It is well known that the Preisach model is useful to approximate the effect of hysteresis behavior in smart materials, such as piezoactuators and Shape Memory Alloy(SMA) wire actuators. For tracking control, many researchers estimate a Preisach model and then compute its inverse model for hysteresis compensation. However, the inverse of its hysteresis behavior also shows hysteresis behavior. From this idea, the inverse model with Kransnoselskii-Pokrovskii(KP) model, a developed version of Preisach model, can be used directly for SMA position control and avoid the inverse operation. Also, we propose another method for the tracking control by approximating the inverse model using an orthogonal polynomial network. To estimate and update the weight parameters in both inverse models, a gradient-based learning algorithm is used. Finally, for the SMA position control, PID controller, adaptive controllers with KP model and adaptive nonlinear inverse model controller are compared experimentally.

We propose novel methods to utilize orthogonal polynomial approximation in higher dimension spaces, which enable us to modify classical differential equation solvers to perform high precision, long-term orbit propagation. These methods have immediate application to efficient propagation of catalogs of Resident Space Objects (RSOs) and improved accounting for the uncertainty in the ephemeris of these objects. More fundamentally, the methodology promises to be of broad utility in solving initial and two point boundary value problems from a wide class of mathematical representations of problems arising in engineering, optimal control, physical sciences and applied mathematics. We unify and extend classical results from function approximation theory and consider their utility in astrodynamics. Least square approximation, using the classical Chebyshev polynomials as basis functions, is reviewed for discrete samples of the to-be-approximated function. We extend the orthogonal approximation ideas to n-dimensions in a novel way, through the use of array algebra and Kronecker operations. Approximation of test functions illustrates the resulting algorithms and provides insight into the errors of approximation, as well as the associated errors arising when the approximations are differentiated or integrated. Two sets of applications are considered that are challenges in astrodynamics. The first application addresses local approximation of high degree and order geopotential models, replacing the global spherical harmonic series by a family of locally precise orthogonal polynomial approximations for efficient computation. A method is introduced which adapts the approximation degree radially, compatible with the truth that the highest degree approximations (to ensure maximum acceleration error < 10^−9ms^−2, globally) are required near the Earths surface, whereas lower degree approximations are required as radius increases. We show that a four order of magnitude speedup is feasible, with both speed and storage efficiency op- timized using radial adaptation. The second class of problems addressed includes orbit propagation and solution of associated boundary value problems. The successive Chebyshev-Picard path approximation method is shown well-suited to solving these problems with over an order of magnitude speedup relative to known methods. Furthermore, the approach is parallel-structured so that it is suited for parallel implementation and further speedups. Used in conjunction with orthogonal Finite Element Model (FEM) gravity approximations, the Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss.

Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-02-25Bitstream added on 2014-06-13T19:06:37Z : No. of bitstreams: 1 barros_mc_me_sjrp.pdf: 547514 bytes, checksum: eb85ffc4b82cf33a3b73f60814c6355f (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Sejam Sn(x); n ¸ 0; os polinômios de Sobolev, ortogonais com relação ao produto interno hf; giS = ZR f(x)g(x)dÃ0(x) + ¸ ZR f0(x)g0(x)dÃ1(x); ¸ > 0; onde fdÃ0; dÃ1g forma um par coerente de medidas relacionadas às medidas de Jacobi ou de Laguerre. Denotemos por PÃ0 n (x) e PÃ1 n (x); n ¸ 0; os polinômios ortogonais com respeito a dÃ0 e dÃ1; respectivamente. Neste trabalho, estudamos o comportamento assintótico, quando n ! 1; das razões entre os polinômios de Sobolev, Sn(x); e os polinômios ortogonais PÃ0 n (x) e PÃ1 n (x); além do comportamento limite da razão entre esses dois últimos polinômios. Propriedades assintóticas para os coeficientes da relação de recorrência satisfeita pelos polinômios de Sobolev também foram estudadas. / Let Sn(x); n ¸ 0; be the Sobolev polynomials, orthogonal with respect to the inner product hf; giS = ZR f(x)g(x)dÃ0(x) + ¸ ZR f0(x)g0(x)dÃ1(x); ¸ > 0; where fdÃ0; dÃ1g forms a coherent pair of measures related to the Jacobi measure or Laguerre measure. Let PÃ0 n (x) and PÃ1 n (x); n ¸ 0; denote the orthogonal polynomials with respect to dÃ0 and dÃ1; respectively. In this work we study the asymptotic behaviour, as n ! 1; of the ratio between the Sobolev polynomials, Sn(x); and the ortogonal polynomials PÃ0 n (x) and PÃ1 n (x); as well as the limit behaviour of the ratio between the last two polynomials. Furthermore, we also give asymptotic results for the coefficients of the recurrence relation satisfied by the Sobolev polynomials.

