Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

Application-oriented Mixed Integer Non-Linear Programming

In the most recent years there is a renovate interest for Mixed Integer Non-Linear Programming (MINLP) problems. This can be explained for different reasons: (i) the performance of solvers handling non-linear constraints was largely improved; (ii) the awareness that most of the applications from the real-world can be modeled as an MINLP problem; (iii) the challenging nature of this very general class of problems. It is well-known that MINLP problems are NP-hard because they are the generalization of MILP problems, which are NP-hard themselves. However, MINLPs are, in general, also hard to solve in practice. We address to non-convex MINLPs, i.e. having non-convex continuous relaxations: the presence of non-convexities in the model makes these problems usually even harder to solve. The aim of this Ph.D. thesis is to give a flavor of different possible approaches that one can study to attack MINLP problems with non-convexities, with a special attention to real-world problems. In Part 1 of the thesis we introduce the problem and present three special cases of general MINLPs and the most common methods used to solve them. These techniques play a fundamental role in the resolution of general MINLP problems. Then we describe algorithms addressing general MINLPs. Parts 2 and 3 contain the main contributions of the Ph.D. thesis. In particular, in Part 2 four different methods aimed at solving different classes of MINLP problems are presented. Part 3 of the thesis is devoted to real-world applications: two different problems and approaches to MINLPs are presented, namely Scheduling and Unit Commitment for Hydro-Plants and Water Network Design problems. The results show that each of these different methods has advantages and disadvantages. Thus, typically the method to be adopted to solve a real-world problem should be tailored on the characteristics, structure and size of the problem. Part 4 of the thesis consists of a brief review on tools commonly used for general MINLP problems, constituted an integral part of the development of this Ph.D. thesis (especially the use and development of open-source software). We present the main characteristics of solvers for each special case of MINLP.

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena

We prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term. We also show the global quenching phenomena for L1 initial datums. Moreover, the free boundary problem is considered in this paper.

Tracking of non-stationary time-series using resource allocating RBF networks

In this paper, we discuss some practical implications for implementing adaptable network algorithms applied to non-stationary time series problems. Using electricity load data and training with the extended Kalman filter, we demonstrate that the dynamic model-order increment procedure of the resource allocating RBF network (RAN) is highly sensitive to the parameters of the novelty criterion. We investigate the use of system noise and forgetting factors for increasing the plasticity of the Kalman filter training algorithm, and discuss the consequences for on-line model order selection. We also find that a recently-proposed alternative novelty criterion, found to be more robust in stationary environments, does not fare so well in the non-stationary case due to the need for filter adaptability during training.

Unsteady free convection flow in the stagnation-point region of a rotating sphere

The unsteady free convection boundary-layer flow in the forward stagnation-point region of a sphere, which is rotating with time-dependent angular velocity in an ambient fluid, has been studied. Both constant wall temperature and constant hear flux conditions have been considered. The non-linear coupled parabolic partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The skin friction and the heat transfer are enhanced by the buoyancy force. The effect of the buoyancy force is found to be more pronounced for smaller Prandtl numbers than for larger Prandtl numbers. For a given buoyancy force, the heat transfer increases with an increase in Prandtl number, but the skin friction decreases.

Unsteady MHD mixed convection flow over an impulsively stretched permeable vertical surface in a quiescent fluid

The unsteady mixed convection flow of an incompressible laminar electrically conducting fluid over an impulsively stretched permeable vertical surface in an unbounded quiescent fluid in the presence of a transverse magnetic field has been investigated. At the same time, the surface temperature is suddenly increased from the surrounding fluid temperature or a constant heat flux is suddenly imposed on the surface. The problem is formulated in such a way that for small time it is governed by Rayleigh type of equation and for large time by Crane type of equation. The non-linear coupled parabolic partial differential equations governing the unsteady mixed convection flow under boundary layer approximations have been solved analytically by using the homotopy analysis method as well as numerically by an implicit finite difference scheme. The local skin friction coefficient and the local Nusselt number are found to decrease rapidly with time in a small time interval and they tend to steady-state values for t* >= 5. They also increase with the buoyancy force and suction, but decrease with injection rate. The local skin friction coefficient increases with the magnetic field, but the local Nusselt number decreases. There is a smooth transition from the unsteady state to the steady state. (C) 2010 Elsevier Ltd. All rights reserved.

On the study of a third-order mechanical oscillator

In this paper, the study of a third-order mechanical oscillator is presented by demonstrating its equivalence to the well-known R.C. multivibrator with two additional reactive elements. The conditions for the oscillator's possession of periodic solutions are presented. It is also shown that under certain conditions, the study of the given third-order autonomous system can be reduced to the study of an equivalent second-order, non-autonomous system.

