Dynamical Theory for Adaptive Systems
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910829152043008 |
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| author | Pham, Tuan Minh Kaneko, Kunihiko |
| author_facet | Pham, Tuan Minh Kaneko, Kunihiko |
| contents | The study of adaptive dynamics, involving many degrees of freedom on two separated timescales, one for fast changes of state variables and another for the slow adaptation of parameters controlling the former's dynamics is crucial for understanding feedback mechanisms underlying evolution and learning. We present a path-integral approach à la Martin-Siggia-Rose-De Dominicis-Janssen (MSRDJ) to analyse nonequilibrium phase transitions in such dynamical systems. As an illustration, we apply our framework to the adaptation of gene-regulatory networks under a dynamic genotype-phenotype map: phenotypic variations are shaped by the fast stochastic gene-expression dynamics and are coupled to the slowly evolving distribution of genotypes, each encoded by a network structure. We establish that under this map, genotypes corresponding to reciprocal networks of coherent feedback loops are selected within an intermediate range of environmental noise, leading to phenotypic robustness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_01403 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamical Theory for Adaptive Systems Pham, Tuan Minh Kaneko, Kunihiko Populations and Evolution Disordered Systems and Neural Networks Adaptation and Self-Organizing Systems Biological Physics The study of adaptive dynamics, involving many degrees of freedom on two separated timescales, one for fast changes of state variables and another for the slow adaptation of parameters controlling the former's dynamics is crucial for understanding feedback mechanisms underlying evolution and learning. We present a path-integral approach à la Martin-Siggia-Rose-De Dominicis-Janssen (MSRDJ) to analyse nonequilibrium phase transitions in such dynamical systems. As an illustration, we apply our framework to the adaptation of gene-regulatory networks under a dynamic genotype-phenotype map: phenotypic variations are shaped by the fast stochastic gene-expression dynamics and are coupled to the slowly evolving distribution of genotypes, each encoded by a network structure. We establish that under this map, genotypes corresponding to reciprocal networks of coherent feedback loops are selected within an intermediate range of environmental noise, leading to phenotypic robustness. |
| title | Dynamical Theory for Adaptive Systems |
| topic | Populations and Evolution Disordered Systems and Neural Networks Adaptation and Self-Organizing Systems Biological Physics |
| url | https://arxiv.org/abs/2306.01403 |