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Fumito Mori, Hiroshi Kori, Noninvasive inference methods for interaction and noise intensities of coupled oscillators using only spike time data, *Proceedings of the National Academy of Sciences*, 10.1073/pnas.2113620119, 119, 6, e2113620119-e2113620119, 2022.02, Measurements of interaction intensity are generally achieved by observing responses to perturbations. In biological and chemical systems, external stimuli tend to deteriorate their inherent nature, and thus, it is necessary to develop noninvasive inference methods. In this paper, we propose theoretical methods to infer coupling strength and noise intensity simultaneously in two well-synchronized noisy oscillators through observations of spontaneously fluctuating events such as neural spikes. A phase oscillator model is applied to derive formulae relating each of the parameters to spike time statistics. Using these formulae, each parameter is inferred from a specific set of statistics. We verify these methods using the FitzHugh–Nagumo model as well as the phase model. Our methods do not require external perturbations and thus can be applied to various experimental systems.. |

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Fumito Mori, Atsushi Mochizuki, Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology, *PHYSICAL REVIEW LETTERS*, 10.1103/PhysRevLett.119.028301, 119, 2, 2017.07, Boolean network models describe genetic, neural, and social dynamics in complex networks, where the dynamics depend generally on network topology. Fixed points in a genetic regulatory network are typically considered to correspond to cell types in an organism. We prove that the expected number of fixed points in a Boolean network, with Boolean functions drawn from probability distributions that are not required to be uniform or identical, is one, and is independent of network topology if only a feedback arc set satisfies a stochastic neutrality condition. We also demonstrate that the expected number is increased by the predominance of positive feedback in a cycle.. |

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Fumito Mori, Necessary Condition for Frequency Synchronization in Network Structures, *PHYSICAL REVIEW LETTERS*, 10.1103/PhysRevLett.104.108701, 104, 10, 2010.03, We present the necessary condition for complete frequency synchronization of phase-coupled oscillators in network structures. The surface area of a set of sites is defined as the number of links between the sites within the set and those outside the set. The necessary condition is that the surface area of any set of cN (0 infinity. We also provide the necessary condition for macroscopic frequency synchronization. Thus, we identify networks in which one or both of the above mentioned types of synchronization do not occur.. |