Integer polyhedra for program analysis

Polyhedra are widely used in model checking and abstract interpretation. Polyhedral analysis is effective when the relationships between variables are linear, but suffers from imprecision when it is necessary to take into account the integrality of the represented space. Imprecision also arises when non-linear constraints occur. Moreover, in terms of tractability, even a space defined by linear constraints can become unmanageable owing to the excessive number of inequalities. Thus it is useful to identify those inequalities whose omission has least impact on the represented space. This paper shows how these issues can be addressed in a novel way by growing the integer hull of the space and approximating the number of integral points within a bounded polyhedron

BOND PERCOLATION ON A NON-P.C.F. SIERPIŃSKI GASKET, ITERATED BARYCENTRIC SUBDIVISION OF A TRIANGLE, AND HEXACARPET

We investigate bond percolation on the iterated barycentric subdivision of a triangle, the hexa-carpet, and the non-p.c.f. Sierpinski gasket. With the use of known results on the diamond fractal, we are able to bound the critical probability of bond percolation on the non-p.c.f. gasket and the iterated barycentric subdivision of a triangle from above by 0.282. We then show how both the gasket and hexacarpet fractals are related via the iterated barycentric subdivisions of a triangle: the two spaces exhibit duality properties although they are not themselves dual graphs. Finally, we show the existence of a non-trivial phase transition on all three graphs. </jats:p

Implications of Components of Income Excluded from Pro Forma Earnings for Future Profitability and Equity Valuation

This study addresses three research questions relating to total exclusions, special items, and other exclusions. Are each of these pro forma exclusion components forecasting irrelevant? Are each of the exclusion components value irrelevant? Are the valuation multiples on the exclusion components justified by their ability to forecast future profitability as predicted by the Ohlson (1999) model? Findings are generally consistent with the market-inefficiency results presented in Doyle et al. (2003) . Total exclusions are valued negatively by the market despite the prediction that total exclusions will be valued positively. Valuation results also suggest that stocks with positive other exclusions are overpriced. Copyright 2007 The Authors Journal compilation (c) 2007 Blackwell Publishing Ltd.

A hybrid constraint model for the routing and wavelength assignment problem

Abstract. In this paper we present a hybrid model for the demand acceptance variant of the routing and wavelength assignment problem in directed networks, an important benchmark problem in optical network design. Our solution uses a decomposition into a MIP model for the routing and optimization aspect, combined with a finite domain constraint model for the wavelength assignment. If a solution to the constraint problem is found, it provides an optimal solution to the overall problem. If the constraint problem is infeasible, we use an extended explanation technique to find a good relaxation of the problem which leads to a near optimal solution. Extensive experiments show that proven optimality is achieved for more than 99.8 % of all cases tested, while run-times are orders of magnitude smaller than the best known MIP solution.