Self-adaptive combination of global tabu search and local search for nonlinear equations

Solving systems of nonlinear equations is a very important task since the problems emerge mostly through the mathematical modelling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a self-adaptive combination of a metaheuristic with a classical local search method is able to converge to some difficult problems that are not solved by Newton-type methods.

Web-based application programming interface to solve nonlinear optimization problems

Nonlinear Optimization Problems are usual in many engineering fields. Due to its characteristics the objective function of some problems might not be differentiable or its derivatives have complex expressions. There are even cases where an analytical expression of the objective function might not be possible to determine either due to its complexity or its cost (monetary, computational, time, ...). In these cases Nonlinear Optimization methods must be used. An API, including several methods and algorithms to solve constrained and unconstrained optimization problems was implemented. This API can be accessed not only as traditionally, by installing it on the developer and/or user computer, but it can also be accessed remotely using Web Services. As long as there is a network connection to the server where the API is installed, applications always access to the latest API version. Also an Web-based application, using the proposed API, was developed. This application is to be used by users that do not want to integrate methods in applications, and simply want to have a tool to solve Nonlinear Optimization Problems.

Visualizing non-linear control system performance by means of multidimensional scaling

This paper addresses the use of multidimensional scaling in the evaluation of controller performance. Several nonlinear systems are analyzed based on the closed loop time response under the action of a reference step input signal. Three alternative performance indices, based on the time response, Fourier analysis, and mutual information, are tested. The numerical experiments demonstrate the feasibility of the proposed methodology and motivate its extension for other performance measures and new classes of nonlinearities.

Neural-network approach to modeling liquid crystals in complex confinement

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy minimization. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the multilayer perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible, and refinable. Furthermore, it can be readily generalized to the richer experimental patterned-substrate geometries that are now experimentally realizable but very problematic to conventional theoretical treatments.

Solving nonlinear equations by a tabu search strategy

Solving systems of nonlinear equations is a problem of particular importance since they emerge through the mathematical modeling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a metaheuristic, called Directed Tabu Search (DTS) [16], is able to converge to the solutions of a set of problems for which the fsolve function of MATLAB® failed to converge. We also show the effect of the dimension of the problem in the performance of the DTS.

Travelling wave profiles in some models with nonlinear diffusion

We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.

Fractional describing function of systems with nonlinear friction

This paper studies the describing function (DF) of systems consisting in a mass subjected to nonlinear friction. The friction force is composed in three components namely, the viscous, the Coulomb and the static forces. The system dynamics is analyzed in the DF perspective revealing a fractional-order behaviour. The reliability of the DF method is evaluated through the signal harmonic content and the limit cycle prediction.

Development of fractional order capacitors based on electrolyte processes

In recent years, significant research in the field of electrochemistry was developed. The performance of electrical devices, depending on the processes of the electrolytes, was described and the physical origin of each parameter was established. However, the influence of the irregularity of the electrodes was not a subject of study and only recently this problem became relevant in the viewpoint of fractional calculus. This paper describes an electrolytic process in the perspective of fractional order capacitors. In this line of thought, are developed several experiments for measuring the electrical impedance of the devices. The results are analyzed through the frequency response, revealing capacitances of fractional order that can constitute an alternative to the classical integer order elements. Fractional order electric circuits are used to model and study the performance of the electrolyte processes.

Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomena

The development of fractional-order controllers is currently one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. This paper reports on the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order PID controllers in the presence of several nonlinearities is discussed. Some results are provided that indicate the superior robustness of such algorithms.

Evaluation of enzyme-linked immunosorbent and alternative assays for detection of HIV antibodies using panels of Brasilian sera

Sera from 472 Brazilian subjects, confirmed to be either positive or negative for HIV antibodies and comprising the total clinical spectrum of HIV infection, were utilized in the evaluation of six commercially available enzyme-linked immunosorbent assays (ELISA), as well as of four alternative assays, namely indirect immunofluorescence (IIF), passive hemagglutination (PHA), dot blot and Karpas AIDS cell test. The sensitivities ranged from 100% (Abbott and Roche ELISA) to 84.2% (PHA) and the specificities ranged from 99.3% (IIF) to 80.2% (PHA). The sensitivity and specificity of the PHA and the sensitivity of the Karpas cell test were significantly lower than those of the other tests. Although the IFF and dot blot had good sensitivities and specificities, the six ELISA were more attractive than those tests when other parameters such as ease of reading and duration of assay were considered.

