6 papers
The strength of a geometric simplex
Olga Anosova, Vitaliy Kurlin
The basic input for many real objects is a finite cloud of unordered points. The strongest equivalence between objects in practice is rigid motion in a Euclidean space. A recent po…
Continuous invariant-based asymmetries of periodic crystals quantify deviations from higher symmetry
Surya Majumder, Daniel Widdowson, Yury Elkin +4
Ideal symmetry is known to break down under almost any noise. One measure of asymmetry in a periodic crystal is the relative multiplicity Z' of geometrically non-equivalent units.…
Complete and bi-continuous invariant of protein backbones under rigid motion
Olga Anosova, Alexey Gorelov, William Jeffcott +2
Proteins are large biomolecules that regulate all living organisms and consist of one or several chains. The primary structure of a protein chain is a sequence of amino acid residu…
Density functions of periodic sequences
Olga Anosova, Vitaliy Kurlin
Periodic point sets model all solid crystalline materials whose structures are determined in a rigid form and should be studied up to rigid motion or isometry preserving inter-poin…
Fast predictions of lattice energies by continuous isometry invariants of crystal structures
Jakob Ropers, Marco M Mosca, Olga Anosova +2
Crystal Structure Prediction (CSP) aims to discover solid crystalline materials by optimizing periodic arrangements of atoms, ions or molecules. CSP takes weeks of supercomputer ti…
Introduction to Periodic Geometry and Topology
Olga Anosova, Vitaliy Kurlin
This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystall…