Made available in DSpace on 2016-04-27T16:58:52Z (GMT). No. of bitstreams: 1 Aloisio Daniel Vendeniatti.pdf: 1272014 bytes, checksum: 1262d89ac2880970c73eca396d22ca43 (MD5) Previous issue date: 2009-04-24 / Secretaria da Educação do Estado de São Paulo / The goal of this essay is to show aspects of genesis of number π, inherent to the question of squaring the circle, which consists in constructing a square which has the same area as a given circle. This problem does not refer to a practical application of mathematics, but to the theoretic question that involves the distinction between a valid approach and thinking accuracy. The first attempt to squaring the circle dates back in the fifth century before Christ. After that, it was established that this construction should be carried through using a finite number of times, also the non-graduated ruler and the drawing compass itself. In the constructions with ruler and drawing compass we are referring to the first three postulates of Euclides Elements: 1) It´s possible to join two points by a straight line, 2) to expand a straight line until the necessary point, and 3) to draw a circumference around any point and with any radius. These postulates are the base of these constructions, sometimes called euclidean´s constructions. A real number α is constructible, if feasible building a segment of legth α with ruler and drawing compass, since a segment is taken as a unity. We show the idea of translating the geometrical problem of constructions made with ruler and drawing compass to the algebraic language and this allowed us to solve the problem of squaring the circle. We exposed that all constructible numbers are algebraic, over the rational numbers, establishing the impossibility of squaring the circle, with Lindemann´s demonstration, in 1882, of the number π transcendence. This problem has been fascinating people for more than twenty centuries. We tried to supply all mathematical tools needed for this demonstration. Demonstrations play a fundamental role in the development of this essay, which purpose is not only to contribute to the math teacher formation, but also to detail the resolution of the problem of squaring the circle / O objetivo deste trabalho é apresentar aspectos da gênese do número π, inerentes à questão da quadratura do círculo, a qual consiste em construir um quadrado de área igual à área de um círculo de raio r dado. Esse problema não diz respeito a uma aplicação prática da matemática, mas sim a uma questão teórica que envolve uma distinção entre uma boa aproximação e a exatidão do pensamento. O registro da primeira tentativa de se quadrar o círculo remonta a Anaxágoras, no século V a.C. Posteriormente, ficou estabelecido que essa construção deveria ser realizada utilizando-se, um número finito de vezes, a régua não graduada e o compasso. Nas construções com régua e compasso, estamos nos referindo aos três primeiros postulados dos Elementos de Euclides: 1) é possível unir dois pontos por uma reta, 2) prolongar uma linha reta até onde seja necessário e 3) traçar uma circunferência em torno de qualquer ponto e com qualquer raio. Esses postulados são a base dessas construções, muitas vezes chamadas de construções euclidianas. Um número real α é construtível, se for possível "construir com régua e compasso um segmento de comprimento igual a α, a partir de um segmento tomado como unidade". Apresentamos a idéia de traduzir o problema geométrico das construções com régua e compasso para a linguagem algébrica, e isso permitiu solucionar o problema da quadratura do círculo. Expomos que todo número construtível é algébrico sobre os racionais, estabelecendo a impossibilidade de quadrar o círculo com a demonstração de Lindemann, em 1882, da transcendência do número π. Vemos que esse problema fascinou estudiosos por mais de 20 séculos. Procuramos fornecer todas as ferramentas matemáticas necessárias para essa demonstração. As demonstrações desempenham um papel fundamental no desenvolvimento deste trabalho, que tem por finalidade não só contribuir para a formação do professor de matemática, mas também detalhar a resolução do problema da quadratura do círculo

