Continuous GRASP with a local active-set method for bound-constrained global optimization

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic-based on the CGRASP and GENCAN methods-for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP-GENCAN on a set of benchmark multimodal test functions.

Repetition-free longest common subsequence

We study the following problem. Given two sequences x and y over a finite alphabet, find a repetition-free longest common subsequence of x and y. We show several algorithmic results, a computational complexity result, and we describe a preliminary experimental study based on the proposed algorithms. We also show that this problem is APX-hard. (C) 2009 Elsevier B.V. All rights reserved.

Approximation algorithms and hardness results for the clique packing problem

For a fixed family F of graphs, an F-packing in a graph G is a set of pairwise vertex-disjoint subgraphs of G, each isomorphic to an element of F. Finding an F-packing that maximizes the number of covered edges is a natural generalization of the maximum matching problem, which is just F = {K(2)}. In this paper we provide new approximation algorithms and hardness results for the K(r)-packing problem where K(r) = {K(2), K(3,) . . . , K(r)}. We show that already for r = 3 the K(r)-packing problem is APX-complete, and, in fact, we show that it remains so even for graphs with maximum degree 4. On the positive side, we give an approximation algorithm with approximation ratio at most 2 for every fixed r. For r = 3, 4, 5 we obtain better approximations. For r = 3 we obtain a simple 3/2-approximation, achieving a known ratio that follows from a more involved algorithm of Halldorsson. For r = 4, we obtain a (3/2 + epsilon)-approximation, and for r = 5 we obtain a (25/14 + epsilon)-approximation. (C) 2008 Elsevier B.V. All rights reserved.

Minimum cycle cover and Chinese postman problems on mixed graphs with bounded tree-width

Let M = (V, E, A) be a mixed graph with vertex set V, edge set E and arc set A. A cycle cover of M is a family C = {C(1), ... , C(k)} of cycles of M such that each edge/arc of M belongs to at least one cycle in C. The weight of C is Sigma(k)(i=1) vertical bar C(i)vertical bar. The minimum cycle cover problem is the following: given a strongly connected mixed graph M without bridges, find a cycle cover of M with weight as small as possible. The Chinese postman problem is: given a strongly connected mixed graph M, find a minimum length closed walk using all edges and arcs of M. These problems are NP-hard. We show that they can be solved in polynomial time if M has bounded tree-width. (C) 2008 Elsevier B.V. All rights reserved.

An all-substrings common subsequence algorithm

Given two strings A and B of lengths n(a) and n(b), n(a) <= n(b), respectively, the all-substrings longest common subsequence (ALCS) problem obtains, for every substring B` of B, the length of the longest string that is a subsequence of both A and B. The ALCS problem has many applications, such as finding approximate tandem repeats in strings, solving the circular alignment of two strings and finding the alignment of one string with several others that have a common substring. We present an algorithm to prepare the basic data structure for ALCS queries that takes O(n(a)n(b)) time and O(n(a) + n(b)) space. After this preparation, it is possible to build that allows any LCS length to be retrieved in constant time. Some trade-offs between the space required and a matrix of size O(n(b)(2)) the querying time are discussed. To our knowledge, this is the first algorithm in the literature for the ALCS problem. (C) 2007 Elsevier B.V. All rights reserved.

A Bayesian Semiparametric Approach for Solving the Discrete Calibration Problem

In this article, we introduce a semi-parametric Bayesian approach based on Dirichlet process priors for the discrete calibration problem in binomial regression models. An interesting topic is the dosimetry problem related to the dose-response model. A hierarchical formulation is provided so that a Markov chain Monte Carlo approach is developed. The methodology is applied to simulated and real data.

Billiards in a General Domain with Random Reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain D R(d) until it hits the boundary and bounces randomly inside, according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord ""picked at random"" in D, and we study the angle of intersection of the process with a (d - 1) -dimensional manifold contained in D.

SPECIAL CHARACTERIZATIONS OF STANDARD DISCRETE MODELS

This article presents important properties of standard discrete distributions and its conjugate densities. The Bernoulli and Poisson processes are described as generators of such discrete models. A characterization of distributions by mixtures is also introduced. This article adopts a novel singular notation and representation. Singular representations are unusual in statistical texts. Nevertheless, the singular notation makes it simpler to extend and generalize theoretical results and greatly facilitates numerical and computational implementation.

