Search results for "Nonlinear system"
showing 10 items of 1446 documents
MuTE: a MATLAB toolbox to compare established and novel estimators of the multivariate transfer entropy.
2014
A challenge for physiologists and neuroscientists is to map information transfer between components of the systems that they study at different scales, in order to derive important knowledge on structure and function from the analysis of the recorded dynamics. The components of physiological networks often interact in a nonlinear way and through mechanisms which are in general not completely known. It is then safer that the method of choice for analyzing these interactions does not rely on any model or assumption on the nature of the data and their interactions. Transfer entropy has emerged as a powerful tool to quantify directed dynamical interactions. In this paper we compare different ap…
Stochastic Nonlinear Time Series Forecasting Using Time-Delay Reservoir Computers: Performance and Universality
2014
International audience; Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay diFFerential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We …
Non-uniform multivariate embedding to assess the information transfer in cardiovascular and cardiorespiratory variability series
2012
The complexity of the short-term cardiovascular control prompts for the introduction of multivariate (MV) nonlinear time series analysis methods to assess directional interactions reflecting the underlying regulatory mechanisms. This study introduces a new approach for the detection of nonlinear Granger causality in MV time series, based on embedding the series by a sequential, non-uniform procedure, and on estimating the information flow from one series to another by means of the corrected conditional entropy. The approach is validated on short realizations of linear stochastic and nonlinear deterministic processes, and then evaluated on heart period, systolic arterial pressure and respira…
Detecting nonlinear causal interactions between dynamical systems by non-uniform embedding of multiple time series.
2010
This study introduces a new approach for the detection of nonlinear Granger causality between dynamical systems. The approach is based on embedding the multivariate (MV) time series measured from the systems X and Y by means of a sequential, non-uniform procedure, and on using the corrected conditional entropy (CCE) as unpredictability measure. The causal coupling from X to Y is quantified as the relative decrease of CCE measured after allowing the series of X to enter the embedding procedure for the description of Y. The ability of the approach to quantify nonlinear causality is assessed on MV time series measured from simulated dynamical systems with unidirectional coupling (the Rössler-…
Adaptive independent vector analysis for multi-subject complex-valued fMRI data.
2017
Abstract Background Complex-valued fMRI data can provide additional insights beyond magnitude-only data. However, independent vector analysis (IVA), which has exhibited great potential for group analysis of magnitude-only fMRI data, has rarely been applied to complex-valued fMRI data. The main challenges in this application include the extremely noisy nature and large variability of the source component vector (SCV) distribution. New method To address these challenges, we propose an adaptive fixed-point IVA algorithm for analyzing multiple-subject complex-valued fMRI data. We exploited a multivariate generalized Gaussian distribution (MGGD)- based nonlinear function to match varying SCV dis…
Non-linear neuro-inspired circuits and systems: Processing and learning issues
2018
In this chapter the main elements useful for the design and realization of the neural architectures reported in the following chapters will be presented. Considering spiking and non-spiking neurons, the models used for implementing each of them, the synaptic models, the basic learning and plasticity algorithms and the network architectures will be introduced and analysed. The key elements that led to their selection and application in the developed neuro-inspired systems will be discussed briefly.
Parameters analysis of FitzHugh-Nagumo model for a reliable simulation
2014
International audience; Derived from the pioneer ionic Hodgkin-Huxley model and due to its simplicity and richness from a point view of nonlinear dynamics, the FitzHugh-Nagumo model has been one of the most successful neuron / cardiac cell model. It exists many variations of the original FHN model. Though these FHN type models help to enrich the dynamics of the FHN model. The parameters used in these models are often in biased conditions. The related results would be questionable. So, in this study, the aim is to find the parameter thresholds for one of the commonly used FHN model in order to pride a better simulation environment. The results showed at first that inappropriate time step and…
Is the Fisher effect non-linear? some evidence for Spain, 1963–2002
2005
In this paper the role of non-linearities in the relationship between nominal interest rates and inflation is examined, in order to shed some additional light on the mostly unfavourable evidence on the presence of a full Fisher effect. The analysis is applied to the case of Spain for the period 1963–2002, which allows previous results on the subject to be re-examined and extended. The empirical methodology makes use of recent developments on threshold cointegration, so that cointegration between a pair of variables should be expected only once a certain threshold was reached.
On the modeling of nonlinear interactions in large complex systems
2010
Abstract This work deals with the modeling of large systems of interacting entities in the framework of the mathematical kinetic theory for active particles. The contents are specifically focused on the modeling of nonlinear interactions which is one of the most important issues in the mathematical approach to modeling and simulating complex systems, and which includes a learning–hiding dynamics. Applications are focused on the modeling of complex biological systems and on immune competition.
Stochastic response of linear and non-linear systems to α-stable Lévy white noises
2005
Abstract The stochastic response of linear and non-linear systems to external α -stable Levy white noises is investigated. In the literature, a differential equation in the characteristic function (CF) of the response has been recently derived for scalar systems only, within the theory of the so-called fractional Einstein–Smoluchowsky equations (FESEs). Herein, it is shown that the same equation may be built by rules of stochastic differential calculus, previously applied by one of the authors to systems driven by arbitrary delta-correlated processes. In this context, a straightforward formulation for multi-degree-of-freedom (MDOF) systems is also developed. Approximate CF solutions to the …