Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme

In this paper, the method of Galerkin and the Askey-Wiener scheme are used to obtain approximate solutions to the stochastic displacement response of Kirchhoff plates with uncertain parameters. Theoretical and numerical results are presented. The Lax-Milgram lemma is used to express the conditions for existence and uniqueness of the solution. Uncertainties in plate and foundation stiffness are modeled by respecting these conditions, hence using Legendre polynomials indexed in uniform random variables. The space of approximate solutions is built using results of density between the space of continuous functions and Sobolev spaces. Approximate Galerkin solutions are compared with results of Monte Carlo simulation, in terms of first and second order moments and in terms of histograms of the displacement response. Numerical results for two example problems show very fast convergence to the exact solution, at excellent accuracies. The Askey-Wiener Galerkin scheme developed herein is able to reproduce the histogram of the displacement response. The scheme is shown to be a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2009 Elsevier Ltd. All rights reserved.

Análise faunística de himenópteros visitantes florais em fragmento de cerradão em Itirapina, SP

Bees are considered one of the most efficient pollinators. Therefore, they have Indisputable role in the plants reproduction, since they increase the quality and quantity of fruit and seeds, and thus they help the ecosystems maintenance. Cerrado is one of the most affected ecosystems due to the growth of human activities, drastically reducing its biodiversity. The faunistic analysis identifies the species and the size of the populations, and can also indicate the degree of environmental Impact on a particular area. Surveys on flower-visiting hymenoptera in a cerradao area, with 40ha, in the Experimental Station of Itiparina (SP), were conducted every fifteen days from March 2003 to February 2004. From 181 insects collected, the Apidae family was represented by the largest number of species and individuals. The species Apis mellifera (55.8%), Trigona spinipes (14.4%) and Exomalopsis (Exomalopsis) sp. (8.3%) were the most prevalent fit the area. Among the bees species collected, 30.8% were classified as sociable and 69.2% as solitary. Considering all hymenoptera collected, 59.7% preferred the morning period and 40.3% the afternoon period for foraging and/or visiting. The Diversity index (Shannon-Wiener) H was 1.6933, V(H) = 0.0123 and Uniformity index E = 0.5652, following pattern found in other areas of cerrado.

Chaos-Galerkin solution of stochastic Timoshenko bending problems

This paper presents an accurate and efficient solution for the random transverse and angular displacement fields of uncertain Timoshenko beams. Approximate, numerical solutions are obtained using the Galerkin method and chaos polynomials. The Chaos-Galerkin scheme is constructed by respecting the theoretical conditions for existence and uniqueness of the solution. Numerical results show fast convergence to the exact solution, at excellent accuracies. The developed Chaos-Galerkin scheme accurately approximates the complete cumulative distribution function of the displacement responses. The Chaos-Galerkin scheme developed herein is a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2011 Elsevier Ltd. All rights reserved.

Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement responses are derived, and compared with corresponding estimates obtained via Monte Carlo simulation. Results show very fast convergence and excellent accuracies in comparison to Monte Carlo simulation. The Askey-Wiener Galerkin scheme presented herein is shown to be a theoretically solid and numerically efficient method for the solution of stochastic problems in engineering.

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

A Class of Channels Resulting in Ill-Convergence for CMA in Decision Feedback Equalizers

This paper analyzes the convergence of the constant modulus algorithm (CMA) in a decision feedback equalizer using only a feedback filter. Several works had already observed that the CMA presented a better performance than decision directed algorithm in the adaptation of the decision feedback equalizer, but theoretical analysis always showed to be difficult specially due to the analytical difficulties presented by the constant modulus criterion. In this paper, we surmount such obstacle by using a recent result concerning the CM analysis, first obtained in a linear finite impulse response context with the objective of comparing its solutions to the ones obtained through the Wiener criterion. The theoretical analysis presented here confirms the robustness of the CMA when applied to the adaptation of the decision feedback equalizer and also defines a class of channels for which the algorithm will suffer from ill-convergence when initialized at the origin.

On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Effects of pasture implantation on the termite (Isoptera) fauna in the Central Brazilian Savanna (Cerrado)

The advance of agricultural frontier may cause the Cerrado (Brazilian savanna) to disappear before 2030. This work focuses on measuring the impact of pasture implantation on a cerrado`s termite fauna. Termites were sampled in a cerrado sensu stricto and a pasture, originally cerrado. All species were classified as their feeder group, accumulation curves were made and Shannon-Wiener indexes and beta diversity were calculated for both areas. Cerrado was richer than pasture and species composition differed considerably, leading beta diversity to a high value. The humivorous was the most representative species, followed by grass/litter feeders, xylophagous and, less representative, the intermediates. There were more xylophagous and intermediates species on cerrado than in pasture; the grass/litter feeders were more abundant in pasture, but didn`t differed in number or species; and humivorous didn`t differed neither in richness nor in abundance. This work shows that the simplification of the habitat is indeed causing the extinction of populations that depend on some specifics resource.

