We present a closed-form solution for the symmetrization problem, solving for the optimal deformation that reconciles a set of local bilateral symmetries. Given as input a set of point-pairs which should be symmetric, we first compute for each local neighborhood a transformation which would produce an approximate bilateral symmetry. We then solve for a single global symmetry which includes all ...

If nature exhibits low energy supersymmetry, discrete (non-Z2) R symmetries may well play an important role. In this paper, we explore such symmetries. We generalize gaugino condensation, constructing large classes of models which are classically scale invariant, and which spontaneously break discrete R symmetries (but not supersymmetry). The order parameters for the breaking include chiral sin...

The Radio science experiment of the BepiColombo mission to the planet Mercury shall allow to solve for the gravity field of the planet up to degree and order 25, for an improved orbit of Mercury and a very accurate verification of Einstein’s theory of gravitation, for measuring the rotation state of the planet, for mapping the topography (in combination with a laser altimeter). To actually obta...

Status of determination of the neutrino masses and mixing is formulated and possible uncertainties, especially due to presence of the sterile neutrinos, are discussed. The data hint an existence of special “neutrino” symmetries. If not accidental these symmetries have profound implications and can substantially change the unification program. The key issue on the way to underlying physics is re...

The existence of symmetries in complex networks has a significant effect on network dynamic behaviour. Nevertheless, beyond topological symmetry, one should consider the fact that real-world are exposed to fluctuations or errors, as well mistaken insertions removals. Therefore, resulting approximate remain hidden standard symmetry analysis - fully accomplished by discrete algebra software. Ther...

Perfect, partial, and approximate symmetries are pervasive in 3D surface meshes of real-world objects. However, current digital geometry processing algorithms generally ignore them, instead focusing on local shape features and differential surface properties. This paper investigates how detection of large-scale symmetries can be used to guide processing of 3D meshes. It investigates a framework...

The axion solution to the strong CP problem makes use of a global Peccei–Quinn U(1) symmetry which is susceptible to violations from quantum gravitational effects. We show how discrete gauge symmetries can protect the axion from such violations. PQ symmetry emerges as an approximate global symmetry from discrete gauge symmetries. Simple models based on ZN symmetries with N = 11, 12, etc are pre...

Enhancing the self-symmetry of a shape is of fundamental aesthetic virtue. In this paper, we are interested in recovering the aesthetics of intrinsic reflection symmetries, where an asymmetric shape is symmetrized while keeping its general pose and perceived dynamics. The key challenge to intrinsic symmetrization is that the input shape has only approximate reflection symmetries, possibly far f...