A Model for Large theta13 Constructed using the Eigenvectors of the S4 Rotation Matrices

A procedure for using the eigenvectors of the elements of the representations of a discrete group in model building is introduced and is used to construct a model that produces a large reactor mixing angle, sin^2(theta13)=2/3 sin^2(pi/16), in agreement with recent neutrino oscillation observations. The model fully constrains the neutrino mass ratios and predicts normal hierarchy with the light neutrino mass, m1~25 meV. Motivated by the model, a new mixing ansatz is postulated which predicts all the mixing angles within 1sigma errors.Comment: 6 pages, 1 figure, contribution to the proceedings of DISCRETE 2012 to appear in the open access Journal of Physics: Conference Series (JPCS), preprint typeset in two-column revtex4 styl

Criteria for homotopic maps to be so along monotone homotopies

The state spaces of machines admit the structure of time. A homotopy theory respecting this additional structure can detect machine behavior unseen by classical homotopy theory. In an attempt to bootstrap classical tools into the world of abstract spacetime, we identify criteria for classically homotopic, monotone maps of pospaces to future homotope, or homotope along homotopies monotone in both coordinates, to a common map. We show that consequently, a hypercontinuous lattice equipped with its Lawson topology is future contractible, or contractible along a future homotopy, if its underlying space has connected CW type.Comment: 7 pages, 5 figures, partially presented at GETCO 2006. title change; strengthened Cor. 3.3. -> Prop. 3.7, Prop. 3.2 -> Lem. 3.2; corrected def of category of continuous lattices in sec. 2; added 5 figures, 8 eg's, Def. 3.4, Lemmas 2.8, 3.5, refs [1],[4],[5]; rewording throughout; conclusion and abstract rewritte

Quasi-local black hole horizons

This article introduces the subject of quasi-local horizons at a level suitable for physics graduate students who have taken a first course on general relativity. It reviews properties of trapped surfaces and trapped regions in some simple examples, general properties of trapped surfaces including their stability properties, the definitions and some applications of dynamical-, trapping-, and isolated-horizons.Comment: 41 pages, 12 Figures. To appear in the Springer Handbook of Spacetime, Springer Verlag (2013