Keywords: Bayesian analysis, Finite mixture, Gibbs sampler, Langevin-Hasting sampler, MH sampler, Model comparison, Nonrecursive nonlinear structural equation model, Path sampling. / Structural equation models (SEMs) have been applied extensively to management, marketing, behavioral, and social sciences, etc for studying relationships among manifest and latent variables. Motivated by more complex data structures appeared in various fields, more complicated models have been recently developed. For the developments of SEMs, there is a usual assumption about the regression coefficient of the underlying latent variables. On themselves, more specifically, it is generally assumed that the structural equation modeling is recursive. However, in practice, nonrecursive SEMs are not uncommon. Thus, this fundamental assumption is not always appropriate. / The main objective of this thesis is to relax this assumption by developing some efficient procedures for some complex nonrecursive nonlinear SEMs (NNSEMs). The work in the thesis is based on Bayesian statistical analysis for NNSEMs. The first chapter introduces some background knowledge about NNSEMs. In chapter 2, Bayesian estimates of NNSEMs are given, then some statistical analysis topics such as standard error, model comparison, etc are discussed. In chapter 3, we develop an efficient hybrid MCMC algorithm to obtain Bayesian estimates for NNSEMs with mixed continuous and ordered categorical data. Also, some statistical analysis topics are discussed. In chapter 4, finite mixture NNSEMs are analyzed with the Bayesian approach. The newly developed methodologies are all illustrated with simulation studies and real examples. At last, some conclusion and discussions are included in Chapter 5. / Li, Yong. / "July 2007." / Adviser: Sik-yum Lee. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0398. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 99-111). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Submitted by Inácio de Oliveira Lima Neto (inacio.neto@inpa.gov.br) on 2018-10-01T14:38:01Z No. of bitstreams: 2 João_Gabriel_Rafaelli.pdf: 2157835 bytes, checksum: 8d523aee7395e3c81de2736e95f7010b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-10-01T14:38:02Z (GMT). No. of bitstreams: 2 João_Gabriel_Rafaelli.pdf: 2157835 bytes, checksum: 8d523aee7395e3c81de2736e95f7010b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-03-02 / Fundação de Amparo à Pesquisa do Estado do Amazonas - FAPEAM / Agroforestry system is a land use technique practiced a long time around the world. Currently, an attention has been paid to this practice, with several projects and organizations working with the optimization of this technique. Among many ways of establishing an agroforestry system, taking into account the species to be used, the environmental conditions and the type of system to be implemented; the understanding of the specific factors that can influence the plantations are of utmost importance for its success. The present work aimed to evaluate the initial development of seedlings from 16 species planted in different lands, influenced by environmental factors and management of local farmers. The study was carried out at the Andirá-Marau Indigenous Reserve (Amazonas - Brazil) in eight different plantations with different agricultural practices. The parameters of plant performance analyzed were: Carbon Stock (CARBON), Absolute Diameter Increment (ADI), Relative Growth Rate (RGR) and Specific Leaf Area (SLA). As factors influencing the performance of seedlings were analyzed: Soil Quality (chemical and physical), percentage of Vegetation Cover (VC), Forest Distance (FD), Above Ground Biomass (AGB), Species Richness (SP_RICH), Litter Biomass, Charcoal Biomass, Nearest Next Neighbor and Competition Index. As a descriptive analysis, the soils were analyzed using ANOVA (two-factor) testing soil depths and areas. Also, the plantations were analyzed in terms of: area size, seedling survival, species composition, spacing, height and biomass. As an exploratory data analysis we used linear regressions between each performance trait and each influence factor. Later, we used the Structural Equation Modeling analysis to test how the factors together influence the performance of the seedlings. Finally, to test how the general models for all species influence in a specie-specific way, we tested models for Carapa guianensis Aubl. As results, it can be observed that during the project 45% of the seedlings died (9% between Dec 2014 and Dec 2015, 32% between Dec 2015 and Aug 2016, 11% between Aug 2016 and Feb 2017), mainly due to large dry season on the 2nd semester. Ingá, Urucum, Andiroba and Graviola species showed great variability in biomass accumulation, while Acerola, Cumaru, Guaraná and Mahogany varied much less. The exploratory analysis showed that RGR was positively influenced by FD and soil nutrients Mn, Ca, Mg, K and CPB and negatively by Fe; the Carbon Stock was positively influenced by FD, Coal Biomass, Nearby Neighbor, by soil nutrients Al, Mg, K, C, N, CEC and negatively by soil Density and Fe; ADI was positively influenced by FD, Neighbor Next, by nutrients Al, Mg, K, C, N, CEC and negatively by soil Density and Fe; SLA was positively influenced by VC and AGB. In the general models for all species, in SEM, we could observe that Carbon Stock had a 14% variation explained by the model, ADI had 14%, RGR had 11% and SLA had 10%. For the specific model (Carapa guianensis) the percentage of variation explained by the models was: Carbon Stock with 31%, ADI with 27%, RGR with 10% and SLA with 71%. We can conclude that soil factors (C, N, P, Mg, CEC, pH, Texture and Density), Biomass of Serrapilheira, VC and Next Neighbor, had greater influence on the initial performance of the seedlings planted in different agroforestry systems, which have to be taken into account for management practices. / Sistemas agroflorestais são formas de uso da terra utilizadas por muito tempo ao redor do mundo. Atualmente tem-se prestado maior atenção a essa prática, com diversos projetos e organizações trabalhando com a otimização das técnicas, para um melhor desenvolvimento desses sistemas. Dentre as diversas maneiras de se estabelecer um sistema agroflorestal, levando em consideração as espécies a serem utilizadas, o ambiente em que se encontra e o tipo de sistema a ser implementado, o entendimento dos fatores que possam influenciar os plantios são de suma importância para um maior sucesso desses. O presente trabalho teve como objetivo avaliar o desenvolvimento inicial de mudas de 16 espécies plantadas em diferentes ambientes, pela influência de fatores ambientais e do manejo de agricultores locais. O estudo foi realizado na Terra Indígena Andirá-Marau (Amazonas - Brasil) e contou com oito diferentes plantios em ambientes com diferentes práticas agrícolas. Foram avaliados os parâmetros de desempenho vegetal o Estoque de Carbono (CARBON), o Incremento Absoluto do Diâmetro (ADI), a Taxa de Crescimento Relativo (RGR) e a Área Foliar Específica (SLA). Como fatores de influência no desempenho das mudas foram avaliados: a Qualidade dos Solos (química e física), a porcentagem de Cobertura Vegetal (VC), a Distância dos plantios para a Floresta (FD), Biomassa Acima do Solo (AGB), Riqueza de Espécies (SP_RICH), Biomassa da Serrapilheira, Biomassa de Carvão, Vizinho Próximo das mudas plantadas e Índice de Competição. Como análise descritiva, os solos foram analisados utilizando o teste ANOVA (two-factor) entre as profundidades e a áreas. Também de forma descritiva foram analisados os plantios quanto: sobrevivência das mudas, composição de espécies, espaçamento, altura e biomassa. Para análise dos dados foram utilizadas regressões lineares entre cada medida de desempenho e cada fator de influência, como forma exploratória dos dados. Posteriormente utilizo-se a análise Structural Equation Modeling (SEM) para testar como os fatores influenciam o desempenho das mudas de forma conjunta. Por fim, para testar como os modelos gerais para todas as espécies influenciam de maneira específica, foi testado modelos para a espécie Carapa guianensis Aubl. Como resultado, pode-se observar que ao longo do projeto 45% das mudas morreram (9% entre Dez 2014 e Dez 2015, 32% entre Dez 2015 e Ago 2016, 11% entre Ago 2016 e Fev 2017), devido principalmente a grande seca no 2o. semestre de 2015. As espécies Ingá, Urucum, Andiroba e Graviola mostraram grande variabilidade no acumulo de biomassa, enquanto Acerola, Cumaru, Guaraná e Mogno variaram muito menos. Já a análise exploratória nos mostrou que o RGR foi influenciado positivamente por FD e pelos nutrientes do solo Mn, Ca, Mg, K e CEC e negativamente por Fe; o Estoque de Carbono foi influenciado positivamente por FD, Biomassa de Carvão, Vizinho Próximo, pelos nutrientes do solo Al, Mg, K, C, N, CEC e negativamente por Densidade do Solo e Fe; o ADI foi influenciado positivamente por FD, Vizinho Próximo, pelos nutrientes Al, Mg, K, C, N, CEC e negativamente por Densidade do Solo e Fe; SLA foi influenciada positivamente por VC e AGB. Nos modelos gerais para todas as espécies, em SEM, vimos que o Estoque de Carbono teve 14% de variação explicada pelo modelo, ADI teve 14%, RGR teve 11% e SLA teve 10%. Para o modelo específico (Carapa guianensis) a porcentagem de variação explicada pelos modelos foram, Estoque de Carbono com 31%, ADI com 27 %, RGR com 10% e SLA com 71%. Podemos concluir que os fatores do solo (C, N, P, Mg, CEC, pH, Textura e Densidade), Biomassa da Serrapilheira, VC e Vizinho Próximo, tiveram maior influência no desempenho inicial das mudas nos sistemas agroflorestais implantados, devendo ser levadas em consideração nas práticas de manejo.

Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2016-08-24T17:57:59Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertaçãosuper_final_(1).pdf: 1088878 bytes, checksum: f1d95f7419b99281751c7ea750e47cf8 (MD5) / Made available in DSpace on 2016-08-24T17:57:59Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertaçãosuper_final_(1).pdf: 1088878 bytes, checksum: f1d95f7419b99281751c7ea750e47cf8 (MD5) Previous issue date: 2011-08-31 / CAPES / Nesta dissertação é apresentada uma solução estacionária para um modelo de dinâmica populacional de uma única espécie, considerando a dispersão da população num espaço heterogêneo e um crescimento logístico da população. No primeiro capítulo, para dar ao leitor alguma intimidade com os conceitos apresentados estudamos alguns modelos de dinâmica populacional de uma única espécie. Referimo-nos a uma única população para dizer que não analisamos aqui a interação entre diversas espécies. No segundo capítulo concentra-se a parte substancial do nosso trabalho. Na seção 1 apresentamos o modelo, na seção 2 apresentamos a solução estacionária para o problema e na seção 3 fazemos uma discussão sobre efeitos de isolamento para uma população. / This thesis presents a stationary solution to a model of population dynamics of a single species, considering the dispersion of biological population in a heterogeneous space and a logistic population growth. In the rst chapter, to give the reader some familiarity with the concepts presented study some models of population dynamics of a single species. We refer to a single population to say we do not analyze the interaction between di erent species. The second chapter focuses on the substantial part of our work. In Section 1 presents the problem and the model, section 2 presents the stationary solution to the problem and in Section 3 we make a discussion about isolation e ects on a population

