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Single-particle cryo-electron microscopy: Mathematical theory, computational challenges, and opportunities
T Bendory, A Bartesaghi… - IEEE signal processing …, 2020 - ieeexplore.ieee.org
In recent years, an abundance of new molecular structures have been elucidated using cryo-
electron microscopy (cryo-EM), largely due to advances in hardware technology and data …
electron microscopy (cryo-EM), largely due to advances in hardware technology and data …
Computational methods for single-particle electron cryomicroscopy
A Singer, FJ Sigworth - Annual review of biomedical data …, 2020 - annualreviews.org
Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for
elucidating the three-dimensional (3D) structure of proteins and other biologically significant …
elucidating the three-dimensional (3D) structure of proteins and other biologically significant …
A group-theoretic framework for data augmentation
S Chen, E Dobriban, JH Lee - Journal of Machine Learning Research, 2020 - jmlr.org
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 original data, properly transformed data are also added to the training set. However, to …
Autocorrelation analysis for cryo-EM with sparsity constraints: improved sample complexity and projection-based algorithms
The number of noisy images required for molecular reconstruction in single-particle
cryoelectron microscopy (cryo-EM) is governed by the autocorrelations of the observed …
cryoelectron microscopy (cryo-EM) is governed by the autocorrelations of the observed …
Group-invariant max filtering
J Cahill, JW Iverson, DG Mixon, D Packer - Foundations of Computational …, 2024 - Springer
Given a real inner product space V and a group G of linear isometries, we construct a family
of G-invariant real-valued functions on V that we call max filters. In the case where V= R d …
of G-invariant real-valued functions on V that we call max filters. In the case where V= R d …
The sample complexity of multireference alignment
A Perry, J Weed, AS Bandeira, P Rigollet… - SIAM Journal on …, 2019 - SIAM
The growing role of data-driven approaches to scientific discovery has unveiled a large
class of models that involve latent transformations with a rigid algebraic constraint. Three …
class of models that involve latent transformations with a rigid algebraic constraint. Three …
Method of moments for 3D single particle ab initio modeling with non-uniform distribution of viewing angles
Single-particle reconstruction in cryo-electron microscopy (cryo-EM) is an increasingly
popular technique for determining the 3D structure of a molecule from several noisy 2D …
popular technique for determining the 3D structure of a molecule from several noisy 2D …
Mathematics for cryo-electron microscopy
A Singer - Proceedings of the International Congress of …, 2018 - World Scientific
Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography
and NMR spectroscopy as a high-resolution structural method for biological …
and NMR spectroscopy as a high-resolution structural method for biological …
Average-case complexity of tensor decomposition for low-degree polynomials
AS Wein - Proceedings of the 55th Annual ACM Symposium on …, 2023 - dl.acm.org
Suppose we are given an n-dimensional order-3 symmetric tensor T∈(ℝ n)⊗ 3 that is the
sum of r random rank-1 terms. The problem of recovering the rank-1 components is possible …
sum of r random rank-1 terms. The problem of recovering the rank-1 components is possible …
Explaining conformational diversity in protein families through molecular motions
V Lombard, S Grudinin, E Laine - Scientific Data, 2024 - nature.com
Proteins play a central role in biological processes, and understanding their conformational
variability is crucial for unraveling their functional mechanisms. Recent advancements in …
variability is crucial for unraveling their functional mechanisms. Recent advancements in …