Orientador: Fernando Eduardo Torres Orihuela / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-27T14:35:36Z (GMT). No. of bitstreams: 1 Paula_AnaRachelBritode_M.pdf: 1519694 bytes, checksum: 61b845f0f57e58e56f6a1f759fc9a382 (MD5) Previous issue date: 2015 / Resumo: A dissertação "Polinômios de Permutação e Palavras Balanceadas" tem como principal objetivo estudar a influência dos polinômios de permutação na teoria de códigos mediante o conceito de palavra balanceada. A base do trabalho é o artigo "Permutacion polynomials and aplications to coding theory" de Yann Laigke-Chapuy. Expomos os conceitos básicos de polinômios de permutação como algumas de suas características, exemplos e métodos para identificação dos mesmos. Em seguida trataremos dos códigos lineares com ênfase nos binários explorando particularmente a conjectura de Helleseth / Abstract: The main goal in writing this dissertation is the study of the influence of the Theory of Permutation Polynomials in the context of Coding Theory via the concept of balanced word. Our basic reference is the paper "Permutation polynomials and applications to coding theory" by Y. Laigke- Chapury. Our plan is to introduce the basic concepts in Coding Theory, Permutation Polynomials; then we mainly consider the long-standing open Helleseth¿s conjecture / Mestrado / Matematica Aplicada / Mestra em Matemática Aplicada

Made available in DSpace on 2016-04-27T16:57:13Z (GMT). No. of bitstreams: 1 Carlos Eduardo de Campos.pdf: 1683164 bytes, checksum: 1dd97a1301e188ce53dd5d495c3b2f0e (MD5) Previous issue date: 2011-11-09 / Secretaria da Educação do Estado de São Paulo / This dissertation is focused on the teaching and learning of the Combinatorial Analysis, specifically mentioning, Counting Problems. The report is about a documentary research, as a result of the analysis of the coursebook, thus the methodological procedures are the most appropriate to this kind of investigation. The aim of this research is to evaluate the types of Counting Problems, which are included in the student s book, Secondary school second grade third term from the Department of Education of the state of São Paulo, in the view of the combinatorial research, taking into account that is the presupposition of the Curriculum of the state of São Paulo, the resolution of the problems in a teaching approach for the combinatorial concepts. The studied problems are the simple ones, in other words, those which could be solved by using only one combinatorial operation. The yardsticks of the content analysis accomplished in the book are the task variables used by Batanero, Navarro-Pelayo, implicit combinatorial model, combinatorial operation, the nature of the elements to be combined and the values of the parameter m and n. They are supported by the theory of the conceptual fields developed by Vergnaud, in which those concepts couldn t be learnt with the approach of a single type of problem. Our investigation led us to the conclusion that, even working with an important list of issues, many of them involved similar situations. It is because not all the considered variables were found in this list / Esta dissertação tem por foco o ensino e a aprendizagem da Análise Combinatória ou, mais especificamente, dos Problemas de Contagem. Trata-se do relatório minucioso de pesquisa documental de análise de material didático e, sobretudo, os procedimentos metodológicos são os adequados a essa modalidade de investigação. O objetivo da investigação é avaliar os tipos de Problemas de Contagem, que figuram no Caderno do Aluno do 3º bimestre do 2º ano do Ensino Médio, da Rede Estadual Paulista de Ensino, com vistas à formação do raciocínio combinatório, levando em conta o pressuposto da Proposta Curricular em questão que entende a resolução de problemas como uma abordagem de ensino eficaz para os conceitos combinatórios. Os problemas estudados são entendidos e classificados como simples, ou seja, aqueles que podem ser resolvidos usando somente uma operação combinatória. Os balizadores da análise de conteúdo realizada no Caderno são as variáveis de tarefa usadas por Batanero e Navarro-Pelayo: modelo combinatório implícito, operação combinatória, natureza dos elementos que se combinam e valores dados aos parâmetros m e n. Os mesmos são respaldados na Teoria dos Campos Conceituais de Verganaud, para a qual conceitos não podem ser apreendidos com a abordagem de um único tipo de problema. Nossa investigação nos levou a constatar que, mesmo com um elenco importante de problemas, muitos deles envolviam situações semelhantes. Isso se deu porque nem todas as variáveis consideradas foram encontradas nesse rol

