相关论文: Semi-algebraic geometry of common lines

Concrete is the standard construction material for buildings, bridges, and roads. As safety plays a central role in the design, monitoring, and maintenance of such constructions, it is important to understand the cracking behavior of…

Semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities. In this paper, we consider the problem of deciding whether two given points in a semi-algebraic set are connected. We restrict to the case…

A pseudoline arrangement graph is a planar graph induced by an embedding of a (simple) pseudoline arrangement. We study the corresponding graph realization problem and properties of pseudoline arrangement graphs. In the first part, we give…

Ab initio electronic structure methods give accurate results for small systems, but do not scale well to large systems. Chemical insight tells us that molecular functional groups will behave approximately the same way in all molecules,…

Transmission electron microscopy (TEM) is a powerful imaging tool that has found broad application in materials science, nanoscience and biology(1-3). With the introduction of aberration-corrected electron lenses, both the spatial…

The application of PhotoEmission Electron Microscopy (PEEM) and Low Energy Electron Microscopy (LEEM) techniques to the study of the electronic and chemical structure of ferroelectric materials is reviewed. Electron optics in both…

A pseudoline is a homeomorphic image of the real line in the plane so that its complement is disconnected. An arrangement of pseudolines is a set of pseudolines in which every two cross exactly once. A drawing of a graph is pseudolinear if…

Electron tomography offers important three-dimensional (3D) structural information which cannot be observed by two-dimensional imaging. By combining annular dark field scanning transmission electron microscopy (ADF-STEM) with aberration…

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…

Cryo-electron microscopy (cryo-EM) enables single-particle analysis of biological macromolecules under strict low-dose imaging conditions, but the resulting micrographs often exhibit extremely low signal-to-noise ratios and weak particle…

Cylindrical algebraic decomposition is a classical construction in real algebraic geometry. Although there are many algorithms to compute a cylindrical algebraic decomposition, their practical performance is still very limited. In this…

Transmission electron microscopy (TEM) is a potent technique for the determination of three-dimensional atomic scale structure of samples in structural biology and materials science. In structural biology, three-dimensional structures of…

Here a new microscopic method is proposed to image and characterize very thin samples like few-layer materials, organic molecules, and nanostructures with nanometer or sub-nanometer resolution using electron beams of energies lower than 20…

Electron cryo-tomography (cryo-ET) enables 3D imaging of complex, radiation-sensitive structures with molecular detail. However, image contrast from the interference of scattered electrons is nonlinear with atomic density and multiple…

A practical method utilising three-dimensional image pattern matching is proposed which, in principle, is capable of unambiguous determination of the types and positions of atoms in small molecules from defocus series collected at only a…

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…

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…

Semialgebraic graphs are graphs whose vertices are points in $\mathbb{R}^d$, and adjacency between two vertices is determined by the truth value of a semialgebraic predicate of constant complexity. We show how to harness polynomial…

This paper proposes a machine learning (ML) method to predict stable molecular geometries from their chemical composition. The method is useful for generating molecular conformations which may serve as initial geometries for saving time…

This paper presents a systematic study of the structure of non-solvable cyclic metric Lie algebras. A cyclic metric is a symmetric bilinear form satisfying a cyclic cocycle condition, which arises naturally in the contexts of…