Related papers: Representation theoretic patterns in three dimensi…

Cryo-electron microscopy (cryo-EM) has revolutionized structural biology by enabling near-atomic-level visualization of biomolecular assemblies. However, the exponential growth in cryo-EM data throughput and complexity, coupled with diverse…

The analysis of neural representation has become an integral part of research aiming to better understand the inner workings of neural networks. While there are many different approaches to investigate neural representations, an important…

A key goal of computer vision is to recover the underlying 3D structure from 2D observations of the world. In this paper we learn strong deep generative models of 3D structures, and recover these structures from 3D and 2D images via…

Difficulties in replication and reproducibility of empirical evidences in machine learning research have become a prominent topic in recent years. Ensuring that machine learning research results are sound and reliable requires…

The fundamental matrix and trifocal tensor are convenient algebraic representations of the epipolar geometry of two and three view configurations, respectively. The estimation of these entities is central to most reconstruction algorithms,…

We review our recently developed methods for large-scale electronic structure calculations, both in one-electron theory and many-electron theory. The method are based on the density matrix representation, together with the Wannier state…

The Representation Theorem by Zomorodian and Carlsson has been the starting point of the study of persistent homology under the lens of algebraic representation theory. In this work, we give a more accurate statement of the original theorem…

We give an algorithm that learns a representation of data through compression. The algorithm 1) predicts bits sequentially from those previously seen and 2) has a structure and a number of computations similar to an autoencoder. The…

We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…

Cryo-electron microscopy (cryo-EM) studies using single particle reconstruction is extensively used to reveal structural information of macromolecular complexes. Aiming at the highest achievable resolution, state of the art electron…

Cryo-electron microscopy (cryo-EM) emerges as a pivotal technology for determining the architecture of cells, viruses, and protein assemblies at near-atomic resolution. Traditional particle picking, a key step in cryo-EM, struggles with…

Decomposing a scene into its reflectance and shading is a challenge due to the lack of extensive ground-truth data for real-world scenes. We introduce a novel physics-based approach for intrinsic image decomposition using a pair of visible…

This short paper being devoted to some aspects of the inverse problem of the representation theory treats several themes, which have their origins in the researches of F.A.Berezin, D.P.Zhelobenko, V.P.Maslov and his group, in context of the…

Single-particle cryo-electron microscopy (cryo-EM) is a leading technology to resolve the structure of molecules. Early in the process, the user detects potential particle images in the raw data. Typically, there are many false detections…

The simple entropic method to statistical reconstructing of heterogeneous three-dimensional media from a single two-dimensional image is briefly reported. We apply the entropic descriptor quantifying spatial inhomogeneity that depends on…

Proteins typically undergo conformational dynamics on the microsecond to millisecond timescale as they perform their function, which is much faster than the time-resolution of cryo-electron microscopy and has thus prevented real-time…

The numerical algorithm of the inverse quantum scattering is developed. This algorithm is based on the Marchenko theory, and includes three steps. The first one is the algebraic Pade approximation of the unitary S-matrix, what is realized…

We present the first three-dimensional theoretical model of microparticle-assisted super-resolution imaging, enabling accurate simulation of virtual image formation. The model reveals that accounting for partial spatial coherence of…

This paper is devoted to an intrinsic geometrical classification of three-mirror telescopes. The problem is formulated as the study of the connected components of a semi-algebraic set. Under first order approximation, we give the general…

Ptychography is a computational imaging technique that has risen in popularity in the x-ray and electron microscopy communities in the past half decade. One of the reasons for this success is the development of new high performance electron…