Made available in DSpace on 2016-04-27T16:58:55Z (GMT). No. of bitstreams: 1 Carlos Francisco Borges.pdf: 2604675 bytes, checksum: 815cc9155f159a14b24957f9b7ed0342 (MD5) Previous issue date: 2009-10-23 / Secretaria da Educação do Estado de São Paulo / The purpose of this essay was to contribute to Trigonometry teaching, specially, to the transition of the trigonometric reasons in the rectangle triangle for the trigonometric circle. A sequence was elaborated with 12 activities, from which ten were created worrying about guiding the student to understand the trigonometric reasons of the rectangle triangle to the trigonometric circle using the dynamic geometry software Geogebra. An activity was made with the objective of working with the radian definition and the conversion of the unit circle (radians) to the angle unit (degrees) and, at last, an activity which had as purpose to create a tool to be used in the classroom when it was not possible to use the calculator, or the computer. The activities were applied to 12th graders in a school from the city of Francisco Morato, Great São Paulo. For such, 4 meetings were used to do the application; the students did the activities in pairs and were not done during the lessons. The Theory of the Didactic Situations and other basis of the Didactic Engineering were used in the elaboration, analysis, application and data survey of the teaching sequence. The experimentation pointed that the students did not make use of some necessary previous knowledge and presented some difficulties to expose their written observations. However, it also showed that there was improvement in the students learning, because while doing the activities using the dynamic geometry, they showed interest and focus / Esse trabalho teve por objetivo contribuir com o ensino de trigonometria, em especial, na transição das razões trigonométricas no triângulo retângulo para o círculo trigonométrico. Foi elaborada uma sequência com 12 atividades, das quais dez foram criadas com a preocupação de conduzir o aluno a compreender as razões trigonométricas do triângulo retângulo para o círculo trigonométrico utilizando, o software de geometria dinâmica Geogebra. Uma atividade foi criada com o intuito de trabalhar com a definição de radianos e a conversão da unidade de arcos (radianos) para unidade de ângulos (graus) e, por fim, uma atividade que tinha por objetivo construir um dispositivo para ser utilizado em sala de aula quando não fosse possível utilizar a calculadora, ou o computador. As atividades foram aplicadas para oito alunos do 2º ano do Ensino Médio de uma escola da cidade de Francisco Morato, Grande São Paulo. Para tal foram usados quatro encontros para realizar a aplicação; os alunos fizeram as atividades em duplas e fora do horário de aula. A Teoria das Situações Didáticas e alguns pressupostos da Engenharia Didática foram usados na elaboração, análise, aplicação e coleta de dados da sequência de ensino. A experimentação aponta que os alunos não mobilizaram alguns conhecimentos prévios necessários e apresentam algumas dificuldades para exporem suas observações por escrito. Mas também mostrou que houve avanços na aprendizagem dos alunos, pois ao executarem as atividades utilizando a geometria dinâmica, mostraram interesse e concentração