Identification of TGFβ signaling, p53, and actin stress fibers as targets of LKB1 tumor suppressor activity

Tumorigenesis is a consequence of inactivating mutations of tumor suppressor genes and activating mutations of proto-oncogenes. Most of the mutations compromise cell autonomous and non-autonomous restrains on cell proliferation by modulating kinase signal transduction pathways. LKB1 is a tumor suppressor kinase whose sporadic mutations are frequently found in non-small cell lung cancer and cervical cancer. Germ-line mutations in the LKB1 gene lead to Peutz-Jeghers syndrome with an increased risk of cancer and development of benign gastrointestinal hamartomatous polyps consisting of hyperproliferative epithelia and prominent stromal stalk composed of smooth muscle cell lineage cells. The tumor suppressive function of LKB1 is possibly mediated by 14 identified LKB1 substrate kinases, whose activation is dependent on the LKB1 kinase complex. The aim of my thesis was to identify cell signaling pathways crucial for tumor suppression by LKB1. Re-introduction of LKB1 expression in the melanoma cell line G361 induces cell cycle arrest. Here we demonstrated that restoring the cytoplasmic LKB1 was sufficient to induce the cell cycle arrest in a tumor suppressor p53 dependent manner. To address the role of LKB1 in gastrointestinal tumor suppression, Lkb1 was deleted specifically in SMC lineage in vivo, which was sufficient to cause Peutz-Jeghers syndrome type polyposis. Studies on primary myofibroblasts lacking Lkb1 suggest that the regulation of TGFβ signaling, actin stress fibers and smooth muscle cell lineage differentiation are candidate mechanisms for tumor suppression by LKB1 in the gastrointestinal stroma. Further studies with LKB1 substrate kinase NUAK2 in HeLa cells indicate that NUAK2 is part of a positive feedback loop by which NUAK2 expression promotes actin stress fiber formation and, reciprocally the induction of actin stress fibers promote NUAK2 expression. Findings in this thesis suggest that p53 and TGFβ signaling pathways are potential mediators of tumor suppression by LKB1. An indication of NUAK2 in the promotion of actin stress fibers suggests that NUAK2 is one possible mediator of LKB1 dependent TGFβ signaling and smooth muscle cell lineage differentiation.

Analysis of continuum using boundary compatibility conditions of integrated force method

Static and vibration problems of an indeterminate continuum are traditionally analyzed by the stiffness method. The force method is more or less non-existent for such problems. This situation is primarily due to the incomplete state of development of the compatibility conditions which are essential for the analysis of indeterminate structures by the flexibility method. The understanding of the Compatibility Conditions (CC) has been substantially augmented. Based on the understanding of CC, a novel formulation termed the Integrated Force Method (IFM) has been established. In this paper IFM has been extended for the static and vibration analyses of a continuum. The IFM analysis is illustrated taking three examples: 1. (1) rectangular plate in flexure 2. (2) analysis of a cantilevered dam 3. (3) free vibration analysis of a beam. From the examples solved it is observed that the force response of an indeterminate continuum with mixed boundary conditions can be generated by IFM without any reference to displacements in the field or on the boundary. Displacements if required can be calculated by back substitution.

Free vibration analysis Of stochastic strings

The free vibration of strings with randomly varying mass and stiffness is considered. The joint probability density functions of the eigenvalues and eigenfunctions are characterized in terms of the solution of a pair of stochastic non-linear initial value problems. Analytical solutions of these equations based on the method of stochastic averaging are obtained. The effects of the mean and autocorrelation of the mass process are included in the analysis. Numerical results for the marginal probability density functions of eigenvalues and eigenfunctions are obtained and are found to compare well with Monte Carlo simulation results. The random eigenvalues, when normalized with respect to their corresponding deterministic values, are observed to tend to become first order stochastically stationary with respect to the mode count.

Optimal uncertainty quantification via convex optimization and relaxation

Many engineering applications face the problem of bounding the expected value of a quantity of interest (performance, risk, cost, etc.) that depends on stochastic uncertainties whose probability distribution is not known exactly. Optimal uncertainty quantification (OUQ) is a framework that aims at obtaining the best bound in these situations by explicitly incorporating available information about the distribution. Unfortunately, this often leads to non-convex optimization problems that are numerically expensive to solve.

This thesis emphasizes on efficient numerical algorithms for OUQ problems. It begins by investigating several classes of OUQ problems that can be reformulated as convex optimization problems. Conditions on the objective function and information constraints under which a convex formulation exists are presented. Since the size of the optimization problem can become quite large, solutions for scaling up are also discussed. Finally, the capability of analyzing a practical system through such convex formulations is demonstrated by a numerical example of energy storage placement in power grids.

When an equivalent convex formulation is unavailable, it is possible to find a convex problem that provides a meaningful bound for the original problem, also known as a convex relaxation. As an example, the thesis investigates the setting used in Hoeffding's inequality. The naive formulation requires solving a collection of non-convex polynomial optimization problems whose number grows doubly exponentially. After structures such as symmetry are exploited, it is shown that both the number and the size of the polynomial optimization problems can be reduced significantly. Each polynomial optimization problem is then bounded by its convex relaxation using sums-of-squares. These bounds are found to be tight in all the numerical examples tested in the thesis and are significantly better than Hoeffding's bounds.

