The structure-property relationship plays a central role in materials science. Understanding the structure-property relationship in solid-state materials is crucial for structure design with optimized properties. The past few years witnessed remarkable progress in correlating structures with properties in crystalline materials, such as machine learning methods and particularly graph neural networks as a natural representation of crystal structures. However, significant challenges remain, including predicting properties with complex unit cells input and material-dependent, variable-length output. Here we present the virtual node graph neural network to address the challenges. By developing three types of virtual node approaches -the vector, matrix, and momentum-dependent matrix virtual nodes, we achieve direct prediction of Γ-phonon spectra and full dispersion only using atomic coordinates as input. We validate the phonon bandstructures on various alloy systems, and further build a Γ-phonon database containing over 146,000 materials in the Materials Project. Our work provides an avenue for rapid and high-quality prediction of phonon spectra and bandstructures in complex materials, and enables materials design with superior phonon properties for energy applications. The virtual node augmentation of graph neural networks also sheds light on designing other functional properties with a new level of flexibility.

Motivation Single-molecule localization microscopy (SMLM) is a super-resolution technique capable of rendering nanometer scale images of cellular structures. Recently, much effort has gone into developing algorithms for extracting quantitative features from SMLM datasets such as the abundance and stoichiometry of macromolecular complexes. These algorithms often require knowledge of the complicated photophysical properties of photoswitchable flourophores. Results Here we develop a calibration-free approach to quantitative SMLM built upon the observation that most photswitchable fluorophores emit a geometrically distributed number of blinks before photobleaching. From a statistical model of a mixture of monomers, dimers and trimers, the method employs an adapted Expectation-Maximization (EM) algorithm to learn the protomer fractions while simultaneously determining the single-fluorophore blinking distribution. To illustrate the utility of our approach, we benchmark it on both simulated datasets and experimental datasets assembled from SMLM images of fluorescently labeled DNA nanostructures. Availability An implementation of our algorithm written in Python is available at: https://www.utm.utoronto.ca/milsteinlab/resources/Software/MMCode/ Supplementary information Supplementary data are available at Bioinformatics Advances online.

Single-molecule localization microscopy (SMLM) is a super-resolution technique capable of rendering nanometer scale images of cellular structures. Recently, much effort has gone into developing SMLM into a quantitative method capable of determining the abundance and stoichiometry of macromolecular complexes. These methods often require knowledge of the complex photophysical properties of photoswitchable flourophores. We previously developed a simpler method built upon the observation that most photswitchable fluorophores emit an exponentially distributed number of blinks before photobleaching, but its utility was limited by the need to calibrate for the blinking distribution. Here we extend this method by incorporating a machine learning technique known as Expectation-Maximization (EM) and apply it to a statistical mixture model of monomers, dimers and trimers. We show that the protomer fractions and the underlying single-fluorophore blinking distributions can be inferred, simultaneously, from SMLM datasets, obviating the need for an additional calibration and greatly expanding the applicability of this technique. To illustrate the utility of our approach, we benchmark the method on both simulated datasets and experimental datasets assembled from dSTORM images of Alexa-647 labeled DNA nanostructures.