Made available in DSpace on 2016-04-27T16:59:03Z (GMT). No. of bitstreams: 1 Ricardo Uchoa Fernandes.pdf: 2015098 bytes, checksum: 6b4dff7832d9c478d3fbc8376b57a470 (MD5) Previous issue date: 2010-05-19 / Secretaria da Educação do Estado de São Paulo / The effective learning of the student is the main goal of a reflective teacher, so it is not enough simply to have all the technical knowledge, you need something more, namely mediation, have a clear and objective, to mobilize material resources for the success of this process . Just thought, this work was to build a meaningful learning the basics of trigonometry in circumference. use this research to teaching engineering, a research methodology that is considered as an experimental scheme based on achievements in teaching classroom. The research has two analytical tools, giving great importance to the training analysis of the error. The first instrument directs for construction of the trigonometric circle, using ruler, protractor and pencil, the second instrument construction is done in dynamic geometry software GeoGebra. The activities of this research tool, as applied to twelve students in the 2nd grade of high school to a state school in Guaratinguetá, interior of Sao Paulo, in the Paraiba Valley. Were two meetings for the application, the students worked individually in the first assessment tool and trio in the second evaluation instrument. The trial shows that prior knowledge have been mobilized to carry out these activities, and information technology as a pedagogical resource, ie, activity with GeoGebra aroused the interest of students because they were more focused and performance was better / O aprendizado efetivo do educando é o principal objetivo de um professor reflexivo, para isso, não basta simplesmente ter todo o conhecimento técnico, é necessário algo a mais, saber mediar, ter uma linguagem clara e objetiva, mobilizar recursos materiais para o sucesso desse processo. Assim pensado, este trabalho teve por objetivo construir uma aprendizagem significativa dos conceitos básicos da trigonometria na circunferência. Esta pesquisa utiliza a engenharia didática, uma metodologia de pesquisa que é considera como um esquema experimental com base em realizações didáticas em sala de aula. A pesquisa possui dois instrumentos de análise, dando grande importância para a análise didática do erro. O primeiro instrumento direciona para a construção da circunferência trigonométrica, utilizando régua, transferidor e lápis; no segundo instrumento, a construção é feita no software de geometria dinâmica Geogebra. As atividades desse instrumento de pesquisa, forma aplicadas para doze alunos da 2ª série do Ensino Médio de uma escola estadual de Guaratinguetá, interior de São Paulo, no vale do Paraíba. Foram dois encontros para a aplicação, sendo que os alunos trabalharam individualmente no primeiro instrumento de avaliação e em trio no segundo instrumento avaliativo. A experimentação evidencia que conhecimentos prévios foram mobilizados para a realização dessas atividades e a informática como recurso pedagógico, isto é, atividade com o Geogebra despertou o interesse dos alunos, pois ficaram mais concentrados e o desempenho foi melhor. Além disso, pode-se entender que tanto a mobilização dos conhecimentos prévios quanto a aquisição de novos pode ser incrementada a partir da adoção de uma estratégia pedagógica com uso de tecnologias e de uma abordagem que considera que a construção dos conhecimentos de forma significativa não prescinde do uso reconstrutivo do erro como ferramenta didática

We study the relationship between subdivision rules, 3-dimensional manifolds, and circle packings. We find explicit subdivision rules for closed right-angled hyperbolic manifolds, a large family of hyperbolic manifolds with boundary, and all 3-manifolds of the E^3,H^2 x R, S^2 x R, SL_2(R), and S^3 geometries (up to finite covers). We define subdivision rules in all dimensions and find explicit subdivision rules for the n-dimensional torus as an example in each dimension. We define a graph and space at infinity for all subdivision rules, and use that to show that all subdivision rules for non-hyperbolic manifolds have mesh not going to 0. We provide an alternate proof of the Combinatorial Riemann Mapping Theorem using circle packings (although this has been done before). We provide a new definition of conformal for subdivision rules of unbounded valence, show that the subdivision rules for the Borromean rings complement are conformal and show that barycentric subdivision is almost conformal. Finally, we show that subdivision rules can be degenerate on a dense set, while still having convergent circle packings.

<p>Among the great challenges in biology are the precise quantification of specific sets of proteins and analyses of their patterns of interaction on a much larger scale than is possible today. </p><p>This thesis presents a novel protein detection technique - proximity ligation - and reports the development and application of a nucleic acid amplification technique, RCA. Proximity ligation converts information about the presence or co-localization of specific proteins to unique sets of nucleic acid sequences. For detection of target proteins or protein complexes the coincident binding by pairs or triplets of specific protein-binding reagents are required. Oligonucleotide-extensions attached to those binding reagents are joined by a DNA ligase and subsequently analyzed by standard molecular genetic techniques. The technique is shown to sensitively detect an assortment of proteins using different types of binders converted to proximity probes, including SELEX aptamers and mono- and polyclonal antibodies. I discuss factors important for using the technique to analyze many proteins simultaneously.</p><p>Quantification of target molecules requires precise amplification and detection. I show how rolling circle amplification, RCA, can be used for precise quantification of circular templates using modified molecular beacons with real-time detection. The combination of proximity-probe templated circularization and RCA results in a sensitive method with high selectivity, capable of visualizing individual immobilized proteins. This technique is used for localized detection of a set of individual proteins and protein complexes at sub-cellular resolution.</p>

