Related papers: Causal Emergence in Discrete and Continuous Dynami…
The study of causal structure in complex systems has gained increasing attention, with many recent studies exploring causal networks that capture cause-effect relationships across diverse fields. Despite increasing empirical evidence…
Consciousness spans macroscopic experience and microscopic neuronal activity, yet linking these scales remains challenging. Prevailing theories, such as Integrated Information Theory, focus on a single scale, overlooking how causal power…
The classic studies of causal emergence have revealed that in some Markovian dynamical systems, far stronger causal connections can be found on the higher-level descriptions than the lower-level of the same systems if we coarse-grain the…
Classical causal models, such as Granger causality and structural equation modeling, are largely restricted to acyclic interactions and struggle to represent cyclic and higher-order dynamics in complex networks. We introduce a causal…
We present a theory of causality in dynamical systems using Koopman operators. Our theory is grounded on a rigorous definition of causal mechanism in dynamical systems given in terms of flow maps. In the Koopman framework, we prove that…
Microbial ecosystems exhibit a surprising amount of functionally relevant diversity at all levels of taxonomic resolution, presenting a significant challenge for most modeling frameworks. A long-standing hope of theoretical ecology is that…
We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of…
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…
Emergence in machine learning refers to the spontaneous appearance of complex behaviors or capabilities that arise from the scale and structure of training data and model architectures, despite not being explicitly programmed. We introduce…
Emergent behavior in complex systems arises from nonlinear interactions among components, yet the intricate nature of self-organization often obscures the underlying causal relationships, long regarded as the "holy grail" of complexity…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
Causal phenomena associated with rare events occur across a wide range of engineering problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal…
Most work on causality in machine learning assumes that causal relationships are driven by a constant underlying process. However, the flexibility of agents' actions or tipping points in the environmental process can change the qualitative…
Emergent effect is crucial to understanding the properties of complex systems that do not appear in their basic units, but there has been a lack of theories to measure and understand its mechanisms. In this paper, we consider emergence as a…
Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic,…
Complex systems universally exhibit emergence, where macroscopic dynamics arise from local interactions, but a predictive law governing this process has been absent. We establish and verify such a law. We define a system's causal power at a…
Understanding the functional architecture of complex systems is crucial to illuminate their inner workings and enable effective methods for their prediction and control. Recent advances have introduced tools to characterise emergent…
Causal reasoning is essential for understanding decision-making about the behaviour of complex `ecosystems' of systems that underpin modern society, with security -- including issues around correctness, safety, resilience, etc. -- typically…
Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A…
The dynamic instability of the living systems and the "superposition" of different forms of randomness are viewed as a component of the contingently increasing organization of life along evolution. We briefly survey how classical and…