We study two models for the formation and packing of helices and sheets in globular (compact) proteins. These models, based on weighted Hamiltonian paths on a regular lattice both exhibit a first order transition between a compact high temperature phase, with no extended secondary structures, and a quasi-frozen compact phase, with secondary structures invading the whole lattice. The quasi-froze...

We complete the quasi-isometric classification of irreducible lattices in semisimple Lie groups over nondiscrete locally compact fields of characteristic zero by showing that any quasi-isometry of a rank one S-arithmetic lattice in a semisimple Lie group over nondiscrete locally compact fields of characteristic zero is a finite distance in the sup-norm from a commensurator.

M. Gromov has shown that any two finitely generated groups Γ and Λ are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions Γ y X x Λ on a locally compact Hausdorff space. This result is extended here to all (compactly generated) locally compact second-countable groups. In his seminal monograph on geometric group theory ...

1 Generalities on Spectral Algebraic Spaces 5 1.1 Scallop Decompositions in the Separated Case . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Quasi-Finite Morphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Quasi-Separatedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4 Points of Spectral Algebr...