Let k be a diierence eld with automorphism. Let b be an element of k, and L be a linear ordinary diierence operator with coeecients in k. A classical problem in the theory of diierence equations is to compute all the solutions in k of the equation L(y) = b. If C denotes a constant eld and if k = C(n) and n = n + 1 or n = qn, there are known algorithms (see 2] for example). Manuel Bronstein pres...

This paper provides evidence on the impact of paid leave legislation on female employment outcomes. Using a di erence-in-di erences and di erence-in-di erence-in-di erences strategy, I study the impact of two state-level programs in California and New Jersey. This paper is rst to exploit the fact that the cost of paid leave in these states is larger for rms with 50 or more employees (who are fo...

We present a new approach to automated reasoning based on di erence identi cation and reduction. Di erence identi cation is based on a generalization of uni cation so that terms are made equal not only by nding substitutions for variables but also by hiding term structure. This annotation of structural di erences serves to direct rippling, a type of rewriting designed to reduce and remove di er...

We study the space of linear di↵erence equations with periodic coe cients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations of points in the projective space. We define the notion of combinatorial Gale transform which is a duality between periodic di↵erence equations of di↵erent orde...

In this paper two recursive constructions for optimal optical orthogonal codes are presented by means of incomplete di/erence matrices and perfect cyclic di/erence packings. These improve the known existence results concerning optimal (v; 4; 1)-OOCs. c © 2002 Elsevier Science B.V. All rights reserved.

In this paper we will consider two algorithms which allow us to obtain second order linear di erence equations for certain families of polynomials. The corresponding algorithms can be implemented in any computer algebra system in order to obtain explicit expressions of the coe cients of the di erence equations. c © 1998 Elsevier Science B.V. All rights reserved. AMS classi cation: 33C45; 42C05

We present a tree di erence algorithm with expected sequential execution timeO(n log log n) and expected parallel execution time of O(log n), for trees of size n. The algorithm assumes unique labels and permits operations only on leaves and frontier subtrees. Despite these limitations, it can be useful in the analysis of structured text. 1 Applications of Tree Di erence In this paper we describ...

TD( ) is a popular family of algorithms for approximate policy evaluation in large MDPs. TD( ) works by incrementally updating the value function after each observed transition. It has two major drawbacks: it makes ine cient use of data, and it requires the user to manually tune a stepsize schedule for good performance. For the case of linear value function approximations and = 0, the Least-Squ...

It is shown that there does not exist a reversible abelian Hadamard diierence set in

Conventional numerical di erentiation formulas based on interpolating polynomials, operators and lozenge diagrams can be simpli ed to one of the nite di erence approximations based on Taylor series, and closed-form expressions of these nite di erence formulas have already been presented. In this paper, we present new nite di erence formulas, which are more accurate than the available ones, espe...