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Eckert, Andreas. "Contributing to develop contributions : - a metaphor for teaching in the reform mathematics classroom." Doctoral thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-64024.
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This thesis aims at contributing to the theoretical research discourse on teaching mathematics. More precise, to explore a teacher’s role and actions while negotiating meaning of mathematical objects in discursive transformative practices in mathematics. The focus is to highlight the teacher as an active contributor to the classroom mathematical discourse, having an important role in shaping the mathematics. At the same time, the teacher is acknowledged as an individual who learns and develops as a lesson and semester progress. Three research papers illustrate the state, at that time, of an inductive analysis of three teachers, teaching a series of lessons based on probability theory at two Swedish primary schools. The teachers worked together with the students to explore an unknown sample space, made up out of an opaque bottle with coloured marbles within that showed one marble at each turn of the bottle. They had to construct mathematical tools together to help them solve the mystery. The analysis focused on teacher–student interactions during this exploration, revealing complex connections in the process of teaching. The three papers presented the development of a theoretical framework named Contributing to Develop Contributions (CDC). The frameworks’ fundamental idea is that teachers learn as they teach, using the teaching metaphor learning to develop learning. That metaphor was developed, in light of the ongoing empirical analysis, into CDC by drawing on a theoretical idea that learning can be viewed as contributing to the collaborative meaning making in the classroom. Teaching and teacher learning are described and understood as reflexive processes in relation to in-the-moment teacher-student interaction. Contributing to develop contributions consists of three different ways of contributing. The analytical categories illustrate how students’ opportunities to contribute to the negotiation of mathematical meaning are closely linked to teachers’ different ways of contributing. The different ways are Contributing one’s own interpretations of mathematical objects, Contributing with others’ interpretations of mathematical objects, and Contributing by eliciting contributions. Each way of contributing was found to have the attributes Transparency, Role-taking and Authority. Together, these six categories show teacher– student interaction as a complex dynamical system where they draw on each other and together negotiate meaning of mathematical objects in the classroom. This thesis reveals how the teaching process can be viewed in terms of learning on different levels. Learning as thought of in terms of contributing to the negotiation of meaning in the moment-to-moment interaction in the classroom. By contributing you influence the collective’s understanding as well as your own. A teacher exercises and develops ways of contributing to the negotiation of meaning of mathematical objects, in order to develop students’ contributions. In a wider perspective, the analysis showed development over time in terms of transformation. The teachers were found to have transformed their understanding of classroom situations in light of the present interactions. Contributing to the negotiation of meaning in the classroom was understood as a process in such transformation, in the ever ongoing becoming of a mathematics teacher.
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Heninger, Alicia Marie. "Ambiguous Student Contributions and Teacher Responses to Clarifiable Ambiguity in Secondary Mathematics Classrooms." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8471.
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Different types of ambiguous student contributions occur in mathematics classrooms. In this study I identified (1) different types of ambiguous student contributions and (2) the different ways teachers respond to one particular kind of ambiguous contribution, clarifiable ambiguity. Note that clarifiable ambiguity is ambiguity that stems from a student who uses an unclear referent in their contribution and can be clarified in the moment by the particular student. Literature has focused only on ambiguity that has the potential to further the development of mathematical concepts and has only theorized about teacher responses to this specific type of ambiguity. This study identified an additional three types of ambiguous student contributions: Student Appropriation of Teacher Ambiguity, Irrelevant Ambiguity, and General Ambiguity. It was important to identify all the different types of ambiguous student contributions because teacher responses should likely be different to the different types of ambiguity. In addition, through analyzing the teacher responses to the clarifiably ambiguous student contributions, this study found that teachers addressed the clarifiably ambiguous student contributions about half the time. When the teachers did address the clarifiable ambiguity, the majority of the time the teacher clarified the ambiguity themselves with the most common response being the teacher honed in on the clarifiably ambiguity and asked for confirmation from the student on the accuracy of the clarification.
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Marcus, Sherry Elizabeth 1966. "Contributions to higher recursion theory." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/28018.
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Seetapun, David. "Contributions to recursion theory." Thesis, University of Cambridge, 1991. https://www.repository.cam.ac.uk/handle/1810/251510.
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Carlström, Jesper. "Partiality and Choice : Foundational Contributions." Doctoral thesis, Stockholm University, Department of Mathematics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-475.
