The Optimal Set and Optimal Partition Approach to Linear and Quadratic Programming

In this chapter we describe the optimal set approach for sensitivity analysis for LP. We show that optimal partitions and optimal sets remain constant between two consecutive transition-points of the optimal value function. The advantage of using this approach instead of the classical approach (using optimal bases) is shown. Moreover, we present an algorithm to compute the partitions, optimal sets and the optimal value function. This is a new algorithm and uses primal and dual optimal solutions. We also extend some of the results to parametric quadratic programming, and discuss differences and resemblances with the linear programming case

Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory

In this paper we consider parafermionic Liouville field theory. We study integral representations of three-point correlation functions and develop a method allowing us to compute them exactly. In particular, we evaluate the generalization of Selberg integral obtained by insertion of parafermionic polynomial. Our result is justified by different approach based on dual representation of parafermionic Liouville field theory described by three-exponential model

New solutions with accelerated expansion in string theory

Abstract: We present concrete solutions with accelerated expansion in string theory, requiring a small, tractable list of stress energy sources. We explain how this construction (and others in progress) evades previous no go theorems for simple accelerating solutions. Our solutions respect an approximate scaling symmetry and realize discrete sequences of values for the equation of state, including one with an accumulation point at w = −1 and another accumulating near w = −1/3 from below. In another class of models, a density of defects generates scaling solutions with accelerated expansion. We briefly discuss potential applications to dark energy phenomenology, and to holography for cosmology.Fil: Dodelson, Matthew. University of Stanford; Estados UnidosFil: Dong, Xi. University of Stanford; Estados UnidosFil: Silverstein, Eva. University of Stanford; Estados Unidos. Fermi National Accelerator Laboratory; Estados UnidosFil: Torroba, Gonzalo. University of Stanford; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentin