No description available.

Many complex systems in Nature are multifractal, a feature closely related to scale invariance. Multifractality is ubiquitous and so it can be found in systems as diverse as marine turbulence, econometric series, heartbeat dynamics and the solar magnetic field. In recent years, there has been growing interest in modelling the multifractal structure in these systems. This has improved our understanding of certain phenomena and has opened the way for applications such as reduction of coding redundancy, reconstruction of data gaps and forecasting of multifractal variables. Exhaustive multifractal characterization of experimental data is needed for tuning parameters of the models. The design of appro- priate algorithms to achieve this purpose remains a major challenge, since discretization, gaps, noise and long-range correlations require ad- vanced processing, especially since multifractal signals are not smooth: due to scale invariance, they are intrinsically uneven and intermittent. In the present study, we introduce a formalism for multifractal data based on microcanonical cascades. We show that with appropri- ate selection of the representation basis, we greatly improve inference capabilities in a robust fashion. In addition, we show two applications of microcanonical cascades: first, forecasting of stock market series; and second, detection of interscale heat transfer in the ocean.

In this thesis we give two different proofs of the result chromatic number of a special graph is 4. The first proof is derived by analysing the structure of the special graph. The second proof is a method which was first studied in [1].

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2018-12-12T09:26:29Z No. of bitstreams: 1 Fernanda Leite Lopes Beyer.pdf: 767950 bytes, checksum: 8f821f59b6aad5ff2cc10370b97ea585 (MD5) / Made available in DSpace on 2018-12-12T09:26:29Z (GMT). No. of bitstreams: 1 Fernanda Leite Lopes Beyer.pdf: 767950 bytes, checksum: 8f821f59b6aad5ff2cc10370b97ea585 (MD5) Previous issue date: 2018-10-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The objective of this study was to map the contributions, approaches and trends of the researches in Mathematics Education elaborated between 1997 and 2016 in Brazil that analyzed the processes of teaching and learning of multiplicative structures from the conceptions of Conceptual Field and Multiplicative Field proposed by Vergnaud . It is a mapping that seeks to inventory, systematize and evaluate scientific production in this area of knowledge. Thus, thirty-two studies (six theses and twenty-six dissertations) were found, which were categorized into three distinct axes of analysis: student axis, composed of researches that had an approach regarding the learning process; axis Professor, formed by the research that focused on the teaching knowledge required for teaching, in initial or continuing teacher training and the Material axis, formed by the researches that studied the approach of the Multiplicative Field in official documents and / or didactic materials. After the files and reviews of the works, it was possible to verify some challenges and tendencies regarding the teaching and learning of Multiplicative Field. With the mapping carried out, we observed in the research results that the misconceptions present in the students are also present in the conceptions of teacher education, because there is a belief of continuity between the additive field and the multiplicative field. We have also identified that the Guides, National Curriculum Parameters and didactic materials suggest the teaching of the concepts inherent to the Multiplicative Conceptual Field, but do not present enough mathematical and didactic organizations to build students' knowledge / O objetivo deste estudo foi mapear as contribuições, enfoques e tendências das pesquisas em Educação Matemática elaboradas entre 1997 e 2016 no Brasil que analisaram os processos de ensino e de aprendizagem de estruturas multiplicativas a partir das concepções de Campo Conceitual e de Campo Multiplicativo propostas por Vergnaud. Trata-se de um mapeamento que busca inventariar, sistematizar e avaliar a produção científica nessa área de conhecimento. Desse modo, foram encontrados trinta e dois trabalhos (seis teses e vinte e seis dissertações), que foram categorizadas em três eixos distintos de análise: eixo Aluno, composto por pesquisas que tiveram uma abordagem a respeito do processo de aprendizagem; eixo Professor, formado pelas pesquisas que focaram nos saberes docentes necessários para o ensino, em formação inicial ou continuada de docentes e o eixo Material, formado pelas pesquisas que estudaram a abordagem do Campo Multiplicativo em documentos oficiais e/ou em materiais didáticos. Após os fichamentos e resenhas dos trabalhos, foi possível verificar alguns desafios e tendências no que diz respeito ao ensino e a aprendizagem do Campo Multiplicativo. Com o mapeamento realizado, observamos, nos resultados das pesquisas que os conceitos equivocados presentes nos alunos também estão presentes nas concepções de ensino de professores, pois existe uma crença de continuidade entre o campo aditivo e campo multiplicativo. Identificamos também que os Guias, Parâmetros Curriculares Nacionais e os materiais didáticos sugerem o ensino dos conceitos inerentes ao Campo Conceitual Multiplicativo, porém não apresentam organizações matemáticas e didáticas suficientemente completas para construção de conhecimentos por parte dos estudantes

In algebraic topology, we work to classify objects. My research aims to build a better understanding of one important notion of classification of differentiable manifolds called cobordism. Cobordism is an equivalence relation, and the equivalence classes in cobordism form a graded ring, with operations disjoint union and Cartesian product. My dissertation studies this graded ring in two ways: 1. by attempting to find preferred class representatives for each class in the ring. 2. by computing the image of the ring under an interesting ring homomorphism called the Witten Genus.

Studien fokuserar på multiplikativt tänkande hos elever i årskurs 3. Multiplikativt tänkande är abstrakt (Clark & Kamii, 1996) och innebär användning av strategier för lösningar av multiplikations- och divisionsuppgifter. Syftet med studien är att undersöka hur elever använder sig av olika strategier inom multiplikativt tänkande vid multiplikation och division. Studien har inspirerats av Grounded Theory. Utifrån teorierna gjordes en semistrukturerad intervju, observationer samt en analys av data. I studien deltog åtta elever i intervjuerna och en pilotstudie inledde undersökningen. Materialet som samlades in bestod av elevernas lösningar av multiplikations- och divisionsuppgifter, anteckningar från observationer av elevernas lösningar samt ljudinspelade intervjuer. Resultatet visar att nästan alla elever använde sig av en additiv strategi i lösningar av multiplikations- och divisionsuppgifter. Det visade även att det endast var fyra av åtta elever som kunde uppvisa förståelse av ett samband mellan de två räknesätten. Resultatet visar att eleverna har olika strategier och lösningar inom multiplikativt tänkande även om de har haft samma matematikundervisning. / This study focuses on multiplicative thinking among pupils in grade 3. Multiplicative thinking is abstract (Clark & Kamii, 1996), involving applying strategies to solve multiplication and division tasks. The purpose of this study is to examine how pupils use different strategies within multiplicative thinking for multiplication and division. This study was inspired by Grounded Theory. From this theory, a number of semi-structured interviews, observations and analysis of data were made. Eight pupils participated in the interviews, after an initial pilot study. The collected material was based on the pupils' solutions of tasks in multiplication and division, notes from observations of the pupils' solutions and audiotaped interviews. The results show that almost every pupil uses an additive strategy in their solutions of multiplication and division tasks. It also show that only four out of eight pupils could show understanding 0f the connection between the two basic arithmetic operations. From the results, the pupils showed different strategies and solutions within multiplicative thinking, even though they have had the same mathematic education.

QC 351 A7 no. 65 / The significance of signal-dependent noise is discussed. Particular emphasis is placed on the type of multiplicative noise present in the density variations in a photographic emulsion. A theoretical treatment of the effect of multiplicative noise on signal detection and signal discrimination problems is presented. Optimum test statistics are derived for processing a sampled message to detect the presence of a known signal. Multiplicative noise described by Poisson and Gaussian statistics is considered. The expressions are extended to include the two-signal discrimination problem. Two-dimensional signal fields in the presence of multiplicative noise are simulated in a computer and processed for optimum signal detection according to the two derived methods. These results are compared to the results of processing based on the assumption of stationary noise statistics. This comparison reveals that modest improvements (20% to 30% reduction in false alarm rate) are obtained when the signal-dependent nature of the noise statistics is considered. The effects of signal-to-noise ratio, signal structure, and changing background level are also investigated. An example of optimum signal discrimination using circles and squares as signals in multiplicative noise is reported. An improvement in the percentage of correctly identified signals is again observed when the proper test statistic is used. Two examples of signal filtering in the presence of signal-dependent noise are included. The first concerns the processing of a real star field to determine the location of weak stars. The second is an illustration of the signal information contained in the noise spectrum of a message recorded on a common photographic film.

