Orientador: Rubens de Figueiredo Camargo / Coorientador: Paulo Fernando de Arruda Mancera / Banca: Edmundo de Oliveira Capela / Banca: Alexys Bruno Alfonso / Resumo: Este trabalho trata do Cálculo Fracionário e suas aplicações em problemas biológicos. Nas aplicações nos concentramos no sistema de Lotka-Volterra clássico e fracionário, para depois analisar o controle biológico da praga da cana-de-açúcar. Como trabalho futuro, propomos analisar as aplicações do sistema de Lotka-Volterra fracionário em problemas reais do câncer, com saturação de crescimento tumoral enfocando tratamento quimioterápico / Abstract: This work is about Fractional Calculus and its applications in biological problems. In the applications we focus on the classical Lotka-Volterra system and into the corresponding fractional order version to examine the biological control of sugar cane's pest. As future work, we analyze the fractional system in real problems of cancer, with saturation of tumor growth with a focus on chemotherapy / Mestre

Orientador: Wagner Caradori do Amaral, Ricardo José Gabrielli Barreto Campello / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-18T18:57:59Z (GMT). No. of bitstreams: 1 Braga_MarcioFeliciano_M.pdf: 1946648 bytes, checksum: 782ab3e1f3a89e6527c7b9c090b00ac0 (MD5) Previous issue date: 2011 / Resumo: Enfoca-se a modelagem de sistemas não-lineares usando modelos de Volterra com bases de funções ortonormais (Orthonormal Basis Functions - OBF) distintas para cada direção do kernel. Os modelos de Volterra constituem uma classe de modelos polinomiais não-recursivos, modelos sem realimentação da saída. Tais modelos são parametrizados por funções multidimensionais, chamadas kernels de Volterra, e representam uma generalização do bem conhecido modelo de resposta ao impulso (FIR) para a descrição de sistemas não-lineares. Como os modelos de Volterra não possuem realimentação do sinal de saída, um número elevado de parâmetros é necessário para representar os kernels de Volterra, especialmente quando o comportamento não-linear do sistema depende fortemente do sinal de saída. No entanto, é possível contornar esta desvantagem por descrever cada kernel por meio de uma expansão em bases de funções ortonormais (OBF). Resultando num modelo que, em geral, possui um número menor de termos para representar o sistema. O modelo resultante, conhecido como modelo OBF-Volterra, pode ser truncado em um número menor de termos se as funções da base forem projetadas adequadamente. O problema reside na questão de como selecionar os polos livres que completamente parametrizam estas funções de forma a reduzir o número de termos a serem utilizados em cada base. Uma abordagem já utilizada envolve a otimização numérica das bases de funções ortonormais usadas para a aproximação de sistemas dinâmicos. Esta estratégia é baseada no cálculo de expressões analíticas para os gradientes da saída dos filtros ortonormais com relação aos polos da base. Estes gradientes fornecem direções de busca exatas para otimizar uma dada base ortonormal. As direções de busca, por sua vez, podem ser usadas como parte de um procedimento de otimização para obter o mínimo de uma função de custo que leva em consideração o erro de estimação da saída do sistema. Esta abordagem considerou apenas os modelos lineares e não-lineares cujas direções dos kernels foram todas parametrizadas por um mesmo conjunto de polos. Neste trabalho, estes resultados foram estendidos de forma a permitir o uso de uma base independente para cada direção dos kernels. Isto permite reduzir ainda mais o erro de truncamento quando as dinâmicas dominantes do kernel ao longo das múltiplas direções são diferentes entre si. As expressões dos gradientes relativas à base de Kautz e à base GOBF são obtidas recursivamente o que permite uma redução no tempo de processamento. Esta metodologia utiliza somente dados de entrada-saída medidos do sistema a ser modelado, isto é, não exige nenhuma informação prévia sobre os kernels de Volterra. Exemplos de simulação ilustram a aplicação dessas abordagens para a modelagem de sistemas não-lineares. Por último, apresentam-se resultados referentes à identificação robusta de modelos não-lineares sob a hipótese de erro desconhecido mas limitado, cujo objetivo é definir os limites superior e inferior dos parâmetros de modelos (intervalos de pertinência paramétrica). É analisado o caso em que se tem informação somente sobre a incerteza na saída do sistema, fornecendo-se o cálculo dos limitantes das incertezas para modelos OBF-Volterra. Estuda-se também os processos que possuem incerteza estruturada, i.e., os parâmetros do modelo, ou os kernels de Volterra, são definidos por meio de intervalos de pertinência e a ordem do modelo é conhecida. Apresenta-se uma solução exata para este problema, eliminando restrições impostas por metodologias anteriores / Abstract: It focuses in the modeling of nonlinear systems using Volterra models with distinct orthonormal basis functions (OBF) to each kernel direction. The Volterra models are a class of nonrecursive polynomial models, models without output feedback. Such models are parameterized by multidimensional functions, called Volterra kernels, they represent a generalization of the well-known impulse response model and are used to describe nonlinear systems. As the Volterra models do not have output feedback, it is required a large number of parameters to represent the Volterra kernels, especially when the nonlinear behavior strongly depends of the output signal. However, such drawback can be overwhelmed by describing each kernel by un expansion in orthonormal basis functions (OBF). Resulting in a model that, in general, requires fewer parameters to represent the system. The resulting model, so-called OBF-Volterra, can be truncated into fewer terms if the basis functions are properly designed. The underlying problem is how to select de free-design poles that fully parameterize these functions in order to reduce the number of terms to be used in each bases. An approach, already used, involves the numeric optimization of orthonormal bases of function used for approximation of dynamic systems. This strategy is based on the computation of analytical expressions for the gradient of the orthonormal filters output with respect to the basis poles. Such gradient provides exact search directions for optimizing the poles of a given orthonormal basis. The search direction can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into consideration the estimation error of the system output. Although, that approach took in count only the linear models and nonlinear models which kernels directions were parameterized by a single set of poles. In this work, these results are extended in such a way to allows a use of an independent basis to each kernel direction. It can reduce even more the truncation error when dominant dynamics of the kernel are different along its directions. The gradient expressions to Kautz and GOBF bases are obtained in a recursive way which allows reducing the time processing. This methodology relies solely on input-output data measured from the system to be modeled, i.e., no previous information about the Volterra kernels is required. Simulation examples illustrate the application of this approach to the modeling of nonlinear systems. At last, it is presented some results about robust identification of nonlinear models under the hypothesis of unknown but bounded error, whose aim is to define the upper and lower bounds of the model parameters (parameter uncertainty interval). It is analyzed the case where the information available is about the uncertainty in the system output signal, providing the calculation for the uncertainty intervals to OBF-Volterra models. The process having structured uncertainty, i.e., the models parameters, or the Volterra kernels, are defined by intervals and the model order is known, is also studied. An exact solution to this problem is developed, eliminating restrictions imposed by previous approach / Mestrado / Automação / Mestre em Engenharia Elétrica

