A framework for using real data with distributed low cost sensors

Currently, due to the widespread use of computers and the internet, students are trading libraries for the World Wide Web and laboratories with simulation programs. In most courses, simulators are made available to students and can be used to proof theoretical results or to test a developing hardware/product. Although this is an interesting solution: low cost, easy and fast way to perform some courses work, it has indeed major disadvantages. As everything is currently being done with/in a computer, the students are loosing the “feel” of the real values of the magnitudes. For instance in engineering studies, and mainly in the first years, students need to learn electronics, algorithmic, mathematics and physics. All of these areas can use numerical analysis software, simulation software or spreadsheets and in the majority of the cases data used is either simulated or random numbers, but real data could be used instead. For example, if a course uses numerical analysis software and needs a dataset, the students can learn to manipulate arrays. Also, when using the spreadsheets to build graphics, instead of using a random table, students could use a real dataset based, for instance, in the room temperature and its variation across the day. In this work we present a framework which uses a simple interface allowing it to be used by different courses where the computers are the teaching/learning process in order to give a more realistic feeling to students by using real data. A framework is proposed based on a set of low cost sensors for different physical magnitudes, e.g. temperature, light, wind speed, which are connected to a central server, that the students have access with an Ethernet protocol or are connected directly to the student computer/laptop. These sensors use the communication ports available such as: serial ports, parallel ports, Ethernet or Universal Serial Bus (USB). Since a central server is used, the students are encouraged to use sensor values results in their different courses and consequently in different types of software such as: numerical analysis tools, spreadsheets or simply inside any programming language when a dataset is needed. In order to do this, small pieces of hardware were developed containing at least one sensor using different types of computer communication. As long as the sensors are attached in a server connected to the internet, these tools can also be shared between different schools. This allows sensors that aren't available in a determined school to be used by getting the values from other places that are sharing them. Another remark is that students in the more advanced years and (theoretically) more know how, can use the courses that have some affinities with electronic development to build new sensor pieces and expand the framework further. The final solution provided is very interesting, low cost, simple to develop, allowing flexibility of resources by using the same materials in several courses bringing real world data into the students computer works.

Mathematics inspired by Darwin. Adaptive dynamics of dispersal and cooperation

In 1859, Charles Darwin published his theory of evolution by natural selection, the process occurring based on fitness benefits and fitness costs at the individual level. Traditionally, evolution has been investigated by biologists, but it has induced mathematical approaches, too. For example, adaptive dynamics has proven to be a very applicable framework to the purpose. Its core concept is the invasion fitness, the sign of which tells whether a mutant phenotype can invade the prevalent phenotype. In this thesis, four real-world applications on evolutionary questions are provided. Inspiration for the first two studies arose from a cold-adapted species, American pika. First, it is studied how the global climate change may affect the evolution of dispersal and viability of pika metapopulations. Based on the results gained here, it is shown that the evolution of dispersal can result in extinction and indeed, evolution of dispersalshould be incorporated into the viability analysis of species living in fragmented habitats. The second study is focused on the evolution of densitydependent dispersal in metapopulations with small habitat patches. It resulted a very surprising unintuitive evolutionary phenomenon, how a non-monotone density-dependent dispersal may evolve. Cooperation is surprisingly common in many levels of life, despite of its obvious vulnerability to selfish cheating. This motivated two applications. First, it is shown that density-dependent cooperative investment can evolve to have a qualitatively different, monotone or non-monotone, form depending on modelling details. The last study investigates the evolution of investing into two public-goods resources. The results suggest one general path by which labour division can arise via evolutionary branching. In addition to applications, two novel methodological derivations of fitness measures in structured metapopulations are given.

Analysis of applications and of conceptions for an application-oriented mathematics instruction

In connection with the (revived) demand for considering applications in the teaching of mathematics, various schemata or lists of criteria have been developed since the end of the sixties, which set up requirements about closeness to the real world or about the type of mathematics being used, and which have made it possible to analyze the available applications in their light. After having stated the problem (in section 1), we present (in section 2) a sketch of some of the best known of these and of some earlier schemata, although we are not aiming for a complete picture. Then (in section 3) we distinguish among different dimensions.in the analysis of applications. With this as a basis, we develop (in section 4) our own suggestion for categorizing types of applications and conceptions for an application-oriented mathematics instruction. Then (in section 5) we illustrate our schemata by some examples of performed evaluations. Finally (in section 6), we present some preliminary first results of the analysis of teaching conceptions.

Mathematics as a tool in the Life Sciences

Teaching mathematics to students in the biological sciences is often fraught with difficulty. Students often discover mathematics to be a very 'dry' subject in which it is difficult to see the motivation of learning it given its often abstract application. In this paper I advocate the use of mathematical modelling as a method for engaging students in understanding the use of mathematics in helping to solve problems in the Biological Sciences. The concept of mathematics as a laboratory tool is introduced and the importance of presenting students with relevant, real-world examples of applying mathematics in the Biological Sciences is discussed.