Background: Survival analysis is sometimes called time-to-event analysis. The Cox model is used widely in survival analysis, where the covariates act multiplicatively on unknown baseline hazards. However, the Cox model requires the proportionality assumption, which limits its applications. The additive hazards model has been used as an alternative to the Cox model, where the covariates act additively on unknown baseline hazards. Objectives and methods: In this thesis, performance of the Cox multiplicative hazards model and the additive hazards model have been demonstrated and applied to the transfer, lifting and repositioning (TLR) injury prevention study. The TLR injury prevention study was a retrospective, pre-post intervention study that utilized a non-randomized control group. There were 1,467 healthcare workers from six hospitals in Saskatchewan, Canada who were injured from January 1, 1999 to December 1, 2006. De-identified data sets were received from the Saskatoon Health Region and Regina Quappelle Health Region. Time to repeated TLR injury was considered as the outcome variable. The models goodness of fit was also assessed. Results: Of a total of 1,467 individuals, 149 (56.7%) in the control group and 114 (43.3%) in the intervention group had repeated injuries during the study period. Nurses and nursing aides had the highest repeated TLR injuries (84.8%) among occupations. Back, neck and shoulders were the most common body parts injured (74.9%). These covariates were significant in both Cox multiplicative and additive hazards models. The intervention group had 27% fewer repeated injuries than the control group in the multiplicative hazards model (HR= 0.63; 95% CI=0.48-0.82; p-value=0.0002). In the additive model, the hazard difference between the intervention and the control groups was 0.002. Conclusion: Both multiplicative and additive hazards models showed similar results, indicating that the TLR injury prevention intervention was effective in reducing repeated injuries. The additive hazards model is not widely used, but the coefficient of the covariates is easy to interpret in an additive manner. The additive hazards model should be considered when the proportionality assumption of the Cox model is doubtful.

Background: Survival analysis is sometimes called time-to-event analysis. The Cox model is used widely in survival analysis, where the covariates act multiplicatively on unknown baseline hazards. However, the Cox model requires the proportionality assumption, which limits its applications. The additive hazards model has been used as an alternative to the Cox model, where the covariates act additively on unknown baseline hazards. Objectives and methods: In this thesis, performance of the Cox multiplicative hazards model and the additive hazards model have been demonstrated and applied to the transfer, lifting and repositioning (TLR) injury prevention study. The TLR injury prevention study was a retrospective, pre-post intervention study that utilized a non-randomized control group. There were 1,467 healthcare workers from six hospitals in Saskatchewan, Canada who were injured from January 1, 1999 to December 1, 2006. De-identified data sets were received from the Saskatoon Health Region and Regina Quappelle Health Region. Time to repeated TLR injury was considered as the outcome variable. The models goodness of fit was also assessed. Results: Of a total of 1,467 individuals, 149 (56.7%) in the control group and 114 (43.3%) in the intervention group had repeated injuries during the study period. Nurses and nursing aides had the highest repeated TLR injuries (84.8%) among occupations. Back, neck and shoulders were the most common body parts injured (74.9%). These covariates were significant in both Cox multiplicative and additive hazards models. The intervention group had 27% fewer repeated injuries than the control group in the multiplicative hazards model (HR= 0.63; 95% CI=0.48-0.82; p-value=0.0002). In the additive model, the hazard difference between the intervention and the control groups was 0.002. Conclusion: Both multiplicative and additive hazards models showed similar results, indicating that the TLR injury prevention intervention was effective in reducing repeated injuries. The additive hazards model is not widely used, but the coefficient of the covariates is easy to interpret in an additive manner. The additive hazards model should be considered when the proportionality assumption of the Cox model is doubtful.