Made available in DSpace on 2016-04-27T16:59:02Z (GMT). No. of bitstreams: 1 Ricardo Dezso Sabo.pdf: 6509941 bytes, checksum: b45f4f13e333775bac308dd846292805 (MD5) Previous issue date: 2010-03-24 / Given the scenario described by academic research, which provides us with the difficulties faced by students when understanding the concepts of combinatorial analysis and the hypothesis that the students misconceptions might result from the teacher s knowledge and methodology, this work aims at investigating, by means of semi-structured interviews, the knowledge of mathematics teachers of secondary school education in relation to this subject. We believe that resorting to semi-structured interviews as a tool for data collection favored the interpretative process of the teacher's speech, thus emphasizing its meanings. In this context, we formulated the following research question: What knowledge can be identified by the high school teacher s speech, using semi-structured interviews, regarding the teaching of the concepts of combinatorial analysis? The theoretical framework was outlined with the use of Yves Chevallard s Anthropological Theory of Didactic as to analyze and organize the mathematical object; Tardif's theories so as to guide us in relation to the teacher's knowledge and the works of Ponte, Nacarato and others, in order to understand how the training and professional development of teachers is carried out. This research has shown that, among the teachers that were interviewed, they reproduce the teaching practices and knowledge inherited from the teachers who participated in their own school experiences taking into account that that the exchange of experiences among colleagues favors the constructions of new knowledge and/or the sedimentation and evolution of old knowledge. Regarding the use of formulas, we see a divergent situation, as some teachers say they value the use of the Multiplicative Principle and others value the use of formulas, although the latter don t seem to be able to justify or explain their validity. There were teachers who said that, when reading the instructions for class exercises, have difficulty figuring out whether the order of the elements is relevant or not. Thus, our results highlighted the importance of providing teachers with opportunities of participation in continuing education or discussion groups that lead to a reassessment of a teacher's knowledge and the construction of new knowledge, in a way that a teacher s practice may also be modified / Diante do cenário descrito por pesquisas acadêmicas que apresentam as dificuldades dos alunos em apropriar-se dos conceitos de análise combinatória e tendo como hipótese que os equívocos dos alunos possam emergir dos saberes e da prática do professor. Este trabalho teve o objetivo de investigar, por meio de entrevistas semiestruturadas os saberes do professor de Matemática do Ensino Médio com relação ao ensino desse tema. Entende-se que lançar mão de entrevistas semiestruturadas, como instrumento de coleta de dados, privilegiou o processo interpretativo da fala do professor, ressaltando, assim, os significados que ele possui. Nesse contexto, formulou-se a seguinte questão de pesquisa: Quais saberes podem ser identificáveis por meio da fala do professor do Ensino Médio, utilizando-se de entrevistas semiestruturadas, em relação ao ensino dos conceitos de análise combinatória? O quadro teórico construiu-se pela utilização da Teoria Antropológica do Didático de Yves Chevallard, com o objetivo de analisar e organizar o objeto matemático; das teorias de Tardif a fim de orientar com relação aos Saberes Docentes e dos trabalhos de Ponte, Nacarato e outros, com o objetivo de entender como se dá a formação e o desenvolvimento profissional do professor. Esta pesquisa revelou que, entre os entrevistados, observou-se a reprodução pelo professor da prática docente, e o saber herdado dos professores que participaram de suas experiências escolares, pois a troca de experiências entre os colegas de profissão favorece a construção de novos saberes e/ou a sedimentação e a evolução de saberes antigos. Com relação ao uso de fórmulas, observou-se uma situação divergente, visto que alguns professores afirmaram que valorizam o uso do Princípio Multiplicativo, e outros, o emprego de fórmula, e estes demonstraram não saber justificar e explicar a validade das mesmas. Houve professores que afirmaram ter dificuldades para distinguir, quando leem os enunciados dos problemas, se a ordem dos elementos é ou não relevante. Assim sendo, os resultados apontaram para a importância das oportunidades de participação em grupos de formação continuada ou grupos de discussão que propiciem uma reavaliação dos saberes docentes e a construção de novos saberes, podendo favorecer, nesse contexto, mudanças na prática docente

