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HMM perturbations

The PPP algorithm adjusts parameters of its hidden Markov model (HMM) by random amounts. These adjustments are called perturbations. The range of adjustments ("amplitude") is set to the largest value that does not degrade accuracy on benchmark tests. A large amplitude is preferred to maximize variation in an alignment ensemble.

HMM parameters are probabilities in the range 0 to 1.

First, each probability is adjusted in the range -25% to +25% of its original value, selecting a value uniformly from that range. In other words, the amplitude is fixed at 25%.

Then, probabilities are normalized to ensure that the values are in the range zero to one and sum to one for all mutually exclusive events, e.g. all possible letters emitted from an insert state or all transitions out of the match state.

Different perturbations are obtained by using different integer seed values for a pseudo-random number generator. By convention, a zero value for the seed indicates that no perturbations are introduced so that default HMM probabilities are used.