Hidden Markov model analysis for fluorescent time series of quantum dots

Abstract

We present a hidden Markov model analysis for fluorescent time series of quantum dots. A fundamental quantity to measure optical performance of the quantum dots is a distribution function for the light-emission duration. So far, to estimate it, a threshold value for the fluorescent intensity was introduced, and the light-emission state was evaluated as a state above the threshold. With this definition, the light-emission duration was estimated, and its distribution function was derived as a blinking plot. Due to the noise in the fluorescent data, however, this treatment generates a large number of artificially short-lived emission states, thus leading to an erroneous blinking plot. In the present paper, we propose a hidden Markov model to eliminate these artifacts. The hidden Markov model introduces a hidden variable specifying the light-emission and quenching states behind the observed fluorescence. We found that it is possible to avoid the above artifacts by identifying the state from the hidden-variable time series. We found that, from the analysis of experimental and theoretical benchmark data, the accuracy of our hidden Markov model is beyond human cognitive ability.