Nonautonomous mixed mKdV-sinh-Gordon hierarchy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Negative even grade mKdV hierarchy and its soliton solutions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Construction of time-dependent dynamical invariants: A new approach

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

THE REDUCTIVE PERTURBATION METHOD AND THE KORTEWEG-DE VRIES HIERARCHY

By using the reductive perturbation method of Taniuti with the introduction of an infinite sequence of slow time variables tau(1), tau(3), tau(5), ..., we study the propagation of long surface-waves in a shallow inviscid fluid. The Korteweg-de Vries (KdV) equation appears as the lowest order amplitude equation in slow variables. In this context, we show that, if the lowest order wave amplitude zeta(0) satisfies the KdV equation in the time tau(3), it must satisfy the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1), With n = 2, 3, 4,.... AS a consequence of this fact, we show with an explicit example that the secularities of the evolution equations for the higher-order terms (zeta(1), zeta(2),...) of the amplitude can be eliminated when zeta(0) is a solitonic solution to the KdV equation. By reversing this argument, we can say that the requirement of a secular-free perturbation theory implies that the amplitude zeta(0) satisfies the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1) This essentially means that the equations of the KdV hierarchy do play a role in perturbation theory. Thereafter, by considering a solitary-wave solution, we show, again with an explicit, example that the elimination of secularities through the use of the higher order KdV hierarchy equations corresponds, in the laboratory coordinates, to a renormalization of the solitary-wave velocity. Then, we conclude that this procedure of eliminating secularities is closely related to the renormalization technique developed by Kodama and Taniuti.

A hierarchy of adaptive (X)over-bar control charts

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Multiple-time higher-order perturbation analysis of the regularized long-wavelength equation

By considering the long-wavelength limit of the regularized long wave (RLW) equation, we study its multiple-time higher-order evolution equations. As a first result, the equations of the Korteweg-de Vries hierarchy are shown to play a crucial role in providing a secularity-free perturbation theory in the specific case of a solitary-wave solution. Then, as a consequence, we show that the related perturbative series can be summed and gives exactly the solitary-wave solution of the RLW equation. Finally, some comments and considerations are made on the N-soliton solution, as well as on the limitations of applicability of the multiple-scale method in obtaining uniform perturbative series.

The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation

We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity-free perturbation theory, we show that the well known N-soliton dynamics of the shallow water wave equation, in the particular case of α = 2β, can be reduced to the N-soliton solution that satisfies simultaneously all equations of the Korteweg-de Vries hierarchy.

PI Stabilization of a Class of Time Delay Systems

In this paper we use the Hermite-Biehler theorem to establish results for the design of proportional plus integral (PI) controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. A signature for the quasipolynomials in this class is derived and used in the proposed approach which yields the complete set of the stabilizing PI controllers.

Division of labor in stable social hierarchy of the independent-founding wasp Mischocyttarus (Monocyttarus) cassununga, von Ihering (Hymenoptera, Vespidae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The dynamic behavior of a parametrically excited time-periodic MEMS taking into account parametric errors

Micro-electromechanical systems (MEMS) are micro scale devices that are able to convert electrical energy into mechanical energy or vice versa. In this paper, the mathematical model of an electronic circuit of a resonant MEMS mass sensor, with time-periodic parametric excitation, was analyzed and controlled by Chebyshev polynomial expansion of the Picard interaction and Lyapunov-Floquet transformation, and by Optimal Linear Feedback Control (OLFC). Both controls consider the union of feedback and feedforward controls. The feedback control obtained by Picard interaction and Lyapunov-Floquet transformation is the first strategy and the optimal control theory the second strategy. Numerical simulations show the efficiency of the two control methods, as well as the sensitivity of each control strategy to parametric errors. Without parametric errors, both control strategies were effective in maintaining the system in the desired orbit. On the other hand, in the presence of parametric errors, the OLFC technique was more robust.

Modeling random corrosion processes via polynomial chaos expansion

Polynomial Chaos Expansion (PCE) is widely recognized as a flexible tool to represent different types of random variables/processes. However, applications to real, experimental data are still limited. In this article, PCE is used to represent the random time-evolution of metal corrosion growth in marine environments. The PCE coefficients are determined in order to represent data of 45 corrosion coupons tested by Jeffrey and Melchers (2001) at Taylors Beach, Australia. Accuracy of the representation and possibilities for model extrapolation are considered in the study. Results show that reasonably accurate smooth representations of the corrosion process can be obtained. The representation is not better because a smooth model is used to represent non-smooth corrosion data. Random corrosion leads to time-variant reliability problems, due to resistance degradation over time. Time variant reliability problems are not trivial to solve, especially under random process loading. Two example problems are solved herein, showing how the developed PCE representations can be employed in reliability analysis of structures subject to marine corrosion. Monte Carlo Simulation is used to solve the resulting time-variant reliability problems. However, an accurate and more computationally efficient solution is also presented.

