Digital predistorter design using B-Spline neural network and inverse of De Boor algorithm

This contribution introduces a new digital predistorter to compensate serious distortions caused by memory high power amplifiers (HPAs) which exhibit output saturation characteristics. The proposed design is based on direct learning using a data-driven B-spline Wiener system modeling approach. The nonlinear HPA with memory is first identified based on the B-spline neural network model using the Gauss-Newton algorithm, which incorporates the efficient De Boor algorithm with both B-spline curve and first derivative recursions. The estimated Wiener HPA model is then used to design the Hammerstein predistorter. In particular, the inverse of the amplitude distortion of the HPA's static nonlinearity can be calculated effectively using the Newton-Raphson formula based on the inverse of De Boor algorithm. A major advantage of this approach is that both the Wiener HPA identification and the Hammerstein predistorter inverse can be achieved very efficiently and accurately. Simulation results obtained are presented to demonstrate the effectiveness of this novel digital predistorter design.

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

Asymptotic behavior at infinity of solutions of multidimensional second kind integral equations

We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the kernel k(s,t) decays like |s — t|-q as |s — t| → ∞ for some sufficiently large q (and some other mild conditions on k are satisfied), then K ∈ B(XP) (the set of bounded linear operators on Xp), for 0 ≤ p ≤ q. If also (I - K)-1 ∈ B(X0) then (I - K)-1 ∈ B(XP) for 0 < p < q, and (I- K)-1∈ B(Xq) if further conditions on k hold. Thus, if k(s, t) = O(|s — t|-q). |s — t| → ∞, and y(s)=O(|s|-p), s → ∞, the asymptotic behaviour of the solution x may be estimated as x (s) = O(|s|-r), |s| → ∞, r := min(p, q). The case when k(s,t) = к(s — t), so that the equation is of Wiener-Hopf type, receives especial attention. Conditions, in terms of the symbol of I — K, for I — K to be invertible or Fredholm on Xp are established for certain cases (Ω a half-space or cone). A boundary integral equation, which models three-dimensional acoustic propaga-tion above flat ground, absorbing apart from an infinite rigid strip, illustrates the practical application and sharpness of the above results. This integral equation mod-els, in particular, road traffic noise propagation along an infinite road surface sur-rounded by absorbing ground. We prove that the sound propagating along the rigid road surface eventually decays with distance at the same rate as sound propagating above the absorbing ground.

On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

Fractional order and non-linear system identification algorithms for biomedical applications

We discuss the modelling of dielectric responses of amorphous biological samples. Such samples are commonly encountered in impedance spectroscopy studies as well as in UV, IR, optical and THz transient spectroscopy experiments and in pump-probe studies. In many occasions, the samples may display quenched absorption bands. A systems identification framework may be developed to provide parsimonious representations of such responses. To achieve this, it is appropriate to augment the standard models found in the identification literature to incorporate fractional order dynamics. Extensions of models using the forward shift operator, state space models as well as their non-linear Hammerstein-Wiener counterpart models are highlighted. We also discuss the need to extend the theory of electromagnetically excited networks which can account for fractional order behaviour in the non-linear regime by incorporating nonlinear elements to account for the observed non-linearities. The proposed approach leads to the development of a range of new chemometrics tools for biomedical data analysis and classification.

Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities

We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a large deviation principle (LDP) for capacities for such Gaussian rough paths. Together with Lyons' universal limit theorem, our results yield immediately the corresponding results for pathwise solutions to stochastic differential equations driven by such Gaussian process in the sense of rough paths. Moreover, our LDP result implies the result of Yoshida on the LDP for capacities over the abstract Wiener space associated with such Gaussian process.

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.

Comunidades de tripes (Insecta : Thysanoptera) em flores e ramos, com ênfase em Asteraceae no Parque Estadual de Itapuã, Viamão, RS

