We give three examples of large intervals in the lattice of (local) clones on an infinite set X, by exhibiting clones C1, C2, C3 such that: (1) the interval [C1, O] in the lattice of local clones is (as a lattice) isomorphic to {0, 1, 2, . . .} under the divisibility relation, (2) the interval [C2, O] in the lattice of local clones is isomorphic to the congruence lattice of an arbitrary semilat...

Few examples of macromolecular crystals containing lattice-translocation defects have been published in the literature. Lattice translocation and twinning are believed to be two common but different crystal-growth anomalies. While the successful use of twinned data for structure determination has become relatively routine in recent years, structure determination of crystals with lattice-translo...

We use conference matrices to define an action of the complex numbers on the real Euclidean vector space R. In certain cases, the lattice D n becomes a module over a ring of quadratic integers. We can then obtain new unimodular lattices, essentially by multiplying the lattice D n by a non-principal ideal in this ring. We show that lattices constructed via quadratic residue codes, including the ...