Cryo-electron microscopy (cryo-EM) is an emerging experimental method to characterize the structure of large biomolecular assemblies. Single particle cryo-EM records 2D images (so-called micrographs) of projections of the three-dimensional particle, which need to be processed to obtain the three-dimensional reconstruct…
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New method for analyzing complex data spaces.
Adaptive orthogonalization of data for clustering and visualization.
Cryo-electron microscopy (cryo-EM) is capable of producing reconstructed 3D images of biomolecules at near-atomic resolution. As such, it represents one of the most promising imaging techniques in structural biology. However, raw cryo-EM images are only highly corrupted - noisy and band-pass filtered - 2D projections o…
Geometric framework for inverse problems using foliations and dual connections.
Cryo-electron microscopy (cryoEM) is an increasingly popular method for protein structure determination. However, identifying a sufficient number of particles for analysis (often >100,000) can take months of manual effort. Current computational approaches are limited by high false positive rates and require significant…
Confirmation bias leads to biased estimates in noisy data analysis.
We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other non-linear dimensionality reduction methods. MFVDM combines different nonlinear emb…
We introduce a novel co-learning paradigm for manifolds naturally equipped with a group action, motivated by recent developments on learning a manifold from attached fibre bundle structures. We utilize a representation theoretic mechanism that canonically associates multiple independent vector bundles over a common bas…
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of unknown shapes in the case of nonparametric noise. The noise density is unknown and ca…
K-means fails in high dimensions with noise and few samples.
Data augmentation is a widely used trick when training deep neural networks: in addition to the original data, properly transformed data are also added to the training set. However, to the best of our knowledge, a clear mathematical framework to explain the performance benefits of data augmentation is not available. In…
Single particle reconstruction (SPR) from cryo-electron microscopy (EM) is a technique in which the 3D structure of a molecule needs to be determined from its contrast transfer function (CTF) affected, noisy 2D projection images taken at unknown viewing directions. One of the main challenges in cryo-EM is the typically…
Researchers use shape analysis to recover protein structures from Cryo-EM data.
Constructing of molecular structural models from Cryo-Electron Microscopy (Cryo-EM) density volumes is the critical last step of structure determination by Cryo-EM technologies. Methods have evolved from manual construction by structural biologists to perform 6D translation-rotation searching, which is extremely comput…
A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although they are not presented this way, can be viewed as spectral methods on matrices bui…
A deep neural network based architecture was constructed to predict amino acid side chain conformation with unprecedented accuracy. Amino acid side chain conformation prediction is essential for protein homology modeling and protein design. Current widely-adopted methods use physics-based energy functions to evaluate s…
Cryo-em images are found to be low-dimensional.
Study on estimating signals from shifted and noisy copies in high dimensions, revealing a phase transition.
Motivated by the task of 2-D classification in single particle reconstruction by cryo-electron microscopy (cryo-EM), we consider the problem of heterogeneous multireference alignment of images. In this problem, the goal is to estimate a (typically small) set of target images from a (typically large) collection of obser…
Cryo-electron microscopy (cryo-EM) is a powerful technique for determining the structure of proteins and other macromolecular complexes at near-atomic resolution. In single particle cryo-EM, the central problem is to reconstruct the three-dimensional structure of a macromolecule from noisy and randomly orien…
Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or SO(3). The goal of such problems is to estimate an unknown vector of group eleme…
Fluorescence microscopy has enabled a dramatic development in modern biology. Due to its inherently weak signal, fluorescence microscopy is not only much noisier than photography, but also presented with Poisson-Gaussian noise where Poisson noise, or shot noise, is the dominating noise source. To get clean fluorescence…
SOLVAR efficiently analyzes cryo-EM data's structural variability.
Method recovers particle orientations from cryo-EM projections.
Deep learning improves 3D microscopy resolution without matched target images.
Convolutional neural networks (CNN) have achieved state of the art performance on both classification and segmentation tasks. Applying CNNs to microscopy images is challenging due to the lack of datasets labeled at the single cell level. We extend the application of CNNs to microscopy image classification and segmentat…
A new diffusion model improves cryo-EM structure sampling.
Cryo-electron microscopy (cryo-EM) studies using single particle reconstruction are extensively used to reveal structural information on macromolecular complexes. Aiming at the highest achievable resolution, state of the art electron microscopes automatically acquire thousands of high-quality micrographs. Particles are…
Method estimates section thickness and XY anisotropy in ssEM images.
We discuss recently emerging applications of the state-of-art deep learning methods on optical microscopy and microscopic image reconstruction, which enable new transformations among different modes and modalities of microscopic imaging, driven entirely by image data. We believe that deep learning will fundamentally ch…
Paper addresses group synchronization with incomplete measurements and proves linear convergence of GPM.
Machine learning classifies colorectal tissue using photoacoustic microscopy.
Cryo-EM reconstruction is reformulated as a stochastic inverse problem to handle structural heterogeneity.
DISPR uses diffusion models to predict 3D cell shapes from 2D images.
Machine learning speeds up FLIM analysis in biomedical research.
Deconvolution microscopy has been extensively used to improve the resolution of the widefield fluorescent microscopy. Conventional approaches, which usually require the point spread function (PSF) measurement or blind estimation, are however computationally expensive. Recently, CNN based approaches have been explored a…
Multi-StyleGAN simulates live cell microscopy imagery.
Novel higher-order group synchronization for noisy local measurements on hypergraphs.
Malaria is a life-threatening disease affecting millions. Microscopy-based assessment of thin blood films is a standard method to (i) determine malaria species and (ii) quantitate high-parasitemia infections. Full automation of malaria microscopy by machine learning (ML) is a challenging task because field-prepared sli…
New method extracts biological concepts from cell microscopy images.
Study improves pollen detection in optical and holographic images using deep learning.
Prototype for adaptive electron microscopy scans reduces dose and time.
UDVD uses deep learning to denoise videos without supervision.
A novel method detects multiple mitosis events and mitigates annotation gaps in phase-contrast microscopy.
An image dataset of 10 different size molecules, where each molecule has 2,000 structural variants, is generated from the 2D cross-sectional projection of Molecular Dynamics trajectories. The purpose of this dataset is to provide a benchmark dataset for the increasing need of machine learning, deep learning and image p…
Deep learning methods are becoming widely used for restoration of defects associated with fluorescence microscopy imaging. One of the major challenges in application of such methods is the availability of training data. In this work, we propose a unified method for reconstruction of multi-defect fluorescence microscopy…
Improves spline quality and accuracy in computational microscopy.