The problem of finding an appropriate geometrical/physical index for measuring a degree of inhomogeneity for a given space-time manifold is posed. Interrelations with the problem of understanding the gravitational/informational entropy are pointed out. An approach based on the notion of approximate symmetry is proposed. A number of related results on definitions of approximate symmetries known ...

Engineering geometric models are often designed to have symmetries and other regularities. In knowledge based reuse, creative design and design for mass customization, to have the information of such symmetries and other regularities from a geometric model is very useful. And this can make us understand more about the geometric model. In reverse engineering, B-rep models are created by fitting ...

We revisit general arguments for the absence of exact continuous global symmetries in string compactifications and extend them to D-brane models. We elucidate the various ways approximate continuous global symmetries arise in the 4-dimensional effective action. In addition to two familiar methods axionic Peccei-Quinn symmetries and remnant global abelian symmetries from Green-Schwarz gauge symm...

The quark and lepton mass matrices possess approximate flavor symmetries. Several results follow if the interactions of new scalars possess these approximate symmetries. Present experimental bounds allow these exotic scalars to have a weak scale mass. The Glashow-Weinberg criterion is rendered unnecessary. Finally, rare leptonic B meson decays provide powerful probes of these scalars, especiall...

We propose a rigorous definition of approximate symmetry and of its spontaneous breakdown in connection with a phase transition. We show that this definition is of interest in the case of the Ising model with a small three-spin perturbation.

We study the relationship between Quantum Approximate Optimization Algorithm (QAOA) and underlying symmetries of objective function to be optimized. Our approach formalizes connection quantum symmetry properties QAOA dynamics group classical function. The is general includes but not limited problems defined on graphs. show a series results exploring highlight examples hard problem classes where...

It is an open question whether fluctuations at the Planck scale in a non-perturbative theory of quantum gravity behave such way that resulting semi-classical geometry can be modelled by space admits (approximate) Killing symmetries. We have investigated notion approximate vector fields suitable to address this lattice theories gravity, as (Causal) Dynamical Triangulations. show it possible cons...