Related papers: Embedding protein 3D-structures in a cubic lattice…
We describe a polynomial time algorithm for, given an undirected graph G, finding the minimum dimension d such that G may be isometrically embedded into the d-dimensional integer lattice Z^d.
Proteins play crucial roles in every cellular process by interacting with each other, with nucleic acids, metabolites, and other molecules. The resulting assemblies can be very large and intricate and pose challenges to experimental…
Several more and more efficient component--by--component (CBC) constructions for suitable rank-1 lattices were developed during the last decades. On the one hand, there exist constructions that are based on minimizing some error functional.…
A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…
The electrical properties of a set of seven-helix transmembrane proteins, whose space arrangement (3D structure) is known, are investigated by using regular arrays of the amino acids. These structures, specifically cubes, have topological…
Understanding of the evolutionary origins of protein structures represents a key component of the understanding of molecular evolution as a whole. Here we seek to elucidate how the features of an underlying protein structural "space" might…
Superposing multiple plane waves can generate helicity lattices in which the optical helicity varies regularly in space. Here we propose an inverse design method for constructing arbitrary helicity structures based on placing a digital…
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…
A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the…
Structure determination is key to understanding protein function at a molecular level. Whilst significant advances have been made in predicting structure and function from amino acid sequence, researchers must still rely on expensive,…
Proteins are the fundamental macromolecules that play diverse and crucial roles in all living matter and have tremendous implications in healthcare, manufacturing, and biotechnology. Their functions are largely determined by the sequences…
Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present a new algorithm for…
Despite the significant increase in computational power, molecular modeling of protein structure using classical all-atom approaches remains inefficient, at least for most of the protein targets in the focus of biomedical research. Perhaps…
Lattice surgery is a method to perform quantum computation fault-tolerantly by using operations on boundary qubits between different patches of the planar code. This technique allows for universal planar-code computation without eliminating…
We present a quantum-in-quantum embedding strategy coupled to machine learning potentials to improve on the accuracy of quantum-classical hybrid models for the description of large molecules. In such hybrid models, relevant structural…
Lattice rules are among the most prominently studied quasi-Monte Carlo methods to approximate multivariate integrals. A rank-1 lattice rule to approximate an $s$-dimensional integral is fully specified by its generating vector $\mathbf{z}…
We study a fundamental problem in structure-based drug design -- generating molecules that bind to specific protein binding sites. While we have witnessed the great success of deep generative models in drug design, the existing methods are…
Protein folding is a central challenge in computational biology, with important applications in molecular biology, drug discovery and catalyst design. As a hard combinatorial optimisation problem, it has been studied as a potential target…
A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…
Gupta et al. [1, 2] describe a very beautiful application of algebraic geometry to lattice structures composed of quadric of revolution (quador) implicit surfaces. However, the shapes created have concave edges where the stubs meet, and…