Integrative Learning of Intensity Fluctuations of Quantum Dots under Excitation via a Tailored Mixture Hidden Markov Model

Semiconductor nano-crystals, known as quantum dots (QDs), have garnered significant interest in various scientific fields due to their unique fluorescence properties. One captivating characteristic of QDs is their ability to emit photons under continuous excitation. The intensity of photon emission fluctuates during the excitation, and such a fluctuation pattern can vary across different dots even under the same experimental conditions. What adding to the complication is that the processed intensity series are non-Gaussian and truncated due to necessary thresholding and normalization. As such, conventional approaches in the chemistry literature, typified by single-dot analysis of raw intensity data with Gaussian hidden Markov models (HMM), cannot meet the many analytical challenges and may fail to capture any novel yet rare fluctuation patterns among QDs. Collaborating with scientists in the chemistry field, we have developed an integrative learning approach to simultaneously analyzing intensity series of multiple QDs. Our approach still inherits the HMM as the skeleton to model the intensity fluctuations of each dot, and based on the data structure and the hypothesized collective behaviors of the QDs, our approach asserts that (i) under each hidden state, the normalized intensity follows a 0/1 inflated Beta distribution, (ii) the state distributions are shared across all the QDs, and (iii) the patterns of transitions can vary across QDs. These unique features allow for a precise characterization of the intensity fluctuation patterns and facilitate the clustering of the QDs. With experimental data collected on 128 QDs, our methods reveal several QD clusters characterized by unique transition patterns across three intensity states. The results provide deeper insight into QD behaviors and their design/application potentials.