Duality is an important notion for constrained optimization which provides a theoretical foundation for a number of constraint decomposition schemes such as separable programming and for deriving lower bounds in space decomposition algorithms such as branch and bound. However, the conventional duality theory has the fundamental limit that it leads to duality gaps for nonconvex optimization prob...

Quark-hadron duality addresses some of the most fundamental issues in strong interaction physics, in particular the nature of the transition from the perturbative to non-perturbative regions of QCD. I summarize recent developments in quark-hadron duality in lepton–hadron scattering, and outline how duality can be studied at future high-luminosity facilities such as Jefferson Lab at 12 GeV or an...

We apply a recent duality theorem for tangles in abstract separation systems to derive tangle-type duality theorems for width-parameters in graphs and matroids. We further derive a duality theorem for the existence of clusters in large data sets. Our applications to graphs include new, tangle-type, duality theorems for tree-width, path-width, and tree-decompositions of small adhesion. Conversel...

The partition function of Ramond-Ramond p-form fields in Type IIA supergravity on a ten-manifold X contains subtle phase factors that are associated with T-duality, self-duality, and the relation of the RR fields to K-theory. The analogous partition function of M-theory on X × S 1 contains subtle phases that are similarly associated with E 8 gauge theory. We analyze the detailed phase factors o...

In this talk we give an overview of some recent developments in gauge and gravity theories, focusing on a new duality between color and kinematics. This duality allows us to construct gravity amplitudes by a simple replacement of color factors by kinematic numerator factors. Applications of these ideas for determining the ultraviolet compatibility of supersymmetric versions of Einstein gravity ...

I ascribe the origin of Bloom-Gilman duality in DIS to a separation of scales between the hard subprocess and soft resonance formation. The success of duality indicates that the subprocesses of exclusive form factors are the same as in DIS. The observed dominance of the longitudinal structure function at large x in πN → µ + µ − X can explain why local duality works for DIS with a pion target. T...