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Cryo-electron microscopy (cryo-EM) has emerged as a powerful technique for determining the three-dimensional structures of biological molecules at near-atomic resolution. However, reconstructing helical assemblies presents unique challenges…

The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained…

The Kolmogorov-Arnold representation is a proven adequate replacement of a continuous multivariate function by an hierarchical structure of multiple functions of one variable. The proven existence of such representation inspired many…

Ergodic theory includes several notions of entropy for probability-preserving actions of countable groups. These include Kolmogorov--Sinai entropy based on F\o lner sequences for amenable groups, entropy defined using a random ordering of…

The cryo-electron microscope (cryo-EM) is increasingly popular these years. It helps to uncover the biological structures and functions of macromolecules. In this paper, we address image denoising problem in cryo-EM. Denoising the cryo-EM…

Cryo-electron microscopy (cryo-EM) has become a major experimental technique to determine the structures of large protein complexes and molecular assemblies, as evidenced by the 2017 Nobel Prize. Although cryo-EM has been drastically…

To cluster, classify and represent are three fundamental objectives of learning from high-dimensional data with intrinsic structure. To this end, this paper introduces three interpretable approaches, i.e., segmentation (clustering) via the…

Cryo-electron microscopy (EM) single particle reconstruction is an entirely general technique for 3D structure determination of macromolecular complexes. However, because the images are taken at low electron dose, it is extremely hard to…

A major challenge in single particle reconstruction from cryo-electron microscopy is to establish a reliable ab-initio three-dimensional model using two-dimensional projection images with unknown orientations. Common-lines based methods…

Constructing a quantum description of crystals from scattering experiments is of paramount importance to explain their macroscopic properties and to evaluate the pertinence of theoretical ab-initio models. While reconstruction methods of…

We apply recent advances in machine learning and computer vision to a central problem in materials informatics: The statistical representation of microstructural images. We use activations in a pre-trained convolutional neural network to…

Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…

Choosing the optimal observable to model dynamical systems for which we do not know the driving equations is nearly always an ad hoc art. Takens' Delay Embedding Theorem guarantees a diffeomorphism between delay-coordinate vectors built…

The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…

Electron cryomicroscopy (cryo-EM) is a technique in structural biology used to reconstruct accurate volumetric maps of molecules. One step of the cryo-EM pipeline involves solving an inverse-problem. This inverse-problem, referred to as…

Multiple approaches to use deep learning for image restoration have recently been proposed. Training such approaches requires well registered pairs of high and low quality images. While this is easily achievable for many imaging modalities,…

Microscopy image analysis is fundamental for different applications, from diagnosis to synthetic engineering and environmental monitoring. Modern acquisition systems have granted the possibility to acquire an escalating amount of images,…

Cryo-electron microscopy is a revolutionary technique that can provide 3D density maps at near-atomic resolution. However, map validation is still an open issue in the field. Despite several efforts from the community, it is possible to…

We propose a method to reconstruct the 3-D molecular structure from micrographs collected at just one sample tilt angle in the random conical tilt scheme in cryo-electron microscopy. Our method uses autocorrelation analysis on the…

Single-particle cryo-electron microscopy (cryo-EM) has become a cornerstone of structural biology, enabling near-atomic resolution analysis of macromolecules through advanced computational methods. However, the development of cryo-EM…