Doctor of Philosophy / Department of Agronomy / Stephen M. Welch / Global crop production must be doubled by 2050 to feed 9 billion people. Novel crop improvement methods and management strategies are the sine qua non for achieving this goal. This requires reliable quantitative methods for predicting the behavior of crop cultivars in novel, time-varying environments. In the last century, two different mathematical prediction approaches emerged (1) quantitative genetics (QG) and (2) ecophysiological crop modeling (ECM). These methods are completely disjoint in terms of both their mathematics and their strengths and weaknesses. However, in the period from 1996 to 2006 a method for melding them emerged to support breeding programs. The method involves two steps: (1) exploiting ECM’s to describe the intricate, dynamic and environmentally responsive biological mechanisms determining crop growth and development on daily/hourly time scales; (2) using QG to link genetic markers to the values of ECM constants (called genotype-specific parameters, GSP’s) that encode the responses of different varieties to the environment. This can require huge amounts of computation because ECM’s have many GSP’s as well as site-specific properties (SSP’s, e.g. soil water holding capacity). Moreover, one cannot employ QG methods, unless the GSP’s from hundreds to thousands of lines are known. Thus, the overall objective of this study is to identify better ways to reduce the computational burden without minimizing ECM predictability. The study has three parts: (1) using the extended Fourier Amplitude Sensitivity Test (eFAST) to globally identify parameters of the CERES-Sorghum model that require accurate estimation under wet and dry environments; (2) developing a novel estimation method (Holographic Genetic Algorithm, HGA) applicable to both GSP and SSP estimation and testing it with the CROPGRO-Soybean model using 182 soybean lines planted in 352 site-years (7,426 yield observations); and (3) examining the behavior under estimation of the anthesis data prediction component of the CERES-Maize model. The latter study used 5,266 maize Nested Associated Mapping lines and a total 49,491 anthesis date observations from 11 plantings. Three major problems were discovered that challenge the ability to link QG and ECM’s: 1) model expressibility, 2) parameter equifinality, and 3) parameter instability. Poor expressibility is the structural inability of a model to accurately predict an observation. It can only be solved by model changes. Parameter equifinality occurs when multiple parameter values produce equivalent model predictions. This can be solved by using eFAST as a guide to reduce the numbers of interacting parameters and by collecting additional data types. When parameters are unstable, it is impossible to know what values to use in environments other than those used in calibration. All of the methods that will have to be applied to solve these problems will expand the amount of data used with ECM’s. This will require better optimization methods to estimate model parameters efficiently. The HGA developed in this study will be a good foundation to build on. Thus, future research should be directed towards solving these issues to enable ECM’s to be used as tools to support breeders, farmers, and researchers addressing global food security issues.

The motivation for this research was to apply methods of vibrations testing in order to determine axial loads in the pin-ended truss members of the Breeding Bam. This method of vibrations testing was necessary in order to determine the in-situ axial loads of the truss members in the bam. Other common methods, such as strain gauges, were not useful for this application. This is because strain gauges can only detect changes in strain and therefore only changes in load. However due to the size and weight of the roof at the Breeding Bam, significant axial loads are produced in the truss members. This in-situ axial load due to the dead load of the roof is a significant portion of any additional loading and cannot be ignored. The ultimate goal of determining the axial loads in the truss members was to develop a model for the roof structure of the bam that accurately predicts axial loads in the truss members over a range of loading conditions. Developing such a model was important in order to make a structural assessment ofthe Breeding Bam's roof structure. In order to determine the axial loads in the truss members, acceleration time histories of the individual truss members were collected using wireless accelerometers provided by MicroStrain of Williston, Vermont. Using the Fourier transform, power spectral densities were produced from the raw acceleration time histories. It was from these plots that the resonant frequencies of the truss members were determined. Knowing the resonant frequencies for a member and the beam vibration equation developed for pin-ended members, the axial load of the truss member were calculated. This process was done for each wrought iron truss member for three separate loading conditions. The purpose of this was to provide enough experimental data so that it could be compared with predictions of several proposed frame models of the bam's roof structure. Ultimately a model was chosen that best predicted the axial loads in the truss members based upon the three loading combinations tested. Using this frame model, an assessment of the bam's roof structure could be made.