Since they appeared, wireless technologies have deeply transformed our society. Today, wireless internet access and other wireless applications demandincreasingly more traffic. However, the continuous traffic increase can be unbearableand requires rethinking and redesigning the wireless technologies inmany different aspects. Aiming to respond to the increasing needs of wirelesstraffic, we are witnessing a rapidly evolving wireless technology scenario.This thesis addresses various aspects of the transmitters used in wireless communications.Transmitters present several hardware (HW) impairments thatcreate distortions, polluting the radio spectrum and decreasing the achievabletraffic in the network. Digital platforms are now flexible, robust and cheapenough to enable compensation of HW impairments at the digital base-bandsignal. This has been coined as ’dirty radio’. Dirty radio is expected in future transmitters where HW impairments may arise to reduce transmitter cost or to enhance power efficiency. This thesis covers the software (SW) compensation schemes of dirty radio developed for wireless transmitters. As describedin the thesis, these schemes can be further enhanced with knowledge of thespecific signal transmission or scenarios, e.g., developing cognitive digital compensationschemes. This can be valuable in today’s rapidly evolving scenarioswhere multiple signals may co-exist, sharing the resources at the same radiofrequency (RF) front-end. In the first part, this thesis focuses on the instrumentation challenges andHWimpairments encountered at the transmitter. A synthetic instrument (SI)that performs network analysis is designed to suit the instrumentation needs.Furthermore, how to perform nonlinear network analysis using the developedinstrument is discussed. Two transmitter HW impairments are studied: themeasurement noise and the load impedance mismatch at the transmitter, asis their coupling with the state-of-the-art digital compensation techniques.These two studied impairments are inherent to measurement systems and areexpected in future wireless transmitters. In the second part, the thesis surveys the area of behavioral modeling and digital compensation techniques for wireless transmitters. Emphasis is placed on low computational complexity techniques. The low complexity is motivated by a predicted increase in the number of transmitters deployed in the network, from base stations (BS), access points and hand-held devices. A modeling methodology is developed that allows modeling transmitters to achieve both reduced computational complexity and low modeling error. Finally, the thesis discusses the emerging architectures of multi-channel transmittersand describes their digital compensation techniques. It revises the MIMOVolterra series formulation to address the general modeling problem anddrafts possible solutions to tackle its dimensionality. In the framework of multi-channel transmitters, a technique to compensate nonlinear multi-carrier satellite transponders is presented. This technique is cognitive because it uses the frequency link planning and the pulse-shaping filters of the individual carriers. This technique shows enhanced compensation ability at reduced computational complexity compared to the state-of-the-art techniques and enables the efficient operation of satellite transponders. / <p>QC 20150526</p>

