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Parametric correlations of energy spectra of quantum chaotic systems are presented in the orthogonal-unitary and symplectic-unitary crossover region. The spectra are allowed to disperse as a function of two external perturbations: one of…
Causal discovery problems use a set of observations to deduce causality between variables in the real world, typically to answer questions about biological or physical systems. These observations are often recorded at regular time…
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques,…
We propose a general method for the construction and analysis of unweighted $\epsilon$ - recurrence networks from chaotic time series. The selection of the critical threshold $\epsilon_c$ in our scheme is done empirically and we show that…
In this paper, we consider the problem of causal order discovery within the framework of monotonic Structural Causal Models (SCMs), which have gained attention for their potential to enable causal inference and causal discovery from…
Three state-space based methods were tested in relation to the ability to detect unidirectional coupling and synchronization of interconnected dynamical systems. The first method, based on measure named M, was introduced by Andrzejak et al.…
From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to itself. Interesting dynamics arise on the invariant diagonal,…
We use the cross correlation sum introduced recently by H. Kantz to study symmetry properties of chaotic attractors. In particular, we apply it to a system of six coupled nonlinear oscillators which was shown by Kroon et al. to have…
Understanding causal relationships among features is fundamental for explaining machine learning model decisions. However, traditional causal discovery methods face challenges with categorical variables due to numerical instability in…
Learning causal relationships between pairs of complex traits from observational studies is of great interest across various scientific domains. However, most existing methods assume the absence of unmeasured confounding and restrict causal…
Understanding causal relationships within a system is crucial for uncovering its underlying mechanisms. Causal discovery methods, which facilitate the construction of such models from time-series data, hold the potential to significantly…
Causal discovery from data affected by latent confounders is an important and difficult challenge. Causal functional model-based approaches have not been used to present variables whose relationships are affected by latent confounders,…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
Discovering causal relationships in complex multivariate time series is a fundamental scientific challenge. Traditional methods often falter, either by relying on restrictive linear assumptions or on conditional independence tests that…
The idea that chaos could be a useful tool for analyze nonlinear systems considered in this paper and for the first time the two time scale property of singularly perturbed systems is analyzed on chaotic attractor. The general idea…
Causality defines the relationship between cause and effect. In multivariate time series field, this notion allows to characterize the links between several time series considering temporal lags. These phenomena are particularly important…
We study a deterministic dynamics with two time scales in a continuous state attractor network. To the usual (fast) relaxation dynamics towards point attractors (``patterns'') we add a slow coupling dynamics that makes the visited patterns…
This paper focuses on causal structure estimation from time series data in which measurements are obtained at a coarser timescale than the causal timescale of the underlying system. Previous work has shown that such subsampling can lead to…
This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the…
Inferring causal relationships from observational data is rarely straightforward, but the problem is especially difficult in high dimensions. For these applications, causal discovery algorithms typically require parametric restrictions or…