The effectiveness of an intelligent tutoring system on the attitude and achievement of developmental mathematics students in a community college

This study examined the effectiveness of intelligent tutoring system instruction, grounded in John Anderson's ACT theory of cognition, on the achievement and attitude of developmental mathematics students in the community college setting. The quasi-experimental research used a pretest-posttest control group design. The dependent variables were problem solving achievement, overall achievement, and attitude towards mathematics. The independent variable was instructional method.^ Four intact classes and two instructors participated in the study for one semester. Two classes (n = 35) served as experimental groups; they received six lessons with real-world problems using intelligent tutoring system instruction. The other two classes (n = 24) served as control groups; they received six lessons with real-world problems using traditional instruction including graphing calculator support. It was hypothesized that students taught problem solving using the intelligent tutoring system would achieve more on the dependent variables than students taught without the intelligent tutoring system.^ Posttest mean scores for one teacher produced a significant difference in overall achievement for the experimental group. The same teacher had higher means, not significantly, for the experimental group in problem solving achievement. The study did not indicate a significant difference in attitude mean scores.^ It was concluded that using an intelligent tutoring system in problem solving instruction may impact student's overall mathematics achievement and problem solving achievement. Other factors must be considered, such as the teacher's classroom experience, the teacher's experience with the intelligent tutoring system, trained technical support, and trained student support; as well as student learning styles, motivation, and overall mathematics ability. ^

The effectiveness of an intelligent tutoring system on the attitude and achievement of developmental mathematics students in a community college

This study examined the effectiveness of intelligent tutoring system instruction, grounded in John Anderson's ACT theory of cognition, on the achievement and attitude of developmental mathematics students in the community college setting. The quasi-experimental research used a pretest-posttest control group design. The dependent variables were problem solving achievement, overall achievement, and attitude towards mathematics. The independent variable was instructional method. Four intact classes and two instructors participated in the study for one semester. Two classes (n = 35) served as experimental groups; they received six lessons with real-world problems using intelligent tutoring system instruction. The other two classes (n = 24) served as control groups; they received six lessons with real-world problems using traditional instruction including graphing calculator support. It was hypothesized that students taught problem solving using the intelligent tutoring system would achieve more on the dependent variables than students taught without the intelligent tutoring system. Posttest mean scores for one teacher produced a significant difference in overall achievement for the experimental group. The same teacher had higher means, not significantly, for the experimental group in problem solving achievement. The study did not indicate a significant difference in attitude mean scores. It was concluded that using an intelligent tutoring system in problem solving instruction may impact student's overall mathematics achievement and problem solving achievement. Other factors must be considered, such as the teacher's classroom experience, the teacher's experience with the intelligent tutoring system, trained technical support, and trained student support; as well as student learning styles, motivation, and overall mathematics ability.

A note on S-asymptotically periodic functions

In [Haiyin Gao, Ke Wang, Fengying Wei, Xiaohua Ding, Massera-type theorem and asymptotically periodic Logistic equations, Nonlinear Analysis: Real World Applications 7 (2006) 1268-1283, Lemma 2.1] it is established that a scalar S-asymptotically to-periodic function (that is, a continuous and bounded function f : [0, infinity) -> R such that lim(t ->infinity)(f (t + omega) - f (t)) = 0) is asymptotically omega-periodic. In this note we give two examples to show that this assertion is false. (C) 2008 Elsevier Ltd. Ail rights reserved.

Database technologies for l-system simulations in virtual plant applications on bioinformatics

One of the most important advantages of database systems is that the underlying mathematics is rich enough to specify very complex operations with a small number of statements in the database language. This research covers an aspect of biological informatics that is the marriage of information technology and biology, involving the study of real-world phenomena using virtual plants derived from L-systems simulation. L-systems were introduced by Aristid Lindenmayer as a mathematical model of multicellular organisms. Not much consideration has been given to the problem of persistent storage for these simulations. Current procedures for querying data generated by L-systems for scientific experiments, simulations and measurements are also inadequate. To address these problems the research in this paper presents a generic process for data-modeling tools (L-DBM) between L-systems and database systems. This paper shows how L-system productions can be generically and automatically represented in database schemas and how a database can be populated from the L-system strings. This paper further describes the idea of pre-computing recursive structures in the data into derived attributes using compiler generation. A method to allow a correspondence between biologists' terms and compiler-generated terms in a biologist computing environment is supplied. Once the L-DBM gets any specific L-systems productions and its declarations, it can generate the specific schema for both simple correspondence terminology and also complex recursive structure data attributes and relationships.

Grupos de simetria: identificação de padrões no património açoriano

Dissertação de Mestrado, Matemática para Professores, 3 de Abril de 2014, Universidade dos Açores.