La biologie structurale est la branche de la biologie qui étudie la structure et l'organisation spatiale des macromolécules.La biologie structurale concerne en particulier la détermination à l'échelle atomiquede la structure 3D, aux changement de conformation des macromolécules, et à la dynamique de ces structures.De nos jours, les techniques expérimentales modernes telles que la résonance magnétique nucléaire, la cristallographie aux rayons X et plus récemmentla microscopie cryoélectronique peuvent produire des cartes de densité à haute résolution, qui combinées aux informations sur la séquence d'une moléculepermettent aux biologistes de résoudre les structures 3D de la molécule à l'étude.Cependant, dans certains cas, la résolution des cartes de densité n'est pas suffisante.Dans un tel cas, on alignegénéralement des sous-unités individuelles, obtenues à haute résolution, dans la carte de densité de base résolution.Mentionnons qu'il est également également possible de déterminer la structure 3D d'un assemblage biologique en ancrant plusieurs sous-unités ensemble.C'est cependant un problème beaucoup plus difficile.Ces problèmes d'amarrage et d'alignement peuvent être formulés comme un problème d'optimisation dont la fonction de coût est écrite comme la corrélation croisée de deux autres fonctions.Les algorithmes d'ancrage originaux ont été formulés comme des problèmes de "clé et verrou", dans lesquels les protéines étaient considérées comme des corps rigides.Il est cependant naïf de considérer les macromolécules comme des corps rigides. Les protéines sont flexibles et peuventsubir de grands changements conformationnels lors de la liaison à d'autres molécules. Considérer les problèmes d'ancrage comme des problèmes de"clé et verrou" n'est donc pas suffisant.Une méthode d'ancrage flexible standard utilise donc l'approche "aligner puis affiner", qui, dans certains cas, peut omettre de bonnes conformations.Cette thèse se concentre sur deux axes principaux.Le premier axe est le développement d'une nouvelle méthode qui échantillonne de manière exhaustive les mouvements de corps rigides et les mouvements collectifs, calculés par analyse en modes propres (AMP).Nous présentons d'abord une méthode qui utilise la transformée de Fourier rapide pour échantillonner une approximation quadratique de la fonction coût. Ensuite, la méthode effectuela recherche flexible en maximisant l'approximation quadratique de la fonction de coût dans un certain domaine de recherche. Cette méthode garantit de trouver la meilleure conformation flexible.Nous présentons ensuite une version en itterative de notre algorithme, qui trouve les mouvements collectifs qui maximisent le score d'amarrage par rapport aux degrés de liberté (DDLs) du corps rigide.La méthode échantillonne de manière exhaustive à la fois les mouvements de corps rigides et les mouvements collectifs en maximisant le maximum lisse selon les DDls correspondant aux transformations rigides de la fonction coût.Les deux méthodes ont été appliquées à des problèmes d'alignement sur des exemples réels et artificiels.De plus, nous présentons un exemple dans lequel l'approche "aligner puis raffiner" n'est pas capable de trouver la bonne conformation tandis quenotre méthode peut trouver ladite conformation.Le deuxième axe est le développement d'une nouvelle extrapolation des mouvements calculés par l'AMP.Nous montrons qu'il est possible, avec des calculs minimaux, d'extrapoler les mouvements instantanés calculés par l'AMP dans le sous espaces des rotations-traslations des blocs (RTB) comme une rotationpresque pure autour d'un certain axe.Nous avons appliqué cette méthode appelée NOLB sur différents systèmes biologiques et avons pu, d'une part, récupérer des mouvements biologiquement pertinents et d'autre part démontrer que la méthode NOLB génère des structures avec une meilleure topologie qu'une méthode d'AMP linéaire. / Structural biology is a branch of molecular biology, biochemistry, and biophysics concerned with the molecular structure of macromolecules, how they acquire the structures they have,and how alterations in their structures affect their function.These molecules are a topic of interest because they serve to keep the cellsalive and functioning.Nowadays, modern experimental techniques, such as nuclear magnetic resonance (NMR), X-ray crystallography and more recently cryo-electron microscopy (cryo-EM) canproduce high resolution density maps, which combined with the information about the sequence of a molecule allows biologists to solve thethree-dimensional (3D) structures of the molecule under study. However, when studding large biological assemblies, experimental techniques are notalways able to generate density maps with a high enough resolution. In such a case, one typically fits individual sub-units, which weresolved using at a higher resolution, into the lower-resolution density map.Let us also mention that it is also possible determine the 3D structure of a biological assembly by docking several sub-units together.This is a much more difficult problem though.These docking and fitting problems can be reformulated as an optimization problem whose cost function can be written as the cross-correlation of two functions.The first fitting and docking algorithms were formulated as "lock and key" problems, in which the proteins were considered as rigid body.However, considering macromolecules, especially proteins, as rigid bodies is not realistic.Proteins are indeed flexible and can undergo large conformational changesupon binding to other molecules.Considering docking and fitting problems as "lock and key" problems is therefore not sufficient.Therefore, a standard flexible docking/fitting method first uses a six-dimensional (6D) rigid body docking/fitting algorithm and then flexibly relaxes the top docking/fitting poses.This approach will be thus refereed to as to the fit then refine approach.However, in some cases, such an approach can miss good conformations.This thesis focuses on two main axes.The first axis is the development of a new method that exhaustively samples both rigid-body and collective motions computed via normal mode analysis (NMA).We first present a method that combines the advantages of the Fourier transform (FFT)-based exhaustive search, which samples all the conformations of a system under study on a grid, with a local optimization technique thatguarantees to find the nearest optimal off-grid and flexible conformation.The algorithm first samples a quadratic approximation of a scoring function on a 6D grid. Then, the method performs the flexible search by maximizing the quadratic approximation of the cost functionwithin a certain search space.We then present a multi-step version of our algorithm, which finds the collective motions that maximize the docking score with respect to the rigid-body degrees of freedom (DOFs).The method exhaustively samples both rigid-body and collective motions by maximizing the soft maximum over the rigid body DOFs of the docking/fitting cost function.Both methods were applied to docking problems on both real and artificial example and we were able to design a benchmark in which the fit then refine approach fails at finding the correct conformation whileour method succeeds.The second axis is the development of a new extrapolation of motions computed by NMA.We show that it is possible, with minimal computations, to extrapolate the instantaneous motions computed by NMA in the the rotations-translations of blocks (RTB) subspace as an almost pure rotation around a certain axis.We applied this non-linear block (NOLB) method on various biological systems and were able to, firstly, retrieve biologically relevant motions andsecondly, to demonstrate that the NOLB method generates structures with a better topology than a linear NMA method.

