Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing

We investigate the possibility of using icosahedral symmetry as a family symmetry group in the lepton sector. The rotational icosahedral group, which is isomorphic to A5, the alternating group of five elements, provides a natural context in which to explore (among other possibilities) the intriguing hypothesis that the solar neutrino mixing angle is governed by the golden ratio. We present a basic toolbox for model-building using icosahedral symmetry, including explicit representation matrices and tensor product rules. As a simple application, we construct a minimal model at tree level in which the solar angle is related to the golden ratio, the atmospheric angle is maximal, and the reactor angle vanishes to leading order. The approach provides a rich setting in which to investigate the flavor puzzle of the Standard Model.Comment: 22 pages, version to be published in Phys. Rev.

Dynamical Reduction of Discrete Systems Based on the Renormalization Group Method

The renormalization group (RG) method is extended for global asymptotic analysis of discrete systems. We show that the RG equation in the discretized form leads to difference equations corresponding to the Stuart-Landau or Ginzburg-Landau equations. We propose a discretization scheme which leads to a faithful discretization of the reduced dynamics of the original differential equations.Comment: LaTEX. 12pages. 1 figure include

Unification in 5D SO(10)

Gauge unification in a five dimensional supersymmetric SO(10) model compactified on an orbifold $S^1/(Z_2 \times Z_2^{\prime})$ is studied. One orbifolding reduces N=2 supersymmetry to N=1, and the other breaks SO(10) to the Pati-Salam gauge group \ps. Further breaking to the standard model gauge group is made through the Higgs mechanism on one of the branes. The differences of the three gauge couplings run logarithmically even in five dimensions and we can keep the predictability for unification as in four dimensional gauge theories. We obtain an excellent prediction for gauge coupling unification with a cutoff scale $M_* \sim 3 \times 10^{17}$ GeV and a compactification scale $M_c \sim 1.5 \times 10^{14}$ GeV. Finally, although proton decay due to dimension 5 operators may be completely eliminated, the proton decay rate in these models is sensitive to the placement of matter multiplets in the 5th dimension, as well as to the unknown physics above the cutoff scale.Comment: 33 pages, one reference added and fig. 3 caption correcte

Design of the liraglutide effect and action in diabetes: evaluation of cardiovascular outcome results (LEADER) trial.

BACKGROUND: Diabetes is a multisystem disorder associated with a nearly twofold excess risk for a broad range of adverse cardiovascular outcomes including coronary heart disease, stroke, and cardiovascular death. Liraglutide is a human glucagon-like peptide receptor analog approved for use in patients with type 2 diabetes mellitus (T2DM). STUDY DESIGN: To formally assess the cardiovascular safety of liraglutide, the Liraglutide Effect and Action in Diabetes: Evaluation of cardiovascular outcome Results (LEADER) trial was commenced in 2010. LEADER is a phase 3B, multicenter, international, randomized, double-blind, placebo-controlled clinical trial with long-term follow-up. Patients with T2DM at high risk for cardiovascular disease (CVD) who were either drug naive or treated with oral antihyperglycemic agents or selected insulin regimens (human NPH, long-acting analog, or premixed) alone or in combination with oral antihyperglycemics were eligible for inclusion. Randomized patients are being followed for up to 5 years. The primary end point is the time from randomization to a composite outcome consisting of the first occurrence of cardiovascular death, nonfatal myocardial infarction, or nonfatal stroke. CONCLUSIONS: LEADER commenced in September 2010, and enrollment concluded in April 2012. There were 9,340 patients enrolled at 410 sites in 32 countries. The mean age of patients was 64.3 ± 7.2 years, 64.3% were men, and mean body mass index was 32.5 ± 6.3 kg/m2. There were 7,592 (81.3%) patients with prior CVD and 1,748 (18.7%) who were high risk but without prior CVD. It is expected that LEADER will provide conclusive data regarding the cardiovascular safety of liraglutide relative to the current standard of usual care for a global population of patients with T2DM

SUSY GUT Model Building

I discuss an evolution of SUSY GUT model building, starting with the construction of 4d GUTs, to orbifold GUTs and finally to orbifold GUTs within the heterotic string. This evolution is an attempt to obtain realistic string models, perhaps relevant for the LHC. This review is in memory of the sudden loss of Julius Wess, a leader in the field, who will be sorely missed.Comment: 24 pages, 14 figures, lectures given at PiTP 2008, Institute for Advanced Study, Princeton, to be published in the European Physical Journal