A ordem Thysanoptera reúne cerca de 5.500 espécies descritas, das quais, mais de 2.000 estão registradas para a região Neotropical. Apesar da grande diversidade de tripes existente no Brasil - que engloba quase 10% das espécies do mundo inteiro - há uma lacuna no conhecimento dessa fauna em ambientes naturais e de sua biologia e ecologia. Os poucos estudos já realizados sugerem que a família Asteraceae apresenta uma tisanopterofauna mais rica que as demais e que flores e ramos são utilizados diferencialmente pelas espécies de tripes. Este estudo objetivou contribuir para o levantamento da tisanopterofauna nativa e averiguar a flora explorada por estes insetos, quanto à utilização de flores e ramos e sua ocorrência em Asteraceae e outras famílias. A área de estudo foi o Parque Estadual de Itapuã (PEI), Viamão (50º 50’- 51º 05’W e 30º 20’- 30º 27’ S), RS. Quatro saídas de campo foram realizadas de junho de 2003 a abril de 2004. Foram determinadas três trilhas de aproximadamente 500 m em diferentes tipos de vegetação. As trilhas estabelecidas foram a da praia da Pedreira (TP) (mata baixa e vegetação rupestre), a do morro do Araçá (TA) (vegetação rupestre, vassourais e mata baixa) e a do morro da Grota (TG) (vegetação rupestre, butiazais e vassourais). Cada uma destas foi dividida em quatro subáreas, de igual extensão. A cada saída foram sorteadas duas destas subáreas, nas quais foram amostrados aleatoriamente três indivíduos de Asteraceae e três de qualquer outra família. De cada indivíduo era retirado um ramo com flores (F) e um sem flores (R). Cada ramo escolhido constituiu uma unidade amostral (UA). Para o total de 279 UAs, foram coletados 1.695 indivíduos - 870 adultos (583 ♀ e 287 ♂) e 825 larvas - de 31 espécies de Thysanoptera, em 19 gêneros e três famílias. Os Terebrantia representaram mais de 90% dos adultos e 76% dos imaturos coletados e compreenderam a maioria das espécies (26). Dentre as famílias, a mais rica e abundante foi Thripidae, com 757 indivíduos e 23 espécies. Frankliniella (9 spp.), Heterothrips (3 spp.) e Neohydatothrips (3 spp.), foram os gêneros mais ricos. Frankliniella foi também o mais abundante, perfazendo cerca de 64% do total da amostra. Os tisanópteros mais comuns foram Frankliniella rodeos e Paraleucothrips minusculus Johansen, 1983, com 363 e 92 indivíduos coletados. Os Índices de Shannon-Wiener (H’) e de dominância de Simpson (D) estimados para a tisanopterofauna do PEI foram de 2,19 e 0,211, respectivamente. Foram coletados 690 adultos e 572 larvas de tripes em F, distribuídos em 29 espécies. Já em R foram capturados 180 adultos e 253 imaturos, sendo registradas 22 espécies. O Índice de Shannon-Wiener aponta uma maior diversidade em R (H’ = 2,33) do que em F (H’ = 2,01), pois a dominância foi notadamente maior em F (D = 0,255) do que em R (D = 0,133) devido a grande abundância de Frankliniella spp. nos mesmos. Em 46 das 61 espécies vegetais coletadas foi constatada a presença de tisanópteros. Entre as famílias de plantas com maior número de espécies associadas com tripes, destacam-se Asteraceae (22), Myrtaceae (4) e Rubiaceae (4). Das 31 espécies de tripes identificadas, 19 ocorrem em Asteraceae e quatro foram registradas exclusivamente nesta família. Observou-se diferenças marcantes nos valores de H’ e D entre a tisanopterofauna habitante de asteráceas (H’ = 1,68; D = 0,311) e aquela das demais famílias (H’ = 2,11; D = 0,178).

Hedging de opções com ativos : base cujos preços seguem processos de difusão com salto

Na presente dissertação foi implementado um modelo para execução de hedging de mínima variância de opções de compra européias em mercados incompletos, considerando um espaço de tempo discreto e contínuo de estados. O desempenho foi medido de forma comparativa tomando como base a popular estratégia delta-hedging em um grande número de simulações, a partir de cenários definidos com o objetivo de submeter o modelo a diversas situações. A trajetória do preço do ativo objeto foi representada por um processo de difusão com saltos, composto por duas parcelas: (i) um processo de Wiener, cuja principal característica é ser uma função contínua e diferenciável em todos os pontos, e (ii) por um processo de Poisson, responsável por inserir descontinuidades na trajetória.

Estrutura e dinâmica do fitoplânctone bacterioplâncton em cultivos de camarão no Rio Grande do Norte-Brasil: impacto sobre o ambiente natural

This work aimed to study the structure and dynamic of Phytoplankton and Bacterioplankton in a complete cycle of shrimp cultivation (Litopenaeus vannamei) and determine the environmental factors responsible for the structural changes of these communities. The study was realized in a saltwater shrimp farm (Macaíba, RN), between September/2005 and February/2006, and in a freshwater shrimp farm (Ceará Mirim, RN), between May/2007 and September 2007. The samplings were collected weekly in saltwater farm and every fifteen days in freshwater farm. Total phosphorus, chlorophyll a and environmental parameters (pH, dissolved oxygen, salinity, temperature, depth and water transparency) were measured. Qualitative and quantitative analysis of the phytoplankton and bacterioplankton were carried out. The Shannon-Wiener ecologic indexes of diversity and the Pielou equitability indexes were calculated to the phytoplankton. Bacterial density was determined by epifluorescence microscopy. The data were statistically analyzed by Pearson correlation and t-Test. Chlorophycea were predominat in salt water and in the captation/drainage point (24 to 99%). Diatoms had higher wealth. The species Choricystis minor had the highest occurrence (100%) and dominance (90-100%), thus showing its adaptation to the high temperatures, salinity and low water transparency conditions. Filamentous Cyanobacteria like Oscillatoria sp., Pseudoanabaena sp. and Phormidium sp. had constant levels. The negative correlation between chlorophycea and water transparency, and the positive correlation between chlorophyll a and salinity, showed that the phytoplankton was well adapted to the low transparency and to the high salinity. The bacterioplankton was negatively correlated with the total phosphorus and salinity. In freshwater, Cyanobacteria were predominant (>80%), presenting some producers of toxins species like Microcystis sp., Aphanizomenon sp., Cylindrospermopsis raciborskii e Anabaena circinalis. Cyanobacterial density and total phosphorus and chlorophyll a concentrations exceeded the maximum value allowed by legislation. The means of total phosphorus varied from 264 to 627 Wg.L-1 and the means of chlorophyll a oscillated between 22 and 182 Wg.L-1. The phytoplankton species were selected by low availability of the light, high pH, temperature and high availability of total phosphorus. The bacterioplankton showed high densities (5,13 x 107 to 8,50 x107 Bac.mL-1). The studied environments (ponds and rivers) presented a high level of trophic state based on the high concentrations of chlorophyll a and total phosphorus and cyanobacteria dominance. The composition of species in the ponds and rivers was similar, as well as high concentrations of total phosphorus and chlorophyll a, highlighting the pollution caused by the discharges of the farms in natural environment

Diversidade e distribuição espacial de artrópodes associados ao solo em agroecossistemas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)