1,270 research outputs found
Comment on "Dynamic range of nanotube- and nanowire-based electromechanical systems"
We investigate the role of quantum effects (e.g. zero-point energy
fluctuations) in the physics of nanotube- and nanowire-based electromechanical
sensors as discussed in a recent article [Postma et al., Appl. Phys. Lett. 86,
223105 (2005)]. Employing the quantum fluctuation-dissipation theorem we find
that these effects pose additional limits on the dynamic range of
nanomechanical resonators.Comment: 1 page, 1 figure, Appl. Phys. Lett. (in print
Cumulants of Hawkes point processes
We derive explicit, closed-form expressions for the cumulant densities of a
multivariate, self-exciting Hawkes point process, generalizing a result of
Hawkes in his earlier work on the covariance density and Bartlett spectrum of
such processes. To do this, we represent the Hawkes process in terms of a
Poisson cluster process and show how the cumulant density formulas can be
derived by enumerating all possible "family trees", representing complex
interactions between point events. We also consider the problem of computing
the integrated cumulants, characterizing the average measure of correlated
activity between events of different types, and derive the relevant equations.Comment: 11 pages, 4 figure
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