Abstract Not Provided. / Thesis / Master of Science (MSc)

In the first part of the dissertation, we construct two-dimensional TQFTs which categorify the evaluations of circles in Kuperberg’s 𝐵₂ spider. We give a purely combinatorial evaluation formula for these TQFTs and show that it is compatible with the trace map on the corresponding commutative Frobenius algebras. Furthermore, we develop a theory of Θ-foams and their combinatorial evaluations to lift the ungraded evaluation of the Θ-web, thus paving a way for categorifying 𝐵₂ webs to 𝐵₂ foams. In the second part of the dissertation, we study the calculus of unoriented 𝔰𝔩₃ webs and foams. We focus on webs with a small number of boundary points. We obtain reducible collections and consider bilinear forms on these collections given by pairings of webs. We give web categories stable under the action of certain endofunctors and derive relations between compositions of these endofunctors.

RNA-cleaving DNAzymes (RCDs) are a class of functional nucleic acids that can bind various targets ranging in size from small molecules to large proteins, which results in activation of cleavage activity. The activation of RCDs results in the cleavage of a ribonucleotide site in an otherwise all-DNA substrate, leading to two cleavage fragments. In this work, a previously identified DNAzyme that binds to a protein biomarker endogenous to Helicobacter pylori (J99) crude extracellular matrix was evaluated for coupling to an isothermal amplification method termed rolling circle amplification (RCA) as a way to improve the originally reported detection limit. Three RCD constructs were designed with the goal of generating a cleavage fragment that could act as a primer to initiate RCA. The first method used the original HP DNAzyme, which liberated a short cleavage fragment that could be used as a primer. However, the primer fragment was rapidly digested by the bacterial matrix, preventing RCA. A second method evaluated use of a circularized substrate and separate RCD to generate a primer, however this system was not capable of generating a cleavage fragment. A final method redesigned the original RCD to move the substrate region from the 3’ to the 5’ end of the RCD, causing the longer RCD-containing fragment to be the primer for RCA. In this case, target-triggered cleavage was observed and the resulting primer was sufficiently resistant to digestion to allow its use as a primer for RCA. Preliminary characterization of the rearranged RCD showed that it retained selectivity similar to the original RCD, but that the cleavage rate was slower. In addition, the RCA based reaction, while successful, did not produce improved detection sensitivity relative to unamplified assays. Methods to further improve RCA performance are discussed for future work. / Thesis / Master of Science (MSc)

No description available.

No description available.

Renormalization is a powerful tool showing up in different contexts of mathematics and physics. In the context of circle diffeomorphisms, the renormalization operator acts like a microscope and allows to study the dynamics of a circle diffeomorphism on a small scale. The convergence of renormalization leads to a proof of the so-called rigidity theorem, which classifies the dynamics of circle diffeomorphisms geometrically: the conjugacy between $C^3$ circle diffeomorphism with Diophantine rotation number and the corresponding rotation is $C^1$. In this thesis, we define the renormalization of circle diffeomorphisms and study its dynamics. In particular, we prove that the renormalization of orientation preserving $C^3$ circle diffeomorphisms with irrational rotation number of bounded type converges to rotations at exponential speed. We also introduce the necessary relevant concepts such as rotation number, distortion and non-linearity and discuss some of their properties. This thesis is a summary and supplement to the book One-Dimensional Dynamics: from Poincaré to Renormalization. / Omnormalisering är en kraftfull teknik som dyker upp i olika sammanhang inom matematik och fysik. I samband med cirkeldiffeomorfier är omnormaliseringsoperatorn ett dynamiskt system, som fungerar som ett mikroskop och gör att vi kan studera dynamiken hos en cirkeldiffeomorfi på en liten skala. Omnormaliseringens konvergens leder till ett bevis för det så kallade rigiditetssatsen, som klassificerar dynamiken hos cirkeldiffeomorfier geometriskt: konjugatet mellan $C^3$ cirkeldiffeomorfi med diofantiska rotationstal och den motsvarande rotationen är $C^1$. I denna avhandling definierar vi omnormaliseringen av cirkeldiffeomorfier och studerar dess dynamik. I synnerhet bevisar vi att omnormaliseringen av orienteringsbevarande $C^3$ cirkeldiffeomorfier med irrationellt rotationstal av begränsad typ konvergerar till rotationer med exponentiell hastighet. Vi introducerar också nödvändiga och relevanta begrepp så som rotationstal, distorsion och icke-linjäritet och diskuterar några av deras egenskaper. Denna avhandling är en sammanfattning och ett komplement till boken One- Dimensional Dynamics: from Poincaré to Renormalization.

the work that follows is a study in material and the nature of its construction. i chose a site that was rich in tradition of building, but chose to not mimic tradition. the arctic circle of norway has a tradition of stone and wood construction. the remote qualities of the site lead me to choose a house, of local stone and wood. the extreme conditions of the environment posed the challenges in design and construction. i did not test the limits of the stone, but let the stone do what is natural to it. i chose not to force the stone to be anything other than itself, and working with these natural tendencies to make the decisions of construction. / Master of Architecture