With the advent of autonomous systems and deep learning systems, safety pertaining to these systems has become a major concern. The existing failure analysis techniques are not enough to thoroughly analyze the safety in these systems. Moreover, because these systems are created to operate in various conditions, they are susceptible to unknown safety issues. Hence, we need mechanisms which can take into account the complexity of operational design domains, identify safety issues other than failures, and expose unknown safety issues. Moreover, existing safety analysis approaches require a lot of effort and time for analysis and do not consider machine learning (ML) safety. To address these limitations, in this dissertation, we discuss an artificial-intelligence driven model-based methodology that aids in identifying unknown safety issues and analyzing ML safety. Our methodology consists of 4 major tasks: 1) automated model generation, 2) automated analysis of component state transition model specification, 3) undesired states analysis, and 4) causal factor analysis. In our methodology we identify unknown safety issues by finding undesired combinations of components' states and environmental entities' states as well as causes resulting in these undesired combinations. In our methodology, we refer to the behaviors that occur because of undesired combinations as off-nominal behaviors (ONBs). To identify undesired combinations and ONBs that aid in exposing unknown safety issues with less effort and time we proposed various approaches for each of the task and performed corresponding empirical studies. We also discussed machine learning safety analysis from the perspective of machine learning engineers as well as system and software safety engineers. The results of studies conducted as part of our research shows that our proposed methodology helps in identifying unknown safety issues effectively. Our results also show that combinatorial methods are effective in reducing effort and time for analysis of off-nominal behaviors without overlooking any dependencies among components and environmental entities of a system. We also found that safety analysis of machine learning components is different from analysis of conventional software components and detail the aspects we need to consider for ML safety.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work aims to support Basic Education teachers by providing a detailed materials for teaching Combinatorial Analysis, Probability and Probabilistic Models, taking into account aspects related to day-to- day using mathematical concepts in problem situations. We also propose a teaching sequence on the topics mentioned above for the Basic Education teachers to broaden and diversify their strategies education. / Este trabalho tem como objetivo dar suporte ao professor da Educação Básica fornecendo um material detalhado para o ensino da Análise Combinatória, Probabilidade e Modelos Probabilísticos, levando-se em consideração aspectos relacionados ao dia-a-dia, utilizando conceitos matemáticos em situações problemas. Propomos ainda uma sequência didática sobre os temas acima citados para que os professores da Educação Básica possam ampliar e diversificar as suas estratégias de ensino.

Un stable (ou ensemble indépendant) est un ensemble de sommets qui sont deux à deux non adjacents. De nombreux résultats classiques en optimisation combinatoire portent sur le nombre de stabilité (défini comme la plus grande taille d'un stable), et les stables se classent certainement parmi les structures les plus simples et fondamentales en théorie des graphes.<p><p>La thèse est divisée en deux parties, toutes deux liées à la notion de stables dans un graphe. Dans la première partie, nous étudions un problème de coloration de graphes, c'est à dire de partition en stables, où le but est de minimiser l'entropie de la partition. C'est une variante du problème classique de minimiser le nombre de couleurs utilisées. Nous considérons aussi une généralisation du problème aux couvertures d'ensembles. Ces deux problèmes sont appelés respectivement minimum entropy coloring et minimum entropy set cover, et sont motivés par diverses applications en théorie de l'information et en bioinformatique. Nous obtenons entre autres une caractérisation précise de la complexité de minimum entropy set cover :le problème peut être approximé à une constante lg e (environ 1.44) près, et il est NP-difficile de faire strictement mieux. Des résultats analogues sont prouvés concernant la complexité de minimum entropy coloring.<p><p>Dans la deuxième partie de la thèse, nous considérons les graphes dont le nombre de stabilité augmente dès qu'une arête est enlevée. Ces graphes sont dit être "alpha-critiques", et jouent un rôle important dans de nombreux domaines, comme la théorie extrémale des graphes ou la combinatoire polyédrique. Nous revisitons d'une part la théorie des graphes alpha-critiques, donnant à cette occasion de nouvelles démonstrations plus simples pour certains théorèmes centraux. D'autre part, nous étudions certaines facettes du polytope des ordres totaux qui peuvent être vues comme une généralisation de la notion de graphe alpha-critique. Nous étendons de nombreux résultats de la théorie des graphes alpha-critiques à cette famille de facettes.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

