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An acyclic causal structure can be described with directed acyclic graph (DAG), where arrows indicate the possibility of direct causation. The task of learning this structure from data is known as "causal discovery." Diverse populations or…
Nowadays, the need for causal discovery is ubiquitous. A better understanding of not just the stochastic dependencies between parts of a system, but also the actual cause-effect relations, is essential for all parts of science. Thus, the…
In the present study, we investigate the dynamics of impulsive differential equations driven by a chaotic system. We rigorously prove that, likewise the drive, the response impulsive system is also chaotic. Our results are based on the…
Synchronization of chaos arises between coupled dynamical systems and is very well understood as a temporal phenomena which leads the coupled systems to converge or develop a dependence with time. In this work, we provide a complementary…
Real world systems evolve in continuous-time according to their underlying causal relationships, yet their dynamics are often unknown. Existing approaches to learning such dynamics typically either discretize time -- leading to poor…
The Nikolaevskiy model for pattern formation with continuous symmetry exhibits spatiotemporal chaos with strong scale separation. Extensive numerical investigations of the chaotic attractor reveal unexpected scaling behavior of the…
We present a sound and complete algorithm, called iterative causal discovery (ICD), for recovering causal graphs in the presence of latent confounders and selection bias. ICD relies on the causal Markov and faithfulness assumptions and…
The ability to understand causality from data is one of the major milestones of human-level intelligence. Causal Discovery (CD) algorithms can identify the cause-effect relationships among the variables of a system from related…
In this paper, based on the classic Chua's circuit, a charge-controlled memristor is introduced to design a novel four-dimensional chaotic system. The complex dynamics of the novel chaotic system such as equilibrium points, stability,…
Convergent Cross-Mapping (CCM) has shown high potential to perform causal inference in the absence of models. We assess the strengths and weaknesses of the method by varying coupling strength and noise levels in coupled logistic maps. We…
The study of cause-and-effect is of the utmost importance in many branches of science, but also for many practical applications of intelligent systems. In particular, identifying causal relationships in situations that include hidden…
We write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with M statistically equivalent channels at nonideal coupling to that for ideal coupling. Unfolding the phases by…
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated…
For low-dimensional chaotic attractors there is usually a single number of unstable dimensions for all of its periodic orbits and we can say such attractors exhibit "mono-chaos". In high-dimensional chaotic attractors, trajectories are…
Identifying causality is fundamental for human understanding of the world, where complex non-autonomous systems such as species population changes, brain activities, etc. are extensively existed. Since the phase spaces of such systems are…
We introduce Causal Computational Asymmetry (CCA), a principle for causal direction identification based on optimization dynamics in which one neural network is trained to predict $Y$ from $X$ and another to predict $X$ from $Y$, and the…
Change point detection in time series aims to identify moments when the probability distribution of time series changes. It is widely applied in many areas, such as human activity sensing and medical science. In the context of multivariate…
In this work, we relate the geometry of chaotic attractors of typical analytic unimodal maps to the behavior of the critical orbit. Our main result is an explicit formula relating the combinatorics of the critical orbit with the exponents…
To uncover the city's fundamental functioning mechanisms, it is important to acquire a deep understanding of complicated relationships among citizens, location, and mobility behaviors. Previous research studies have applied direct…
The method of generating of high-dimensional oscillations on the basis of summing of low-dimensional chaotic signals of noncoupled dynamical systems is investigated. It is shown that the correlation dimension of attractor reconstructed from…