A fusão de dois mundos: convergência do mundo real e digital nas acções de marketing na rede

No passado, as acções publicitárias eram rotuladas como above the line e below the line, referindo-se à dicotomia de pontos de contacto com os públicos-alvo via Meios de Comunicação Social ou via Ponto de Venda. A esta dicotomia de meios e instrumentos, os anos 90 vieram trazer um terceiro ponto de contacto, crescentemente omnipresente e hegemónico, a world wide web ou rede, a que se acedia via computador. As acções de marketing e comunicação passaram então a rotular-se como online e offline, passando, não já a referir-se aos pontos de contacto, mas aos canais pelos quais circulavam as mensagens e acções das marcas. Desde o início deste século, o poder do digital veio crescendo, em software e hardware, em terminais e tecnologias, assistindo-se a uma transferência de esforços de comunicação, da esfera real para a esfera do digital. O deslumbramento pelo digital conquistou mesmo algumas marcas de dimensão mundial que hoje apostam integralmente o seu orçamento nesta forma de marketing, nas suas múltiplas facetas. Contudo, e porque se tem tornado óbvio que os públicos distribuem os seus favores por múltiplos touch points, para maximizar o impacto, assiste-se agora a um fenómeno único, potenciado por novas tecnologias que surgem todos os dias: em estratégias que se podem denominar de all-line, verifica-se a fusão entre dois mundos, mundo real e mundo digital, em múltiplas actividades de marketing que fazem convergir estas duas realidades em plataformas que vão do computador ao tablet, do smartphone à vending machine interactiva, do facebook ao Google maps, da imprensa tradicional ao pinterest. É esta convergência mundo real - mundo digital que abre agora novas oportunidades à comunicação publicitária, potenciando os ingredientes das marcas de sucesso no futuro: sensações (estímulo dos sentidos), intimidade e mistério, num cocktail suportado por uma nova criatividade.

Real time manufacturing systems simulator

A área da simulação computacional teve um rápido crescimento desde o seu apareciment, sendo actualmente uma das ciências de gestão e de investigação operacional mais utilizadas. O seu princípio baseia-se na replicação da operação de processos ou sistemas ao longo de períodos de tempo, tornando-se assim uma metodologia indispensável para a resolução de variados problemas do mundo real, independentemente da sua complexidade. Das inúmeras áreas de aplicação, nos mais diversos campos, a que mais se destaca é a utilização em sistemas de produção, onde o leque de aplicações disponível é muito vasto. A sua aplicação tem vindo a ser utilizada para solucionar problemas em sistemas de produção, uma vez que permite às empresas ajustar e planear de uma maneira rápida, eficaz e ponderada as suas operações e os seus sistemas, permitindo assim uma rápida adaptação das mesmas às constantes mudanças das necessidades da economia global. As aplicações e packages de simulação têm seguindo as tendências tecnológicas pelo que é notório o recurso a tecnologias orientadas a objectos para o desenvolvimento das mesmas. Este estudo baseou-se, numa primeira fase, na recolha de informação de suporte aos conceitos de modelação e simulação, bem como a respectiva aplicação a sistemas de produção em tempo real. Posteriormente centralizou-se no desenvolvimento de um protótipo de uma aplicação de simulação de ambientes de fabrico em tempo real. O desenvolvimento desta ferramenta teve em vista eventuais fins pedagógicos e uma utilização a nível académico, sendo esta capaz de simular um modelo de um sistema de produção, estando também dotada de animação. Sem deixar de parte a possibilidade de integração de outros módulos ou, até mesmo, em outras plataformas, houve ainda a preocupação acrescida de que a sua implementação recorresse a metodologias de desenvolvimento orientadas a objectos.

Potencialidades de uma abordagem com Interdisciplinaridade entre matemática e estudo do meio e centrada no ambiente

