Related papers: Ordinal Patterns in the Duffing Oscillator: Analyz…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
White noise is a fundamental and fairly well understood stochastic process that conforms the conceptual basis for many other processes, as well as for the modeling of time series. Here we push a fresh perspective toward white noise that,…
In this communication, the approach of phenomenological universalities of growth are considered to describe the behaviour of a system showing oscillatory growth. Two phenomenological classes are proposed to consider the behaviour of a…
Specially customised Entropies are widely applied in measuring the degree of uncertainties existing in the frame of discernment. However, all of these entropies regard the frame as a whole that has already been determined which dose not…
We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can…
Research on the distribution of prime numbers has revealed a dual character: deterministic in definition yet exhibiting statistical behavior reminiscent of random processes. In this paper we show that it is possible to use an image-focused…
Determinantal point processes (DPPs) are probability models over subsets of a ground set that favor diverse selections while suppressing redundancy. That is, they tend to assign higher likelihood to collections whose elements complement one…
Identifying structural parameters in linear simultaneous-equation models is a longstanding challenge. Recent work exploits information in higher-order moments of non-Gaussian data. In this literature, the structural errors are typically…
The asymmetrically forced, damped Duffing oscillator is introduced as a prototype model for analyzing the homoclinic tangle of symmetric dissipative systems with \textit{symmetry breaking} disturbances. Even a slight fixed asymmetry in the…
Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…
This paper introduces a framework for modeling cyclical and feedback-driven information flow through a generalized family of entropy-modulated transformations called derangetropy functionals. Unlike scalar and static entropy measures such…
We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric, objective, and the required data processing is parsimonious. Main ingredients are a…
Estimation of permutation entropy (PE) using Bayesian statistical methods is presented for systems where the ordinal pattern sampling follows an independent, multinomial distribution. It is demonstrated that the PE posterior distribution is…
Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of…
A general, variational approach to derive low-order reduced systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes the more classical notions of invariant or slow manifold when…
We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral…
Distinguishing cause from effect is a scientific challenge resisting solutions from mathematics, statistics, information theory and computer science. Compression-Complexity Causality (CCC) is a recently proposed interventional measure of…
In [Haruna, T. and Nakajima, K., 2011. Physica D 240, 1370-1377], the authors introduced the duality between values (words) and orderings (permutations) as a basis to discuss the relationship between information theoretic measures for…
Out-of-time-order correlators (OTOCs) are central probes of quantum scrambling, and their generalizations have recently become key primitives for both benchmarking quantum advantage and learning the structure of Hamiltonians. Yet their…
We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.