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→Simplification of Markov chains
For specific methods of coarse-graining Markov chains, please refer to coarse-graining of Markov chains.
For specific methods of coarse-graining Markov chains, please refer to coarse-graining of Markov chains.
==References==
<references />
==Editor's Recommendation==
Here are some links that can help readers better understand the relevant information of causal emergence:
===Causal Emergence Reading Club===
*[https://campus.swarma.org/course/3110 Introduction to the Causal Emergence Reading Club]
[[File:Reading Club deepens our understanding of concepts such as causality and emergence by reading frontier literature; focuses on finding research directions that combine concepts such as causality and emergence, and multi-scale; and explores the research direction of multi-scale automatic modeling of complex systems..jpg|Thumbnail|370x370px|Reading Club deepens our understanding of concepts such as causality and emergence by reading frontier literature; focuses on finding research directions that combine concepts such as causality and emergence, and multi-scale; and explores the research direction of multi-scale automatic modeling of complex systems.]]Share some recently developed theories and tools, including causal emergence theory, machine learning-driven renormalization technology, and a cross-scale analysis framework being developed by self-referential dynamics.
*[https://pattern.swarma.org/study_group/7 Causal Emergence Reading Club Season 1]
Emergence phenomenon is undoubtedly one of the most mysterious phenomena among many phenomena in complex systems. The "causal emergence" theory proposed by Erik Hoel provides a new possible explanatory approach for this wonderful cross-level emergence phenomenon. Through cross-level coarse-graining (or renormalization) operations, we can obtain completely different dynamics on the same dynamic system at different scales. Through the review of this season's reading club, we hope to explore the frontier progress in this emerging field and derive more new research topics.
*[https://pattern.swarma.org/study_group/16 Causal Emergence Reading Club Season 2]
The combination of emergence and causality creates the concept of causal emergence. This is a theoretical system that uses causality to quantitatively characterize emergence. In this season's reading club, by reading frontier literature, we deepen our understanding of concepts such as causality and emergence; focus on finding research directions that combine concepts such as causality and emergence, and multi-scale; and explore the research direction of multi-scale automatic modeling of complex systems. The second season reading club is more focused on discussing the relationship between causal science and causal emergence, and quantitatively characterizing emergence, focusing on finding research directions that combine concepts such as causality and emergence, and multi-scale; and exploring the research direction of multi-scale automatic modeling of complex systems.
*[https://pattern.swarma.org/study_group/28 Causal Emergence Reading Club Season 3]
In the third season reading club of causal emergence, we will further conduct in-depth learning and discussion around the core research questions of causal emergence, namely "the definition of causal emergence" and "the identification of causal emergence". We will conduct in-depth discussions and analyses on the core theories of causal emergence such as Causal Emergence and Causal Geometry proposed by Erik Hoel, and carefully sort out the methodologies involved, including learning and drawing on relevant research ideas from other research fields such as dynamic reduction and latent space dynamic learning. Finally, we will discuss the applications of causal emergence, including expanding on issues such as biological networks, brain networks, or emergence detection to explore more practical application scenarios.
===Path Recommendation===
*The learning path about causal emergence sorted out by teacher Zhang Jiang according to the first season of the causal emergence reading club: https://pattern.swarma.org/article/153
*The entry path of causal emergence sorted out by teacher Zhang Jiang based on the first five seasons of the causal emergence reading club: https://pattern.swarma.org/article/296.
This entry is written by [[Wang Zhipeng]], [[Zhang Jiang]], and [[Liu Kaiwei]], and proofread and revised by [[Zhang Jiang]] and [[Wang Zhipeng]].
'''The content of this entry is derived from wikipedia and public materials and complies with the CC3.0 agreement.'''
[[Category:Causal emergence]]
[[Category:Information theory]]
[[Category:Causal measure]]