Solving discrete ordered median problems with induced order: preliminary results

The Discrete Ordered Median Problem with Induced Order (DOMP+IO) is a multi-level version of the classical DOMP, which has been widely studied. In this work, a DOMP+IO with two types of facilites (levels) is considered and some preliminary results are provided.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A Genetic Algorithm for solving the Discrete Ordered Median Problem with Induced Order

The Discrete Ordered Median Problem with Induced Ordered (DOMP+IO) is a multi-facility version of the classical discrete ordered median problem (DOMP), which has been widely studied. Several exact methods have been proposed to solve the DOMP, however these methods could only solve small-scale problems, which are far of real-life problems. In this work, a DOMP+IO with two kinds of facilities is considered and a heuristic method is proposed for its solving. The proposed procedure is based on a genetic algorithm and the preliminary results show the efficiency and capability to obtain good solutions for large-scale problems.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

On approximate solutions of semilinear evolution equations

A general framework is presented to discuss the approximate solutions of an evolution equation in a Banach space, with a linear part generating a semigroup and a sufficiently smooth nonlinear part. A theorem is presented, allowing to infer from an approximate solution the existence of an exact solution. According to this theorem, the interval of existence of the exact solution and the distance of the latter from the approximate solution can be evaluated solving a one-dimensional "control" integral equation, where the unknown gives a bound on the previous distance as a function of time. For example, the control equation can be applied to the approximation methods based on the reduction of the evolution equation to finite-dimensional manifolds: among them, the Galerkin method is discussed in detail. To illustrate this framework, the nonlinear heat equation is considered. In this case the control equation is used to evaluate the error of the Galerkin approximation; depending on the initial datum, this approach either grants global existence of the solution or gives fairly accurate bounds on the blow up time.Comment: 33 pages, 10 figures. To appear in Rev. Math. Phys. (Shortened version; the proof of Prop. 3.4. has been simplified

On a Spector ultrapower of the Solovay model

We prove that a Spector--like ultrapower extension \gN of a countable Solovay model \gM (where all sets of reals are Lebesgue measurable) is equal to the set of all sets constructible from reals in a generic extension \gM[\al] where \al is a random real over \gM. The proof involves an almost everywhere uniformization theorem in the Solovay model

Deterministic Consistency: A Programming Model for Shared Memory Parallelism

The difficulty of developing reliable parallel software is generating interest in deterministic environments, where a given program and input can yield only one possible result. Languages or type systems can enforce determinism in new code, and runtime systems can impose synthetic schedules on legacy parallel code. To parallelize existing serial code, however, we would like a programming model that is naturally deterministic without language restrictions or artificial scheduling. We propose "deterministic consistency", a parallel programming model as easy to understand as the "parallel assignment" construct in sequential languages such as Perl and JavaScript, where concurrent threads always read their inputs before writing shared outputs. DC supports common data- and task-parallel synchronization abstractions such as fork/join and barriers, as well as non-hierarchical structures such as producer/consumer pipelines and futures. A preliminary prototype suggests that software-only implementations of DC can run applications written for popular parallel environments such as OpenMP with low (<10%) overhead for some applications.Comment: 7 pages, 3 figure