Computing maximal copies of polytopes contained in a polytope

Kepler (1619) and Croft (1980) have considered largest homothetic copies of one regular polytope contained in another regular polytope. For arbitrary pairs of polytopes we propose to model this as a quadratically constrained optimization problem. These problems can then be solved numerically; in case the optimal solutions are algebraic, exact optima can be recovered by solving systems of equations to very high precision and then using integer relation algorithms. Based on this approach, we complete Croft's solution to the problem concerning maximal inclusions of regular three-dimensional polyhedra by describing inclusions for the six remaining cases.Comment: 13 pages, 7 figure

General Gauge Mediation and Deconstruction

We locate a supersymmetry breaking hidden sector and supersymmetric standard model on different lattice points of an orbifold moose. The hidden sector is encoded in a set of current correlators and the effects of the current correlators are mediated by the lattice site gauge groups with "lattice hopping" functions and through the bifundamental matter that links the lattice sites together. We show how the gaugino mass, scalar mass and Casimir energy of the lattice can be computed for a general set of current correlators and then give specific formulas when the hidden sector is specified to be a generalised messenger sector coupled to a supersymmetry breaking spurion. The results reproduce the effect of five dimensional gauge mediation from a purely four dimensional construction.Comment: 20 pages, 1 figure. Version accepted by JHE

Low-energy electron diffraction from disordered surfaces

Model calculations are presented of L E E D intensities diffracted by a onedimensionally disordered overlayer adsorbed on a well ordered substrate. Multiple scattering amplitudes are calculated by an extension of Beeby's multiple scattering method. The surface layers are divided into overlapping configurations of atoms, the diffraction of each of which is described by individual scattering amplitudes. In this way the surrounding of each adsorbed atom is divided into two parts: the immediate vicinity, in which multiple scattering is treated self-consistently, and the outer region which is represented by an averaged Τ matrix. The results of the model calculations indicate that the intensities are not correctly described if only averaged Τ matrices are used, and that in a first approximation the half-widths of the diffuse streaks observed in the experiment can be analysed using the kinematic theory

Monoidal derivators and additive derivators

One aim of this paper is to develop some aspects of the theory of monoidal derivators. The passages from categories and model categories to derivators both respect monoidal objects and hence give rise to natural examples. We also introduce additive derivators and show that the values of strong, additive derivators are canonically pretriangulated categories. Moreover, the center of additive derivators allows for a convenient formalization of linear structures and graded variants thereof in the stable situation. As an illustration of these concepts, we discuss some derivators related to chain complexes and symmetric spectra

The perfect integrator driven by Poisson input and its approximation in the diffusion limit

In this note we consider the perfect integrator driven by Poisson process input. We derive its equilibrium and response properties and contrast them to the approximations obtained by applying the diffusion approximation. In particular, the probability density in the vicinity of the threshold differs, which leads to altered response properties of the system in equilibrium.Comment: 7 pages, 3 figures, v2: corrected authors in referenc