HOMEOMORPHISMS OF THE ANNULUS WITH A TRANSITIVE LIFT II

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift (f) over tilde to the in finite strip (A) over tilde which is transitive. We show that, if the rotation number of (f) over tilde restricted to both boundary components of A is strictly positive, then there exists a closed nonempty connected set Gamma subset of (A) over tilde such that Gamma subset of] - infinity,0] x [0,1], Gamma is unbounded, the projection of to Gamma A is dense, Gamma - (1, 0) subset of Gamma and (f) over tilde(Gamma) subset of Gamma. Also, if p(1) is the projection on the first coordinate of (A) over tilde, then there exists d > 0 such that, for any (z) over tilde is an element of Gamma, lim sup (n ->infinity) p(1)((f) over tilde (n) ((Z) over tilde)) - p(1) ((Z) over tilde)/n < -d.

Metastable Periodic Patterns in Singularly Perturbed Delayed Equations

We consider the scalar delayed differential equation epsilon(x) over dot(t) = -x(t) + f(x(t-1)), where epsilon > 0 and f verifies either df/dx > 0 or df/dx < 0 and some other conditions. We present theorems indicating that a generic initial condition with sign changes generates a solution with a transient time of order exp(c/epsilon), for some c > 0. We call it a metastable solution. During this transient a finite time span of the solution looks like that of a periodic function. It is remarkable that if df/dx > 0 then f must be odd or present some other very special symmetry in order to support metastable solutions, while this condition is absent in the case df/dx < 0. Explicit epsilon-asymptotics for the motion of zeroes of a solution and for the transient time regime are presented.

SUPPORT OF MAXIMIZING MEASURES FOR TYPICAL C(0) DYNAMICS ON COMPACT MANIFOLDS

Given a compact manifold X, a continuous function g : X -> IR, and a map T : X -> X, we study properties of the T-invariant Borel probability measures that maximize the integral of g. We show that if X is a n-dimensional connected Riemaniann manifold, with n >= 2, then the set of homeomorphisms for which there is a maximizing measure supported on a periodic orbit is meager. We also show that, if X is the circle, then the ""topological size"" of the set of endomorphisms for which there are g maximizing measures with support on a periodic orbit depends on properties of the function g. In particular, if g is C(1), it has interior points.

Boundary and internal conditions for adjoint fluid-flow problems

The ever-increasing robustness and reliability of flow-simulation methods have consolidated CFD as a major tool in virtually all branches of fluid mechanics. Traditionally, those methods have played a crucial role in the analysis of flow physics. In more recent years, though, the subject has broadened considerably, with the development of optimization and inverse design applications. Since then, the search for efficient ways to evaluate flow-sensitivity gradients has received the attention of numerous researchers. In this scenario, the adjoint method has emerged as, quite possibly, the most powerful tool for the job, which heightens the need for a clear understanding of its conceptual basis. Yet, some of its underlying aspects are still subject to debate in the literature, despite all the research that has been carried out on the method. Such is the case with the adjoint boundary and internal conditions, in particular. The present work aims to shed more light on that topic, with emphasis on the need for an internal shock condition. By following the path of previous authors, the quasi-1D Euler problem is used as a vehicle to explore those concepts. The results clearly indicate that the behavior of the adjoint solution through a shock wave ultimately depends upon the nature of the objective functional.

A DISCRETIZATION SCHEME FOR AN ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH DELAY AND ITS DYNAMICS

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.

Fibonacci bimodal maps

We introduce the Fibonacci bimodal maps on the interval and show that their two turning points are both in the same minimal invariant Cantor set. Two of these maps with the same orientation have the same kneading sequences and, among bimodal maps without central returns, they exhibit turning points with the strongest recurrence as possible.

On the extent of star countable spaces

For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y aS, X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelof spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelof. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense sigma-compact subspace can have arbitrary extent. It is proved that for any omega (1)-monolithic compact space X, if C (p) (X)is star countable then it is Lindelof.