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If the transition matrix associated with the substitution model is doubly stochastic, then we find a set of permutations which give rise to the model.
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In contrast to current models which assume a fixed spatio-temporal receptive field or simple temporal averaging for sequential processing, recurrent convolutional models are "doubly deep" in that they can be compositional in spatial and temporal "layers".
A hidden Markov model is a "doubly embedded stochastic process with an underlying stochastic process that is not observable, but can only be observed through another set of stochastic process that produce the sequence of observations" [25].
This model is labelled doubly stochastic as it accounts for measurement error in xt−1 by defining the observation series yt−1, while xt−1 is defined as the latent variable series.
This is doubly unconvincing.
This is doubly confused.
That is doubly cruel.
This is doubly unfortunate.
Which is doubly unfortunate.
Mary is doubly isolated.
This is doubly daft.
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