Qualidade de vida das pessoas que vivem com o HIV/Aids no município de Rio das Ostras

Este estudo teve como objetivo geral analisar a qualidade de vida e suas representações em momentos distintos de diagnóstico entre pessoas que vivem com o HIV/aids, no município de Rio das Ostras, Rio de Janeiro. O estudo foi apoiado na teoria das representações sociais associada ao constructo da qualidade de vida. Realizou-se estudo quali-quantitativo, desenvolvido no Programa de DST, AIDS e Hepatites Virais do município de Rio das Ostras, tendo como sujeitos e amostra 100 pessoas que viviam com HIV/aids. A amostra foi estratificada, contando com 50 pessoas com tempo de diagnóstico de até 6 meses e 50 superior a 6 meses. A coleta de dados se deu através da aplicação de um questionário de caracterização socioeconômica e clínica, instrumento WHOQOL-HIV-Bref e entrevistas semiestruturadas, durante o período compreendido entre os meses de maio de 2013 a janeiro de 2014. Todos os sujeitos responderam aos dois primeiros instrumentos, e para as entrevistas foi constituída uma subamostra de 40 pessoas, igualmente distribuídas em dois grupos de acordo com o tempo de diagnóstico. A análise dos dados foi realizada através de estatística descritiva e inferencial utilizando o software SPSS 17.0. A análise das representações sociais foi apoiada pelo software Alceste 4.10. O grupo estudado caracterizou-se igualitariamente entre os sexos, com orientação religiosa evangélica (36%), média de idade de 37,6 anos, residentes no município de tratamento (89%), escolaridade fundamental e média incompleta (48%), empregados (65%), com renda pessoal média de R$ 1.077,00, com tempo de diagnóstico menor que quatro anos (68%), em uso de terapia antirretroviral (74%) e tempo de uso de terapia antirretroviral menor que quatro anos (52%). Os resultados da análise da qualidade de vida demonstraram que os escores dos domínios espiritualidade/religião/crenças pessoais (14,61) e relações sociais (14,52) apresentaram as maiores médias brutas, dentre aquelas com tendência positiva de avaliação. As médias mais baixas recaíram nos domínios nível de independência (13,77) e meio ambiente (13,29). Observou-se que o tempo de diagnóstico não interferiu nos escores de qualidade de vida da amostra. A representação da qualidade de vida revelou-se constituída por conteúdos associados às expectativas futuras, qualidade de vida frente ao diagnóstico, enfrentamento, uso do antirretroviral, transmissão e prevenção. Nesses conteúdos observou-se que essa representação compartilha significados, apontando para a hipótese de representação não autônoma em relação a representação social da aids. Conclui-se que o grupo possui mecanismos de adaptação à situação vivenciada, revelando percepção da necessidade de autocuidado e manutenção de uma rede de apoio alicerçada na espiritualidade/religiosidade e nas relações sociais, o que faz crer existir um caminhar progressivo para novos sistemas de interpretação, regendo relações mais positivas e objetivadas na representação social da qualidade de vida.

A miniature insertion element transposable in Microcystis sp FACHB 854

A 186-bp sequence with imperfect terminal inverted repeats and target direct repeats but without any transposase-encoding capacity was found to be transposable in an isolate derived from Microcystis sp. FACHB 854. This miniature insertion element, designated as ISM854-1, and with its homologues present at least 10 copies in the genome of Microcystis FACHB 854, is inserted into the 8-bp long and AT-rich target sequences, but none or few in other Microcystis strains. A variant of ISM854-1, denoted ISM854-1A, has perfect inverted repeat sequences and may transpose in pairs in a structure like a composite transposon. This is the first report of non-autonomous transposition of a mini-IS in a cyanobacterium.

Comparative genomic analysis reveals species-dependent complexities that explain difficulties with microsatellite marker development in molluscs

Reliable population DNA molecular markers are difficult to develop for molluscs, the reasons for which are largely unknown. Identical protocols for microsatellite marker development were implemented in three gastropods. Success rates were lower for Gibbula cineraria compared to Littorina littorea and L. saxatilis. Comparative genomic analysis of 47.2?kb of microsatellite containing sequences (MCS) revealed a high incidence of cryptic repetitive DNA in their flanking regions. The majority of these were novel, and could be grouped into DNA families based upon sequence similarities. Significant inter-specific variation in abundance of cryptic repetitive DNA and DNA families was observed. Repbase scans show that a large proportion of cryptic repetitive DNA was identified as transposable elements (TEs). We argue that a large number of TEs and their transpositional activity may be linked to differential rates of DNA multiplication and recombination. This is likely to be an important factor explaining inter-specific variation in genome stability and hence microsatellite marker development success rates. Gastropods also differed significantly in the type of TEs classes (autonomous vs non-autonomous) observed. We propose that dissimilar transpositional mechanisms differentiate the TE classes in terms of their propensity for transposition, fixation and/or silencing. Consequently, the phylogenetic conservation of non-autonomous TEs, such as CvA, suggests that dispersal of these elements may have behaved as microsatellite-inducing elements. Results seem to indicate that, compared to autonomous, non-autonomous TEs maybe have a more active role in genome rearrangement processes. The implications of the findings for genomic rearrangement, stability and marker development are discussed.