M.Sc. (Applied Mathematics) / Numerous studies on linear and nonlinear Volterra integral equations (VIEs), have been performed. These studies mainly considered the existence and uniqueness of the solution, and numerical solutions of these equations. In this work, a class of nonlinear (nonstandard) Volterra integral equation that has received very little attention in the literature is considered. The existence and uniqueness of the solution for the nonlinear VIE is proved using the contraction mapping theorem in the space C[0; d]. Collocation methods, repeated trapezoidal rule and repeated Simpson's rule are used to solve the nonlinear (nonstandard) VIE. For the collocation solutions we considered two cases: implicit Euler method and implicit midpoint method. Examples are used to compare the performance of these methods and the results show that the repeated Simpson's rule performs better than the other methods. An analysis of the collocation solution and the solution by the repeated trapezoidal rule is performed. Su cient conditions for existence and uniqueness of the numerical solution are given. The collocation methods and repeated trapezoidal rule yield convergence of order one.

O objetivo deste trabalho e encontrar uma solução exata para um sistema de equações integrais de Volterra. Para isso, usaremos a teoria de espacos de reprodução e núcleos positivos definidos, visto que as técnicas usuais de resoluções de equações diferenciais e integrais possuem restrições. Grande parte do estudo voltado a solução de equações se baseia em analisar o comportamento das soluções, o chamado estudo qualitativo. Este não e o nosso interesse, queremos aproximar a solução do problema usando a representa c~ao dessa solução em uma base ortonormal especial de um espaço de Hilbert de reprodução gerado por um núcleo positivo de nido adequado. Dessa forma, truncando a serie encontrada para a solução do sistema de Volterra podemos exibir uma boa aproxima c~ao para a solução do sistema. As equações integrais de Volterra, foco deste trabalho, s~ao importantes para a modelagem de fenômenos físicos, demográficos ou epidemiológicos. Para a resolução de tais equações, faremos um estudo introdutório sobre conceitos de álgebra linear, análise e teoria da medida com o intuito de abranger temas como: existência de base de um espaço vetorial, o processo de ortogonaliza c~ao de Gram-Schmidt, os espaços Lp, entre outros. Faremos uma breve análise sobre a transformada de Laplace, assim como resolveremos uma equação diferencial e integral usando este método. Tambem resolveremos um sistema de equações integrais através da transformada de Laplace para exemplificar o método. Cabe lembrar que a maioria das equações não pode ser resolvida por meio da transformada de Laplace. Faremos um estudo de resolução de equações lineares de Volterra e então abrangeremos esse estudo para equa c~oes n~ao lineares. / The aim of this study is to give the exact solution to a system of linear Volterra integral equations. So do it, we will use the theory of reproduction Kernel method and positive de nite kernels, since the usual method to solve di erential and integral equations have restrictions. Much of the study about solving equations is based on analyzing the behavior of solutions, called qualitative study. This is not our interest, we want to approach the solution of the problem using the representation of the solution in a special orthonormal basis of the reproduction kernel Hilbert space generated by an appropriate positive de nite kernel. Thus, truncating the series found for the solution of the Volterra system, we can give a good approximation to the system solution. The Volterra integral equations, focus of this work, are important to modeling physical, demographic or epidemiological phenomena. For solving such equations, we make an introductory study of linear algebra, analysis and measure theory in order to comprehend topics such as: existence of a base in a vector space, the Gram-Schmidt orthogonalization process, the spaces Lp, and others. We make a brief analysis of the Laplace transform, as well as solve a di erential and integral equation using this method. We also solve a system of integral equations by Laplace transform to illustrate the method. It should be noted that most of the equations can not be solved by means of the Laplace transform. We will study how to solve linear Volterra equations and then extend the study to nonlinear equations.

