Related papers: Differential symbolic entropy in nonlinear dynamic…

The identification of complex periodic windows in the two-dimensional parameter space of certain dynamical systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic…

Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down…

It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…

The histogram is a key method for visualizing data and estimating the underlying probability distribution. Incorrect conclusions about the data result from over or under-binning. A new method based on the Shannon entropy of the histogram…

The information detection of complex systems from data is currently undergoing a revolution, driven by the emergence of big data and machine learning methodology. Discovering governing equations and quantifying dynamical properties of…

This paper considers the problem of appearance indication of useful acoustic signal in the signal/noise mixture. Various information characteristics (information entropy, Jensen-Shannon divergence, spectral information divergence and…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…

The theoretical explanation for deep neural network (DNN) is still an open problem. In this paper DNN is considered as a discrete-time dynamical system due to its layered structure. The complexity provided by the nonlinearity in the…

Non-deterministic chaos is a form of low-dimensional dynamics which is characterized by the existence of a countable set of {\em sensitive decision points} (SDP's). Away from these points, the dynamics is well-behaved. Near these points,…

The structure of a complex network plays a crucial role in determining its dynamical properties. In this work, we show that the the degree to which a network is directed and hierarchically organised is closely associated with the degree to…

We measure the influence of different time-scales on the dynamics of financial market data. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying…

The analysis of chaotic signals with time-frequency methods is considered. For this purpose, two new transformations are presented which consist in the decomposition of a signal onto an orthogonal set of respectively linear and hyperbolic…

The problem of defining and studying complexity of a time series has interested people for years. In the context of dynamical systems, Grassberger has suggested that a slow approach of the entropy to its extensive asymptotic limit is a sign…

Traditional system identification with multisine inputs relies on uniform sampling and periodic excitation to preserve Fourier orthogonality and avoid spectral leakage, limiting its use in scenarios with irregular sampling or nonperiodic…

An efficient technique is introduced for model inference of complex nonlinear dynamical systems driven by noise. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is…

This paper introduces a new fundamental characteristic, \ie, the dynamic range, from real-world metric tools to deep visual recognition. In metrology, the dynamic range is a basic quality of a metric tool, indicating its flexibility to…

The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…

There is a whole range of emergent phenomena in non-equilibrium behaviors can be well described by a set of stochastic differential equations. Inspired by an insight gained during our study of robustness and stability in phage lambda…

Ensuring reliable data collection in large-scale particle physics experiments demands Data Quality Monitoring (DQM) procedures to detect possible detector malfunctions and preserve data integrity. Traditionally, this resource-intensive task…

Process anomaly detection is an important application of process mining for identifying deviations from the normal behavior of a process. Neural network-based methods have recently been applied to this task, learning directly from event…