This thesis is primarily focused on problems in extremal combinatorics, although we will also consider some questions of analytic and algorithmic nature. The d-dimensional hypercube is the graph with vertex set {0,1}^d where two vertices are adjacent if they differ in exactly one coordinate. In Chapter 2 we obtain an upper bound on the 'saturation number' of Q_m in Q_d. Specifically, we show that for m &ge; 2 fixed and d large there exists a subgraph G of Q_d of bounded average degree such that G does not contain a copy of Q_m but, for every G' such that G &subne; G' &sube; Q_d, the graph G' contains a copy of Q_m. This result answers a question of Johnson and Pinto and is best possible up to a factor of O(m). In Chapter 3, we show that there exists &epsilon; &gt; 0 such that for all k and for n sufficiently large there is a collection of at most 2^{(1-&epsilon;)k} subsets of [n] which does not contain a chain of length k+1 under inclusion and is maximal subject to this property. This disproves a conjecture of Gerbner, Keszegh, Lemons, Palmer, P&aacute;lv&ouml;lgyi and Patk&oacute;s. We also prove that there exists a constant c &isin; (0,1) such that the smallest such collection is of cardinality 2^{(1+o(1))^ck} for all k. In Chapter 4, we obtain an exact expression for the 'weak saturation number' of Q_m in Q_d. That is, we determine the minimum number of edges in a spanning subgraph G of Q_d such that the edges of E(Q_d)\E(G) can be added to G, one edge at a time, such that each new edge completes a copy of Q_m. This answers another question of Johnson and Pinto. We also obtain a more general result for the weak saturation of 'axis aligned' copies of a multidimensional grid in a larger grid. In the r-neighbour bootstrap process, one begins with a set A₀ of 'infected' vertices in a graph G and, at each step, a 'healthy' vertex becomes infected if it has at least r infected neighbours. If every vertex of G is eventually infected, then we say that A₀ percolates. In Chapter 5, we apply ideas from weak saturation to prove that, for fixed r &ge; 2, every percolating set in Q_d has cardinality at least (1+o(1))(d choose r-1)/r. This confirms a conjecture of Balogh and Bollob&aacute;s and is asymptotically best possible. In addition, we determine the minimum cardinality exactly in the case r=3 (the minimum cardinality in the case r=2 was already known). In Chapter 6, we provide a framework for proving lower bounds on the number of comparable pairs in a subset S of a partially ordered set (poset) of prescribed size. We apply this framework to obtain an explicit bound of this type for the poset &Vscr;(q,n) consisting of all subspaces of &Fopf;_qⁿordered by inclusion which is best possible when S is not too large. In Chapter 7, we apply the result from Chapter 6 along with the recently developed 'container method,' to obtain an upper bound on the number of antichains in &Vscr;(q,n) and a bound on the size of the largest antichain in a p-random subset of &Vscr;(q,n) which holds with high probability for p in a certain range. In Chapter 8, we construct a 'finitely forcible graphon' W for which there exists a sequence (&epsilon;_i)^&infin;_i=1 tending to zero such that, for all i &ge; 1, every weak &epsilon;_i-regular partition of W has at least exp(&epsilon;_i^-2/2^{5log&lowast;&epsilon;_i^-2}) parts. This result shows that the structure of a finitely forcible graphon can be much more complex than was anticipated in a paper of Lov&aacute;sz and Szegedy. For positive integers p,q with p/q &VerticalSeparator;&ge; 2, a circular (p,q)-colouring of a graph G is a mapping V(G) &rarr; &Zopf;_p such that any two adjacent vertices are mapped to elements of &Zopf;_p at distance at least q from one another. The reconfiguration problem for circular colourings asks, given two (p,q)-colourings f and g of G, is it possible to transform f into g by recolouring one vertex at a time so that every intermediate mapping is a p,q-colouring? In Chapter 9, we show that this question can be answered in polynomial time for 2 &le; p/q &LT; 4 and is PSPACE-complete for p/q &ge; 4.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-06-01T10:57:51Z No. of bitstreams: 2 Dissertação - Matheus Rudolfo Diedrich Ullmann - 2016.pdf: 1264745 bytes, checksum: 65f8378224bd7fd700216a920f2da7a0 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-06-01T11:00:53Z (GMT) No. of bitstreams: 2 Dissertação - Matheus Rudolfo Diedrich Ullmann - 2016.pdf: 1264745 bytes, checksum: 65f8378224bd7fd700216a920f2da7a0 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-06-01T11:00:53Z (GMT). No. of bitstreams: 2 Dissertação - Matheus Rudolfo Diedrich Ullmann - 2016.pdf: 1264745 bytes, checksum: 65f8378224bd7fd700216a920f2da7a0 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2016-02-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The MassiveOpenOnlineCourses(MOOCs)areonlinecourseswithopenenrollment that involvingahugeamountofstudentsfromdifferentlocations,withdifferentback- grounds andinterests.Thelargenumberofstudentsimpliesahugeandunmanageable number ofinteractions.Thisfact,alongwiththedifferentinterestsofstudents,resulting in low-qualityinteractions.Duetothelargenumberofstudents,alsobecomesunviable