Investigating the Co-Regulatory Role of Midline and Extramacrochaetae In Regulating Eye Development and Vision in \u3ci\u3eDrosophila melanogaster\u3c/i\u3e

The Honors thesis research focused on the roles of extramacrochaetae and midline in regulating eye development and the vision of Drosophila melanogaster. It is known from previous studies that extramacrochaetae (emc) and midline (mid) independently regulate the formation of ommatidial units in the Drosophila compound eye. However, the thesis focuses on the interaction of these two genes and their co-dependent roles in regulating eye development. This study also attempts to explain the recovered formation of ommatidial units and interommatidial bristles when the expression of both of these genes is reduced and whether flies doubly mutant for these genes have recovered phototactic ability. Specific genotypes of flies were subjected to larval and adult phototaxis assays to assay their phototactic ability. A Western analysis was performed on extramacrochaetae mutants, midline mutants, and wild-type flies to determine whether the Emc and Mid proteins interacted in a co-regulatory fashion within developing larval tissues. The larval phototaxis assays revealed a slight decrease in photoreception in the mid-RNAi larvae when compared to the wild-type larvae. However the data was not conclusive to definitively determine if the mid-RNAi mutants displayed a significant decrease in photoreceptive ability. The adult phototaxis assays were more definitive than the larval assays. The emc1 flies displayed a slight decrease in photoreceptive ability. Both the mid-RNAi and the flies doubly mutant for midGA174 and emc1 displayed a significant decrease in photoreceptive ability. The Western blot and immunofluorescence studies revealed an interaction between mid and emc, and the future nature of this interaction will be resolved in greater detai

Iterative Solution Methods for Reduced-Order Models of Parameterized Partial Differential Equations

This dissertation considers efficient computational algorithms for solving parameterized discrete partial differential equations (PDEs) using techniques of reduced-order modeling. Parameterized equations of this type arise in numerous mathematical models. In some settings, e.g. sensitivity analysis, design optimization, and uncertainty quantification, it is necessary to compute discrete solutions of the PDEs at many parameter values. Accuracy considerations often lead to algebraic systems with many unknowns whose solution via traditional methods can be expensive. Reduced-order models use a reduced space to approximate the parameterized PDE, where the reduced space is of a significantly smaller dimension than that of the discrete PDE. Solving an approximation of the problem on the reduced space leads to reduction in cost, often with little loss of accuracy. In the reduced basis method, an offline step finds an approximation of the solution space and an online step utilizes this approximation to solve a smaller reduced problem, which provides an accurate estimate of the solution. Traditionally, the reduced problem is solved using direct methods. However, the size of the reduced system needed to produce solutions of a given accuracy depends on the characteristics of the problem, and it may happen that the size is significantly smaller than that of the original discrete problem but large enough to make direct solution costly. In this scenario, it is more effective to use iterative methods to solve the reduced problem. To demonstrate this we construct preconditioners for the reduced-order models or construct well-conditioned reduced-order models. We demonstrate that by using iterative methods, reduced-order models of larger dimension can be effective. There are several reasons that iterative methods are well suited to reduced- order modeling. In particular, we take advantage of the similarity of the realizations of parameterized systems, either by reusing preconditioners or by recycling Krylov vectors. These two approaches are shown to be effective when the underlying PDE is linear. For nonlinear problems, we utilize the discrete empirical interpolation method (DEIM) to cheaply evaluate the nonlinear components of the reduced model. The method identifies points in the PDE discretization necessary for representing the nonlinear component of the reduced model accurately. This approach incurs online computational costs that are independent of the spatial dimension of the discretized PDE. When this method is used to assemble the reduced model cheaply, iterative methods are shown to further improve efficiency in the online step. Finally, when the traditional offline/online approach is ineffective for a given problem, reduced-order models can be used to accelerate the solution of the full model. We follow the solution model of Krylov subspace recycling methods for sequences of linear systems where the coefficient matrices vary. A Krylov subspace recycling method contains a reduced-order model and an iterative method that searches the space orthogonal to the reduced space. We once again use iterative solution techniques for the solution of the reduced models that arise in this context. In this case, the iterative methods converge quickly when the reduced basis is constructed to be naturally well conditioned

Properties and preservers of the pseudospectrum

The interplay between the algebraic and analytic properties of a matrix and the geometric properties of its pseudospectrum is investigated. It is shown that one can characterize Hermitian matrices, positive semi-definite matrices, orthogonal projections, unitary matrices, etc. in terms of the pseudospectrum. Also, characterizations are given to maps on matrices leaving invariant the pseudospectrum of the sum, difference, or product of matrix pairs. It is shown that such a map is always a unitary similarity transform followed by some simple operations such as adding a constant matrix, taking the matrix transpose, or multiplying by a scalar in {1, -1}. (C) 2011 Elsevier Inc. All rights reserved

Solving the steady state diffusion equation with uncertainty

Abstract The goal of this project is to efficiently solve a steady state diffusion equation with a random coefficient. Although, such equations can be solved using Monte-Carlo methods, the lengthy computation time can be constraining. Using a Karhunen-Loéve expansion allows the random coefficient to be approximated with a finite sum of random variables. This expansion combined with a Galerkin method or stochastic collocation method reduces computation time

