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.

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.

Non-planar double-box, massive and massless pentabox Feynman integrals in the negative-dimensional approach

The negative-dimensional integration method is a technique which can be applied, with success, in usual covariant gauge calculations. We consider three two-loop diagrams: the scalar massless non-planar double-box with six propagators and the scalar pentabox in two cases, where six virtual particles have the same mass, and in the case all of them are massless. Our results are given in terms of hypergeometric functions of Mandelstam variables and also for arbitrary exponents of propagators and dimension D.

Controlling Excitation Inversion of a Cooper Pair Box Interacting with a Nanomechanical Resonator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Influence of cavity preparation and curing method on the marginal seal of resin composite restorations: an in vitro evaluation.

OBJECTIVE: To evaluate the influence of cavity design and photocuring method on the marginal seal of resin composite restorations. METHOD AND MATERIALS: Seventy-two bovine teeth were divided into 2 groups: group 1 received box-type cavity preparations, and group 2 received plate-type preparations. Each group was divided into 3 subgroups. After etching and bonding, Z250 resin composite (3M Espe) was applied in 2 equal increments and cured with 1 of 3 techniques: (1) conventional curing for 30 seconds at 650 mW/cm2; (2) 2-step photocuring, in which the first step was performed 14 mm from the restoration for 10 seconds at 180 mW/cm2 and the second step was performed in direct contact for 20 seconds at 650 mW/cm2; or (3) progressive curing using Jetlite 4000 (J. Morita) for 8 seconds at 125 mW/cm2 and then 22 seconds at 125 mW/cm2 up to 500 mW/cm2. The specimens were thermocycled for 500 cycles and then submitted to dye penetration with a 50% silver nitrate solution. Microleakage was assessed using a stereomicroscope. Data were analyzed using analysis of variance and Tukey test (5% level of significance). RESULTS: A statistically significant difference was found between groups when a double interaction between photocuring and cavity preparation was considered (P = .029). CONCLUSIONS: No one type of cavity preparation or photocuring method prevented micro-leakage. The plate-type preparation showed the worst dye penetration when conventional and progressive photocuring methods were used. The best results were found using the 2-step photocuring with the plate-type preparation.

The bias in reversing the Box-Cox transformation in time series forecasting: An empirical study based on neural networks

The Box-Cox transformation is a technique mostly utilized to turn the probabilistic distribution of a time series data into approximately normal. And this helps statistical and neural models to perform more accurate forecastings. However, it introduces a bias when the reversion of the transformation is conducted with the predicted data. The statistical methods to perform a bias-free reversion require, necessarily, the assumption of Gaussianity of the transformed data distribution, which is a rare event in real-world time series. So, the aim of this study was to provide an effective method of removing the bias when the reversion of the Box-Cox transformation is executed. Thus, the developed method is based on a focused time lagged feedforward neural network, which does not require any assumption about the transformed data distribution. Therefore, to evaluate the performance of the proposed method, numerical simulations were conducted and the Mean Absolute Percentage Error, the Theil Inequality Index and the Signal-to-Noise ratio of 20-step-ahead forecasts of 40 time series were compared, and the results obtained indicate that the proposed reversion method is valid and justifies new studies. (C) 2014 Elsevier B.V. All rights reserved.

Structural characterization of Li-MN doped powders prepared by Pechini's method

Pechini's method has been successfully used to prepare Li-doped MgNb2O6(MN) at short time and low temperature. It consists in the preparation of metal citrate solution, which is polymerized at 250°C to form a high viscous resin. This resin was burned in a box type furnace at 400°C/2h and ground in a mortar. Successive steps of calcination up to 900°C were used to form a crystalline precursor. SEM, DTA and XRD were used to characterize the powders. MN precursor powders containing from 0.1 to 5.0 mol% of LiNbO3 additive was prepared aiming better dielectric properties and microstructural characteristics of the PMN prepared from columbite route. SEM analysis showed that particles increased by sintering, forming large agglomerates. The surface area is also substantially reduced with the increase in additive amount above 1.0 mol%. In XRD pattern of the precursor material with 5.0 mol% of additive was observed the LiNbO3 phase of trigonal structure. XRD data were used for Rietveld refinement and a decrease in microstrain and pronounced increase in crystallite size with the increase of LiNbO3 were observed. It is in agreement with the particle morphologies observed by SEM analysis.

Spray Congealing of Pharmaceuticals: Study on Production of Solid Dispersions Using Box-Behnken Design

This work aimed at evaluating the spray congealing method for the production of microparticles of carbamazepine combined with a polyoxylglyceride carrier. In addition, the influence of the spray congealing conditions on the improvement of drug solubility was investigated using a three-factor, three-level Box-Behnken design. The factors studied were the cooling air flow rate, atomizing pressure, and molten dispersion feed rate. Dependent variables were the yield, solubility, encapsulation efficiency, particle size, water activity, and flow properties. Statistical analysis showed that only the yield was affected by the factors studied. The characteristics of the microparticles were evaluated using X-ray powder diffraction, scanning electron microscopy, differential scanning calorimetry, and hot-stage microscopy. The results showed a spherical morphology and changes in the crystalline state of the drug. The microparticles were obtained with good yields and encapsulation efficiencies, which ranged from 50 to 80% and 99.5 to 112%, respectively. The average size of the microparticles ranged from 17.7 to 39.4 mu m, the water activities were always below 0.5, and flowability was good to moderate. Both the solubility and dissolution rate of carbamazepine from the spray congealed microparticles were remarkably improved. The carbamazepine solubility showed a threefold increase and dissolution profile showed a twofold increase after 60 min compared to the raw drug. The Box-Behnken fractional factorial design proved to be a powerful tool to identify the best conditions for the manufacture of solid dispersion microparticles by spray congealing.

Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization

At each outer iteration of standard Augmented Lagrangian methods one tries to solve a box-constrained optimization problem with some prescribed tolerance. In the continuous world, using exact arithmetic, this subproblem is always solvable. Therefore, the possibility of finishing the subproblem resolution without satisfying the theoretical stopping conditions is not contemplated in usual convergence theories. However, in practice, one might not be able to solve the subproblem up to the required precision. This may be due to different reasons. One of them is that the presence of an excessively large penalty parameter could impair the performance of the box-constraint optimization solver. In this paper a practical strategy for decreasing the penalty parameter in situations like the one mentioned above is proposed. More generally, the different decisions that may be taken when, in practice, one is not able to solve the Augmented Lagrangian subproblem will be discussed. As a result, an improved Augmented Lagrangian method is presented, which takes into account numerical difficulties in a satisfactory way, preserving suitable convergence theory. Numerical experiments are presented involving all the CUTEr collection test problems.

Evaluation of Wave energy transmission through a floating breakwater using the SPH method

[EN]Energy transmission through a box-shaped floating breakwater (FB) is examined, under simplified conditions, by using the smoothed particle hydrodynamics (SPH) method, a mesh-free particle numerical approach. The efficiency of the structure is assessed in terms of the coefficient of transm ission as a function of the wave period and the location of the floating breakwater relative to the zone to be protected. Preliminary results conceming wave energy transmission reveals a clear improvement of the efficiency as wave period decreases andan important role ofthe bathymetry.

A Ladder Operator Solution to the Particle in a Box Problem

A ladder operator solution to the particle in a box problem of elementary quantum mechanics is presented, although the pedagogical use of this method for this problem is questioned.