In this paper we start an investigation to check the best we can do with SAT encodings for solving two important hard arithmetic problems, integer factorization and discrete logarithm. Given the current success of using SAT encodings for solving problems with linear arithmetic constraints, studying the suitability of SAT for solving non-linear arithmetic problems was a natural step. However, ou...

The increasing share of distributed energy resources poses a challenge to the distribution network operator (DNO) to maintain the current availability of the system while limiting the investment costs. Related to this, there is a clear trend in DNOs trying to better monitor their grid by installing a distribution management system (DMS). This DMS enables the DNOs to remotely switch their networ...

This paper discusses issues on the estimation of consumer demand equations subject to binding non-negative constraints. We propose computationally feasible specifications and a simulated maximum likelihood (SML) method for demand systems. Our study shows that the econometric implementation of the SML estimates can avoid high-dimensional integration problems. As contrary to the simulation method...

The facility location problem is a strategic decision-making for a supply chain, which determines the profitability and sustainability of its components. This paper deals with a scenario where two supply chains, consisting of a producer, a number of distribution centers and several retailers provided with similar products, compete to maintain their market shares by opening new distribution cent...

It was recently discovered by Baik, Deift and Johansson [4] that the asymptotic distribution of the length of the longest increasing subsequence in a permutation chosen uniformly at random from Sn, properly centred and normalised, is the same as the asymptotic distribution of the largest eigenvalue of an n × n GUE random matrix, properly centred and normalised, as n → ∞. This distribution had e...

In a famous paper 8] Hammersley investigated the length L n of the longest increasing subsequence of a random n-permutation. Implicit in that paper is a certain one-dimensional continuous-space interacting particle process. By studying a hydrodynamical limit for Hammersley's process we show by fairly \soft" arguments that limn ?1=2 EL n = 2. This is a known result, but previous proofs (Vershik-...

We compute the limit distribution for the (centered and scaled) length of the longest increasing subsequence of random colored permutations. The limit distribution function is a power of that for usual random permutations computed recently by Baik, Deift, and Johansson (math.CO/9810105). In the two–colored case our method provides a different proof of a similar result by Tracy and Widom about t...