A research report submitted to the Faculty of Science, in partial fulfilment of the requirements for the degree of Master of Science, University of the Witwatersrand, Johannesburg, 2015. / This dissertation analyses the reaction-di usion equations, in particular the modi ed Huxley model, arising in population dynamics. The focus is on determining the classical Lie point symmetries, and the construction of the conservation laws and group-invariant solutions for reaction-di usion equations. The invariance criterion for determination of classical Lie point symmetries results in a system of linear determining equations which can be solved analytically. Furthermore, the Lie point symmetries associated with the conservation laws are determined. Reductions by associated Lie point symmetries are carried out. Nonclassical symmetry techniques are also employed. Here the invariance criterion for symmetry determination results in a system of nonlinear determining equations which may be solved albeit di cult. Nonclassical symmetries results in exact solutions which may not be constructed by classical Lie point symmetries. The highlight in construction of exact solution using nonclassical symmetries is the introduction of the modi ed Hopf-Cole transformation. In this dissertation, the di usion term and the coe cient of the source term are given as quadratic functions of space variable in one case, and the coe cient as the generalised power law in the other. These equations admit a number of classical Lie point symmetries. The genuine nonclassical symmetries are admitted when the source term of the reaction-di usion equation is a cubic.

Burgers’ Equation ut + cuux = νuxx is a nonlinear partial differential equation which arises in models of traffic and fluid flow. It is perhaps the simplest equation describing waves under the influence of diffusion. We consider the large time behavior of solutions with exponentially localized initial conditions, analyzing the rate of convergence to a known self similar single-hump solution. We use the Cole-Hopf Transformation to convert the problem into a heat equation problem with exponentially localized initial conditions. The solution to this problem converges to a Gaussian. We then find an optimal Gaussian approximation which is accurate to order t−2. Transforming back to Burgers’ Equation yields a solution accurate to order t−2.

In a thermally equilibrated system, electron behavior in a metal is described by the Fermi-Dirac equation. With ultrafast lasers, electrons can be excited into temporary distributions which are not described by the Fermi-Dirac equation and are therefore not at a well-defined temperature. These nonthermal distributions quickly equilibrate through two primary processes: electron-electron scattering and electron-phonon scattering. In most situations, these effects are unnoticeable, since they are completed within 5 ps. A probabilistic numerical model for electron-electron scattering is presented. The model is robust, scaleable, and requires only one parameter. The success of the model suggests future work on a similar electron-phonon scattering model, which would provide a complete description of the elctron distribution during thermalization. Once complete, this model can be tested by measuring the amount of second harmonic light generated by an ultrafast laser in a pump-probe experiment.

We analyze a pair of nonlinear PDEs describing viscoelastic fluid flow in one dimension. We give a summary of the physical derivation and nondimensionlize the PDE system. Based on the boundary conditions and parameters, we are able to classify three different categories of traveling wave solutions, consistent with the results in [?]. We extend this work by analyzing the stability of the traveling waves. We thoroughly describe the numerical schemes and software program, VISCO, that were designed specifically to analyze the model we study in this paper. Our simulations lead us to conjecture that the traveling wave solutions found in [?] are globally stable for all sets of initial conditions with the appropriate asymptotic boundary conditions. We are able give some analytical evidence in support of this hypothesis but are unsuccessful in providing a complete proof.

We explore the behavior of an integrodifferential equation used to model one-dimensional biological swarms. In this model, we assume the motion of the swarm is determined by pairwise interactions, which in a continuous setting corresponds to a convolution of the swarm density with a pairwise interaction kernel. For a large class of interaction kernels, we derive conditions that lead to solutions which spread, blow up, or reach a steady state. For a smaller class of interaction kernels, we are able to make more quantitative predictions. In the spreading case, we predict the approximate shape and scaling of a similarity profile, as well as the approximate behavior at the endpoints of the swarm (via solutions to a traveling wave problem). In the blow up case, we derive an upper bound for the time to blow up. In the steady state case, we use previous results to predict the equilibrium swarm density. We support our predictions with numerical simulations. We also consider an extension of the original model which incorporates external forces. By analyzing and simulating particular cases, we determine that the addition of an external force can qualitatively change the behavior of the system.

In this study, the hydrodynamic performance of anguilliform swimming motion is computed using Morison’s equation. This method was shown to predict the servo motor torques well. The anguilliform swimming motion is sinusoidal with increasing amplitude from head to tail. A “wakeless” swimming motion proposed by Vorus and Taravella (2011) with zero net circulation is considered. This method is compared to the existing slender body theory and is validated with reference to the experimental results of NEELBOT-1.1 (Potts, 2015). The results for the study indicates that self-propulsion speed of the motion is independent of the oscillating tail amplitude at a constant advance ratio. At a constant wave speed, the self-propulsion speed attains a local maximum at an advance ratio of 0.5. Where the nominal length is equal to half the wavelength.

This thesis is concerned with stochastic heat equation with memory and nonlinear energy supply. The main motivation to study such systems comes from Thermodynamics, see [85]. The main objective of this work is to study the existence and uniqueness of solutions to such equations and to investigate some fundamental properties of solutions like continuous dependence on initial conditions. In our approach we follow the seminal papers by Da Prato and Clement [10], where the stochastic heat equation with memory is tranformed into an integral equation in a function space and the so-called mild solutions are studied. In the aforementioned papers only linear equations with additive noise were investigated. The main contribution of this work is the extension of this approach to nonlinear equations. Our main tools are the theory of stochastic convolutions as developed in [33] and the theory of resolvent kernels for deterministic linear heat equations with memory, see[10]. Since the solution at time t depends on the whole history of the process up to time t, the resolvent kernel does not define a semigroup of operators in the state space of the process and therefore a ???standard??? theory of stochastic evolution equations as presented in the monograph [33] does not apply. A more delicate analysis of the resolvent kernles and the associated stochastic convolutions is needed. We will describe now content of this thesis in more detail. Introductory Chapters 1 and 2 collect some basic and essentially well known facts about the Wiener process, stochastic integrals, stochastic convolutions and integral kernels. However, some results in Chapter 2 dealing with stochastic convolution with respect to non-homogenous Wiener process are extensions of the existing theory. The main results of this thesis are presented in Chapters 3 and 4. In Chapter 3 we prove the existence and uniqueness of solutions to heat equations with additive noise and either Lipschitz or dissipative nonlinearities. In both cases we prove the continuous dependence of solutions on initial conditions. In Chapter 4 we prove the existence and uniqueness of solutions and continuous dependence on initial conditions for equations with multiplicative noise. The diffusion coefficients defined by unbounded operators are allowed.