The next generation of toxic chemicals and hazardous wastes from sophisticated chemical industries will demand the environmental agencies to employ biological methods over the conventional physical and chemical remediation methods. Over the past decade, natural metallo-enzymes have been identified to degrade some of the major chemical contaminants through electron transfer pathways. However, these natural enzymes are less stable in organic solvents and they are not effective for the degradation of toxic compounds such as polychlorinated biphenyls or dioxins. This thesis explores the use of protein design approaches to produce chemically and molecularly modified enzymes, which are highly stable, possess little substrate specificity, and have higher activity than the natural enzymes. The experiments presented in this thesis make use of solid phase synthesis and site-directed mutagenesis for the synthesis and production of these enzymes and popular chromatographic techniques for their purification. The partial characterization of these proteins revealed the essential structural features of these proteins, and their catalytic activity was demonstrated by the use of peroxidase assays. / Master of Science

This thesis presents a new method for improved resolution of stereoscopic 3D terrain mapping by local dense bundling of disparity maps. The Unmanned Systems Lab (USL) at Virginia Tech is designing an unmanned aerial vehicle (UAV) first-response system capable of 3D terrain mapping in the wake of a nuclear event. The UAV is a helicopter, and is equipped with a stereo boom imaging system, GPS, and an inertial measurement system (IMU) for low-altitude aerial mapping. Previous 3D reconstruction algorithms on the project used two-frame rectified stereo correspondence to create a local 3D map, which was geo-located by raw GPS and IMU data. The new local dense bundling algo-rithm combines multiple pairs of stereo images by SURF feature point matching, image rectification, matching of dense points with semi-global block matching, and optimization of camera pose and dense 3D point location using a stereo-constrained local bundle adjustment. The performance of the algorithm is evaluated numerically on synthetic im-agery and qualitatively on real aerial flight data. Results indicate the algorithm produces marked improvement in accuracy and vertical resolution, given a proper helicopter flight path and sufficient image overlap. With synthetic imagery and precise pose supplied, the algorithm shows a 1.2x to 6x reduction in vertical error. / Master of Science

A agricultura de precisão tem agregado alto valor para os agricultores por causa das tecnologias que estão ligadas a ela. Sistemas que extraem informações de imagens digitais são extremamente utilizados para que o agricultor tome decisões a fim de aumentar sua produtividade. Uma das técnicas de realizar o monitoramento é a construção de um mosaico de imagens aéreas, onde são utilizadas aeronaves voando em baixa altitude. Esta técnica pode levar dezenas de horas para ser concluída, dependendo da configuração do computador que a executa. Com o intuito de reduzir o tempo nessa construção e tornar possível o embarque a essa aplicação, este trabalho apresenta uma maneira simplificada de construir o mosaico de imagens aéreas baseada na técnica de georreferenciamento direto, no qual utiliza a computação heterogênea para acelerar o desempenho. Essa abordagem é composta por apenas três técnicas que também compõem a abordagem clássica para a construção de mosaicos (warping, extração de características e combinação de características), além de inserir em seus cálculos os dados fornecidos pelos sensores GPS e IMU com a finalidade de direcionar e posicionar cada imagem pertencente ao conjunto que formará o mosaico. A plataforma de computação heterogênea utilizada neste trabalho é a NVIDIA Jetson TK1 escolhida pelo fato de disponibilizar de uma GPU que suporta a linguagem de programação CUDA. Utilizando esta abordagem, a falta de correção da perspectiva do conteúdo (geometria) da imagem gera um resultado inesperado, pois os dados fornecidos pela IMU, ao contrário do que se imagina, apenas servem para corrigir a posição das coordenadas do GPS registradas no momento de captura de cada imagem que compõem o mosaico. O tempo de execução da aplicação desenvolvida é satisfatório tornando possível a adoção desta abordagem. / Accuracy agriculture has added value to farmers thanks to the new technologies that are linked to it. Systems that extract information from digital images are very usefull to help farmers making decisions in order to increase their productivity. One of the techniques to perform this kind of monitoring is the construction of an aerial imagery mosaic where aircrafts flies in low altitude. This technique may take hours to be completed, depending on computer\'s configuration. With the purpose of reducing time in this construction, this thesis presents a simplified way to make aerial imagery mosaic based on direct georeferencing. This approach is composed by three techniques that also make up the classic approach to building mosaics (warping, extraction of characteristics and combination of characteristics), the difference is with this technique here presented is also possible to insert into the calculations the data provided by the GPS and IMU sensors with the purpose of directing and positioning each image to the belonging set to form the mosaic. The heterogeneous computing platform used in this work is the NVIDIA JetsonTK1, this platform was chosen because it offers a GPU that supports the language of CUDA programming. If the images\' geometry errors weren\'t rectfyed, using this approach, an unexpected result happens, because the data provided by IMU, contrary to what is imagined, only serve to correct the position of the GPS coordinates recorded at the moment of capture of each image that composes the mosaic. The developing time in this application is satisfactory making the adoption of this approch favorable.

