  Network structures are reconstructed from dynamical data by respectively
naive mean field (nMF) and Thouless-Anderson-Palmer (TAP) approximations. For
TAP approximation, we use two methods to reconstruct the network: a) iteration
method; b) casting the inference formula to a set of cubic equations and
solving it directly. We investigate inference of the asymmetric Sherrington-
Kirkpatrick (S-K) model using asynchronous update. The solutions of the sets
cubic equation depend of temperature T in the S-K model, and a critical
temperature Tc is found around 2.1. For T < Tc, the solutions of the cubic
equation sets are composed of 1 real root and two conjugate complex roots while
for T > Tc there are three real roots. The iteration method is convergent only
if the cubic equations have three real solutions. The two methods give same
results when the iteration method is convergent. Compared to nMF, TAP is
somewhat better at low temperatures, but approaches the same performance as
temperature increase. Both methods behave better for longer data length, but
for improvement arises, TAP is well pronounced.
