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• W2775993691 abstract "We expand the theory of Hawkes processes to the nonstationary case, in which the mutually exciting point processes receive time-dependent inputs. We derive an analytical expression for the time-dependent correlations, which can be applied to networks with arbitrary connectivity, and inputs with arbitrary statistics. The expression shows how the network correlations are determined by the interplay between the network topology, the transfer functions relating units within the network, and the pattern and statistics of the external inputs. We illustrate the correlation structure using several examples in which neural network dynamics are modeled as a Hawkes process. In particular, we focus on the interplay between internally and externally generated oscillations and their signatures in the spike and rate correlation functions." @default.
• W2775993691 created "2018-01-05" @default.
• W2775993691 creator A5020365810 @default.
• W2775993691 creator A5050330911 @default.
• W2775993691 date "2017-12-26" @default.
• W2775993691 modified "2023-10-15" @default.
• W2775993691 title "Theory of nonstationary Hawkes processes" @default.
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• W2775993691 doi "https://doi.org/10.1103/physreve.96.062314" @default.
• W2775993691 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/29347353" @default.
• W2775993691 hasPublicationYear "2017" @default.
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