相关论文: Semi-algebraic geometry of common lines

Quasicrystals are aperiodically ordered solids that exhibit long-range order without translational periodicity, bridging the gap between crystalline and amorphous materials. Due to their lack of translational periodicity, information on…

Serial section electron microscopy (ssEM) is a widely used technique for obtaining volumetric information of biological tissues at nanometer scale. However, accurate 3D reconstructions of identified cellular structures and volumetric…

An image line segment is a fundamental low-level visual feature that delineates straight, slender, and uninterrupted portions of objects and scenarios within images. Detection and description of line segments lay the basis for numerous…

Observing the individual building blocks of matter is one of the primary goals of microscopy. The invention of the scanning tunneling microscope [1] revolutionized experimental surface science in that atomic-scale features on a solid-state…

Cryo-EM reconstruction algorithms seek to determine a molecule's 3D density map from a series of noisy, unlabeled 2D projection images captured with an electron microscope. Although reconstruction algorithms typically model the 3D volume as…

Single-particle cryo-Electron Microscopy (EM) has become a popular technique for determining the structure of challenging biomolecules that are inaccessible to other technologies. Recent advances in automation, both in data collection and…

In this paper, we describe and study a mathematical framework for cryo-elecron microscopy. The main result, is a a proof of the admissability (correctness) and the numerical stability of the intrinsic reconstitution algorithm which was…

Background: Single-particle cryo-electron microscopy (cryo-EM) has become a popular tool for structural determination of biological macromolecular complexes. High-resolution cryo-EM reconstruction often requires hundreds of thousands of…

Revealing the structure of complex biological macromolecules, such as proteins, is an essential step for understanding the chemical mechanisms that determine the diversity of their functions. Synchrotron based x-ray crystallography and…

A Cartan geometry of the General Linear symmetry is formulated by dividing out the displacements from the group. The resulting action is quadratic in curvature, polynomial in all the (minimal) variables, and describes an observer space…

The three-dimensional structure of proteins plays a crucial role in determining their function. Protein structure prediction methods, like AlphaFold, offer rapid access to a protein structure. However, large protein complexes cannot be…

Compressed sensing algorithms are used to decrease electron microscope scan time and electron beam exposure with minimal information loss. Following successful applications of deep learning to compressed sensing, we have developed a…

Advances on cryo-electron imaging technologies have led to a rapidly increasing number of density maps. Alignment and comparison of density maps play a crucial role in interpreting structural information, such as conformational…

DNA segments and sequences have been studied thoroughly during the past decades. One of the main problems in computational biology is the identification of exon-intron structures inside genes using mathematical techniques. Previous studies…

The Boundary Element Method (BEM) is a powerful numerical approach for solving 3D elastostatic problems, particularly useful for crack propagation in fracture mechanics and half-space problems. A key challenge in BEM lies in handling…

Automated and semi-automated techniques in biomedical electron microscopy (EM) enable the acquisition of large datasets at a high rate. Segmentation methods are therefore essential to analyze and interpret these large volumes of data, which…

Electrocardiogram (ECG) delineation, the segmentation of meaningful waveform features, is critical for clinical diagnosis. Despite recent advances using deep learning, progress has been limited by the scarcity of publicly available…

Secondary electron (SE) imaging offers a powerful complementary capabilities to conventional scanning transmission electron microscopy (STEM) by providing surface-sensitive, pseudo-3D topographic information. However, contrast…

Semialgebraic splines are bivariate splines over meshes whose edges are arcs of algebraic curves. They were first considered by Wang, Chui, and Stiller. We compute the dimension of the space of semialgebraic splines in two extreme cases. If…

The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…