Submitted by Caroline Falcao (caroline.rfalcao@ufpe.br) on 2017-06-19T17:49:08Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) 2011-Dissertacao-Tatyane-Veras-De-Queiroz.pdf: 1221590 bytes, checksum: 8a4a86ea3d37c88bdae2dfff9f39feee (MD5) / Made available in DSpace on 2017-06-19T17:49:08Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) 2011-Dissertacao-Tatyane-Veras-De-Queiroz.pdf: 1221590 bytes, checksum: 8a4a86ea3d37c88bdae2dfff9f39feee (MD5) Previous issue date: 2011-05-27 / Estudo envolvendo a compreensão dos conceitos matemáticos emcrianças e adolescentes surdos tem se tornado relevantedevido à proposta de uma educação inclusiva. A presente pesquisa tem porobjetivoinvestigar o efeito de diferentes formas de apresentação de problemas (português, interlíngua e Libras) e dos suportes de representação (material concreto definido, lápis e papel e representação visual) na resolução de problemas de multiplicação por crianças surdas. Para tal foram entrevistados 88 estudantes, surdos e ouvintes, do Ensino Fundamental de escolas públicas do Recife, alocadosigualmente em quatro grupos (G1 –surdos sem instrução; G2 –surdos com instrução; G3 –ouvintes sem instrução; G4 –ouvintes com instrução), que realizaram quatro tarefas (T1-Sondagem, T2-Português, T3-Interlíngua e T4-Libras, sendo esta última aplicada apenas com os surdos). Os principais resultados foram os seguintes: (a) o efeito da forma como o problema é apresentado:os participantes apresentaram desempenhos diferentes em relação às tarefas (T2, T3 e T4), diferindo em relação àforma como o problema estava escrito ou era apresentado. A forma escrita da Tarefa 2 favoreceu o desempenho dos ouvintes enquanto aforma da Tarefa 3 e Tarefa 4 favoreceu aos surdos; (b) efeito dos suportes de representação de acordo com as situações propostas:osdados apontaram que os suportes interferiram no desempenho juntamente com a forma escrita dos problemas, ou seja, nas tarefas em que o grupo teve dificuldade em relação à escrita, o suporte parecia auxiliar na resolução, como o lápis e papel para os surdos na Tarefa 2. Nas Tarefas 3 e 4, em que os grupos não apresentaram dificuldades, o desempenho em relação aos suportes era semelhante, não havendo diferenças significativas; (c) estratégias adotadas por surdos:dependia do nível de instrução de cada grupo e da situação proposta em cada tarefa, assim, as estratégias mais elaboradas emergiram nos grupos com instrução formal da multiplicação, enquanto que as estratégias mais simples foram adotadas por grupos sem instrução. A partir desses resultados, é possível dizer que aproximar a forma de apresentação dos enunciados matemáticos à realidade dos surdos contribui para o desempenhoe para o surgimento de estratégias mais elaboradas, principalmente quando associada a alguns suportes de representação, como o material concreto definido (para os sem instrução) e o lápis e papel (para os com instrução). Portanto, é necessário pensar em rotas alternativas de ensino, em salas de aula inclusivas, para aquisição de conceitos matemáticos por surdos. / Studies involving the understanding of mathematical concepts in deaf children and teenagers have become increasingly relevant due to the proposed inclusive education. This research aims to investigate the effect of different ways of presenting problems (Portuguese, Interlingua and Sign Language) and the representational supports (specific material, pencil and paper and visual representation) in solving multiplication problems by deafchildren. To this end, 88 deaf and hearing students from Elementary Public Schools in Recife were interviewed and allocated equally into four groups (Group 1 -deaf without instruction; Group 2 -deaf with instruction; Group 3 -listeners without instruction; Group 4 -listeners with instruction) that performed four tasks (T1 -Sounding out, T2 -Portuguese, T3 –Interlingua, T4 –Pounds, latter applied only with deaf people). The main results were as follows: (a) the effect of how the problem is presented: the participants had different performances related to the tasks 2, 3 and 4, according to how the problem was wrote or presented. The written form in Task 2 favored the listeners’ performance while the Task 3 and 4 helped the deaf. (b) the effect of the representational supports according to proposed situations:the collected data indicated that the performance was interfered along with the problems in written form, in other words, the tasks in which the group had writing difficulties, the representation tools seemed to help solving the situation, like the paper and pencil helped the deaf ones in the Task 2. In the tasks 3 and 4, in which the groups had no difficulties, the performance related to the representation supports was similar, not having major differences; (c) the strategies used by the deaf:it depended on the education level of each group and the situation presented on each task, so the most refined strategies appeared in the groups with formal instruction in multiplication, while the simplest strategies have been adopted by groups without instruction. From these results, it is possible to say that making the way of presenting mathematics questions closer to the reality of deaf people helps their performance and the creation of refined strategies, mainly when is using the representational support such as the concret materials (to the deaf without instruction) and pencil and paper (to the deaf with instruction). Therefore, it is necessary to think in new alternative ways of teaching in inclusive classrooms, so the deaf students can understand mathematical concepts.