Medical imagery is increasingly evolving towards higher resolution and throughput. The increasing volume of data and the usage of multiple and often novel imaging modalities necessitates the use of mathematical and computational techniques for quicker, more accurate and more robust analysis of medical imagery. The fields of computer vision and machine learning provide a rich set of techniques that are useful in medical image analysis, in tasks ranging from segmentation to classification and population analysis, notably by integrating the qualitative knowledge of experts in anatomy and the pathologies of various disorders and making it applicable to the analysis of medical imagery going forward. The object of the proposed research is exactly to explore various computer vision and machine learning methods with a view to the improved analysis of multiple modalities of brain and cardiac imagery, towards enabling the clinical goals of studying schizophrenia, brain tumors (meningiomas and gliomas in particular) and cardiovascular disorders. In the first project, a framework is proposed for the segmentation of tubular, branched anatomical structures. The framework uses the tubular surface model which yields computational advantages and further incorporates a novel automatic branch detection algorithm. It is successfully applied to the segmentation of neural fiber bundles and blood vessels. In the second project, a novel population analysis framework is built using the shape model proposed as part of the first project. This framework is applied to the analysis of neural fiber bundles towards the detection and understanding of schizophrenia. In the third and final project, the use of mass spectrometry imaging for the analysis of brain tumors is motivated on two fronts, towards the offline classification analysis of the data, as well as the end application of intraoperative detection of tumor boundaries. SVMs are applied for the classification of gliomas into one of four subtypes towards application in building appropriate treatment plans, and multiple statistical measures are studied with a view to feature extraction (or biomarker detection). The problem of intraoperative tumor boundary detection is formulated as a detection of local minima of the spatial map of tumor cell concentration which in turn is modeled as a function of the mass spectra, via regression techniques.

The vector bundles with the basic structure space with affine connection. It is shown that in the present bundles the linear inducts the affine connection, and the curvature of the objects of the present connection is traced. Having defined the concept of the first differential extension of the vector bundles, an indication is made that the linear connection of vector bundles inducts the elongated linear connection of space and linear co-connection, expression form of the linear co-connection components and their interrelation. There are derived commutative formulas of the inducted connection and forms of its components of curvature objects.

In an attempt to prove Amitsur's Conjecture for cyclic subgroups of the Brauer group, we look at rational embeddings of the Severi Brauer variety of an algebra into its norm hypersurface. We enlarge the collection of such embeddings, and generalize them to embeddings of generalized Severi Brauer varieties into determinantal varieties. / text

