Homological perturbation theory for nonperturbative integrals

We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In particular, we explain that phenomena usually thought of as particular to asymptotic integrals in fact also occur exactly: integrals of the type appearing in quantum field theory can be reduced in a totally algebraic fashion to integrals over an Euler--Lagrange locus, provided this locus is understood in the scheme-theoretic sense, so that imaginary critical points and multiplicities of degenerate critical points contribute.Comment: 22 pages. Minor revisions from previous versio

Asymptotics of multivariate sequences, part III: quadratic points

We consider a number of combinatorial problems in which rational generating functions may be obtained, whose denominators have factors with certain singularities. Specifically, there exist points near which one of the factors is asymptotic to a nondegenerate quadratic. We compute the asymptotics of the coefficients of such a generating function. The computation requires some topological deformations as well as Fourier-Laplace transforms of generalized functions. We apply the results of the theory to specific combinatorial problems, such as Aztec diamond tilings, cube groves, and multi-set permutations.Comment: substantial correction

Computing equilibria in general equilibrium models via interior-point method

In this paper we study new computational methods to find equilibria in general equilibrium models. We first survey the algorithms to compute equilibria that can be found in the literature on computational economics and we indicate how these algorithms can be improved from the computational point of view. We also provide alternative algorithms that are able to compute the equilibria in an efficient manner even for large-scale models, based on interior-point methods. We illustrate the proposed methods with some examples taken from the literature on general equilibrium modelsPublicad