In an anisotropic adaptive finite element algorithm one usually needs an error estimator that yields the error size but also the stretching directions and stretching ratios of the elements of a (quasi) optimal anisotropic mesh. However the last two ingredients can not be extracted from any of the known anisotropic a posteriori error estimators. Therefore a heuristic approach is pursued here, namely, the desired information is provided by the so-called Hessian strategy. This strategy produces favourable anisotropic meshes which result in a small discretization error. The focus of this paper is on error estimation on anisotropic meshes. It is known that such error estimation is reliable and efficient only if the anisotropic mesh is aligned with the anisotropic solution. The main result here is that the Hessian strategy produces anisotropic meshes that show the required alignment with the anisotropic solution. The corresponding inequalities are proven, and the underlying heuristic assumptions are given in a stringent yet general form. Hence the analysis provides further inside into a particular aspect of anisotropic error estimation.

In an anisotropic adaptive finite element algorithm one usually needs an error estimator that yields the error size but also the stretching directions and stretching ratios of the elements of a (quasi) optimal anisotropic mesh. However the last two ingredients can not be extracted from any of the known anisotropic a posteriori error estimators. Therefore a heuristic approach is pursued here, namely, the desired information is provided by the so-called Hessian strategy. This strategy produces favourable anisotropic meshes which result in a small discretization error. The focus of this paper is on error estimation on anisotropic meshes. It is known that such error estimation is reliable and efficient only if the anisotropic mesh is aligned with the anisotropic solution. The main result here is that the Hessian strategy produces anisotropic meshes that show the required alignment with the anisotropic solution. The corresponding inequalities are proven, and the underlying heuristic assumptions are given in a stringent yet general form. Hence the analysis provides further inside into a particular aspect of anisotropic error estimation.

Doctor of Philosophy / Department of Plant Pathology / Bikram S. Gill / H13, a dominant resistance gene transferred from Aegilops tauschii into wheat (Triticum aestivum), confers a high level of antibiosis against a wide range of Hessian fly (HF, Mayetiola destructor) biotypes. Previously, H13 was mapped to the distal arm of chromosome 6DS, where it is flanked by markers Xcfd132 and Xgdm36. A mapping population of 1,368 F2 individuals derived from the cross: PI372129 (h13h13) / PI562619 (Molly, H13H13) was genotyped and H13 was flanked by Xcfd132 at 0.4cM and by Xgdm36 at 1.8cM. Screening of BAC-based physical maps of chromosome 6D of Chinese Spring wheat and Ae. tauschii coupled with high resolution genetic and Radiation Hybrid mapping identified nine candidate genes co-segregating with H13. Candidate gene validation was done on an EMS-mutagenized TILLING population of 2,296 M₃ lines in Molly. Twenty seeds per line were screened for susceptibility to the H13-virulent HF GP biotype. Sequencing of candidate genes from twenty-eight independent susceptible mutants identified three nonsense, and 24 missense mutants for CNL-1 whereas only silent and intronic mutations were found in other candidate genes. 5’ and 3’ RACE was performed to identify gene structure and CDS of CNL-1 from Molly (H13H13) and Newton (h13h13). Increased transcript levels were observed for H13 gene during incompatible interactions at larval feeding stages of GP biotype. The predicted coding sequence of H13 gene is 3,192 bp consisting of two exons with 618 bp 5’UTR and 2,260 bp 3’UTR. It translates into a protein of 1063 amino acids with an N-terminal Coiled-Coil (CC), a central Nucleotide-Binding adapter shared by APAF-1, plant R and CED-4 (NB-ARC) and a C-terminal Leucine-Rich Repeat (LRR) domain. Conserved domain analysis revealed shared domains in Molly and Newton, except for differences in sequence, organization and number of LRR repeat in Newton. Also, the presence of a transposable element towards the C terminal of h13 was indicative of interallelic recombination, recent tandem duplications and gene conversions in the CNL rich region near H13 locus. Comparative analysis of candidate genes in the H13 region indicated that gene duplications in CNL encoding genes during divergence of wheat and barley led to clustering and diversity. This diversity among CNL genes may have a role in defining differences in the recognition specificities of NB-LRR encoding genes. Allele mining for the H13 gene in the core collection of Ae. tauschii and hexaploid wheat cultivars identified different functional haplotypes. Screening of these haplotypes using different HF biotypes would help in the identification of the new sources of resistance to control evolving biotypes of HF. Cloning of H13 will provide perfect markers to breeders for HF resistance breeding programs. It will also provide an opportunity to study R-Avr interactions in the hitherto unexplored field of insect-host interaction.

Master of Science / Entomology / Ming-Shun Chen / Robert "Jeff" J. Whitworth / MicroRNA (miRNA) plays a role in nearly all the biological pathways and therefore may provide opportunities to develop new means to combat the Hessian fly, Mayetiola destructor, a destructive pest of wheat. This study presents a comprehensive analysis of miRNA species via deep-sequencing samples from Hessian fly second instar larvae, pupae and adults. A total of 921 unique miRNA species were identified from approximately 30 million sequence reads. Among the 921 miRNA species, only 22 were conserved among Hessian fly and other insect species, and 242 miRNA species were unique to Hessian fly, the remaining 657 share certain sequence similarities with pre-miRNA genes identified from various insect species. The abundance of the 921 miRNA species based on sequence reads varies greatly among the three analyzed stages, with 20 exclusively expressed in adults, two exclusively expressed in pupae and two exclusively expressed in second instar larvae. For miRNA species expressed in all stages, 722 were with reads lower than 10. The abundance of the remaining 199 miRNA species varied from zero to more than eight-fold differences among different stages. Putative miRNA-encoding genes were analyzed for each miRNA species. A single putative gene was identified for 594 miRNA species. Two putative genes were identified for 138 miRNA species. Three or more putative genes were identified for 86 miRNA species. The three largest families had 14, 23 and 34 putative coding genes, respectively. No gene was identified for the remaining 103 miRNA species. In addition, 1516 putative target genes were identified for 490 miRNA species based on known criteria for miRNA targets. The putative target genes are involved in a wide range of processes from nutrient metabolism to encoding effector proteins. Analysis of the expression patterns of miRNA and pre-miRNA for the miRNA family PC-5p-67443, which contains 91 genes, revealed that miRNA and pre-miRNA were expressed differently in different developmental stages, suggesting that different isogenes are regulated by different mechanisms, or pre-miRNAs had other functions in addition to as an intermediate for miRNA biogenesis. The large set of miRNA species identified here provides a foundation for future research on miRNA functions in Hessian fly and for comparative studies in other species. The differential expression patterns between a pre-miRNA and its encoded mature miRNA in a multigene family is an initial step toward understanding the functional significance of isogenes in dramatically expanded miRNA families.

Doctor of Philosophy / Genetics Interdepartmental Program / Jesse A. Poland / Wheat is perhaps the most important component in human diet introduced since the conception of modern agriculture, which provides about 20% of the daily protein and calorie intake to billions of people. Adaptable to wide range of climates, wheat is grown worldwide, lending it the potential to mitigate the imminent risk of food security for future population of 9.5 billion people. For developing improved crop varieties in the future, genetic diversity is a key factor in plant breeding. Constraints in wheat evolution and artificial selection practices have resulted in erosion of this ingredient in elite germplasm. However, wheat wild relatives, such as Ae. tauschii, D-genome donor of wheat, are a storehouse for unexploited genetic diversity that can be used for improving wheat for disease and insect resistance, yield, quality, and tolerance to abiotic stresses. More than 1700 genebanks around the world hold over 7 million accessions of these wild relatives. These genebanks are expensive to maintain, therefore, efficient curation is necessary. We developed and implemented a protocol to identify duplicate accessions using genomic tools. Implementing this approach with three genebanks, we identified over 50% duplicated accessions across genebanks. There are over a million Triticeae accessions held collectively, and it is likely as more number of genebanks are tested, there will be decreasing number of unique accessions. Selecting and utilizing the wild genetic diversity is no easy task. Historically, breeders and geneticists have chosen the accessions primarily based on associated phenotypic data. Unless focusing on a targeted trait, this practice is imperfect in capturing the genetic diversity with some other limitations, such as confounding phenotypic data with the testing environment. Utilizing next-generation sequencing methods, we selected a MiniCore consisting of only 40 accessions out of 574 capturing more than 95% of the allelic diversity. This MiniCore will facilitate the use of genetic diversity present in Ae. tauschii for wheat improvement including resistance to leaf rust, stem rust, Hessian fly, and tolerance to abiotic stresses. Hessian fly is an important insect pest of wheat worldwide. Out of 34 known resistance genes, only six have been mapped on the D sub-genome. With swift HF evolution, we need to rapidly map and deploy the resistance genes. Some of the undefeated HF resistance genes, such as H26 and H32, were introgressed from Ae. tauschii. In this study, we mapped three previously known genes, and a new gene from Ae. tauschii accession KU2147. Genes were mapped on chromosomes 6B, 3D, and 6D. Further, identification and cloning of resistance genes will enhance our understanding about its function and mode of action. In conclusion, wild wheat relatives are genetically diverse species, and utilizing the novel genetic diversity in Ae. tauschii will be fruitful for wheat improvement in the wake of climate change to ensure future food security to expected 2 billion newcomers by 2050.

Doctor of Philosophy / Department of Entomology / Brian P. McCornack / Timely enactment of insect pest management and incursion mitigation protocols requires development of time-sensitive monitoring approaches. Numerous passive monitoring methods exist (e.g., insect traps), which offer an efficient solution to monitoring for pests across large geographic regions. However, given the number of different monitoring tools, from specific (e.g., pheromone lures) to general (e.g., sticky cards), there is a need to develop protocols for deploying methods to effectively and efficiently monitor for a multitude of potential pests. The non-random movement of the Hessian fly, Mayetiola destructor (Say) (Diptera: Cecidomyiidae), toward several visual, chemical, and tactile cues, makes it a suitable study organism to examine new sensor technologies and deployment strategies that can be tailored for monitoring specific pests. Therefore, the objective was to understand Hessian fly behavior toward new sensor technologies (i.e., light emitting diodes (LEDs) and laser displays) to develop monitoring and deployment strategies. A series of laboratory experiments and trials were conducted to understand how the Hessian fly reacts to the technologies and how environmental factors may affect the insect’s response. Hessian fly pupae distribution within commercial wheat fields was also analyzed to determine deployment of monitoring strategies. Laboratory experiments demonstrated Hessian fly attraction to green spectrum (502 and 525 nm) light (LEDs), that response increased with light intensity (16 W/m2), and that they responded in the presence of wheat odor and the Hessian fly female sex-pheromone, but, response was reduced under ambient light. These laboratory experiments can be used to build a more targeted approach for Hessian fly monitoring by utilizing the appropriate light wavelength and intensity with pheromone and wheat odor to attract both sexes, and mitigating exposure to ambient light. Together this information suggested that light could be used with natural cues to increase attraction. Therefore, a light source (green laser display) was applied to a wheat microcosm, which resulted in greater oviposition in wheat covered by the laser display. Examination of Hessian fly pupal distribution within commercial wheat fields showed that proportion of wheat within a 1 km buffer of the field affected distribution between fields. This helps to inform deployment of monitoring strategies as it identified fields with a lower proportion of wheat within a 1 km buffer to be at higher risk Hessian fly infestation, and therefore monitoring efforts should be focused on those fields. Together this work demonstrates Hessian fly behavior toward new sensor technologies, how those technologies interact with environmental cues, and how environmental composition affects pupal distribution. Collectively this information will enable cheaper, more accurate and more efficient monitoring of this destructive pest.

Made available in DSpace on 2015-05-15T11:46:26Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 980914 bytes, checksum: a5914e595687839b602a1d3280515022 (MD5) Previous issue date: 2011-02-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Hesse said in one of his articles that a hypersurface in the projective space Pn that has null hessian polynomial is a cone. Later, Gordam and Noether prove that the statement of Hesse is valid only for n 3, presenting counter-examples for n 4. Initially we tried to solve the problem in a direct and elementary form, been well succeeding only in the case of P1, so we set out to study the dual of variety and polar map associated to the hypersurface X = Z(F) Pn. Having mind that X IF , where IF is the polar map image, and that X is a cone if and only if, X is degenerate. Which brings us to display a series of technical results in order to conclude that IF is a linear variety, speci cally a line if n = 2 and a plane or line if n = 3. Thus we prove for a given hypersurface X = Z(F) Pn. If n 3, then X is a Cone () det [Hess (F)] = 0. / Hesse a rmou em um dos seus artigos que uma hipersuperfície no espaço projetivo Pn que tenha o hessiano polinomial nulo é um cone. Mais tarde, Gordam e Noether provam que a a rmação de Hesse é valida apenas para n 3, apresentando contra- exemplos para n 4. Inicialmente tentamos resolver o problema de maneira direta e elementar, tendo sucesso só no caso de P1, então partimos para o estudo de dual de uma variedade e de mapa polar associado a uma hipersuperfície X = Z(F) Pn. Tendo em consideração que X IF , onde IF é a imagem do mapa polar, e que X é um Cone se, e somente se, X é degenerado. Somos levados a mostrar uma série de resultados técnicos a m de concluir que IF é uma variedade linear, especi camente uma reta se n = 2 e um plano ou uma reta se n = 3. Provando assim que dada uma hipersuperfície X = Z(F) Pn. Se n 3, então X é um cone () det [Hess (F)] = 0.

Orientador: Margarida Pinheiro Mello / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T06:57:47Z (GMT). No. of bitstreams: 1 Gower_RobertMansel_M.pdf: 908087 bytes, checksum: f8067f63c68dadafecf74e1387966331 (MD5) Previous issue date: 2011 / Resumo: Dentro do contexto de programação não linear, vários algoritmos resumem-se à aplicação do método de Netwon aos sistemas constituídos pelas condições de primeira ordem de Lagrange. Nesta classe de métodos é necessário calcular a matriz hessiana. Nosso foco é o cálculo exato, dentro da precisão da máquina, de matrizes hessianas usando diferenciação automática. Para esse fim, exploramos o cálculo da matriz hessiana sob dois pontos de vista. O primeiro é um modelo de grafo que foca nas simetrias que ocorrem no processo do cálculo da hessiana. Este ângulo propicia a intuição de como deve ser calculada a hessiana e leva ao desenvolvimento de um novo método de modo reverso para o cálculo de matrizes hessianas denominado edge pushing. O segundo ponto de vista é uma representação puramente algébrica que reduz o cálculo da hessiana à avaliação de uma expressão. Esta expressão pode ser usada para demonstrar algoritmos já existentes e projetar novos. Para ilustrar, deduzimos dois novos algoritmos, edge pushing e um novo algoritmo de modo direto, e uma série de outros métodos conhecidos [1], [20, p.157] e [9]. Apresentamos estudos teóricos e empíricos sobre o algoritmo edge pushing. Analisamos sua complexidade temporal e de uso de memória. Implementamos o algoritmo como um driver do pacote ADOL-C [19] e efetuamos testes computacionais, comparando sua performance com à de dois outros drivers em dezesseis problemas da coleção CUTE [5]. Os resultados indicam que o novo algoritmo é muito promissor. Pequenas modificações em edge pushing produzem um novo algoritmo, edge pushing sp, para o cálculo da esparsidade de matrizes hessianas, um passo necessário de uma classe de métodos que calculam a matriz hessiana usando colorações de grafos, [14, 19, 30]. Estudos de complexidade e testes numéricos são realizados comparando o novo método contra um outro recentemente desenvolvido [30] e os testes favorecem o novo algoritmo edge pushing sp. No capítulo final, motivado pela disponibilidade crescente de computadores com multiprocesadores, investigamos o processamento em paralelo do cálculo de matrizes hessianas. Examinamos o cálculo em paralelo de matrizes hessianas de funções parcialmente separáveis. Apresentamos uma abordagem desenvolvida para o cômputo em paralelo que pode ser usando em conjunto com qualquer método de cálculo de hessiana e outra estratégia específica para métodos de modo reverso. Testes são executados em um computador com memória compartilhada usando a interface de programação de aplicativo OpenMP / Abstract: In the context of nonlinear programming, many algorithms boil down to the application of Newton's method to the system constituted by the first order Lagrangian conditions. The calculation of Hessian matrices is necessary in this class of solvers. Our focus is on the exact calculation, within machine precision, of Hessian matrices through automatic differentiation. To this end, we detail the calculations of the Hessian matrix under two points of view. The first is an intuitive graph model that focuses on what symmetries occur throughout the Hessian calculation. This provides insight on how one should calculate the Hessian matrix, and we use this enlightened perspective to deduce a new reverse Hessian algorithm called edge pushing. The second viewpoint is a purely algebraic representation of the Hessian calculation via a closed formula. This formula can be used to demonstrate existing algorithms and design new ones. In order to illustrate, we deduce two new algorithms, edge pushing and a new forward algorithm, and a series of other known Hessian methods [1], [20, p.157] and [9]. We present theoretical and empirical studies of the edge pushing algorithm, establishing memory and temporal bounds, and comparing the performance of its computer implementation against that of two algorithms available as drivers of the software ADOL-C [14, 19, 30] on sixteen functions from the CUTE collection [5]. Test results indicate that the new algorithm is very promising. As a by-product of the edge pushing algorithm, we obtain an efficient algorithm, edge pushing sp, for automatically obtaining the sparsity pattern of Hessian matrices, a necessary step in a class of methods used for computing Hessian matrices via graph coloring, [14, 19, 30]. Complexity bounds are developed and numerical tests are carried out comparing the new sparsity detection algorithm against a recently developed method [30] and the results favor the new edge pushing sp algorithm. In the final chapter, motivated by the increasing commercial availability of multiprocessors, we investigate the implementation of parallel versions of the edge pushing algorithm. We address the concurrent calculation of Hessian matrices of partially separable functions. This includes a general approach to be used in conjunction with any Hessian software, and a strategy specific to reverse Hessian methods. Tests are carried out on a shared memory computer using the OpenMP paradigm / Mestrado / Analise Numerica / Mestre em Matemática Aplicada

