Applications of Page Ranking in P Systems

Abstract

The page rank of a webpage is a numerical estimate of its authority. In Google’s PageRank algorithm the ranking is derived as the invariant probability distribution of a Markov chain random surfer model. The crucial point in this algorithm is the addition of a small probability transition for each pair of states to render the transition matrix irreducible and aperiodic. The same idea can be applied to P systems, and the resulting invariant probability distribution characterizes their dynamical behavior, analogous to recurrent states in deterministic dynamical systems. The modification made to the original P system gives rise to a new class of P systems with the property that their computations need to be robust against random mutations. Another application is the pathway identification problem, where a metabolite graph is constructed from information about biochemical reactions available in public databases. The invariant distribution of this graph, properly interpreted as a Markov chain, should allow to search pathways more efficiently than current algorithms. Such automatic pathway calculations can be used to derive appropriate P system models of metabolic processes.