<p>Padlock probes are useful in a variety of genetic applications, some of which require that the probes are amplified in order to generate detectable signals. Two general padlock amplification methods, RCA and PCR, are discussed in this thesis.</p><p>The isothermal rolling circle amplification (RCA) mechanism is described in detail as well as how a target strand affects primer extension. A mechanism to resolve the topological constraint imposed by the target strand, to which a padlock probe has been linked, is also discussed. We also present a more powerful amplification technique, termed serial circle amplification, which provides a highly precise tool for nucleic acid studies. Rolling circle products are digested to unit lengths, and each monomer converted to new circular oligonucleotides that can serve as templates in consecutive rounds of RCA. The final products are single-stranded DNA molecules, readily available for hybridization-based detection, for instance using molecular beacons or array hybridization.</p><p>Padlock probes have the potential to be combined in large numbers for parallel gene analysis. A significant improvement of the level of multiplexed genotyping is presented using padlock probes and a molecular inversion strategy. Padlock probes containing common primer sequences along with locus-specific tag sequences were combined in multiplexed ligation reactions. After exonucleolytic selection for circular molecules, the probes were cleaved at uracil residues situated between the primer sequences, which facilitated release from the genomic DNA. A single PCR primer pair amplified all molecularly inverted probes, and the products were finally sorted on microarrays for simultaneous readout. Up to 1,500 genotypes could be detected in parallel, with sufficient signal strength for further scale-up. Finally, an application of the same parallel genotyping strategy is described where a set of padlock probes was used to study tumor induced immune responses. The distribution of TCR Vβ transcripts in tumor infiltrating T-cells and in normal control tissues were investigated in a microarray format.</p>

Padlock probes are useful in a variety of genetic applications, some of which require that the probes are amplified in order to generate detectable signals. Two general padlock amplification methods, RCA and PCR, are discussed in this thesis. The isothermal rolling circle amplification (RCA) mechanism is described in detail as well as how a target strand affects primer extension. A mechanism to resolve the topological constraint imposed by the target strand, to which a padlock probe has been linked, is also discussed. We also present a more powerful amplification technique, termed serial circle amplification, which provides a highly precise tool for nucleic acid studies. Rolling circle products are digested to unit lengths, and each monomer converted to new circular oligonucleotides that can serve as templates in consecutive rounds of RCA. The final products are single-stranded DNA molecules, readily available for hybridization-based detection, for instance using molecular beacons or array hybridization. Padlock probes have the potential to be combined in large numbers for parallel gene analysis. A significant improvement of the level of multiplexed genotyping is presented using padlock probes and a molecular inversion strategy. Padlock probes containing common primer sequences along with locus-specific tag sequences were combined in multiplexed ligation reactions. After exonucleolytic selection for circular molecules, the probes were cleaved at uracil residues situated between the primer sequences, which facilitated release from the genomic DNA. A single PCR primer pair amplified all molecularly inverted probes, and the products were finally sorted on microarrays for simultaneous readout. Up to 1,500 genotypes could be detected in parallel, with sufficient signal strength for further scale-up. Finally, an application of the same parallel genotyping strategy is described where a set of padlock probes was used to study tumor induced immune responses. The distribution of TCR Vβ transcripts in tumor infiltrating T-cells and in normal control tissues were investigated in a microarray format.