En esta tesis se analiza la formación de patrones debido a inestabilidades en un sistema de reacción - difusión - advección generadas mediante un flujo de corte. Las inestabilidades son similares a la formación de patrones de Turing en un sistema de activador - inhibidor donde una condición necesaria es que la difusividad del inhibidor es mayor que la difusividad del activador. En presencia de un flujo de corte, nosotros encontramos que esta condición no es necesaria. Nosotros analizamos dos modelos para un flujo de corte, uno de ellos consiste en dos capas moviéndose con diferentes velocidades, el otro correspondiente a un flujo de Poiseuille dentro de un tubo bidimensional. La inestabilidad aparece cuando la velocidad promedio del flujo aumenta por encima de cierta velocidad umbral, conduciendo así a los patrones que se mueven según el marco de referencia del flujo. Nuestros resultados, patrones aislados de Turing, pueden ser obtenidos usando una difusividad efectiva por efecto de la dispersión de Taylor. / Tesis

by Siu-Chung Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 98-100). / Abstract also in Chinese. / Chapter CHAPTER 1 --- INTRODUCTION --- p.3 / Chapter CHAPTER 2 --- BACKGROUND THEORY --- p.6 / Chapter 2.1 --- Passive LC Low-pass Filter --- p.6 / Chapter 2.1.1 --- Butterworth Low-pass Filter --- p.6 / Chapter 2.1.2 --- Chebyshev Low-pass Filter --- p.8 / Chapter 2.2 --- Low-pass to Band-pass Transformation --- p.10 / Chapter 2.2.1 --- Impedance Inverter --- p.12 / Chapter 2.2.2 --- Admittance Inverter --- p.14 / Chapter 2.3 --- Coupled Resonator Band-pass Filter --- p.15 / Chapter 2.4 --- Active Filter Techniques --- p.19 / Chapter 2.4.1 --- Actively-coupled Passive Resonators --- p.20 / Chapter 2.4.2 --- Negative Resistance for Q-enhancement --- p.21 / Chapter 2.4.3 --- Transversal & Recursive Filters --- p.22 / Chapter 2.4.4 --- Active Inductors --- p.24 / Chapter 2.5 --- Chapter Summary --- p.27 / Chapter CHAPTER 3 --- NEGATIVE RESISTANCE BASED ACTIVE FILTER --- p.28 / Chapter 3.1 --- Lossy Coupled-Resonator Band-pass Filter --- p.28 / Chapter 3.2 --- Negative Resistance Circuit --- p.32 / Chapter 3.2.1 --- Capacitive Feedback Configuration of CS MESFET --- p.33 / Chapter 3.2.2 --- Active LC-Resonator --- p.35 / Chapter 3.3 --- Design Criteria of Active Filter --- p.39 / Chapter 3.3.1 --- Choices of Feedback Capacitance --- p.40 / Chapter 3.3.2 --- Derivation of Design Requirements --- p.44 / Chapter 3.4 --- Chapter Summary --- p.46 / Chapter CHAPTER 4 --- INTERMODULATION ANALYSIS BY VOLTERRA-SERIES --- p.47 / Chapter 4.1 --- volterra-series analysis --- p.47 / Chapter 4.1.1 --- Nonlinear Transfer Functions --- p.48 / Chapter 4.1.2 --- Harmonic-Input Method --- p.50 / Chapter 4.2 --- Derivation of Intermodulation Products in Active Filter --- p.52 / Chapter 4.2.1 --- Modeling of Nonlinear MESFETs --- p.52 / Chapter 4.2.2 --- First Order Kernel --- p.56 / Chapter 4.2.3 --- Second Order Kernel --- p.58 / Chapter 4.2.4 --- Third Order Kernel --- p.61 / Chapter 4.3 --- Simplified Nonlinear Model of Active Filter --- p.66 / Chapter 4.4 --- Minimization of Intermodulation in Active Filter --- p.67 / Chapter 4.5 --- Chapter Summary --- p.73 / Chapter CHAPTER 5 --- DESIGN OF 900MHZ HYBRID ACTIVE FILTER --- p.74 / Chapter 5.1 --- Material Considerations --- p.74 / Chapter 5.1.1 --- Choice of MESFET --- p.75 / Chapter 5.1.2 --- Choice of Inductors --- p.75 / Chapter 5.1.3 --- Choice of Capacitors --- p.75 / Chapter 5.1.4 --- Choice of PCB Material --- p.76 / Chapter 5.2 --- Design of Hybrid Active Filters --- p.76 / Chapter 5.2.1 --- General Filter Structure --- p.76 / Chapter 5.2.2 --- Gate-Source & Feedback Capacitance Control --- p.78 / Chapter 5.2.3 --- Stability Issues --- p.79 / Chapter 5.2.4 --- PCB Layout --- p.82 / Chapter 5.2.5 --- Design Variants --- p.82 / Chapter 5.3 --- Measurements & Results --- p.84 / Chapter 5.3.1 --- Passive Filter Frequency Response Measurement --- p.85 / Chapter 5.3.2 --- Active Filter Frequency Response Measurement --- p.86 / Chapter 5.3.3 --- Two-Tone Intermodulation Measurement --- p.88 / Chapter 5.3.4 --- Gain-Compression Measurement --- p.92 / Chapter 5.4 --- Chapter Summary --- p.95 / Chapter CHAPTER 6 --- CONCLUSION --- p.96 / Chapter CHAPTER 7 --- FUTURE WORKS --- p.97 / REFERENCE --- p.98 / PUBLICATION LIST --- p.100 / APPENDIX --- p.101