Preservers of eigenvalue inclusion sets of matrix products

For a square matrix A, let S(A) be an eigenvalue inclusion set such as the Gershgorin region, the union of Cassini ovals, and the Ostrowski\u27s set. Characterization is obtained for maps Phi on n x n matrices satisfying S(Phi(A)Phi(B)) = S(AB) for all matrices A and B. (C) 2010 Elsevier Inc. All rights reserved

Índices de qualidade biológica do solo em área sob manejo de adubos verdes

In the search for a sustainable agriculture the use of plant species that promotes soil biological properties has been considered as an alternative to soil conservation practices. Our aim here was to evaluate the effects of plant species cultivation on both the soil macroarthropods and arbuscular mycorrhizal fungi communities in a semiarid ecoregion. The study was developed in field conditions, using a randomized blocks design with ten treatments (Crotalaria juncea L., C. spectabilis Roth, C. ochroleuca G. Don, Canavalia ensiformis (L.) DC., Dolichos lablab L., Mucuna pruriens (L.) DC., Stilozobium aterrimum Piper & Tracy, Neonotonia wightii (Wight & Arn.) J.A. Lackey, Pennisetum glaucum (L.) R. Br., and a control treatment (a mix of Brachiaria decumbens Stapf cv. Basilisk and native weeds), in three independent blocks. In order to evaluate the effects of plant species cultivation on both the soil macroarthropod and arbuscular mycorrhizal fungal communities, we evaluated the plant dry biomass production, soil pH, soil total organic carbon, species richness (S), Shannon’s diversity index (H') and Simpson’s dominance index (C). For the effects of plant species cultivation on arbuscular mycorrhizal fungi (AMF) communities, we compared our results with two additional control treatments (Eucalyptus globulus Labill and a tropical moist forest). The Shapiro-Wilk test was applied to assess the normality of the data distribution. Two-way ANOVA was used to test significant differences between species richness, H’ index, and C index. The Bonferroni’s test was applied at 5% probability. Based on our results, we generated two equations to estimate the soil biological quality index (IQBS), as well as the mycorrhizal quality index (IQM). We found the highest values of soil macroarthropod richness and H’ index in the plots where C. spectabilis and C. ochroleuca were cultivated. The plant species with the best results in the ecological indexes were P. glaucum, C. ensiformis, S. aterrimum and N. wightii, when compared with Eucalyptus globulus Labill and tropical moist forest.Na busca da sustentabilidade na agricultura, a utilização de espécies vegetais com características botânicas benéficas às propriedades biológicas do solo tem sido considerada como alternativa às práticas convencionais. Objetivou-se avaliar o efeito do cultivo de espécies de plantas das famílias Fabaceae e Poaceae nas comunidades de macroartrópodes e fungos micorrízicos arbusculares do solo em ambiente semiárido. O estudo foi desenvolvido em condições de campo, em 3 blocos (DBC); constituído por 10 tratamentos. Os tratamentos foram: Crotalaria juncea L., C. spectabilis Roth, C. ochroleuca G. Don, Canavalia ensiformis (L.) DC., Dolichos lablab L., Mucuna pruriens (L.) DC., Stizolobium aterrimum Piper & Tracy, Neonotonia wightii (Wight & Arn.) J.A. Lackey, Pennisetum glaucum (L.) R.Br., e Brachiaria decumbens Stapf cv. Basilisk + plantas espontâneas. Para determinar os efeitos das espécies para adubação verde sobre a comunidade de macroartrópodes e de fungos micorrízicos no solo foram avaliados produção de biomassa seca, pH, carbono orgânico total do solo, riqueza de grupos (S), índice de diversidade de Shannon (H’) e índice de dominância de Simpson (C). Exclusivamente, para avaliação da influência dessas espécies vegetais sobre as comunidades de fungos micorrízicos arbusculares (FMA), foi realizada uma comparação de todas as variáveis analisadas em função de uma plantação de Eucalyptus globulus Labill e uma Floresta tropical úmida. Os dados foram submetidos ao teste Shapiro-Wilk para determinar a normalidade na distribuição dos dados. Para as significâncias dos índices ecológicos foi utilizada ANOVA do tipo “two-way” e aplicado o teste Bonferroni a 5%. Com base nos dados obtidos foram geradas equações para estimar a qualidade biológica do solo (IQBS), assim como o índice de qualidade micorrízica (IQM) nas áreas avaliadas. As espécies de plantas da Família Fabaceae proporcionam condições positivas para a manutenção de uma comunidade de macroartrópodes diversificada, sendo C. spectabilis e C. ochroleuca as espécies com maior riqueza e diversidade nas estações chuvosa e seca, respectivamente. Para as comunidades de FMAs as espécies de plantas que promoveram os melhores resultados nos índices ecológicos foram P. glaucum, C. ensiformis, S. aterrimum e N. wightii, quando comparados com Eucalyptus globulus Labill e a Floresta tropical úmida