Challenges in the creation and development of a mathematics MOOC

The fast development of distance learning tools such as Open Educational Resources (OER) and Massive Open Online Courses (MOOC or MOOCs) are indicators of a shift in the way in which digital teaching and learning are understood. MOOC are a new style of online classes that allow any person with web access, anywhere, usually free of charge, to participate through video lectures, computer graded tests and discussion forums. They have been capturing the attention of many higher education institutions around the world. This paper will give us an overview of the “Introduction to Differential Calculus” a MOOC Project, created by an engaged volunteer team of Mathematics lecturers from four schools of the Polytechnic Institute of Oporto (IPP). The MOOC theories and their popularity are presented and complemented by a discussion of some MOOC definitions and their inherent advantages and disadvantages. It will also explore what MOOC mean for Mathematics education. The Project development is revealed by focusing on used MOOC structure, as well as the quite a lot of types of course materials produced. It ends with a presentation of a short discussion about problems and challenges met throughout the development of the project. It is also our goal to contribute for a change in the way teaching and learning Mathematics is seen and practiced nowadays, trying to make education more accessible to as many people as possible and increase our institution (IPP) recognition.

Visualizing control systems performance: A fractional perspective

This article presents a novel method for visualizing the control systems behavior. The proposed scheme uses the tools of fractional calculus and computes the signals propagating within the system structure as a time/frequency-space wave. Linear and nonlinear closed-loop control systems are analyzed, for both the time and frequency responses, under the action of a reference step input signal. Several nonlinearities, namely, Coulomb friction and backlash, are also tested. The numerical experiments demonstrate the feasibility of the proposed methodology as a visualization tool and motivate its extension for other systems and classes of nonlinearities.

Aplicação das FPAA na realização de sistemas de ordem fraccionária

Esta tese de dissertação tem como principal objetivo a implementação de controladores fracionários utilizando diapositivos analógicos FPAA (Field Programable Analog Array). Embora estes dispositivos já não sejam um tecnologia recente, não tiveram grande aceitação comercial, daí não ter sido grande a sua evolução nesta última década. Mas para a elaboração de alguns circuitos analógicos, nomeadamente filtros, amplificadores e mesmo controladores PID (Proporcional-Integrativo-Derivativo) analógicos torna-se numa ferramenta que pode facilitar o projeto e implementação. Para a realização deste estudo, utilizou-se a placa de desenvolvimento da Anadigm AN231K04-DVLP3 juntamente com o software disponibilizado pela mesma empresa, o AnadigmDesigner2. Para a simulação e observação dos resultados foi utilizada a DAQ (Data Acquisition) Hilink da Zelton juntamente com o software Matlab. De forma a testar a implementação dos controladores fracionários nas FPAA foram realizados alguns circuitos no software e enviados para a FPAA comparando os resultados obtidos na simulação com os visualizados no osciloscópio. Por último foi projetado um controlador PIlDm recorrendo aos métodos de aproximação inteira descritos neste documento implementados na FPAA recorrendo ao uso de filtros de primeira e segunda ordem.

Projeto de estabilidade de internato masculino

O presente documento corresponde à realização de um projeto de estruturas em betão armado e estrutura metálica. A escolha deste tema teve como propósito aplicar os conhecimentos adquiridos ao longo do percurso académico, sobretudo em disciplinas do ramo de estruturas. O trabalho desenvolvido é um Projeto de Estabilidade de Betão Armado e Estrutura Metálica de um Internato Masculino para Padres em Onameva, Cunene – Angola. A elaboração deste projeto decorre da realização de um estágio formal de 8 meses na empresa CALCULUS, Miguel Barros – Engenharia, LDA, com o objetivo principal de reunir os requisitos necessários à admissão na Ordem dos Engenheiros. No contexto laboral de um gabinete de projetos de engenharia civil, foi feita a integração de forma gradual e sustentada das competências adquiridas ao longo da formação académica e vivenciadas situações reais de trabalho profissional. De entre as atividades desenvolvidas no estágio, foi escolhido o projeto de estabilidade acima referido pela oportunidade de realizar todas as etapas do seu desenvolvimento, desde a análise da arquitetura até à elaboração das peças escritas e desenhadas, dando assim resposta às exigências necessárias para a conclusão do Mestrado em Engenharia Civil, no ramo de Estruturas, pelo Instituto Superior de Engenharia do Porto.