composition manuallylearninggroups.DuetothesecharacteristicspresentinMOOCs, a methodforforminggroupswasdevelopedinthiswork,asanattempttoattendthedi- chotomy existsbetweenthecollective,whichinvolvestheformationofanonlinelearning community onamassivescale,andindividual,withdifferentinterests,priorknowledge and expectationsanddifferentleadershipprofiles.Fortheformationofgroups,anadapta- tion ofParticleSwarmOptimizationalgorithmwasproposedbasedonthreecriteria,kno- wledge level,interestsandleadershipprofiles,formingthengroupswithdifferentlevels of knowledge,similarinterestsanddistributedleadership,providingbetterinteractionand knowledgeconstruction.Werecreatedtwovariationsoftheproblem,withfivestudents and theothersix.Basedoncomputationaltests,thealgorithmdemonstratedthatableto attend thegroupingcriteriainasatisfactorycomputingtimeandismoreefficientthanthe model randomgroupsformation.Thetestsalsodemonstratedthatthealgorithmisrobust taking intoaccountthevariousdatasetsanditerationsvariations.Toevaluatethequality of interactionsandknowledgebuildingingroupsformedbythemethod,Acasestudy wasconducted;andfortheanalysisofthecollecteddiscourses,itwastakenasthebasis twomodelsofdiscourseanalysisfoundintheliterature.Theresultsofthecasestudy demonstrated thatthegroupsformedbytheproposedmethodachievedthebestresultsin the interactionsandknowledgeconstruction,whencomparedwithgroupsthatdonotuse it. / Os Massive OpenOnlineCourses (MOOCs) sãocursos online com inscriçõesabertas que envolvemumaenormequantidadedeestudantesdediferenteslocalidades,comdife- rentes backgrounds e interesses.Ograndenúmerodealunosimplicaemumaenormee não gerenciávelquantidadedeinterações.Estefato,juntamentecomosinteressesdife- rentes dosalunos,resultaeminteraçõesdebaixaqualidade.Devidoàgrandequantidade de alunos,tambémtorna-seinviávelacomposiçãodegruposdeaprendizagemdeforma manual. DevidoàessascaracterísticaspresentesnosMOOCs,ummétodoparaformação de gruposfoidesenvolvidonestetrabalho,comoumatentativaparaatenderadicoto- mia queexisteentreocoletivo,queenvolveaformaçãodeumacomunidade online de aprendizagem emumaescalamaciça,eoindividual,comdiferentesinteresses,conhe- cimentos prévioseexpectativasecomdiferentesperfisdeliderança.Paraaformação dos grupos,umaadaptaçãodoalgoritmo ParticleSwarmOptimization foi propostacom base emtrêscritérios,níveldeconhecimento,interesseseperfisdeliderança,formando então gruposcomníveisdeconhecimentodiferentes,interessessemelhanteseliderança distribuída,proporcionandoumamelhorinteraçãoeconstruçãodeconhecimento.Foram criadas duasvariaçõesdoproblema,umacomcincoalunoseoutracomseis.Combase em testescomputacionais,oalgoritmodemonstrouqueconsegueatenderoscritériosde agrupamento emumtempodecomputaçãosatisfatórioeémaiseficientequeomodelode formação degruposaleatório.Ostestesdemonstraramtambémqueoalgoritmoérobusto levandoemcontaosvariadosconjuntosdedadosevariaçõesdeiterações.Paraavaliara qualidade dasinteraçõeseaconstruçãodeconhecimentonosgruposformadospelomé- todo, umestudodecasofoirealizado;eparaaanálisedosdiscursoscoletados,tomou-se como basedoismodelosdeanálisedediscursopresentesnaliteratura.Oresultadodo estudo decasodemonstrouqueosgruposformadospelométodopropostoobtiveramos melhores resultadosnasinteraçõeseconstruçãodoconhecimento,quandocomparados com osgruposquenãooutilizaram.

Indiana University-Purdue University Indianapolis (IUPUI) / Phormia regina (Meigen), commonly known as the black blow fly is a dipteran that belongs to the family Calliphoridae. Calliphorids play an important role in various research fields including ecology, medical studies, veterinary and forensic sciences. P. regina, a non-model organism, is one of the most common forensically relevant insects in North America and is typically used to assist in estimating postmortem intervals (PMI). To better understand the roles P. regina plays in the numerous research fields, we re-constructed its genome using next generation sequencing technologies. The focus was on generating a reference genome through de novo assembly of high-throughput short read sequences. Following assembly, genetic markers were identified in the form of microsatellites and single nucleotide polymorphisms (SNPs) to aid in future population genetic surveys of P. regina. A total 530 million 100 bp paired-end reads were obtained from five pooled male and female P. regina flies using the Illumina HiSeq2000 sequencing platform. A 524 Mbp draft genome was assembled using both sexes with 11,037 predicted genes. The draft reference genome assembled from this study provides an important resource for investigating the genetic diversity that exists between and among blow fly species; and empowers the understanding of their genetic basis in terms of adaptations, population structure and evolution. The genomic tools will facilitate the analysis of genome-wide studies using modern genomic techniques to boost a refined understanding of the evolutionary processes underlying genomic evolution between blow flies and other insect species.