@article {10.7717/peerj.8533, title = {Ecosystem antifragility: beyond integrity and resilience}, journal = {PeerJ}, volume = {8}, year = {2020}, pages = {e8533}, abstract = {We review the concept of ecosystem resilience in its relation to ecosystem integrity from an information theory approach. We summarize the literature on the subject identifying three main narratives: ecosystem properties that enable them to be more resilient; ecosystem response to perturbations; and complexity. We also include original ideas with theoretical and quantitative developments with application examples. The main contribution is a new way to rethink resilience, that is mathematically formal and easy to evaluate heuristically in real-world applications: ecosystem antifragility. An ecosystem is antifragile if it benefits from environmental variability. Antifragility therefore goes beyond robustness or resilience because while resilient/robust systems are merely perturbation-resistant, antifragile structures not only withstand stress but also benefit from it.}, keywords = {Antifragility, Complexity, Ecosystem integrity, Resilience}, issn = {2167-8359}, doi = {10.7717/peerj.8533}, url = {https://doi.org/10.7717/peerj.8533}, author = {Equihua, Miguel and Espinosa Aldama, Mariana and Gershenson, Carlos and L{\'o}pez-Corona, Oliver and Mungu{\'\i}a, Mariana and P{\'e}rez-Maqueo, Octavio and Ram{\'\i}rez-Carrillo, Elvia} } @article {Cocho2019, title = {Rank-frequency distribution of natural languages: A difference of probabilities approach}, journal = {Physica A: Statistical Mechanics and its Applications}, volume = {532}, year = {2019}, pages = {121795}, abstract = {In this paper we investigate the time variation of the rank k of words for six Indo-European languages using the Google Books N-gram Dataset. Based on numerical evidence, we regard k as a random variable whose dynamics may be described by a Fokker{\textendash}Planck equation which we solve analytically. For low ranks the distinct languages behave differently, maybe due to the syntax rules, whereas for k>50 the law of large numbers predominates. We analyze the frequency distribution of words using the data and their adjustment in terms of time-dependent probability density distributions. We find small differences between the data and the fits due to conflicting dynamic mechanisms, but the data show a consistent behavior with our general approach. For the lower ranks the behavior of the data changes among languages presumably, again, due to distinct dynamic mechanisms. We discuss a possible origin of these differences and assess the novel features and limitations of our work.}, keywords = {Fokker{\textendash}Planck equation, Languages, Master equation, Rank dynamics}, issn = {0378-4371}, doi = {10.1016/j.physa.2019.121795}, url = {https://doi.org/10.1016/j.physa.2019.121795}, author = {Germinal Cocho and Rosal{\'\i}o F. Rodr{\'\i}guez and Sergio S{\'a}nchez and Jorge Flores and Carlos Pineda and Carlos Gershenson} }