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We propose a statistical framework for clustering multiple time series that exhibit nonlinear dynamics into an a-priori-unknown number of sub-groups that each comprise time series with similar dynamics. Our motivation comes from neuroscience where an important problem is to identify, within a large assembly of neurons, sub-groups that respond similarly to a stimulus or contingency. In the neural setting, conditioned on cluster membership and the parameters governing the dynamics, time series within a cluster are assumed independent and generated according to a nonlinear binomial state-space model. We derive a Metropolis-within-Gibbs algorithm for full Bayesian inference that alternates between sampling of cluster membership and sampling of parameters of interest. The Metropolis step is a PMMH iteration that requires an unbiased, low variance estimate of the likelihood function of a nonlinear state- space model. We leverage recent results on controlled sequential Monte Carlo to estimate likelihood functions more efficiently compared to the bootstrap particle filter. We apply the framework to time series acquired from the prefrontal cortex of mice in an experiment designed to characterize the neural underpinnings of fear. 

Abstract The carrier excitation, relaxation, energy transport, and conversion processes during light‐nanocrystal (NC) interactions have been intensively investigated for applications in optoelectronics, photocatalysis, and photovoltaics. However, there are limited studies on the non‐equilibrium heating under relatively high laser excitation that leads to NCs sintering. Here, the authors use femtosecond laser two‐pulse correlation and in‐situ optical transmission probing to investigate the non‐equilibrium heating of NCs and transient sintering dynamics. First, a two‐pulse correlation study reveals that the sintering rate strongly increases when the two heating laser pulses are temporally separated by <10 ps. Second, the sintering rate is found to increase nonlinearly with laser fluence when heating with ≈700 fs laser pulses. By three‐temperature modeling, the NC sintering mechanism mediated by electron induced ligand transformation is suggested. The ultrafast and non‐equilibrium process facilitates sintering in dry (spin‐coated) and wet (solvent suspended) environments. The nonlinear dependence of sintering rate on laser fluence is exploited to print sub‐diffraction‐limited features in NC suspension. The smallest feature printed is ≈200 nm, which is ≈¼ of the laser wavelength. These findings provide a new perspective toward nanomanufacturing development based on probing and engineering ultrafast transport phenomena in functional NCs.