No, she is not my mom, not my aunt, we are not family. Yes, we do look alike, we do live in the same neighborhood, we smell the same coffee beans each morning, and we share the same zip code. The only difference between us is I do have an actual address here, she does not. Yes, she must have lived here much longer than me, she has a history in this town, a lot of the people would recognize her smiling spirit right away, yet she only occupies a corner in a street near a coffee shop most of the year. Everyone knows that space is hers, except the legal papers. Where are you from? The question may seem so simple, but regardless of how many times I am asked the answer has never been so easy for me each time I am asked, and I am asked very often. Belonging, identity, countries, tribes, bloodlines and borders are things that confuse me a lot, and for that I decided to do my thesis about them, trying to find an answer to a simple question, in a very complicated universe. I chose to study these matters through a transitional program, in a transforming neighborhood and for users who are in their most confused age; an international 6 boarding school in Dupont circle. / Master of Architecture

Submitted by Renata Lopes (renatasil82@gmail.com) on 2015-12-11T11:16:50Z No. of bitstreams: 1 giselecardosodelemos.pdf: 1950421 bytes, checksum: 5d956c19538a640bfa5a8e77dcd04747 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2015-12-11T15:02:15Z (GMT) No. of bitstreams: 1 giselecardosodelemos.pdf: 1950421 bytes, checksum: 5d956c19538a640bfa5a8e77dcd04747 (MD5) / Made available in DSpace on 2015-12-11T15:02:15Z (GMT). No. of bitstreams: 1 giselecardosodelemos.pdf: 1950421 bytes, checksum: 5d956c19538a640bfa5a8e77dcd04747 (MD5) Previous issue date: 2015-08-31 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho busca analisar as apropriações que o escritor indiano em língua inglesa Amitav Ghosh faz das noções ocidentais de ciência e religião em suas respectivas obras The Calcutta Chromosome e The Circle of Reason, por meio de diálogos, tensões e negociações destas noções com paradigmas filosófico-religiosos de caráter inclusivista e dialógico da civilização indiana, que são matrizes existenciais que perpassam gerações e influenciam inclusive a contemporaneidade da Índia. Para esse fim, esse trabalho privilegia a literatura ficcional como ferramenta crítica para as discussões sobre ciência e religião, uma vez que a ficção propicia a contextualização das coisas/seres, ou seja, a apreensão destes em sua totalidade. Com isso, também buscamos apresentar uma contextualização histórica, linguística, literária, científica e filosófico-religiosa para que sejam mais bem compreendidas algumas escolhas de Amitav Ghosh, a saber: a língua inglesa, o gênero literário romance, as temáticas da medicina tropical e da frenologia e a apropriação da doutrina da transmigração da alma (ātma), a lei do karma e a teoria dos guṇas, discutidas em fontes como os Upaniṣads e o Bhagavad-gītā. Como ferramentas de análise utilizamos, sobretudo, teorias pós-coloniais de subalternidade, tradições unitaristas da filosofia hindu, as obras não-ficcionais do próprio autor e as obras dos mais importantes críticos literários de Ghosh. Com as análises literárias mostramos que Ghosh, além de por em prática a tradição inclusivista indiana, ele demonstra a superioridade do ―domínio espiritual‖ sobre o ―domínio material‖, (conceitos cunhados por Partha Chatterjee) e reabilita a noção de uma racionalidade ocidental excludente tornando-a uma razão iluminadora e libertadora. / This study analyzes the appropriations of Western notions of science and religion by the Indian writer in English Amitav Ghosh, in his respective works The Calcutta Chromosome and The Circle of Reason, through dialogues, tensions, and negotiations between these notions and religious and philosophical paradigms of the Indian civilization, characterized by its inclusive and dialogical characteristics. These paradigms form an existential matrix that crosses generations and even influences contemporary India. To this end, this work focuses on fictional literature as a critical tool for the discussion on science and religion, since fiction provides contextualization for things/beings, that is, the comprehention of these in their entirety. With this, we also seek to provide a historical, linguistic, literary, scientific, philosophical and religious context in order to better understand some of Amitav Ghosh‘s choices, namely the English language, the novel as literary genre, the themes of tropical medicine and phrenology and the appropriation of the doctrine of transmigration of the soul (saṃsāra), the law of karma and the theory of guṇas discussed in sources such as the Upaniṣads and the Bhagavad-gītā. As tools of analysis, we use especially postcolonial theories of subalternity, unitarian traditions of Hindu philosophy, nonfictional works of the author himself and the works of the most important literary critics of Ghosh‘s work. With literary analysis we show that Ghosh, besides using the inclusivist Indian tradition, demonstrates the superiority of ―spiritual domain‖ over the ―material domain‖ (concepts coined by Partha Chatterjee) and also rehabilitates the notion of an exclusionary Western rationality transforming it into an enlightening and liberating reason.

TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra