The Causal Interaction between Complex Subsystems
Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the <i>bulk</i> information flow between two complex subsystems of a large-dimensional parental system....
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/1/3 |
| _version_ | 1827665703058014208 |
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| author | X. San Liang |
| author_facet | X. San Liang |
| author_sort | X. San Liang |
| collection | DOAJ |
| description | Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the <i>bulk</i> information flow between two complex subsystems of a large-dimensional parental system. Analytical formulas have been obtained in a closed form. Under a Gaussian assumption, their maximum likelihood estimators have also been obtained. These formulas have been validated using different subsystems with preset relations, and they yield causalities just as expected. On the contrary, the commonly used proxies for the characterization of subsystems, such as averages and principal components, generally do not work correctly. This study can help diagnose the emergence of patterns in complex systems and is expected to have applications in many real world problems in different disciplines such as climate science, fluid dynamics, neuroscience, financial economics, etc. |
| first_indexed | 2024-03-10T01:31:50Z |
| format | Article |
| id | doaj.art-9e2456e46d4245dd9c1b2128a0e90e3d |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T01:31:50Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-9e2456e46d4245dd9c1b2128a0e90e3d2023-11-23T13:40:17ZengMDPI AGEntropy1099-43002021-12-01241310.3390/e24010003The Causal Interaction between Complex SubsystemsX. San Liang0Department of Atmospheric & Oceanic Sciences, Institute of Atmospheric Sciences, Fudan University, Shanghai 200438, ChinaInformation flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the <i>bulk</i> information flow between two complex subsystems of a large-dimensional parental system. Analytical formulas have been obtained in a closed form. Under a Gaussian assumption, their maximum likelihood estimators have also been obtained. These formulas have been validated using different subsystems with preset relations, and they yield causalities just as expected. On the contrary, the commonly used proxies for the characterization of subsystems, such as averages and principal components, generally do not work correctly. This study can help diagnose the emergence of patterns in complex systems and is expected to have applications in many real world problems in different disciplines such as climate science, fluid dynamics, neuroscience, financial economics, etc.https://www.mdpi.com/1099-4300/24/1/3bulk information flowcomplex systemcausalitysubspacenetworks of networks |
| spellingShingle | X. San Liang The Causal Interaction between Complex Subsystems Entropy bulk information flow complex system causality subspace networks of networks |
| title | The Causal Interaction between Complex Subsystems |
| title_full | The Causal Interaction between Complex Subsystems |
| title_fullStr | The Causal Interaction between Complex Subsystems |
| title_full_unstemmed | The Causal Interaction between Complex Subsystems |
| title_short | The Causal Interaction between Complex Subsystems |
| title_sort | causal interaction between complex subsystems |
| topic | bulk information flow complex system causality subspace networks of networks |
| url | https://www.mdpi.com/1099-4300/24/1/3 |
| work_keys_str_mv | AT xsanliang thecausalinteractionbetweencomplexsubsystems AT xsanliang causalinteractionbetweencomplexsubsystems |