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In this paper we study the convergence of the multiscale finite element method for nonlinear and random homogenization problems. Error estimates similar to those for linear homogenization problems are obtained here.

This paper analyzes the resolution complexity of two random constraint satisfaction problem (CSP) models (i.e. Model RB/RD) for which we can establish the existence of phase transitions and identify the threshold points exactly. By encoding CSPs into ...

Recent years have seen remarkable progress in propositional satisfiability (SAT). Despite the worst-case exponential run time of all known algorithms, SAT solvers can currently be used to solve hard benchmark problems.This PhD dissertation contributes ...

A recent theoretical result by Achlioptas et al. shows that many models of random binary constraint satisfaction problems become trivially insoluble as problem size increases. This insolubility is partly due to the presence of ‘flawed variables,’ ...

The standard models used to generate random binary constraint satisfaction problems are described. At the problem sizes studied experimentally, a phase transition is seen as the constraint tightness is varied. However, Achlioptas et al. showed that if ...