Orientador: Eliana Xavier Linhares de Andrade / Banca: Ana Paula Peron / Banca: Alagacone Sri Ranga / Resumo: Sejam Sn(x); n ¸ 0; os polinômios de Sobolev, ortogonais com relação ao produto interno hf; giS = ZR f(x)g(x)dÃ0(x) + ¸ ZR f0(x)g0(x)dÃ1(x); ¸ > 0; onde fdÃ0; dÃ1g forma um par coerente de medidas relacionadas às medidas de Jacobi ou de Laguerre. Denotemos por PÃ0 n (x) e PÃ1 n (x); n ¸ 0; os polinômios ortogonais com respeito a dÃ0 e dÃ1; respectivamente. Neste trabalho, estudamos o comportamento assintótico, quando n ! 1; das razões entre os polinômios de Sobolev, Sn(x); e os polinômios ortogonais PÃ0 n (x) e PÃ1 n (x); além do comportamento limite da razão entre esses dois últimos polinômios. Propriedades assintóticas para os coeficientes da relação de recorrência satisfeita pelos polinômios de Sobolev também foram estudadas. / Abstract: Let Sn(x); n ¸ 0; be the Sobolev polynomials, orthogonal with respect to the inner product hf; giS = ZR f(x)g(x)dÃ0(x) + ¸ ZR f0(x)g0(x)dÃ1(x); ¸ > 0; where fdÃ0; dÃ1g forms a coherent pair of measures related to the Jacobi measure or Laguerre measure. Let PÃ0 n (x) and PÃ1 n (x); n ¸ 0; denote the orthogonal polynomials with respect to dÃ0 and dÃ1; respectively. In this work we study the asymptotic behaviour, as n ! 1; of the ratio between the Sobolev polynomials, Sn(x); and the ortogonal polynomials PÃ0 n (x) and PÃ1 n (x); as well as the limit behaviour of the ratio between the last two polynomials. Furthermore, we also give asymptotic results for the coefficients of the recurrence relation satisfied by the Sobolev polynomials. / Mestre

