@article{17c3b4fa77c2493dbdea6876bd42a158,

title = "Inference of time-varying networks through transfer entropy, the case of a Boolean network model",

abstract = "Inferring network topologies from the time series of individual units is of paramount importance in the study of biological and social networks. Despite considerable progress, our success in network inference is largely limited to static networks and autonomous node dynamics, which are often inadequate to describe complex systems. Here, we explore the possibility of reconstructing time-varying weighted topologies through the information-theoretic notion of transfer entropy. We focus on a Boolean network model in which the weight of the links and the spontaneous activity periodically vary in time. For slowly-varying dynamics, we establish closed-form expressions for the stationary periodic distribution and transfer entropy between each pair of nodes. Our results indicate that the instantaneous weight of each link is mapped into a corresponding transfer entropy value, thereby affording the possibility of pinpointing the dominant weights at each time. However, comparing transfer entropy readings at different times may provide erroneous estimates of the strength of the links in time, due to a counterintuitive modulation of the information flow by the non-autonomous dynamics. In fact, this time variation should be used to scale transfer entropy values toward the correct inference of the time evolution of the network weights. This study constitutes a necessary step toward a mathematically-principled use of transfer entropy to reconstruct time-varying networks.",

author = "Maurizio Porfiri and {Ruiz Mar{\'i}n}, Manuel",

note = "Funding Information: This work was supported by the National Science Foundation under Grant Nos. CMMI 1433670, CMMI 1561134, and CBET 1547864, the US Army Research Office under Grant No. W911NF-15-1-0267 with Dr. Samuel C. Stanton and Dr. Alfredo Garcia as the program managers, and Ministerio de Economa y Competitividad de Espana and FEDER funds under Grant No. ECO2015-65637-P. This study is part of the collaborative activities carried out under the program Groups of Excellence of the Region of Murcia, the Fundacion Seneca, Science and Technology Agency of the Region of Murcia Project No. 19884/GERM/15. The authors are thankful to Drs. Shinnosuke Nakayama and Rifat Sipahi for useful discussions on seasonal effects and Mr. Alain Boldini for help in checking the calculations. The authors want to express their gratitude to one anonymous reviewer whose constructive feedback has greatly contributed to improve the technical rigor of the paper. Funding Information: This work was supported by the National Science Foundation under Grant Nos. CMMI 1433670, CMMI 1561134, and CBET 1547864, the US Army Research Office under Grant No. W911NF-15-1-0267 with Dr. Samuel C. Stanton and Dr. Alfredo Garcia as the program managers, and Minis-terio de Econom{\'i}a y Competitividad de Espana and FEDER funds under Grant No. ECO2015-65637-P. This study is part of the collaborative activities carried out under the program Groups of Excellence of the Region of Murcia, the Fundacion Seneca, Science and Technology Agency of the Region of Murcia Project No. 19884/GERM/15. The authors are thankful to Drs. Shinnosuke Nakayama and Rifat Sipahi for useful discussions on seasonal effects and Mr. Alain Boldini for help in checking the calculations. The authors want to express their gratitude to one anonymous reviewer whose constructive feedback has greatly contributed to improve the technical rigor of the paper. Publisher Copyright: {\textcopyright} 2018 Author(s).",

year = "2018",

month = oct,

day = "1",

doi = "10.1063/1.5047429",

language = "English (US)",

volume = "28",

journal = "Chaos",

issn = "1054-1500",

publisher = "American Institute of Physics Publising LLC",

number = "10",

}