Related papers: A Central Partition of Molecular Conformational Sp…
In previous works [physics/0204035, physics/0404052, physics/0509126] a procedure was described for dividing the $3 \times N$-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the…
In a previous work a procedure was decribed for dividing the $3 \times N$-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the building of a combinatorial structure from data…
A combinatorial model of molecular conformational space that was previously developped (J. Gabarro-Arpa, Comp. Biol. and Chem. 27, (2003) 153-159), had the drawback that structures could not be properly embedded beacause it lacked explicit…
On the basis of empirical evidence from molecular dynamics simulations, molecular conformational space can be described by means of a partition of central conical regions characterized by the dominance relations between cartesian…
In a previous work arXiv:physics/0611108v2, it was shown that the volume spanned by a molecular system in its conformational space can be effectively bounded by a polyhedral cone, this cone is described by means of a simple combinatorial…
In previous works it was shown that protein 3D-conformations could be encoded into discrete sequences called dominance partition sequences (DPS), that generated a linear partition of molecular conformational space into regions of molecular…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
Understanding the geometry and topology of configuration or conformational spaces of molecules has relevant applications in chemistry and biology such as the proteins folding problem, drug design and the structure activity relationship…
This paper introduces the conformal model (an extension of the homogeneous coordinate system) for molecular geometry, where 3D space is represented within R^5 with an inner product different from the usual one. This model enables efficient…
Mapping conformational heterogeneity of macromolecules presents a formidable challenge to X-ray crystallography and cryo-electron microscopy, which often presume its absence. This has severely limited our knowledge of the conformations…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose a new point of view, making use of concepts taken from the field of computational geometry,…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
Molecular representation learning has attracted much attention recently. A molecule can be viewed as a 2D graph with nodes/atoms connected by edges/bonds, and can also be represented by a 3D conformation with 3-dimensional coordinates of…
Machine learning models of vastly different modalities and architectures are being trained to predict the behavior of molecules, materials, and proteins. However, it remains unclear whether they learn similar internal representations of…
A topological hyperplane is a subspace of R^n (or a homeomorph of it) that is topologically equivalent to an ordinary straight hyperplane. An arrangement of topological hyperplanes in R^n is a finite set H such that k topological…
The rich information content of measurements in the molecular frame rather than the laboratory frame has motivated the development of several methods for aligning gas phase molecules in space. Even so, for asymmetric tops the problem of…
Molecular property prediction, crucial for early drug candidate screening and optimization, has seen advancements with deep learning-based methods. While deep learning-based methods have advanced considerably, they often fall short in fully…
The conformation space of cyclooctane, a ringlike organic molecule comprising eight carbon atoms, is a two-dimensional algebraic variety, which has been studied extensively for more than 90 years. We propose a cell structure representing…
The prediction of the three-dimensional native structure of proteins from the knowledge of their amino acid sequence, known as the protein folding problem, is one of the most important yet unsolved issues of modern science. Since the…