Micro- or nanometer sized magnetic particles (beads) currently have a vast range of life science applications in, for example, bioseparation techniques, cancer therapy, development of contrast agents and biosensing techniques. In the latter field, magnetic beads offer several unique advantages, including minimal background signals, physical and chemical stability and low manufacturing costs. Because of these properties, magnetic biosensing techniques are potential candidates for low-cost, easy-to-use molecular diagnostic devices. This doctoral thesis focuses mainly on the proof of principle and further development of a new magnetic biosensor platform for detection of DNA targets, a potential candidate for a new generation of low-cost, easy-to-use diagnostic devices: the Volume-Amplified Magnetic Nanobead Detection Assay (VAM-NDA). The VAM-NDA principle combines target recognition by padlock probe ligation followed by rolling circle amplification (RCA) of the reacted probes with changes in Brownian relaxation behaviour of magnetic nanobeads (typically ~100 nm in diameter) induced by a change in hydrodynamic bead volume. More specifically, the RCA products (coils, typically ~1 μm in diameter) are detected magnetically by adding magnetic beads tagged with detection probes complementary to part of the repeating RCA-coil sequence. Thus, depending on the target concentration, a certain quantity of beads binds to the coils by base-pair hybridisation (bead immobilisation), resulting in a dramatic bead volume increase, which is then detected by measuring the complex magnetisation spectrum. Use of a commercial SQUID magnetometer for measuring complex magnetisation resulted in a detection limit in the low pM range for DNA targets with excellent quantification accuracy. Simultaneous multiplexing was also evaluated. The stability and aging of typical commercial ferrofluids (suspensions of magnetic beads) were investigated by measuring the complex magnetisation of and interbead interactions in oligonucleotide-functionalised ferrofluids. In summary, the bead surface characteristics were found to have a strong impact on the measured dynamic magnetic properties.

This thesis describes three readout formats for molecular analyses. A common feature in all works is probing techniques that upon specific target recognition ideally results in equimolar amounts of DNA circles. These are then specifically amplified and detected using any of the techniques presented herein. The first paper presents a method that enables homogeneous digital detection and enumeration of biomolecules, represented as fluorescence-labelled DNA macromolecules. This method offers precise measurements to be performed with a wide linear dynamic range. As an application, two closely related bacterial species were selectively detected. The second paper further investigates and optimizes the properties of the technique presented in paper one. The third paper demonstrates a platform that enables simultaneous quantitative analysis of large numbers of biomolecules. The array format and decoding scheme together propose a digital strategy for decoding of biomolecules. The array and the decoding procedure were characterized and evaluated for gene copy-number measurements. The fourth paper examines a new strategy for non-optical measurements of biomolecules. Characteristics of this technique are investigated, and compared to its optical equivalent, fluorescence polarization.

Fundamental to all biological processes is the interplay between biomolecules such as proteins and nucleic acids. Studies of interactions should therefore be more informative than mere detection of expressed proteins. Preferably, such studies should be performed in material that is as biologically and clinically relevant as possible, i.e. in primary cells and tissues. In addition, to be able to take into account the heterogeneity of such samples, the analyses should be performed in situ to retain information on the sub-cellular localization where the interactions occur, enabling determination of the activity status of individual cells and allowing discrimination between e.g. tumor cells and surrounding stroma. This requires assays with an utmost level of sensitivity and selectivity. Taking these issues into consideration, the in situ proximity-ligation assay (in situ PLA) was developed, providing localized detection of proteins, protein-protein interactions and post-translational modifications in fixed cells and tissues. The high sensitivity and selectivity afforded by the assay's requirement for dual target recognition in combination with powerful signal amplification enables visualization of single protein molecules in intact single cells and tissue sections. To further increase the usefulness and application of in situ PLA, the assay was adapted to high content analysis techniques such as flow cytometry and high content screening. The use of in situ PLA in flow cytometry offers the possibility for high-throughput analysis of cells in solution with the unique characteristics offered by the assay. For high content screening, it was demonstrated that in situ PLA can enable cell-based drug screening of compounds affecting post-translational modifications and protein-protein interactions in primary cells, offering superior abilities over current assays. The methods presented in this thesis provide powerful new tools to study proteins in genetically unmodified cells and tissues, and should offer exciting new possibilities for molecular biology, diagnostics and drug discovery.