Heinrich e Cécile Daniker-Haller - A música doméstica na vida de um casal de negociantes entre Zurique e o Rio de Janeiro na primeira metade do século XIX

O casal de suíços, Heinrich (1795–1866) e Cécile Däniker-Haller (1816–1887), com seus filhos, viveu no Rio de Janeiro entre 1828 e 1852. Comerciantes prósperos, cosmopolitas e melômanos, deixaram grande quantidade de informações sobre suas atividades de música em ambiente doméstico daquele período, mas também depois de terem voltado a se estabelecer na Suíça. O Genealogisches Archiv der Helene und Cécile Rübel Familienstiftung (FA HCR), na cidade de Zurique, documenta a história desta família. As informações registradas pelo casal estudado, principalmente em forma de cartas e diários, permitem-nos conhecer e analisar a prática musical em ambiente doméstico das famílias estrangeiras no Rio de Janeiro, e demonstrar quais eram os repertórios por eles utilizados. Entre as conclusões tiradas, inclui-se o fato de que o romantismo alemão teria feito sua entrada no ambiente musical brasileiro através dos salões musicais das famílias estrangeiras, exatamente como foi o caso em outras cidades do mundo não germânico. Nos documentos deixados pela família Däniker-Haller encontram-se os mais antigos testemunhos até hoje encontrados da execução de Lieder de Schubert em ambiente doméstico no Rio de Janeiro. Por outro lado, a prática da Hausmusik na cidade de Zurique vem descrita e comparada àquela carioca. A análise destes relatos também nos permite descrever a diferença que havia entre os eventos musicais em ambiente doméstico íntimo e informal, e os "salões musicais", onde diletantes se produziam em esfera semi-pública previamente preparados e ensaiados, e a marcante diferença no repertório destes dois tipos de eventos sociais.

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Airway surface liquid volume regulation determines different airway phenotypes in liddle compared with betaENaC-overexpressing mice.

Studies in cystic fibrosis patients and mice overexpressing the epithelial Na(+) channel beta-subunit (betaENaC-Tg) suggest that raised airway Na(+) transport and airway surface liquid (ASL) depletion are central to the pathogenesis of cystic fibrosis lung disease. However, patients or mice with Liddle gain-of-function betaENaC mutations exhibit hypertension but no lung disease. To investigate this apparent paradox, we compared the airway phenotype (nasal versus tracheal) of Liddle with CFTR-null, betaENaC-Tg, and double mutant mice. In mouse nasal epithelium, the region that functionally mimics human airways, high levels of CFTR expression inhibited Liddle epithelial Nat channel (ENaC) hyperfunction. Conversely, in mouse trachea, low levels of CFTR failed to suppress Liddle ENaC hyperfunction. Indeed, Na(+) transport measured in Ussing chambers ("flooded" conditions) was raised in both Liddle and betaENaC-Tg mice. Because enhanced Na(+) transport did not correlate with lung disease in these mutant mice, measurements in tracheal cultures under physiologic "thin film" conditions and in vivo were performed. Regulation of ASL volume and ENaC-mediated Na(+) absorption were intact in Liddle but defective in betaENaC-Tg mice. We conclude that the capacity to regulate Na(+) transport and ASL volume, not absolute Na(+) transport rates in Ussing chambers, is the key physiologic function protecting airways from dehydration-induced lung disease.

A Playful Glance at Hierarchical Questions for Two-Way Alternating Automata

Two-way alternating automata were introduced by Vardi in order to study the satisfiability problem for the modal μ-calculus extended with backwards modalities. In this paper, we present a very simple proof by way of Wadge games of the strictness of the hierarchy of Motowski indices of two-way alternating automata over trees.

Evolutionary synthesis of stochastic gene network models using feature-based search spaces

A feature-based fitness function is applied in a genetic programming system to synthesize stochastic gene regulatory network models whose behaviour is defined by a time course of protein expression levels. Typically, when targeting time series data, the fitness function is based on a sum-of-errors involving the values of the fluctuating signal. While this approach is successful in many instances, its performance can deteriorate in the presence of noise. This thesis explores a fitness measure determined from a set of statistical features characterizing the time series' sequence of values, rather than the actual values themselves. Through a series of experiments involving symbolic regression with added noise and gene regulatory network models based on the stochastic 'if-calculus, it is shown to successfully target oscillating and non-oscillating signals. This practical and versatile fitness function offers an alternate approach, worthy of consideration for use in algorithms that evaluate noisy or stochastic behaviour.

Extending relAPS to first order logic

RelAPS is an interactive system assisting in proving relation-algebraic theorems. The aim of the system is to provide an environment where a user can perform a relation-algebraic proof similar to doing it using pencil and paper. The previous version of RelAPS accepts only Horn-formulas. To extend the system to first order logic, we have defined and implemented a new language based on theory of allegories as well as a new calculus. The language has two different kinds of terms; object terms and relational terms, where object terms are built from object constant symbols and object variables, and relational terms from typed relational constant symbols, typed relational variables, typed operation symbols and the regular operations available in any allegory. The calculus is a mixture of natural deduction and the sequent calculus. It is formulated in a sequent style but with exactly one formula on the right-hand side. We have shown soundness and completeness of this new logic which verifies that the underlying proof system of RelAPS is working correctly.

Generating Relation Algebras for Qualitative Spatial Reasoning

Basic relationships between certain regions of space are formulated in natural language in everyday situations. For example, a customer specifies the outline of his future home to the architect by indicating which rooms should be close to each other. Qualitative spatial reasoning as an area of artificial intelligence tries to develop a theory of space based on similar notions. In formal ontology and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts. We shall introduce abstract relation algebras and present their structural properties as well as their connection to algebras of binary relations. This will be followed by details of the expressiveness of algebras of relations for region based models. Mereotopology has been the main basis for most region based theories of space. Since its earliest inception many theories have been proposed for mereotopology in artificial intelligence among which Region Connection Calculus is most prominent. The expressiveness of the region connection calculus in relational logic is far greater than its original eight base relations might suggest. In the thesis we formulate ways to automatically generate representable relation algebras using spatial data based on region connection calculus. The generation of new algebras is a two pronged approach involving splitting of existing relations to form new algebras and refinement of such newly generated algebras. We present an implementation of a system for automating aforementioned steps and provide an effective and convenient interface to define new spatial relations and generate representable relational algebras.

Optimisation et approximation adiabatique

L'approximation adiabatique en mécanique quantique stipule que si un système quantique évolue assez lentement, alors il demeurera dans le même état propre. Récemment, une faille dans l'application de l'approximation adiabatique a été découverte. Les limites du théorème seront expliquées lors de sa dérivation. Ce mémoire à pour but d'optimiser la probabilité de se maintenir dans le même état propre connaissant le système initial, final et le temps d'évolution total. Cette contrainte sur le temps empêche le système d'être assez lent pour être adiabatique. Pour solutionner ce problème, une méthode variationnelle est utilisée. Cette méthode suppose connaître l'évolution optimale et y ajoute une petite variation. Par après, nous insérons cette variation dans l'équation de la probabilité d'être adiabatique et développons en série. Puisque la série est développée autour d'un optimum, le terme d'ordre un doit nécessairement être nul. Ceci devrait nous donner un critère sur l'évolution la plus adiabatique possible et permettre de la déterminer. Les systèmes quantiques dépendants du temps sont très complexes. Ainsi, nous commencerons par les systèmes ayant des énergies propres indépendantes du temps. Puis, les systèmes sans contrainte et avec des fonctions d'onde initiale et finale libres seront étudiés.

Quantum nonlocality, cryptography and complexity

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Winterreise et Die sieben Todsünden : un regard sur l’aliénation du sujet moderne

La version intégrale de cette thèse est disponible uniquement pour consultation individuelle à la Bibliothèque de musique de l’Université de Montréal (www.bib.umontreal.ca/MU).

Modélisation du carnet d'ordres limites et prévision de séries temporelles

Le contenu de cette thèse est divisé de la façon suivante. Après un premier chapitre d’introduction, le Chapitre 2 est consacré à introduire aussi simplement que possible certaines des théories qui seront utilisées dans les deux premiers articles. Dans un premier temps, nous discuterons des points importants pour la construction de l’intégrale stochastique par rapport aux semimartingales avec paramètre spatial. Ensuite, nous décrirons les principaux résultats de la théorie de l’évaluation en monde neutre au risque et, finalement, nous donnerons une brève description d’une méthode d’optimisation connue sous le nom de dualité. Les Chapitres 3 et 4 traitent de la modélisation de l’illiquidité et font l’objet de deux articles. Le premier propose un modèle en temps continu pour la structure et le comportement du carnet d’ordres limites. Le comportement du portefeuille d’un investisseur utilisant des ordres de marché est déduit et des conditions permettant d’éliminer les possibilités d’arbitrages sont données. Grâce à la formule d’Itô généralisée il est aussi possible d’écrire la valeur du portefeuille comme une équation différentielle stochastique. Un exemple complet de modèle de marché est présenté de même qu’une méthode de calibrage. Dans le deuxième article, écrit en collaboration avec Bruno Rémillard, nous proposons un modèle similaire mais cette fois-ci en temps discret. La question de tarification des produits dérivés est étudiée et des solutions pour le prix des options européennes de vente et d’achat sont données sous forme explicite. Des conditions spécifiques à ce modèle qui permettent d’éliminer l’arbitrage sont aussi données. Grâce à la méthode duale, nous montrons qu’il est aussi possible d’écrire le prix des options européennes comme un problème d’optimisation d’une espérance sur en ensemble de mesures de probabilité. Le Chapitre 5 contient le troisième article de la thèse et porte sur un sujet différent. Dans cet article, aussi écrit en collaboration avec Bruno Rémillard, nous proposons une méthode de prévision des séries temporelles basée sur les copules multivariées. Afin de mieux comprendre le gain en performance que donne cette méthode, nous étudions à l’aide d’expériences numériques l’effet de la force et la structure de dépendance sur les prévisions. Puisque les copules permettent d’isoler la structure de dépendance et les distributions marginales, nous étudions l’impact de différentes distributions marginales sur la performance des prévisions. Finalement, nous étudions aussi l’effet des erreurs d’estimation sur la performance des prévisions. Dans tous les cas, nous comparons la performance des prévisions en utilisant des prévisions provenant d’une série bivariée et d’une série univariée, ce qui permet d’illustrer l’avantage de cette méthode. Dans un intérêt plus pratique, nous présentons une application complète sur des données financières.