Evaluation of Adult Chronic Chagas` Heart Disease Diagnosis by Molecular and Serological Methods

Chagas` disease caused by Trypanosoma cruzi is endemic in Latin America. T. cruzi presents heterogeneous populations and comprises two main genetic lineages, named T. cruzi I and T. cruzi II. Diagnosis in the chronic phase is based on conventional serological tests, including indirect immunofluorescence (IIF) and enzyme-linked immunosorbent assay (ELISA), and diagnosis in the acute phase based on parasitological methods, including hemoculture. The objective of this study was to evaluate the diagnostic procedures of Chagas` disease in adult patients in the chronic phase by using a PCR assay and conventional serological tests, including TESA-blot as the gold standard. Samples were obtained from 240 clinical chronic chagasic patients. The sensitivities, compared to that of TESA-blot, were 70% for PCR using the kinetoplast region, 75% for PCR using the nuclear repetitive region, 99% for IIF, and 95% for ELISA. According to the serological tests results, we recommend that researchers assess the reliability and sensitivity of the commercial kit Chagatest ELISA recombinant, version 3.0 (Chagatest Rec v3.0; Wiener Lab, Rosario, Argentina), due to the lack of sensitivity. Based on our analysis, we concluded that PCR cannot be validated as a conventional diagnostic technique for Chagas` disease. These data have been corroborated by low levels of concordance with serology test results. It is recommended that PCR be used only for alternative diagnostic support. Using the nuclear repetitive region of T. cruzi, PCR could also be applicable for monitoring patients receiving etiologic treatment.

The Diffusion Kernel Filter

A particle filter method is presented for the discrete-time filtering problem with nonlinear ItA ` stochastic ordinary differential equations (SODE) with additive noise supposed to be analytically integrable as a function of the underlying vector-Wiener process and time. The Diffusion Kernel Filter is arrived at by a parametrization of small noise-driven state fluctuations within branches of prediction and a local use of this parametrization in the Bootstrap Filter. The method applies for small noise and short prediction steps. With explicit numerical integrators, the operations count in the Diffusion Kernel Filter is shown to be smaller than in the Bootstrap Filter whenever the initial state for the prediction step has sufficiently few moments. The established parametrization is a dual-formula for the analysis of sensitivity to gaussian-initial perturbations and the analysis of sensitivity to noise-perturbations, in deterministic models, showing in particular how the stability of a deterministic dynamics is modeled by noise on short times and how the diffusion matrix of an SODE should be modeled (i.e. defined) for a gaussian-initial deterministic problem to be cast into an SODE problem. From it, a novel definition of prediction may be proposed that coincides with the deterministic path within the branch of prediction whose information entropy at the end of the prediction step is closest to the average information entropy over all branches. Tests are made with the Lorenz-63 equations, showing good results both for the filter and the definition of prediction.

STRUCTURE OF THE SHRUB-ARBOREAL COMPONENT OF AN ATLANTIC FOREST FRAGMENT ON A HILLOCK IN THE CENTRAL LOWLAND OF RIO DE JANEIRO, BRAZIL

The present study describes and evaluates the horizontal and vertical structures of a lowland forest fragment on a hillock in the municipality of Silva Jardim, Rio de Janeiro State, Brazil (22 degrees 31`56 `` S and 42 degrees 20`46 `` W). Twenty plots (10x2m) totaling 0.5ha were laid out following the slope grade using DBH >= 5cm as the inclusion criterion. A total of 734 individuals were encountered, yielding a total density of 1468 ind./ha and a total basal area of 10783m(2). The richness values (129 species/41 families), Shannon-Wiener diversity (4.22) and equitability (0.87) indices indicated an accentuated floristic heterogeneity and low ecological dominance. Lauraceae, Myrtaceae, Fabaceae and Euphorbiaceae showed the greatest species richness, corroborating other studies that indicated these species as the most representative of Atlantic Forest areas in southeastern Brazil. The species with the greatest importance values (VI) were Aparisthmium cordatum, Guapira opposita, Lacistema pubescens, Xylopia sericea, Tapirira guianensis and Piptocarpha macropoda. The high diversity observed was influenced by earlier anthropogenic actions and by the current successional stage. The forest fragment studied demonstrated closer floristic similarity to areas inventoried in a close-by biological reserve than to fragments dispersed throughout the coastal plain. Similarities in soil type, degree of soil saturation and use-history of forest resources all support these relationships. The fragmented physiognomy of the central lowland in this region and the use-history of the landscape make these small remnant forest areas important in terms of establishing strategies for landscape restoration and species conservation.

Exact Search Directions for Optimization of Linear and Nonlinear Models Based on Generalized Orthonormal Functions

A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

Related changes in biodiversity, insolation and climate in the Atlantic rainforest since the last interglacial

The long-term Colonia record is located in the Atlantic rainforest domain in Brazil (23 degrees 52`S 46 degrees 42`20 `` W 900 m a.s.l.). The 780 cm long core CO3 provides a coverage of a complete interglacial/glacial cycle for the first time in a neotropical rainforest. Information on the behavior of tropical climates compared to global changes in temperatures indicates specific climate responses in terms of precipitation at these latitudes. Winter extratropical circulation was very active during the last interglacial and most of the glacial. Floristic composition of the rainforest changed several times in each phase of expansion, twice during the interglacial, and three times during glacial episodes. Araucaria was well developed in the area of Sao Paulo until the beginning of the first dry phase of the glacial at ca. 50,000 yr B.P. Changes in insolation controlled the expansion of the rainforest and the tropical hydrological cycle as evidenced by a strong precession signal. However precession had no impact on regional climatic features. The two interglacials (MIS 5e and Holocene) showed completely different patterns attesting to the continuous evolution of the forest. The biodiversity index (Shannon-Wiener Index) remained high during both the interglacial and glacial attesting to the permanence of small patches of rainforest refugia during drier phases. The lowest Shannon-Wiener Indexes were recorded between 23,000 and 12,000 yr B.P. and 40,000 and 30,000 yr B.P. and characterize two marked phases of stress for the rainforest. (C) 2008 Elsevier B.V. All rights reserved.