Vienas svarbiausių šiuolaikinės diferencialinės geometrijos skyrių yra glodžių G- struktūrų teorija, kuriai pradžią davė klasikinės Rymano erdvės struktūros nagrinėjimas. G- struktūra glodžioje daugdaroje yra gaunama paėmus jos reperių sluoksniuotės redukciją , atitinkantį neišsigimusių matricų grupės pogrupį G. G-struktūros egzistuoja ne bet kurioje daugdaroje. Šiame darbe yra nagrinėjama tik baigtinio tipo G- struktūrų vidinės sietys. Yra įrodoma, kad kiekvieną baigtinio tipo G- struktūrą atitinka baigtinio tipo diferencialinė lygtis ant daugdaros . G- struktūrų geometrija nagrinėjama netradiciniu būdu nagrinėjant jų infinitezimalių simetrijų diferencialines lygtis. Šiuo metodu yra išnagrinėtos G- struktūrų afininės sietys, taip pat ir normalinės sietys. Paskutiniosios G- struktūrų geometrijoje nebuvo iki šiol tyrinėtos. / The most important part of differential geometry in our days is the theory of smooth G- structures, which started with the analyses of clasical construction of Riemannian space. G-structure in smooth manifold is acquired, when we take reduction of its frame bundle corresponding to subgroup G of non-degeneracy matrix group . It‘s important to note, that G- structures do not exist in every manifold. In this paper are considering intrisic connections only of finite type of G- structures. It is proved, that every finite type of G- structure corresponds to finite type of differential equation on the manifold . The Geometry of G- structures is investigated not traditionally while analyzing differential equations of infetisimal simmetrics of G- structures. There are analysed affine connections of G- structures, also and normal connections. The former haven‘t been investigated in geometry of G- structures.

Bundle Adjustment is a common fine-tuning step used in photogrammetry. It uses different types of parameters, some of which can be considered to be almost linear while others can be considered to be highly nonlinear, e.g. the rotational parameters. However, in the Bundle Adjustment process all parameters are treated equal. In concert with a poor initial estimate, this might cause Bundle Adjustment to diverge. In this report, two novel methods based on the damped Gauss-Newton with Armijo linesearch, modified by giving rotational parameters a special treatment, are tested. These methods, Clamped Alpha and Linear Exponential Search, are compared to Gauss-Newton with Armijo linesearch, as well as to the undamped Gauss-Newton method, also known as the Gauss-Markov method. Parameter sweeps over different perturbation levels for the angular parameters show that each of the three damped methods outperform the Gauss-Newton method. Notably, the Clamped Alpha method also outperforms the other two damped methods, with as much as 16 times as many convergent cases for a given perturbation level. Meanwhile, the average number of iterations is increased by only 1.8 times that of the Gauss-Newton with Armijo linesearch. The results add to existing research arguing for the use of damped methods in Bundle Adjustment. In particular, the simple and cheap Clamped Alpha method is potentially attractive for problems where the uncertainty of the camera angles is significant. While the Clamped Alpha method show promising results, it should be noted that the experiments in this study are on synthetic data. In order to solidify these results, further investigations into the performance of Clamped Alpha using real-world data should be conducted.

Les variétés possédant une orbite dense sous l'opération d'un groupe sont dites presque homogènes. Il s'agit d'objets ayant une géométrie très riche, qui ont été abondamment étudiés ces 50 dernières années ; cela inclut notamment les variétés toriques. L'objectif de cette thèse est d'obtenir une classification des couples (X,G) où X est une courbe ou une surface algébrique, définie sur un corps quelconque, et G est un groupe algébrique lisse connexe opérant fidèlement dans X et possédant une orbite dense. Cette classification passe par l'étude des complétions régulières équivariantes de X.Un premier chapitre regroupe des rappels sur les opérations de groupes algébriques ainsi que plusieurs résultats préliminaires utiles par la suite.L'étude des courbes presque homogènes fait ressortir une classe particulière, celle des courbes seminormales. Nous obtenons une classification complète des couples (X,G) quand X est une courbe seminormale. Nous décrivons aussi les courbes quelconques presque homogènes (sur un corps quelconque), généralisant ainsi un résultat de Vladimir Popov. Enfin, nous déterminons les fibrés en droites linéarisés sur les courbes seminormales presque homogènes.Le dernier chapitre traite le cas des surfaces. À nouveau, nous obtenons une classification des couples (X,G) quand X est une surface et G n'est pas affine. Quand G est affine, la surface est rationnelle. Nous décrivons alors, sur un corps algébriquement clos, les surfaces homogènes et leurs complétions régulières équivariantes relativement minimales. En caractéristique nulle, nous déterminons aussi les groupes qui opèrent. Beaucoup de phénomènes nouveaux se produisent en caractéristique positive, et certains de nos résultats sont incomplets dans ce cadre. / The varieties having a dense orbit under the action of a group are said to be almost homogeneous. Those are objects with a very rich geometry and have been extensively studied for the last 50 years ; this includes toric varieties. The purpose of this thesis is to classify the pairs (X,G) where X is an algebraic curve or surface, defined over an arbitrary field, and G is a smooth connected algebraic group, acting faithfully on X with a dense orbit. The classification relies on the study of the equivariant regular completions of X.The study of almost homogeneous curves highlights the class of seminormal curves. We get a full classification of the pairs (X,G) when X is a seminormal curve. We also describe all almost homogeneous curves (over an arbitrary field), thus generalizing a result of Vladimir Popov. Finally, we determine the linearized line bundles over seminormal almost homogeneous curves.The last chapter deals with the case of surfaces. Again, we get a classification of the pairs (X,G) when X is a surface and G is not affine. When G is affine, the surface is rational. We then describe, over an algebraically closed field, the homogeneous surfaces and their relatively minimal equivariant regular completions. In characteristic zero, we also determine the acting groups. Many new phenomena occur in positive characteristic, and some of our results are incomplete in this setting.