A general class of fluctuation tests for parameter instability in an M-estimation framework is suggested. The tests are based on partial sum processes of M-estimation scores for which functional central limit theorems are derived under the null hypothesis of parameter stability and local alternatives. Special emphasis is given to parameter instability in (generalized) linear regression models and it is shown that the introduced M-fluctuation tests contain a large number of parameter instability or structural change tests known from the statistics and econometrics literature. The usefulness of the procedures is illustrated using artificial data and data for the German M1 money demand, historical demographic time series from Großarl, Austria, and youth homicides in Boston. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Mixed integer programming (MIP) problems are highly parameterized, and finding parameter settings that achieve high performance for specific types of MIP instances is challenging. This paper presents a method to find the information about how CPLEX solver parameter settings perform for the different classes of mixed integer linear programs by using designed experiments and statistical models. Fitting a model through design of experiments helps in finding the optimal region across all combinations of parameter settings. The study involves recognizing the best parameter settings that results in the best performance for a specific class of instances. Choosing good setting has a large effect in minimizing the solution time and optimality gap.

Recursive partitioning is embedded into the general and well-established class of parametric models that can be fitted using M-type estimators (including maximum likelihood). An algorithm for model-based recursive partitioning is suggested for which the basic steps are: (1) fit a parametric model to a data set, (2) test for parameter instability over a set of partitioning variables, (3) if there is some overall parameter instability, split the model with respect to the variable associated with the highest instability, (4) repeat the procedure in each of the daughter nodes. The algorithm yields a partitioned (or segmented) parametric model that can effectively be visualized and that subject-matter scientists are used to analyze and interpret. / Series: Research Report Series / Department of Statistics and Mathematics

A dissertation submitted in fulfilment of the requirements for the degree of Master of Science in Engineering to the Faculty of Engineering and the Built Environment, School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Johannesburg , 2018 / The Discrete Element Method (DEM) models and simulates the flow of gran ular material through confining geometry. The method has the potential to significantly reduce the costs associated with the design and operation of bulk materials handling equipment. The challenge, however, is the difficulty of determining the required input parameters. Previous calibration approaches involved direct measurements and random parameter search. The aim of this research was to develop a sequential DEM calibration framework, identify ap propriate calibration experiments and validate the framework on real flows in a laboratory-scale silo and chute. A systematic and sequential DEM calibration framework was developed. The framework consists of categorising the DEM input parameters into three cat egories of determining the directly measured input parameters, obtaining the literature acquired input parameters, and linking physical experiments with DEM simulations to obtain the calibrated parameter values. The direct mea surement parameters comprised the coefficients of restitution and the particle to wall surface coefficient of rolling friction. Literature obtained parameters were the Young’s Modulus and Poisson’s ratio. The calibrated parameters comprised the particle to wall surface coefficient of sliding friction calibrated from the wall fiction angle, the particle to particle friction coefficients (sliding and rolling) calibrated from two independent angles of repose, particle den sity calibrated from bulk density, and adhesion and cohesion energy densities. The framework was then tested using iron ore with a particle size distribution between +2mm and - 4.75 mm in LIGGGHTS DEM software. i Validation of the obtained input parameter values in the silo and chute showed very good qualitative comparisons between the measured and simulated flows. Quantitative predictions of flow rate were found to be particularly sensitive to variations in the particle to particle coefficient of sliding friction. It was concluded that due to their inherent limitations, angle of repose tests were not totally reliable to calibrate the particle to particle coefficient of sliding friction. Sensitivity tests conducted showed that in the quasi-static flow regime, only the frictional parameters were dominant, while both the frictional and colli sional parameters were dominant in the dynamic flow regime. These results are expected to lay a solid foundation for further research in systematic DEM cali bration and greatly increase the effectiveness of DEM models in bulk materials handling applications. / XL2019

