On the Sufficiency of Pairwise Interactions in Maximum Entropy Models of Networks
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Biological information processing networks consist of many components, which are coupled by an even larger number of complex multivariate interactions. However, analyses of data sets from fields as diverse as neuroscience, molecular biology, and behavior have reported that observed statistics of states of some biological networks can be approximated well by maximum entropy models with only pairwise interactions among the components. Based on simulations of random Ising spin networks with p-spin (\(p>2\)) interactions, here we argue that this reduction in complexity can be thought of as a natural property of densely interacting networks in certain regimes, and not necessarily as a special property of living systems. By connecting our analysis to the theory of random constraint satisfaction problems, we suggest a reason for why some biological systems may operate in this regime.
KeywordsCollective dynamics p-spin models Numerical simulations
We thank Aly Pesic and Daniel Holz, who helped during the early stages of this project, Arthur Lander and Chris Myers, who suggested a possible link to evolution, and Thierry Mora, Aleksandra Walczak, and Gasper Tkacik for useful discussions. We also thank the anonymous referees for their insightful comments. We are grateful to the Emory College Emerson Center for Scientific Computing and its funders for the help with numerical simulations. The authors were partially supported by the James S. McDonnell foundation Complex Systems award, by the Human Frontiers Science Program, and by the National Science Foundation.
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