Related papers: Differential symbolic entropy in nonlinear dynamic…
Neural networks excel at pattern recognition but struggle with constraint reasoning -- determining whether configurations satisfy logical or physical constraints. We introduce Differentiable Symbolic Planning (DSP), a neural architecture…
Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are ``noisy'', heterogeneous and exhibit different types of…
In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…
The seismocardiographic signal is a promising alternative to the traditional ECG in the analysis of the cardiac activity. In particular, the systolic complex is known to be the most informative part of the seismocardiogram, thus requiring…
In current clinical practice, electroencephalograms (EEG) are reviewed and analyzed by well-trained neurologists to provide supports for therapeutic decisions. The way of manual reviewing is labor-intensive and error prone. Automatic and…
We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative weights in a given time series. Two different tools have been advanced in the literature to such effect, namely, i) the…
We give piecewise affine maps on the unit cube whose symbolic representation is the Dyck shift. This leads to a different way of verifying the chaotic nature of this system, including the computation of entropy.
A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…
Objectives: With the technological advancements in the field of tele-health monitoring, it is now possible to gather huge amounts of electro-physiological signals such as electrocardiogram (ECG). It is therefore necessary to develop…
A practical measure for the complexity of sequences of symbols (``strings'') is introduced that is rooted in automata theory but avoids the problems of Kolmogorov-Chaitin complexity. This physical complexity can be estimated for ensembles…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…
An approach to generate the pseudorandom-bit sequence from the asymptotic deterministic randomness system is proposed in this Letter. We study the characteristic of multi-value correspondence of the asymptotic deterministic randomness…
We introduce a two-stage multitask learning framework for analyzing Electroencephalography (EEG) signals that integrates denoising, dynamical modeling, and representation learning. In the first stage, a denoising autoencoder is trained to…
A nonparametric kernel density estimator for directional-linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions…
Approximate entropy (ApEn) has been widely used as an estimator of regularity in many scientific fields. It has proved to be a useful tool because of its ability to distinguish different system's dynamics when there is only available…
How does the information flow between different brain regions during various stimuli? This is the question we aim to address by studying complex cognitive paradigms in terms of Information Theory. To assess creativity and the emergence of…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
In this paper a new method of detection of homogeneous zones and singularity parts of a 1D signal is proposed. The entropy function is used to transform signal in piecewise linear one. The multiple regression permits to detect lines and…
Systems with time-delayed chaotic dynamics are common in nature, from control theory to aeronautical propulsion. The overarching objective of this paper is to compute the stability properties of a chaotic dynamical system, which is…