@article{Pikovskij2018,
  author    = {Pikovskij, Arkadij},
  title     = {Reconstruction of a random phase dynamics network from observations},
  series = {Physics letters : A},
  volume    = {382},
  journal   = {Physics letters : A},
  number    = {4},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0375-9601},
  doi       = {10.1016/j.physleta.2017.11.012},
  pages     = {147 -- 152},
  year      = {2018},
  abstract  = {We consider networks of coupled phase oscillators of different complexity: Kuramoto-Daido-type networks, generalized Winfree networks, and hypernetworks with triple interactions. For these setups an inverse problem of reconstruction of the network connections and of the coupling function from the observations of the phase dynamics is addressed. We show how a reconstruction based on the minimization of the squared error can be implemented in all these cases. Examples include random networks with full disorder both in the connections and in the coupling functions, as well as networks where the coupling functions are taken from experimental data of electrochemical oscillators. The method can be directly applied to asynchronous dynamics of units, while in the case of synchrony, additional phase resettings are necessary for reconstruction.},
  language  = {en}
}
@article{SysoevPonomarenkoPikovskij2017,
  author    = {Sysoev, Ilya V. and Ponomarenko, Vladimir I. and Pikovskij, Arkadij},
  title     = {Reconstruction of coupling architecture of neural field networks from vector time series},
  series = {Communications in nonlinear science \& numerical simulation},
  volume    = {57},
  journal   = {Communications in nonlinear science \& numerical simulation},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {1007-5704},
  doi       = {10.1016/j.cnsns.2017.10.006},
  pages     = {342 -- 351},
  year      = {2017},
  abstract  = {We propose a method of reconstruction of the network coupling matrix for a basic voltage-model of the neural field dynamics. Assuming that the multivariate time series of observations from all nodes are available, we describe a technique to find coupling constants which is unbiased in the limit of long observations. Furthermore, the method is generalized for reconstruction of networks with time-delayed coupling, including the reconstruction of unknown time delays. The approach is compared with other recently proposed techniques.},
  language  = {en}
}