In this thesis, we study a class of multi-stable reaction-diffusion systems used to model competing species. Systems in this class possess uniform stable steady states representing semi-trivial solutions. We start by considering a bistable, interaction, where the interactions are of classic “Lotka-Volterra” type and we consider a particular problem with relevance to applications in population dynamics: essentially, we study under what conditions the interplay of relative motility (diffusion) and competitive strength can cause waves of invasion to be halted and reversed. By establishing rigorous results concerning related degenerate and near-degenerate systems,we build a picture of the dependence of the wave speed on system parameters. Our results lead us to conjecture that this class of competition model has three “zones of response” in which the wave direction is left-moving, reversible and right-moving, respectively and indeed that in all three zones, the wave speed is an increasing function of the relative motility. Moreover, we study the effects of domain size on planar and non-planar interfaces and show that curvature plays an important role in determining competitive outcomes. Finally, we study a 3-species Lotka-Volterra model, where the third species is treated as a bio-control agent or a bio-buffer and investigate under what conditions the third species can alter the existing competition interaction.

Using the nonlinear Volterra series representation, analytical expressions for the third-order intermodulation distortion power and intercept point for a MESFET small-signal amplifier are derived when its equivalent circuit is bilateral and includes the gate-to-drain capacitance (CgJ explicitly as a nonlinear element. Previously developed analytical expressions treated Cgd as a linear element or incorporated it as part of gate-to-source and drainto- source capacitances (Cgs and Cds). These new analytical expressions are then compared with experimental data and good agreement is obtained. The analytical expressions are also used to study the variation of intermodulation distortion with input power, frequency, and source and load impedances. It is shown that the nonlinearity of Cgd contributes significantly to the intermodulation distortion power and the third-order intercept point and therefore should not be neglected in the analysis and design.

Given an algebra of pseudo-differential operators on a manifold, an elliptic element is said to be a reduction of orders, if it induces isomorphisms of Sobolev spaces with a corresponding shift of smoothness. Reductions of orders on a manifold with boundary refer to boundary value problems. We consider smooth symbols and ellipticity without additional boundary conditions which is the relevant case on a manifold with boundary. Starting from a class of symbols that has been investigated before for integer orders in boundary value problems with the transmission property we study operators of arbitrary real orders that play a similar role for operators without the transmission property. Moreover, we show that order reducing symbols have the Volterra property and are parabolic of anisotropy 1; analogous relations are formulated for arbitrary anisotropies. We finally investigate parameter-dependent operators, apply a kernel cut-off construction with respect to the parameter and show that corresponding holomorphic operator-valued Mellin symbols reduce orders in weighted Sobolev spaces on a cone with boundary.