O presente estudo partiu do problema “Como promover aprendizagens da Matemática e do Estudo do Meio numa perspetiva interdisciplinar, explorando o mundo real?”. Neste sentido, tem como objetivos: selecionar recursos e atividades que se revelem motivadoras para os alunos; demonstrar a relevância da inter-relação de diferentes conceitos e a importância da sua ligação com as vivências dos alunos; ativar o envolvimento dos alunos para a aprendizagem da Matemática através do Estudo do meio e de situações do mundo real; estimular a perceção do aluno da presença da Matemática nos conteúdos de Estudo do Meio; fomentar a compreensão da relação dos conteúdos de Matemática e estudo do Meio. Com este propósito formularam-se as seguintes questões: (1) Que tipo de atividades se poderão proporcionar de forma a motivar os alunos para os conteúdos do Estudo do Meio e da Matemática? (2) De que forma a exploração das situações/conceções do quotidiano poderá promover o envolvimento dos alunos na aprendizagem da Matemática e do Estudo do Meio? (3) De que forma o Ensino Experimental das Ciências numa perspetiva interdisciplinar pode contribuir para desenvolver tanto as competências conceptuais (fatores do ambiente: temperatura e humidade/OTD/números racionais), como capacidades de pensamento crítico e tomada de decisão inerente? Tendo em vista os objetivos do estudo, desenvolveram-se, com uma turma do 2º ano de escolaridade, quatro situações formativas, que envolveram as disciplinas de Matemática e Estudo do Meio. O domínio de conteúdos preponderante na área de Estudo do Meio foi À descoberta do Ambiente Natural, enquanto na Matemática os domínios predominantes foram Organização e tratamento de dados e Números e operações. Foram realizadas diversas atividades experimentais, onde os alunos tiveram um papel ativo na construção dos seus conhecimentos. A investigação segue uma metodologia qualitativa, centrando-se num estudo de caso, onde se caracteriza uma experiência interdisciplinar que envolveu as disciplinas de Matemática e Estudo do Meio. Os dados foram recolhidos pela professora investigadora através de gravações de vídeo e áudio, fotografias, trabalhos dos alunos e de registos da professora investigadora. Os resultados demonstraram como os alunos mobilizaram e apropriaram os conteúdos de Matemática e Estudo do Meio. Os dados, através da análise de conteúdo, parecem iv sugerir que houve uma evolução no desempenho dos alunos a vários níveis, nomeadamente: no trabalho cooperativo, no envolvimento da tarefa, nas interações estabelecidas e na motivação para a aprendizagem da Matemática e Estudo do Meio.

As the world turns: short-term human spatial memory in egocentric and allocentric coordinates

We aimed to determine whether human subjects' reliance on different sources of spatial information encoded in different frames of reference (i.e., egocentric versus allocentric) affects their performance, decision time and memory capacity in a short-term spatial memory task performed in the real world. Subjects were asked to play the Memory game (a.k.a. the Concentration game) without an opponent, in four different conditions that controlled for the subjects' reliance on egocentric and/or allocentric frames of reference for the elaboration of a spatial representation of the image locations enabling maximal efficiency. We report experimental data from young adult men and women, and describe a mathematical model to estimate human short-term spatial memory capacity. We found that short-term spatial memory capacity was greatest when an egocentric spatial frame of reference enabled subjects to encode and remember the image locations. However, when egocentric information was not reliable, short-term spatial memory capacity was greater and decision time shorter when an allocentric representation of the image locations with respect to distant objects in the surrounding environment was available, as compared to when only a spatial representation encoding the relationships between the individual images, independent of the surrounding environment, was available. Our findings thus further demonstrate that changes in viewpoint produced by the movement of images placed in front of a stationary subject is not equivalent to the movement of the subject around stationary images. We discuss possible limitations of classical neuropsychological and virtual reality experiments of spatial memory, which typically restrict the sensory information normally available to human subjects in the real world.

Market Index Biases and Minimum Risk Indices

Markets, in the real world, are not efficient zero-sum games where hypotheses of the CAPM are fulfilled. Then, it is easy to conclude the market portfolio is not located on Markowitz"s efficient frontier, and passive investments (and indexing) are not optimal but biased. In this paper, we define and analyze biases suffered by passive investors: the sample, construction, efficiency and active biases and tracking error are presented. We propose Minimum Risk Indices (MRI) as an alternative to deal with to market index biases, and to provide investors with portfolios closer to the efficient frontier, that is, more optimal investment possibilities. MRI (using a Parametric Value-at-Risk Minimization approach) are calculated for three stock markets achieving interesting results. Our indices are less risky and more profitable than current Market Indices in the Argentinean and Spanish markets, facing that way the Efficient Market Hypothesis. Two innovations must be outlined: an error dimension has been included in the backtesting and the Sharpe"s Ratio has been used to select the"best" MRI

Market Index Biases and Minimum Risk Indices

Markets, in the real world, are not efficient zero-sum games where hypotheses of the CAPM are fulfilled. Then, it is easy to conclude the market portfolio is not located on Markowitz"s efficient frontier, and passive investments (and indexing) are not optimal but biased. In this paper, we define and analyze biases suffered by passive investors: the sample, construction, efficiency and active biases and tracking error are presented. We propose Minimum Risk Indices (MRI) as an alternative to deal with to market index biases, and to provide investors with portfolios closer to the efficient frontier, that is, more optimal investment possibilities. MRI (using a Parametric Value-at-Risk Minimization approach) are calculated for three stock markets achieving interesting results. Our indices are less risky and more profitable than current Market Indices in the Argentinean and Spanish markets, facing that way the Efficient Market Hypothesis. Two innovations must be outlined: an error dimension has been included in the backtesting and the Sharpe"s Ratio has been used to select the"best" MRI