In this thesis, we provide convergent numerical solutions to non-linear forward-BSDEs (Backward Stochastic Differential Equations). Applications in mathematical finance, financial economics and financial econometrics are discussed. Numerical examples show the effectiveness of our methods.

Dans la première partie de ce travail nous considérons des problèmes hyperboliques du premier ordre linéaires où des problèmes paraboliques linéaires dégénérés en temps. En utilisant une méthode de matrice de masse singulière, nous proposons une méthode d’élément finis permettant d’avoir des estimations d’erreur en espace optimale pour l’élément fini de Lagrange P1 par exemple. Nous appliquons ces résultats au cas d’un système parabolique utilisé en electroradiologie. La seconde partie est consacrée aux polynômes Lp extrémaux à l’extérieur du cercle unité associés à une mesure de la forme générale α = βa + βs + γ, où βa est régulière, βs singulière et γ discrète. Dans un premier temps nous considérons βs = 0, et nous avons généralisé au cas Lp des résultats connus dans le cas L2. Dans le cas où βs = 0 nous montrons les mêmes résultats (formules d’optimalité) mais en utilisant d’autres fonctions de régularité. / In the first part of this work, we deal with, linear hyperbolic problems of first order or linear parabolic problems, which are degenerated with respect to the time operator. By using a singular mass matrix technique, we propose a finite element method allowing to get optimal error estimates with respect to space for the Lagrange first order finite element for example. Then our method is applied to a parabolic system degenerated with respect to time which is used in electrocardiology. The second part of this work is dedicated to extremal polynomials in Lp , outside to the unit circle associated to a measure α, with a general form given by α = βa + βs + γ. The regular part is denoted βa , the singular part βs and the discrete part γ. In a first step we take βs = 0, and we generalized to the Lp case the known results in the L2 case. When the singular part is non zero, by using different regularity functions, we get the same optimality formulae.

Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-02-27Bitstream added on 2014-06-13T20:16:04Z : No. of bitstreams: 1 nunes_jb_me_sjrp.pdf: 1005590 bytes, checksum: 7da54a97a1f2ab452a315062071f2c4e (MD5) / Este trabalho trata do estudo da localização dos zeros dos polinômios gerados por uma determinada relação de recorrência de três termos. O objetivo principal é estudar limitantes, em termos dos coeficientes da relação de recorrência, para as regiões onde os zeros estão localizados. Os zeros são explorados atravé do problema de autovalor associado a uma matriz de Hessenberg. As aplicações são consideradas para polinômios de Szego fSng, alguns polinômios para- ortogonais ½Sn(z) + S¤n (z) 1 + Sn(0) ¾ e ½Sn(z) ¡ S¤n (z) 1 ¡ Sn+1(0) ¾, especialmente quando os coeficientes de reflexão são reais. Um outro caso especial considerado são os zeros do polinômio Pn(z) = n Xm=0 bmzm, onde os coeficientes bm; para m = 0; 1; : : : ; n, são complexos e diferentes de zeros. / In this work we studied the localization the zeros of polynomials generated by a certain three term recurrence relation. The main objective is to study bounds, in terms of the coe±cients of the recurrence relation, for the regions where the zeros are located. The zeros are explored through an eigenvalue representation associated with a Hessenberg matrix. Applications are considered to Szeg}o polynomials fSng, some para-orthogonal polyno- mials ½Sn(z) + S¤n (z) 1 + Sn(0) ¾and ½Sn(z) ¡ S¤n (z) 1 ¡ Sn+1(0) ¾, especially when the re°ection coe±cients are real. As another special case, the zeros of the polynomial Pn(z) = n Xm=0 bmzm, where the non-zero complex coe±cients bm for m = 0; 1; : : : ; n, were considered.

