Related papers: A central partition of molecular conformational sp…
In the first work of this series [physics/0204035] it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the espace into…
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 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 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…
Deep learning has proven to yield fast and accurate predictions of quantum-chemical properties to accelerate the discovery of novel molecules and materials. As an exhaustive exploration of the vast chemical space is still infeasible, we…
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…
We study how to generate molecule conformations (i.e., 3D structures) from a molecular graph. Traditional methods, such as molecular dynamics, sample conformations via computationally expensive simulations. Recently, machine learning…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
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…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
Molecules have seemed like a natural fit to deep learning's tendency to handle a complex structure through representation learning, given enough data. However, this often continuous representation is not natural for understanding chemical…
The cascade of 2D geometric transformations were exploited to model relations between entities in a knowledge graph (KG), leading to an effective KG embedding (KGE) model, CompoundE. Furthermore, the rotation in the 3D space was proposed as…
Realistic 3D-conformations of protein structures can be embedded in a cubic lattice using exclusively integer numbers, additions, subtractions and boolean operations.
Sequential assembly with geometric primitives has drawn attention in robotics and 3D vision since it yields a practical blueprint to construct a target shape. However, due to its combinatorial property, a greedy method falls short of…
The rational design of molecules with desired properties is a long-standing challenge in chemistry. Generative neural networks have emerged as a powerful approach to sample novel molecules from a learned distribution. Here, we propose a…
Prediction of a molecule's 3D conformer ensemble from the molecular graph holds a key role in areas of cheminformatics and drug discovery. Existing generative models have several drawbacks including lack of modeling important molecular…
I investigate a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
Three-dimensional molecular structure generation is typically performed at the level of individual atoms, yet molecular graph generation techniques often consider fragments as their structural units. Building on the advances in frame-based…