  We analytically study the input-output properties of a neuron whose active
dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to
Poisson stimulus. Both single-site and two-site mean-field approximations
incorrectly predict a non-equilibrium phase transition which is not allowed in
the model. We propose an excitable-wave mean-field approximation which shows
good agreement with previously published simulation results [Gollo et al., PLoS
Comput. Biol. 5(6) e1000402 (2009)] and accounts for finite-size effects. We
also discuss the relevance of our results to experiments in neuroscience,
emphasizing the role of active dendrites in the enhancement of dynamic range
and in gain control modulation.