Este trabalho apresenta um estudo sobre taxas de aniquilação de pósitrons em gases moleculares por meio do cálculo do parâmetro de aniquilação Zeff. O modelo Gribakin-Lee (GL) formula de maneira fenomenológica um mecanismo de captura do pósitron mediado por uma interação dipolar, descrevendo uma contribuição ressonante para Zeff dos modos vibracionais ativos-IR da molécula. Este modelo concorda muito bem quando testado aos halometanos no experimento com feixes de pósitrons, porém, falha quando aplicado ao experimento com pósitrons térmicos. Neste contexto, foram testadas algumas hipóteses para explicar a discordância entre o modelo GL aplicado ao experimento com feixes de pósitrons e ao experimento com pósitrons térmicos. Foi mostrado como o modelo GL pode ser obtido como um caso particular do formalismo dos operadores de projeção de Feshbach. As hipóteses testadas para explicar a discrepância entre os modelos foram: (i) desconsiderar a aproximação de largura zero, para uma convolução mais realista do parâmetro de aniquilação Zeff com a distribuição energética dos pósitrons; (ii) incluir combinações de modos vibracionais e overtones IR-ativos, além de modos com atividade Raman no cálculo de Zeff térmico; (iii) incluir ressonâncias rotacionais no modelo GL; e (iv) propor um modelo simplificado para a densidade eletrônica considerando a sua dependência em relação às coordenadas nucleares da molécula. Verificou-se que considerar larguras finitas na convolução de Zeff térmico e Zeff para o feixe não leva a uma diferença significativa em comparação com o modelo GL, sendo legítimo a utilização da aproximação de largura zero para as ressonâncias vibracionais de Feshbach. Quanto à inclusão de overtones e combinações ativos-IR, verificou-se que apesar deste método ser de extrema importância para ajustar Zeff no caso do experimento com feixes de pósitrons para as moléculas de metanol e etileno, a influência desta contribuição para Zeff térmico é modesta. Moléculas com baixíssimas energias de ligação, como o CH3F, podem apresentar uma possível contribuição rotacional para Zeff, representando quase que a totalidade da contribuição ressonante ao parâmetro de aniquilação. / This work presents a study of the rates of annihilation of positrons in molecular gases by calculating the annihilation parameter Zeff. The Gribakin-Lee (GL) model formulates a dipole-interaction-mediated positron capture mechanism, describing a resonant contribution to Zeff of the active-IR vibrational modes of the molecule. This model agrees very well when tested to the halomethanes in the experiment with positron beams, but fails when applied to the experiment with thermal positrons. In this context, some hypotheses were tested to explain the discrepancy between the GL model applied to the experiment with positron beams and the experiment with thermal positrons. It was shown how the GL model can be obtained as a particular case of the Feshbach projection operators formalism. The hypotheses tested to explain the discrepancy between the models were: (i) to disregard the zero-width approximation for a more realistic convolution of the annihilation parameter Zeff with the energy distribution of the positrons; (ii) to include combinations of IR-active vibrational modes and overtones, in addition to modes with Raman activity in the calculation of thermal Zeff; (iii) to include rotational resonances in the GL model and; (iv) to propose a simplified model for the electron density considering its dependence on the nuclear coordinates of the molecule. It has been found that considering finite widths in the convolution of thermal Zeff and Zeff for the beams does not lead to a significant difference from the GL model, being legitimate the use of the zero width approximation for the vibrational Feshbach resonances. Regarding the inclusion of overtones and combinations IR-active, it was found that although this method is of extreme importance to fit Zeff in the case of the experiment with positron beams for methanol and ethylene, the influence of this contribution to thermal Zeff is modest. Molecules with very low binding energies, such as CH3F, may present a possible rotational contribution to Zeff, representing almost the entire resonant contribution to the annihilation parameter.

