U-curve: A branch-and-bound optimization algorithm for U-shaped cost functions on Boolean lattices applied to the feature selection problem

This paper presents the formulation of a combinatorial optimization problem with the following characteristics: (i) the search space is the power set of a finite set structured as a Boolean lattice; (ii) the cost function forms a U-shaped curve when applied to any lattice chain. This formulation applies for feature selection in the context of pattern recognition. The known approaches for this problem are branch-and-bound algorithms and heuristics that explore partially the search space. Branch-and-bound algorithms are equivalent to the full search, while heuristics are not. This paper presents a branch-and-bound algorithm that differs from the others known by exploring the lattice structure and the U-shaped chain curves of the search space. The main contribution of this paper is the architecture of this algorithm that is based on the representation and exploration of the search space by new lattice properties proven here. Several experiments, with well known public data, indicate the superiority of the proposed method to the sequential floating forward selection (SFFS), which is a popular heuristic that gives good results in very short computational time. In all experiments, the proposed method got better or equal results in similar or even smaller computational time. (C) 2009 Elsevier Ltd. All rights reserved.

Influence of culture conditions on mycelial growth and bioluminescence of Gerronema viridilucens

Herein we describe a procedure for measuring the total light emission of the naturally bioluminescent tropical fungus Gerronema viridilucens and the optimization of culture conditions using multivariate factorial ANOVA. Cultures growing on an agar surface in 35 mm Petri dishes at 90% humidity show optimal bioluminescence emission at 25 degrees C in the presence of 1.0% sugar cane molasses, 0.10% yeast extract and pH 6.0 (nonbuffered). Temperature and pH are the most important factors for both mycelial growth and bioluminescence.

Sensitivity of complex networks measurements

Complex networks obtained from real-world networks are often characterized by incompleteness and noise, consequences of imperfect sampling as well as artifacts in the acquisition process. Because the characterization, analysis and modeling of complex systems underlain by complex networks are critically affected by the quality and completeness of the respective initial structures, it becomes imperative to devise methodologies for identifying and quantifying the effects of the sampling on the network structure. One way to evaluate these effects is through an analysis of the sensitivity of complex network measurements to perturbations in the topology of the network. In this paper, measurement sensibility is quantified in terms of the relative entropy of the respective distributions. Three particularly important kinds of progressive perturbations to the network are considered, namely, edge suppression, addition and rewiring. The measurements allowing the best balance of stability (smaller sensitivity to perturbations) and discriminability (separation between different network topologies) are identified with respect to each type of perturbation. Such an analysis includes eight different measurements applied on six different complex networks models and three real-world networks. This approach allows one to choose the appropriate measurements in order to obtain accurate results for networks where sampling bias cannot be avoided-a very frequent situation in research on complex networks.

Constraining the age of the iporanga formation with SHRIMP U-Pb zircon: Implications for possible ediacaran glaciation in the Ribeira Belt, SE Brazil

The Ribeira belt in SE Brazil is a Neoproterozoic to Early Palaeozoic orogen, whose architecture and history is not yet fully understood. The depositional age of many of the sedimentary sequences in the Ribeira Belt remains unconstrained, and with debate concerning their depositional environment and tectonic setting. In this paper we present SHRIMP zircon U/Pb age constraints for one such problematic unit in the Ribeira Belt the lporanga Formation - and discuss the significance of this age with regards to the timing of Neoproterozoic glacial events in southeast Brazil. Using a felsic volcanic unit immediately under the lporanga Formation and granite cobbles from breccias in its basal parts a reconnaissance SHRIMP U/Pb zircon maximum depositional age of 580 Ma is assigned for the base of this unit. This age is marginally younger than the 625605 Ma ages for intrusions into the Lajeado and Ribeira subgroups, with which the lporanga Formation is in tectonic contact. This indicates that the Lajeado and Ribeira subgroups are not stratigraphically equivalent to the lporanga Formation, as thought previously by some workers. The maximum depositional age of 580 Ma also places a maximum time constraint on the tectonic juxtaposition of the lporanga Formation with other supracrustal units, and on the greenschist facies metamorphism and isoclinal folding that affected it. The potential glacial origin for the lporanga Formation, if correct, would place it in the late Ediacaran - provisionally equivalent to the Gaskiers glaciation. (c) 2007 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.