensitive dependence on initial conditions. From different lead positions (F3, F4, Cz, P3, P4, O1 and O2) we calculated the so-called correlation dimension D2, which i…