相关论文: A Central Partition of Molecular Conformational Sp…

A molecule's 2D representation consists of its atoms, their attributes, and the molecule's covalent bonds. A 3D (geometric) representation of a molecule is called a conformer and consists of its atom types and Cartesian coordinates. Every…

Several systems involve spatial arrangements of elements such as molecules or cells, the characterization of which bears important implications to biological and physical investigations. Traditional approaches to quantify spatial order and…

We calculate correlation functions of exactly-solvable one-dimensional flat-band models by utilizing the "molecular-orbital" representation. The models considered in this paper have a gapped ground state with flat-band being fully occupied,…

We extend the existing idea of "cellular poset", introduce a collection of "cellular methods" for the computation of homology of intersection lattice of a complicated subspace arrangement, and for the computation of multiplicative structure…

A previous study of diatomic molecules revealed that variational second-order density matrix theory has serious problems in the dissociation limit when the N-representability is imposed at the level of the usual two-index (P, Q, G) or even…

This series presents an approach to mathematical biology which makes precise the function of biological molecules. Because biological systems compute, the theory is a general purpose computer language. I build a language for efficiently…

Simplified representations of macromolecules help in rationalising and understanding the outcome of atomistic simulations, and serve to the construction of effective, coarse-grained models. The number and distribution of coarse-grained…

We investigate the structure of two-dimensional partial cubes, i.e., of isometric subgraphs of hypercubes whose vertex set defines a set family of VC-dimension at most 2. Equivalently, those are the partial cubes which are not contractible…

Colour vision has long fascinated scientists, who have sought to understand both the physiology of the mechanics of colour vision and the psychophysics of colour perception. We consider representations of colour in anatomically constrained…

The three-dimensional shape and conformation of small-molecule ligands are critical for biomolecular recognition, yet encoding 3D geometry has not improved ligand-based virtual screening approaches. We describe an end-to-end deep learning…

Diffraction analysis in four dimensional scanning transmission electron microscopy now enables the mapping of local structures including symmetry, strain, and polarization of materials. However, measuring the distribution of these…

Topological orders are a class of phases of matter that beyond the Landau symmetry breaking paradigm. The two (spatial) dimensional (2d) topological orders have been thoroughly studied. It is known that they can be fully classified by a…

For the study of complex synthetic and biological molecular systems by computer simulations one is still restricted to simple model systems or to by far too small time scales. To overcome this problem multiscale techniques are being…

We construct a class of periodic tilings of the plane, which corresponds to toroidal arrangements of trivalent atoms, with pentagonal, hexagonal and heptagonal rings. Each tiling is characterized by a set of four integers and determines a…

This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…

To fully understand the 3D context of a single image, a visual system must be able to segment both the visible and occluded regions of objects, while discerning their occlusion order. Ideally, the system should be able to handle any object…

One of the molecular properties most intuitive to the human perception is the geometrical shape. However, when exploring a large chemical space the determination of shape needs to be automated. We present a fast and simple approach to…

The physical structure of hot molecular cores, where forming massive stars have heated up dense dust and gas, but have not yet ionized the molecules, poses a prominent challenge in the research of high-mass star formation and…

Living organisms rely on molecular networks, such as gene circuits and signaling pathways, for information processing and robust decision-making in crowded, noisy environments. Recent advances show that interacting biomolecules…

Colloids self-assemble into various organized superstructures determined by particle interactions. There is a tremendous progress in both the scientific understanding and applications of self-assemblies of single-type identical particles.…