Maximum Persistency in Energy Minimization

We consider discrete pairwise energy minimization problem (weighted constraint satisfaction, max-sum labeling) and methods that identify a globally optimal partial assignment of variables. When finding a complete optimal assignment is intractable, determining optimal values for a part of variables is an interesting possibility. Existing methods are based on different sufficient conditions. We propose a new sufficient condition for partial optimality which is: (1) verifiable in polynomial time (2) invariant to reparametrization of the problem and permutation of labels and (3) includes many existing sufficient conditions as special cases. We pose the problem of finding the maximum optimal partial assignment identifiable by the new sufficient condition. A polynomial method is proposed which is guaranteed to assign same or larger part of variables than several existing approaches. The core of the method is a specially constructed linear program that identifies persistent assignments in an arbitrary multi-label setting.Comment: Extended technical report for the CVPR 2014 paper. Update: correction to the proof of characterization theore

Absence of gravitational contributions to the running Yang-Mills coupling

The question of a modification of the running gauge coupling of (non-) abelian gauge theories by an incorporation of the quantum gravity contribution has recently attracted considerable interest. In this letter we perform an involved diagrammatical calculation in the full Einstein-Yang-Mills system both in cut-off and dimensional regularization at one loop order. It is found that all gravitational quadratic divergencies cancel in cut-off regularization and are trivially absent in dimensional regularization so that there is no alteration to asymptotic freedom at high energies. The logarithmic divergencies give rise to an extended effective Einstein-Yang-Mills Lagrangian with a counterterm of dimension six. In the pure Yang-Mills sector this counterterm can be removed by a nonlinear field redefinition of the gauge potential, reproducing a classical result of Deser, Tsao and van Nieuwenhuizen obtained in the background field method with dimensional regularization.Comment: 4 pages, 1 figure, uses revtex and feynmf. v2: references adde