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The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich. For medium and large coupling strengths, we find spatially periodic,…
Understanding the latent causal factors of a dynamical system from visual observations is considered a crucial step towards agents reasoning in complex environments. In this paper, we propose CITRIS, a variational autoencoder framework that…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
This article investigates correlational properties of two-dimensional chaotic maps on the unit circle. We give analytical forms of higher-order covariances. We derive the characteristic function of their simultaneous and lagged ergodic…
Graphs are commonly used to represent and visualize causal relations. For a small number of variables, this approach provides a succinct and clear view of the scenario at hand. As the number of variables under study increases, the graphical…
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…
Gradient-based causal discovery shows great potential for deducing causal structure from data in an efficient and scalable way. Those approaches however can be susceptible to distributional biases in the data they are trained on. We…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…
We study a finite uni-directional array of "cascading" or "threshold coupled" chaotic maps. Such systems have been proposed for use in nonlinear computing and have been applied to classification problems in bioinformatics. We describe some…
External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a…
We present a method for generating robust chaos. It is based on the search algorithm weak symmetry violation in the reconstructed attractor. On its basis the smooth functions in the form of a system of finite-difference equations. To ensure…
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during…
Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatio-temporal systems including fluid turbulence is supported by non-chaotic, exactly recurring time-periodic solutions of the…
An important goal across most scientific fields is the discovery of causal structures underling a set of observations. Unfortunately, causal discovery methods which are based on correlation or mutual information can often fail to identify…
This study investigates the application of causal discovery algorithms in equity markets, with a focus on their potential to build investment strategies. An investment strategy was developed based on the causal structures identified by…
Detecting symmetry from data is a fundamental problem in signal analysis, providing insight into underlying structure and constraints. When data emerge as trajectories of dynamical systems, symmetries encode structural properties of the…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
Identifying covariates that modify treatment effects is a central problem in causal inference. Yet existing data-adaptive procedures do not provide finite-sample control over the expected number of false discoveries, risking spurious…
We propose causal isotonic calibration, a novel nonparametric method for calibrating predictors of heterogeneous treatment effects. Furthermore, we introduce cross-calibration, a data-efficient variant of calibration that eliminates the…
Restarting a stochastic search process can accelerate its completion by providing an opportunity to take a more favorable path with each reset. This strategy, known as stochastic resetting, is well studied in random processes. Here, we…