Orientador: Eliana Xavier Linhares de Andrade / Banca: Alagacone Sri Ranga / Banca: Andre Piranhe da Silva / Resumo: Este trabalho trata do estudo da localização dos zeros dos polinômios gerados por uma determinada relação de recorrência de três termos. O objetivo principal é estudar limitantes, em termos dos coeficientes da relação de recorrência, para as regiões onde os zeros estão localizados. Os zeros são explorados atravé do problema de autovalor associado a uma matriz de Hessenberg. As aplicações são consideradas para polinômios de Szeg"o fSng, alguns polinômios para- ortogonais ½Sn(z) + S¤n (z) 1 + Sn(0) ¾ e ½Sn(z) ¡ S¤n (z) 1 ¡ Sn+1(0) ¾, especialmente quando os coeficientes de reflexão são reais. Um outro caso especial considerado são os zeros do polinômio Pn(z) = n Xm=0 bmzm, onde os coeficientes bm; para m = 0; 1; : : : ; n, são complexos e diferentes de zeros. / Abstract: In this work we studied the localization the zeros of polynomials generated by a certain three term recurrence relation. The main objective is to study bounds, in terms of the coe±cients of the recurrence relation, for the regions where the zeros are located. The zeros are explored through an eigenvalue representation associated with a Hessenberg matrix. Applications are considered to Szeg}o polynomials fSng, some para-orthogonal polyno- mials ½Sn(z) + S¤n (z) 1 + Sn(0) ¾and ½Sn(z) ¡ S¤n (z) 1 ¡ Sn+1(0) ¾, especially when the re°ection coe±cients are real. As another special case, the zeros of the polynomial Pn(z) = n Xm=0 bmzm, where the non-zero complex coe±cients bm for m = 0; 1; : : : ; n, were considered. / Mestre

In Paper [I] we use data on Swedish public procurement auctions for internal regularcleaning service contracts to provide novel empirical evidence regarding green publicprocurement (GPP) and its effect on the potential suppliers’ decision to submit a bid andtheir probability of being qualified for supplier selection. We find only a weak effect onsupplier behavior which suggests that GPP does not live up to its political expectations.However, several environmental criteria appear to be associated with increased complexity,as indicated by the reduced probability of a bid being qualified in the postqualificationprocess. As such, GPP appears to have limited or no potential to function as an environmentalpolicy instrument. In Paper [II] the observation is made that empirical evaluations of the effect of policiestransmitted through public procurements on bid sizes are made using linear regressionsor by more involved non-linear structural models. The aspiration is typically to determinea marginal effect. Here, I compare marginal effects generated under both types ofspecifications. I study how a political initiative to make firms less environmentally damagingimplemented through public procurement influences Swedish firms’ behavior. Thecollected evidence brings about a statistically as well as economically significant effect onfirms’ bids and costs. Paper [III] embarks by noting that auction theory suggests that as the number of bidders(competition) increases, the sizes of the participants’ bids decrease. An issue in theempirical literature on auctions is which measurement(s) of competition to use. Utilizinga dataset on public procurements containing measurements on both the actual and potentialnumber of bidders I find that a workhorse model of public procurements is bestfitted to data using only actual bidders as measurement for competition. Acknowledgingthat all measurements of competition may be erroneous, I propose an instrumental variableestimator that (given my data) brings about a competition effect bounded by thosegenerated by specifications using the actual and potential number of bidders, respectively.Also, some asymptotic results are provided for non-linear least squares estimatorsobtained from a dependent variable transformation model. Paper [VI] introduces a novel method to measure bidders’ costs (valuations) in descending(ascending) auctions. Based on two bounded rationality constraints bidders’costs (valuations) are given an imperfect measurements interpretation robust to behavioraldeviations from traditional rationality assumptions. Theory provides no guidanceas to the shape of the cost (valuation) distributions while empirical evidence suggeststhem to be positively skew. Consequently, a flexible distribution is employed in an imperfectmeasurements framework. An illustration of the proposed method on Swedishpublic procurement data is provided along with a comparison to a traditional BayesianNash Equilibrium approach.