Algebraic structures such as groups, rings and modules provide a rigorous framework for organising and manipulating mathematical objects. Graph theory, concerned with vertices connected by edges, has ...

3D configurations of atoms dictate all materials properties. Quantitative predictions of accurate equilibrium structures, 3D coordinates of all atoms, from a chemical graph, a representation of the ...

Crystal structures have a decisive impact on the properties of materials, and research on crystal structures often serves as a starting point for material studies. Crystal structure prediction is a ...

Imagine 100 dots scattered in front of you. In a haphazard variation on connect-the-dots, start drawing lines between the points. How many lines can you draw without producing a triangle? A square? An ...