In the absence of strict complementarity, Monteiro and Wright 7] proved that the convergence rate for a class of Newton interior-point methods for linear complementarity problems is at best linear. They also established an upper bound of 1=4 for the Q 1-factor of the duality gap sequence when the steplengths converge to one. In the current paper, we prove that the Q 1 factor of the duality gap ...

In the absence of strict complementarity, Monteiro and Wright 7] proved that the convergence rate for a class of Newton interior-point methods for linear complementarity problems is at best linear. They also established an upper bound of 1=4 for the Q 1-factor of the duality gap sequence when the steplengths converge to one. In the current paper, we prove that the Q 1 factor of the duality gap ...

We derive the q-deformation of the chiral Gross-Taylor holomorphic string large N expansion of two dimensional SU(N) Yang-Mills theory. Delta functions on symmetric group algebras are replaced by the corresponding objects (canonical trace functions) for Hecke algebras. The role of the Schur-Weyl duality between unitary groups and symmetric groups is now played by q-deformed Schur-Weyl duality o...

A topological duality for monadic n-valued Lukasiewicz algebras introduced by M. Abad (Abad, M.: Estructuras cíclica y monádica de un álgebra de Lukasiewicz nvalente. Notas de Lógica Matemática 36. Instituto de Matemática. Universidad Nacional del Sur, 1988) is determined. When restricted to the category of Q-distributive lattices and Q-homomorphims, it coincides with the duality obtained by R....

Two main families of reinforcement learning algorithms, Q-learning and policy gradients, have recently been proven to be equivalent when using a softmax relaxation on one part, and an entropic regularization on the other. We relate this result to the well-known convex duality of Shannon entropy and the softmax function. Such a result is also known as the Donsker-Varadhan formula. This provides ...

7 We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums 9 involving the Gaussian binomial coefficients. Special cases of these identities—for example, with all parameters equal to 1—have occurred in the literature. The special case with only one pa...

We present some recent developments in the study of quark-hadron duality in structure functions in the resonance region. To understand the workings of local duality we introduce the concept of truncated moments, which are used to describe the Q dependence of specific resonance regions within a QCD framework.

For dyons in heterotic string theory compactified on a six-torus, with electric charge vector Q and magnetic charge vector P , the positive integer I ≡ gcd(Q ∧ P ) is an invariant of the U-duality group. We propose the microscopic theory for computing the spectrum of all dyons for all values of I, generalizing earlier results that exist only for the simplest case of I = 1. Our derivation uses a...