UC Santa Barbara

It is well known that reconstruction problems, as the interdisciplinary subject, have been studied in numerous contexts including statistical physics, information theory and computational biology, to name a few. We consider a 2q-state symmetric model, with two categories of q states in each category, and 3 transition probabilities: the probability to remain in the same state, the probability to change states but remain in the same category, and the probability to change categories. We construct a nonlinear second-order dynamical system based on this model and show that the Kesten–Stigum reconstruction bound is not tight when q≥ 4.