{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T21:57:29Z","timestamp":1768514249127,"version":"3.49.0"},"reference-count":75,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T00:00:00Z","timestamp":1599177600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005739","name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","doi-asserted-by":"publisher","award":["PAPIIT projects IN107919 and IV100120"],"award-info":[{"award-number":["PAPIIT projects IN107919 and IV100120"]}],"id":[{"id":"10.13039\/501100005739","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Robustness and evolvability are essential properties to the evolution of biological networks. To determine if a biological network is robust and\/or evolvable, it is required to compare its functions before and after mutations. However, this sometimes takes a high computational cost as the network size grows. Here, we develop a predictive method to estimate the robustness and evolvability of biological networks without an explicit comparison of functions. We measure antifragility in Boolean network models of biological systems and use this as the predictor. Antifragility occurs when a system benefits from external perturbations. By means of the differences of antifragility between the original and mutated biological networks, we train a convolutional neural network (CNN) and test it to classify the properties of robustness and evolvability. We found that our CNN model successfully classified the properties. Thus, we conclude that our antifragility measure can be used as a predictor of the robustness and evolvability of biological networks.<\/jats:p>","DOI":"10.3390\/e22090986","type":"journal-article","created":{"date-parts":[[2020,9,4]],"date-time":"2020-09-04T11:24:24Z","timestamp":1599218664000},"page":"986","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Antifragility Predicts the Robustness and Evolvability of Biological Networks through Multi-Class Classification with a Convolutional Neural Network"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4856-7415","authenticated-orcid":false,"given":"Hyobin","family":"Kim","sequence":"first","affiliation":[{"name":"Biotech Research and Innovation Centre (BRIC), University of Copenhagen (UCPH), 2200 Copenhagen, Denmark"},{"name":"Novo Nordisk Foundation Center for Stem Cell Biology, DanStem, Faculty of Health Sciences, University of Copenhagen, 2200 Copenhagen, Denmark"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6259-1609","authenticated-orcid":false,"given":"Stalin","family":"Mu\u00f1oz","sequence":"additional","affiliation":[{"name":"Institute for Software Technology (IST), Graz University of Technology, 8010 Graz, Austria"}]},{"given":"Pamela","family":"Osuna","sequence":"additional","affiliation":[{"name":"Facult\u00e9 des Sciences et Ing\u00e9nierie, Sorbonne Universit\u00e9, 75005 Paris, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0193-3067","authenticated-orcid":false,"given":"Carlos","family":"Gershenson","sequence":"additional","affiliation":[{"name":"Centro de Ciencias de la Complejidad, Universidad Nacional Aut\u00f3noma de M\u00e9xico, CDMX 04510, Mexico"},{"name":"Instituto de Investigaciones en Matem\u00e1ticas Aplicadas y en Sistemas, Universidad Nacional Aut\u00f3noma de M\u00e9xico, CDMX 04510, Mexico"},{"name":"Department of High Performance Computing, ITMO University, 199034 St. Petersburg, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,4]]},"reference":[{"key":"ref_1","first-page":"1959","article-title":"Perspective: Evolution and detection of genetic robustness","volume":"57","author":"Hermisson","year":"2003","journal-title":"Evolution"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8420","DOI":"10.1073\/pnas.95.15.8420","article-title":"Evolvability","volume":"95","author":"Kirschner","year":"1998","journal-title":"Proc. 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