Mean-field games (MFGs) study the behavior of rational and indistinguishable agents in a large population. Agents seek to minimize their cost based upon statis- tical information on the population’s distribution. In this dissertation, we study the homogenization of a stationary first-order MFG and seek to find a numerical method to solve the homogenized problem. More precisely, we characterize the asymptotic behavior of a first-order stationary MFG with a periodically oscillating potential. Our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems. Moreover, we prove existence and uniqueness of the solution to these limit problems. Next, we notice that the homogenized problem resembles the problem involving effective Hamiltoni- ans and Mather measures, which arise in several problems, including homogenization of Hamilton–Jacobi equations, nonlinear control systems, and Aubry–Mather theory. Thus, we develop algorithms to solve the homogenized problem, the effective Hamil- tonians, and Mather measures. To do that, we construct the Hessian Riemannian flow. We prove the convergence of the Hessian Riemannian flow in the continuous setting. For the discrete case, we give both the existence and the convergence of the Hessian Riemannian flow. In addition, we explore a variant of Newton’s method that greatly improves the performance of the Hessian Riemannian flow. In our numerical experiments, we see that our algorithms preserve the non-negativity of Mather mea- sures and are more stable than related methods in problems that are close to singular. Furthermore, our method also provides a way to approximate stationary MFGs.

In sufficient dimension reduction (Li, 1991; Cook, 1998b), original predictors are replaced by their low-dimensional linear combinations while preserving all of the conditional information of the response given the predictors. Sliced inverse regression [SIR; Li, 1991] and principal Hessian directions [PHD; Li, 1992] are two popular sufficient dimension reduction methods, and both SIR and PHD estimators involve all of the original predictor variables. To deal with the cases when the linear combinations involve only a subset of the original predictors, we propose a Bayesian model averaging (Raftery et al., 1997) approach to achieve sparse sufficient dimension reduction. We extend both SIR and PHD under the Bayesian framework. The superior performance of the proposed methods is demonstrated through extensive numerical studies as well as a real data analysis. / Statistics