What is it about?

Complex structures in nature often arises from a limited set of simpler elements, such as novels from letters or proteins from amino acids. In musical composition, for example, we experience such construction in time; sounds and silences combine to form motifs; motifs form passages, which in turn form movements. But how can we generally identify nearly conserved long-lived structures from complex dynamics which are measured only incompletely? We introduce a novel framework for the identification of maximally-predictive states, from which we can identify long-lived structures through decomposing the ensemble dynamics into macroscopic structures that evolve on different timescales.

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Why is it important?

Our framework allows us to distil the variables that accurately capture large scale phenomena, which is a fundamental step towards providing simplified interpretable models of complex dynamics.

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This page is a summary of: Maximally predictive states: From partial observations to long timescales, Chaos An Interdisciplinary Journal of Nonlinear Science, February 2023, American Institute of Physics, DOI: 10.1063/5.0129398.
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