Efficient computation of discrete polynomial transforms

This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )

Distributed models in P-Systems architectures to reduce computation time

Membrane systems are computational equivalent to Turing machines. However, their distributed and massively parallel nature obtains polynomial solutions opposite to traditional non-polynomial ones. At this point, it is very important to develop dedicated hardware and software implementations exploiting those two membrane systems features. Dealing with distributed implementations of P systems, the bottleneck communication problem has arisen. When the number of membranes grows up, the network gets congested. The purpose of distributed architectures is to reach a compromise between the massively parallel character of the system and the needed evolution step time to transit from one configuration of the system to the next one, solving the bottleneck communication problem. The goal of this paper is twofold. Firstly, to survey in a systematic and uniform way the main results regarding the way membranes can be placed on processors in order to get a software/hardware simulation of P-Systems in a distributed environment. Secondly, we improve some results about the membrane dissolution problem, prove that it is connected, and discuss the possibility of simulating this property in the distributed model. All this yields an improvement in the system parallelism implementation since it gets an increment of the parallelism of the external communication among processors. Proposed ideas improve previous architectures to tackle the communication bottleneck problem, such as reduction of the total time of an evolution step, increase of the number of membranes that could run on a processor and reduction of the number of processors.

Detecting reliable gene interactions by a hierarchy of Bayesian network classifiers

The main purpose of a gene interaction network is to map the relationships of the genes that are out of sight when a genomic study is tackled. DNA microarrays allow the measure of gene expression of thousands of genes at the same time. These data constitute the numeric seed for the induction of the gene networks. In this paper, we propose a new approach to build gene networks by means of Bayesian classifiers, variable selection and bootstrap resampling. The interactions induced by the Bayesian classifiers are based both on the expression levels and on the phenotype information of the supervised variable. Feature selection and bootstrap resampling add reliability and robustness to the overall process removing the false positive findings. The consensus among all the induced models produces a hierarchy of dependences and, thus, of variables. Biologists can define the depth level of the model hierarchy so the set of interactions and genes involved can vary from a sparse to a dense set. Experimental results show how these networks perform well on classification tasks. The biological validation matches previous biological findings and opens new hypothesis for future studies

Functional Hierarchy of Simultaneously Expressed Adhesion Receptors: Integrin α2β1 but Not CD44 Mediates MV3 Melanoma Cell Migration and Matrix Reorganization within Three-dimensional Hyaluronan-containing Collagen MatricesV⃞

Haptokinetic cell migration across surfaces is mediated by adhesion receptors including β1 integrins and CD44 providing adhesion to extracellular matrix (ECM) ligands such as collagen and hyaluronan (HA), respectively. Little is known, however, about how such different receptor systems synergize for cell migration through three-dimensionally (3-D) interconnected ECM ligands. In highly motile human MV3 melanoma cells, both β1 integrins and CD44 are abundantly expressed, support migration across collagen and HA, respectively, and are deposited upon migration, whereas only β1 integrins but not CD44 redistribute to focal adhesions. In 3-D collagen lattices in the presence or absence of HA and cross-linking chondroitin sulfate, MV3 cell migration and associated functions such as polarization and matrix reorganization were blocked by anti-β1 and anti-α2 integrin mAbs, whereas mAbs blocking CD44, α3, α5, α6, or αv integrins showed no effect. With use of highly sensitive time-lapse videomicroscopy and computer-assisted cell tracking techniques, promigratory functions of CD44 were excluded. 1) Addition of HA did not increase the migratory cell population or its migration velocity, 2) blocking of the HA-binding Hermes-1 epitope did not affect migration, and 3) impaired migration after blocking or activation of β1 integrins was not restored via CD44. Because α2β1-mediated migration was neither synergized nor replaced by CD44–HA interactions, we conclude that the biophysical properties of 3-D multicomponent ECM impose more restricted molecular functions of adhesion receptors, thereby differing from haptokinetic migration across surfaces.