Cryo-EM is a transformational paradigm in molecular biology where computa-1 tional methods are used to infer 3D molecular structure at atomic resolution from2 extremely noisy 2D electron microscope images. At the forefront of research is3 how to model the structure when the imaged particles exhibit non-rigid conforma-4 tional flexibility and compositional variation where parts are sometimes missing.5 We introduce a novel 3D reconstruction framework with a hierarchical Gaussian6 mixture model, inspired in part by Gaussian Splatting for 4D scene reconstruction.7 In particular, the structure of the model is grounded in an initial process that infers8 a part-based segmentation of the particle, providing essential inductive bias in9 order to handle both conformational and compositional variability. The framework,10 called CryoSPIRE, is shown to reveal biologically meaningful structures on com-11 plex experimental datasets, and establishes a new state-of-the-art on CryoBench, a12 benchmark for cryo-EM heterogeneity methods.

Particle Image Velocimetry (PIV) aims to infer underlying velocity fields from time-separated particle images, forming a PDE-constrained inverse problem governed by advection dynamics.

Cryo-EM is a transformational paradigm in molecular biology where computational methods are used to infer 3D molecular structure at atomic resolution from extremely noisy 2D electron microscope images. At the forefront of research is how to model the structure when the imaged particles exhibit non-rigid conformational flexibility and compositional variation where parts are sometimes missing. We introduce a novel 3D reconstruction framework with a hierarchical Gaussian mixture model, inspired in part by Gaussian Splatting for 4D scene reconstruction. In particular, the structure of the model is grounded in an initial process that infers a part-based segmentation of the particle, providing essential inductive bias in order to handle both conformational and compositional variability. The framework, called CryoSPIRE, is shown to reveal biologically meaningful structures on complex experimental datasets, and establishes a new state-of-the-art on CryoBench, a benchmark for cryo-EM heterogeneity methods.

Variational autoencoders (VAEs) are a popular generative model used to approximate distributions. The encoder part of the VAE is used in amortized learning of latent variables, producing a latent representation for data samples. Recently, VAEs have been used to characterize physical and biological systems. In this case study, we qualitatively examine the amortization properties of a VAE used in biological applications. We find that in this application the encoder bears a qualitative resemblance to more traditional explicit representation of latent variables.

Particle image velocimetry (PIV) is essential in experimental fluid dynamics. In the current work, we propose a new velocity field estimation paradigm, which achieves a synergetic combination of the deep learning method and the traditional cross-correlation method. Specifically, the deep learning method is used to optimize and correct a coarse velocity guess to achieve a super-resolution calculation. And the cross-correlation method provides the initial velocity field based on a coarse correlation with a large interrogation window. As a reference, the coarse velocity guess helps with improving the robustness of the proposed algorithm. This fully convolutional network with embedded cross-correlation is named as CC-FCN. CC-FCN has two types of input layers, one is for the particle images, and the other is for the initial velocity field calculated using cross-correlation with a coarse resolution. Firstly, two pyramidal modules extract features of particle images and initial velocity field respectively. Then the fusion module appropriately fuses these features. Finally, CC-FCN achieves the super-resolution calculation through a series of deconvolution layers to obtain the single-pixel velocity field. As the supervised learning strategy is considered, synthetic data sets including ground-truth fluid motions are generated to train the network parameters. Synthetic and real experimental PIV data sets are used to test the trained neural network in terms of accuracy, precision, spatial resolution and robustness. The test results show that these attributes of CC-FCN are further improved compared with those of other tested PIV algorithms. The proposed model could therefore provide competitive and robust estimations for PIV experiments.

Particle picking is currently a critical step in the cryo-EM single particle reconstruction pipeline. Despite extensive work on this problem, for many data sets it is still challenging, especially for low SNR micrographs. We present the KLT (Karhunen Loeve Transform) picker, which is fully automatic and requires as an input only the approximated particle size. In particular, it does not require any manual picking. Our method is designed especially to handle low SNR micrographs. It is based on learning a set of optimal templates through the use of multi-variate statistical analysis via the Karhunen Loeve Transform. We evaluate the KLT picker on publicly available data sets and present high-quality results with minimal manual effort.

Determining the 3D structures of biological molecules is a key problem for both biology and medicine. Electron Cryomicroscopy (Cryo-EM) is a promising technique for structure estimation which relies heavily on computational methods to reconstruct 3D structures from 2D images. This paper introduces the challenging Cryo-EM density estimation problem as a novel application for stochastic optimization techniques. Structure discovery is formulated as MAP estimation in a probabilistic latent-variable model, resulting in an optimization problem to which an array of seven stochastic optimization methods are applied. The methods are tested on both real and synthetic data, with some methods recovering reasonable structures in less than one epoch from a random initialization. Complex quasi-Newton methods are found to converge more slowly than simple gradient-based methods, but all stochastic methods are found to converge to similar optima. This method represents a major improvement over existing methods as it is significantly faster and is able to converge from a random initialization.