Anatase as an alternative application for preventing biodeterioration of mortars: evaluation and comparison with other biocides

International Biodeterioration & Biodegradation 64(2010)388 e 396

Alternative chelating agents: Evaluation of the ready biodegradability and complexation properties

The ready biodegradability of four chelating agents, N,N -(S,S)-bis[1-carboxy-2-(imidazol-4-yl)ethyl]ethylenediamine (BCIEE), N - ethylenedi-L-cysteine (EC), N,N -bis (4-imidazolymethyl)ethylenediamine (EMI) and 2,6-pyridine dicarboxylic acid (PDA), was tested according to the OECD guideline for testing of chemicals. PDA proved to be a readily biodegradable substance. However, none of the other three compounds were degraded during the 28 days of the test. Chemical simulations were performed for the four compounds in order to understand their ability to complex with some metal ions (Ca, Cd, Co, Cu, Fe, Mg, Mn, Ni, Pb, Zn) and discuss possible applications of these chelating agents. Two different conditions were simulated: (i) in the presence of the chelating agent and one metal ion, and (ii) in the simultaneous presence of the chelating agent and all metal ions with an excess of Ca. For those compounds that were revealed not to be readily biodegradable (BCIEE, EC and EMI), applications were evaluated where this property was not fundamental or even not required. Chemical simulations pointed out that possible applications for these chelating agents are: food fortification, food process, fertilizers, biocides, soil remediation and treatment of metal poisoning. Additionally, chemical simulations also predicted that PDA is an efficient chelating agent for Ca incrustations removal, detergents and for pulp metal ions removal process.

Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

‘Thy love afar is spite at home' Emerson, Thoreau and Carey: an alternative perspective of communication in US

The conquest of the West by the stagecoaches and then by railway, Ford and the automobile civilization, the Moon landing by Apollo 11, Microsoft, Apple, CNN, Google and Facebook have appeared to us as celebratory examples of the willingness and ability of the US to overcome the distance and the absence through so-called modern progress of transportation and communication. Undoubtedly, the imaginary and the instrumental power associated to transports and communication of the last century and a half are identified with the mental images that the world has of the US. A world that has eagerly imported and copy their technology and technological culture. Beyond the illusions, this attempting, which has always been praised to transcende space and eclipse the time to get to places and peole increasingly distant and fast, has always a dark side: the political control of population, commercial advertising, the spread of the rumors, noise and gossip. However, since at least the nineteenth century, the political project incorporated in modern transportation and communication technologies was not shared by some of the most remarkable thinkers in the US not only in that century, but also in the 20th century. This paper begins by rescue Ralph W. Emerson and Henry D. Thoreau legacy regarding to communication. Emerson conceived communication as a give-and-take with no coordination between the two, and does not involve contact with the other. Thoreau, in turn, argued that modern trasnportation and communications inventions are but pretty toys which distract attention from serious things, nothing more than 'improved means to an end that is not perfected.' Secondly, we show that this skeptical view of the techological improvement of transport and communication was proceed in an original way with James W. Carey, a media studies thinker who became known for his criticism of the transmission view of communication.

Soliton-type and other travelling wave solutions for an improved class of nonlinear sixth-order Boussinesq equations

An improved class of nonlinear bidirectional Boussinesq equations of sixth order using a wave surface elevation formulation is derived. Exact travelling wave solutions for the proposed class of nonlinear evolution equations are deduced. A new exact travelling wave solution is found which is the uniform limit of a geometric series. The ratio of this series is proportional to a classical soliton-type solution of the form of the square of a hyperbolic secant function. This happens for some values of the wave propagation velocity. However, there are other values of this velocity which display this new type of soliton, but the classical soliton structure vanishes in some regions of the domain. Exact solutions of the form of the square of the classical soliton are also deduced. In some cases, we find that the ratio between the amplitude of this wave and the amplitude of the classical soliton is equal to 35/36. It is shown that different families of travelling wave solutions are associated with different values of the parameters introduced in the improved equations.