This is a preview. Log in through your library . Abstract In the random walk whose state space is a subset of the non-negative integers explicit representations for the generating functions of the ...

Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose ...

Natural selection uses duplicated genes as raw material for functional innovation, co-opting their existing features to new functions. Understanding genetic innovation requires two questions to be ...