Dimensional reduction of a self-dual tensor gauge field in 6d gives an Abelian vector gauge field in 5d. We derive the conditions under which an interacting 5d theory of an Abelian vector gauge field is the dimensional reduction of a 6d Lorentz invariant interacting theory of a self-dual tensor. Then we specialize to the particular 6d theory that gives 5d Born–Infeld theory. The field equation ...

In AdS, scalar fields with masses slightly above the Breitenlohner-Freedman bound admit a variety of possible boundary conditions which are reflected in the Lagrangian of the dual field theory. Generic small changes in the AdS boundary conditions correspond to deformations of the dual field theory by multi-trace operators. Here we extend this discussion to the case of vector gauge fields in the...

This paper presents a new dual formulation for quadratically constrained convex programs (QCCP). The special structure of the derived dual problem allows to apply the gradient projection algorithm to produce a simple explicit method involving only elementary vector-matrix operations, that is proven to converge at a linear rate.

This paper proposes a methodology to calculate both the first and second derivatives of a vector function of one variable in a single computation step. The method is based on the nested application of the dual number approach for first order derivatives. It has been implemented in Fortran language, a module which contains the dual version of elementary functions as well as more complex function...

The bilocal electric field strength correlators in Abelian-projected SU(2)and SU(3)-theories are derived with accounting for the contributions to these quantities brought about by the virtual vortex loops, built out of the dual Nielsen-Olesen strings. Owing to the screening of magnetic charge of the dual vector bosons in the gas of such loops, these bosons become heavier, which leads to the res...

Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove t...

We propose a fault-tolerant routing with its extensions based on limited global information in dual-cube networks. It is based on an early work of Wu’s safety level and safety vector in cube networks. An r-connected dual-cube network consists of 2rþ1 connected r-cubes (also called clusters). Both faulty nodes and faulty links are considered here. First, a depth-first search routing (DSBR) based...

Four-dimensional N=1 supersymmetric Spin(N) gauge theories with matter in the vector and spinor representations are considered. Dual descriptions are known for some of these theories. It is noted that when masses are given to all fields in the spinor representation, the dual gauge group G breaks to a group H such that π2(G/H) = Z2. The quantum numbers of the associated Z2 monopole and those of ...

We examine the low energy structure of N = 1 supersymmetric SO(10) gauge theory with matter chiral superfields in NQ spinor and Nf vector representations. We construct a dual to this model based upon an SU(Nf + 2NQ − 7)×Sp(2NQ − 2) gauge group without utilizing deconfinement methods. This product theory generalizes all previously known Pouliot-type duals to SO(Nc) models with spinor and vector ...

Solutions to optimization problems of convex type are typically characterized by saddle point conditions in which the primal vector is paired with a dual ‘multiplier’ vector. This paper investigates the behavior of such a primal-dual pair with respect to perturbations in parameters on which the problem depends. A necessary and sufficient condition in terms of certain matrices is developed for t...