Paper Info
Title
Markov Chain Computations Using Molecular Reactions
Abstract
Markov chains are commonly used in numerous signal processing and statistical modeling applications. This paper describes an approach to implement any first-order Markov chain using molecular reactions in general and DNA in particular. Markov chain consists of two parts: a set of states, and state transition probabilities. Each state is modeled by a unique molecular type, referred as a data molecule. Each state transition is modeled by a unique molecular type, referred as a control molecule, and a unique molecular reaction. Each reaction consumes data molecules of one state and produces data molecules of another state. The concentrations of control molecules are initialized according to the probabilities of corresponding state transitions in the chain. The steady-state probability of Markov chain is computed by equilibrium concentration of data molecules. We demonstrate our method for the Gambler's Ruin problem as an instance of the Markov chain process. Both stochastic chemical kinetics and mass-action kinetics validate the computed probabilities using the proposed model. The molecular reactions are then mapped to DNA strand displacement reactions. The error in the probability of ruin computed by the proposed model is shown to be less than 1% for DNA strand displacement reactions.
Year
Venue
Keywords
2015
2015 IEEE INTERNATIONAL CONFERENCE ON DIGITAL SIGNAL PROCESSING (DSP)
Molecular computation, Markov chain, Gambler's ruin problem, molecular reaction, DNA strand-displacement
Field
DocType
Citations 
Statistical physics,Markov chain mixing time,Additive Markov chain,Continuous-time Markov chain,Pattern recognition,Markov chain Monte Carlo,Computer science,Markov chain,Balance equation,Discrete phase-type distribution,Artificial intelligence,Examples of Markov chains
Conference
4
PageRank 
References 
Authors
0.44
6
3
Name
Order
Citations
PageRank
Sayed Ahmad Salehi1313.78
Marc D. Riedel252148.65
keshab k parhi33235369.07