Os principais resultados originais relatados ao longo desse texto provêm de observações em experimentos numéricos, entretanto, na maioria dos casos, os resultados são fundamentados com instrumentos teóricos ou com modelos heurísticos. Inicialmente, introduzimos, nas equações que descrevem osciladores caóticos, uma pequena perturbação periódica a fim de observar no espaço de parâmetros a porção de parâmetros cujo comportamento caótico é extinto. Assim, constatamos que o conjunto de parâmetros correspondentes às orbitas caóticas extintas correspondem à replicas de janelas periódicas complexas previamente existentes no sistema não-perturbado. Posteriormente, utilizando as propriedades de torsão do espaço de estados dos osciladores caóticos, visualizamos transições existentes no interior das janelas periódicas complexas. Quando consideramos sequências dessas janelas sob a ótica da torsão do espaço de estados, observamos a existência de regras que relacionam janelas consecutivas ao longo dessa sequência. Adicionalmente, no espaço de parâmetros de osciladores caóticos e sistemas dinâmicos adicionais, fizemos uma estimativa da dimensão da fronteira entre o conjunto de parâmetros que leva às soluções periódicas e o conjunto que leva aos atratores caóticos. Para os sistemas investigados, os valores obtidos para essa dimensão estão no mesmo intervalo de confiança, indicando que essa dimensão é universal. / The main results reported along this text come from observations in numerical experiments, however, in most cases, results are explained by theoretical instruments or heuristic models. Initially we introduced in the equations that describe chaotic oscillators, a small periodic perturbation to observe, in the parameter space, the portion of parameters whose chaotic behavior is extinguished. Thus, we find that the set of parameters corresponding to the extinct chaotic orbits correspond to replicas of previously complex periodic windows existing in the unperturbed system. Subsequently, using the torsion properties of state spaces of chaotic oscillators, we visualize transitions within the complex periodic windows. When we consider sequences of these windows from the perspective of torsion properties of the state space, we observe the existence of rules that relate consecutive windows along these sequences. Additionally, in the parameter space of chaotic oscillators and additional dynamical systems, we estimate the dimension of the boundary between the set of parameters that leads to periodic solutions and the set that leads to chaotic attractors. For the systems considered here, the values for this dimension are in the same confidence interval, indicating that this dimension is universal.

Analyzing life-time data with long-term survivors is an important topic in medical application. Cure models are usually used to analyze survival data with the proportion of cure subjects or long-term survivors. In order to include the propor- tion of cure subjects, mixture and non-mixture cure models are considered. In this dissertation, we utilize both maximum likelihood and Bayesian methods to estimate model parameters. Simulation studies are carried out to verify the nite sample per- formance of the estimation methods. Real data analyses are reported to illustrate the goodness-of- t via Fr echet, Weibull and Exponentiated Exponential susceptible distributions. Among the three parametric susceptible distributions, Fr echet is the most promising. Next, we extend the non-mixture cure model to include a change point in a covariate for right censored data. The smoothed likelihood approach is used to address the problem of a log-likelihood function which is not di erentiable with respect to the change point. The simulation study is based on the non-mixture change point cure model with an exponential distribution for the susceptible subjects. The simulation results revealed a convincing performance of the proposed method of estimation. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

by Siu-fung Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Bibliography: leaves 38-41. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Analysis of the Structural Equation Model with Continuous Data --- p.6 / Chapter §2.1 --- The Model --- p.6 / Chapter §2.2 --- Mehtods of Handling Incomplete Data --- p.8 / Chapter §2.3 --- Design of the Monte-Carlo Study --- p.12 / Chapter §2.4 --- Results of the Monte-Carlo Study --- p.15 / Chapter Chapter 3 --- Analysis of the Structural Equation Model with Polytomous Data --- p.24 / Chapter §3.1 --- The Model --- p.24 / Chapter §3.2 --- Methods of Handling Incomplete Data --- p.25 / Chapter §3.3 --- Design of the Monte-Carlo Study --- p.27 / Chapter §3.4 --- Results of the Monte-Carlo Study --- p.31 / Chapter Chapter 4 --- Summary and Discussion --- p.36 / References --- p.38 / Tables --- p.42 / Figures --- p.78