Les phénomènes d’interaction fluide-structure jouent un rôle important dans le calcul de tenue au séisme des assemblages combustibles. Afin de quantifier les marges de dimensionnement, le modèle de forces fluides utilisé doit être validé et affiné. Pour cela, des campagnes d’essais à l’échelle industrielle ont été réalisées en amont de la thèse. L’objectif ici est de contribuer à l’interprétation des essais industriels pour le cas stationnaire, et de valider les méthodes numériques permettant de simuler ce type d’écoulement. La problématique industrielle s'inscrit dans la tradition de l'étude des structures élancées sous écoulement axial. Le modèle de force fluide locale généralement utilisé, que nous appelons modèle de Taylor-Lighthill-Païdoussis (TLP), consiste en stationnaire à combiner un terme de force fluide potentielle, proportionnel à la courbure, et un terme de force fluide visqueuse, proportionnel à la pente. Des versions dynamiques de ce modèle ont été employées avec succès pour prédire le comportement vibratoire de cylindres flexibles en écoulement axial. Néanmoins, la littérature propose très peu de données de validation directe de cette représentation des forces fluides. Afin d’acquérir de telles données, pour le cas particulier d’un cylindre confiné dans un réseau de cylindres, un nouveau banc d’essai a été conçu et mis en place au laboratoire. Il s’agit d’un faisceau de 3x3 cylindres disposé dans une veine de soufflerie. Le cylindre central possède trois degrés de liberté : rotation, translation, flexion. Les efforts fluides résultants sont mesurés à l’aide d’une balance. Un modèle numérique similaire à la maquette est aussi réalisé et donne accès aux forces fluides locales. Les forces globales obtenues numériquement et expérimentalement sont comparables. Les forces locales obtenues dans les simulations numériques s’expliquent bien à l’aide du modèle TLP, en ignorant les effets de bord à l’entrée et à la sortie du faisceau. La transposition au cas industriel, de géométrie plus complexe, est réalisable par recalage des coefficients du modèle. / Fluid-structure interaction phenomena play a major role in the seismic design of fuel assemblies. In order to evaluate the design margins, the implemented model of fluid forces needs to be carefully assessed. Industrial-scale tests have been carried out with that purpose. Our goal is to contribute to their interpretation in the steady case, and to validate CFD methods usually applied to the type of flow at stake here. This fits in the tradition of the study of slender structures in axial flow. The local steady fluid forces decompose in a potential term, which is proportional to the curvature of the structure, and a viscous term, proportional to the angle of incidence. Adapted versions of this representation, which we call Taylor-Lighthill-Païdoussis (TLP) model, have proved successful in predicting the dynamic behaviour of flexible cylinders in axial flow. However, there is a lack in the literature of sound validation data for the fluid forces themselves. In order to gather such data, a new test rig has been designed and built. It consists in a 3x3 cylinder bundle confined in a wind tunnel. The central cylinder can be rotated, translated or bent. Resultant fluid forces are measured using a load cell. CFD calculations give access to the local fluid forces. CFD and experiments give similar results on the global fluid forces. The TLP model performs well at predicting the local fluid forces, except in the inlet and outlet regions. It can be fitted to the industrial case by adapting its coefficients.