We consider a simple system with a local synchronous generator and a load whose power consumption is a random process. The most probable scenario of system failure (synchronization loss) is considered, and it is argued that its knowledge is virtually
enough to estimate the probability of failure per unit time. We discuss two numerical methods to obtain the optimal evolution leading to failure.
It is speculated that the most probable channel noise realizations (instantons) that cause the iterative decoding of low-density parity-check codes to fail make the decoding not to converge. The Wibergs formula is generalized for the case when the pa
rt of a computational tree that contributes to the output at its center is ambiguous. Two methods of finding the instantons for large number of iterations are presented and tested on Tanners [155, 64, 20] code and Gaussian channel. The inherently dynamic instanton with effective distance of 11.475333 is found.
