ReviewPLoS computational biology2020
Climbing Escher's stairs: A way to approximate stability landscapes in multidimensional systems.
Review in PLoS computational biology, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- Towards Operationalizing Ecological Resilience for Infrastructure Decision-Making.Risk analysis : an official publication of the Society for Risk Analysis · 2026Article
- Reconstructing community dynamics from limited observations.Microbiome · 2026Article
- Modeling cell populations metabolism and competition under maximum power constraints.PLoS computational biology · 2023Article
- Roadmap on plasticity and epigenetics in cancer.Physical biology · 2022Review
- Evolutionary dynamics, evolutionary forces, and robustness: A nonequilibrium statistical mechanics perspective.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
- Kelp-forest dynamics controlled by substrate complexity.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
- Dissecting transition cells from single-cell transcriptome data through multiscale stochastic dynamics.Nature communications · 2021Article
- State-Dependent Regulation of Cortical Processing Speed via Gain Modulation.The Journal of neuroscience : the official journal of the Society for Neuroscience · 2021Article
- Evaluating the performance of multivariate indicators of resilience loss.Scientific reports · 2021Article
- Critical Transitions in Ecosystems and Society. The Contribution of Sociological Systems Theory to the Analysis of Socio-Environmental Transformations.Frontiers in sociology · 2021Article
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Authors and funding
3 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Stability landscapes are useful for understanding the properties of dynamical systems. These landscapes can be calculated from the system's dynamical equations using the physical concept of scalar potential. Unfortunately, it is well known that for most systems with two or more state variables such potentials do not exist. Here we use an analogy with art to provide an accessible explanation of why this happens and briefly review some of the possible alternatives. Additionally, we introduce a novel and simple computational tool that implements one of those solutions: the decomposition of the differential equations into a gradient term, that has an associated potential, and a non-gradient term, that lacks it. In regions of the state space where the magnitude of the non-gradient term is small compared to the gradient part, we use the gradient term to approximate the potential as quasi-potential. The non-gradient to gradient ratio can be used to estimate the local error introduced by our approximation. Both the algorithm and a ready-to-use implementation in the form of an R package are provided.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.