In the community of localization-based super-resolution microscopy (or called localization microscopy), it is generally believed that the emission of single molecules is so weak that an EMCCD (electron multiplying charge coupled device) camera is necessary to be used as the detector by eliminating read noise. Here we evaluate the possibility of a new kind of low light detector, scientific complementary metal-oxide-semiconductor (sCMOS) camera in localization microscopy. We demonstrate experimentally that sCMOS is capable of imaging actin bundles with FWHM diameter of 37 nm, evidencing the capability of sCMOS in localization microscopy. We further characterize the noise performance of sCMOS and find out that, with the use of a bright fluorescence probe such as d2EosFP, localization microscopy imaging is now working in the shot noise limited region.

Policy gradient (PG) methods are a widely used reinforcement learning methodology in many applications such as videogames, autonomous driving, and robotics. In spite of its empirical success, a rigorous understanding of the global convergence of PG methods is lacking in the literature. In this work, we close the gap by viewing PG methods from a nonconvex optimization perspective. In particular, we propose a new variant of PG methods for infinite-horizon problems that uses a random rollout horizon for the Monte-Carlo estimation of the policy gradient. This method then yields an unbiased estimate of the policy gradient with bounded variance, which enables the tools from nonconvex optimization to be applied to establish global convergence. Employing this perspective, we first recover the convergence results with rates to the stationary-point policies in the literature. More interestingly, motivated by advances in nonconvex optimization, we modify the proposed PG method by introducing periodically enlarged stepsizes. The modified algorithm is shown to escape saddle points under mild assumptions on the reward and the policy parameterization. Under a further strict saddle points assumption, this result establishes convergence to essentially locally-optimal policies of the underlying problem, and thus bridges the gap in existing literature on the convergence of PG methods. Results from experiments on the inverted pendulum are then provided to corroborate our theory, namely, by slightly reshaping the reward function to satisfy our assumption, unfavorable saddle points can be avoided and better limit points can be attained. Intriguingly, this empirical finding justifies the benefit of reward-reshaping from a nonconvex optimization perspective.

This paper presents a comprehensive literature review on point set registration. The state-of-the-art modeling methods and algorithms for point set registration are discussed and summarized. Special attention is paid to methods for pairwise registration and groupwise registration. Some of the most prominent representative methods are selected to conduct qualitative and quantitative experiments. From the experiments we have conducted on 2D and 3D data, CPD-GL pairwise registration algorithm and JRMPC groupwise registration algorithm seem to outperform their rivals both in accuracy and computational complexity. Furthermore, future research directions and avenues in the area are identified.

Localization-based super-resolution microscopy (or called localization microscopy) rely on repeated imaging and localization of active molecules, and the spatial resolution enhancement of localization microscopy is built upon the sacrifice of its temporal resolution. Developing algorithms for high-density localization of active molecules is a promising approach to increase the speed of localization microscopy. Here we present a new algorithm called SSM_BIC for such purpose. The SSM_BIC combines the advantages of the Structured Sparse Model (SSM) and the Bayesian Information Criterion (BIC). Through simulation and experimental studies, we evaluate systematically the performance between the SSM_BIC and the conventional Sparse algorithm in high-density localization of active molecules. We show that the SSM_BIC is superior in processing single molecule images with weak signal embedded in strong background.

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