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The subject of the thesis is foundational aspects of partial functions (Papers 1, 2 & 4) and some choice principles (Papers 3 & 4) in the context of constructive mathematics.
Paper 1 studies the inversion functions of commutative rings. The foundational problem of having them only partially defined is overcome by extending them to total functions. This cannot be done constructively unless the rings themselves are extended at the same time. We study such extensions, called wheels. It is investigated how identities for wheels relate to identities for commutative rings.
Paper 2 studies the foundations of partial functions in Martin-Löf's type theory according to the view of subsets as propositional functions, in particular in connection with equivalence relations that the functions are supposed to preserve. The first and second isomorphism theorems of algebra are verified, showing that our approach is flexible enough for some natural mathematical proofs to be carried out.
Paper 3 shows that the difference between the principles of intensional and extensional choice can be described as the principle of excluded middle plus a certain mild extensionality principle, which follows from the principle that functions are identical if they are identical at every point.
Paper 4 studies a constructive calculus of indefinite and definite descriptions. It has the property that it can be interpreted straightforwardly in type theory with all terms referring to individuals. In this respect it differs from other constructive calculi of descriptions, which are known to be conservative extensions of description-free calculi but for which descriptions cannot be interpreted as referring to individuals in general.
The appendix includes a predicative version of Birkhoff's theorem. It states that if a class of algebras is closed under homomorphic images, subalgebras and products and contains a set-indexed family of algebras that satisfies the same identities as the class, then the class can be axiomatized by a set of equations.
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Ferreira, Jose Antonio de Sousa Jorge. "Some contributions to stochastic modelling." Thesis, University of Sheffield, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312790.
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Marais, Magdaleen Suzanne. "Contributions to centralizers in matrix rings." Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/5154.
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Thesis (PhD (Mathematics))--University of Stellenbosch, 2010.ENGLISH ABSTRACT: THE concept of a k-matrix in the full 2 2 matrix ring M2(R=hki), where R is an arbitrary unique factorization domain (UFD) and k is an arbitrary nonzero nonunit in R, is introduced. We obtain a concrete description of the centralizer of a k-matrix bB in M2(R=hki) as the sum of two subrings S1 and S2 ofM2(R=hki), where S1 is the image (under the natural epimorphism fromM2(R) toM2(R=hki)) of the centralizer in M2(R) of a pre-image of bB, and where the entries in S2 are intersections of certain annihilators of elements arising from the entries of bB. Furthermore, necessary and sufficient conditions are given for when S1 S2, for when S2 S1 and for when S1 = S2. It turns out that if R is a principal ideal domain (PID), then every matrix in M2(R=hki) is a k-matrix for every k. However, this is not the case in general if R is a UFD. Moreover, for every factor ring R=hki with zero divisors and every n > 3 there is a matrix for which the mentioned concrete description is not valid. Finally we provide a formula for the number of elements of the centralizer of bB in case R is a UFD and R=hki is finite.
AFRIKAANSE OPSOMMING: DIE konsep van ’n k-matriks in die volledige 2 2 matriksring M2(R=hki), waar R ’n willekeurige unieke faktoriseringsgebied (UFG) en k ’n willekeurige nie-nul nie-inverteerbare element in R is, word bekendgestel. Ons verkry ’n konkrete beskrywing van die sentraliseerder van ’n k-matriks bB in M2(R=hki) as die som van twee subringe S1 en S2 van M2(R=hki), waar S1 die beeld (onder die natuurlike epimorfisme van M2(R) na M2(R=hki)) van die sentraliseerder in M2(R) van ’n trubeeld vanbB is, en die inskrywings van S2 die deursnede van sekere annihileerders van elemente afkomstig van die inskrywings van bB is. Verder word nodige en voldoende voorwaardes gegee vir wanneer S1 S2, vir wanneer S2 S1 en vir wanneer S1 = S2. Dit blyk dat as R ’n hoofideaalgebied (HIG) is, dan is elke matriks in M2(R=hki) ’n k-matriks vir elke k. Dit is egter nie in die algemeen waar indien R ’n UFG is nie. Meer nog, vir elke faktorring R=hki met nuldelers en elke n > 3 is daar ’n matriks waarvoor die bogenoemde konkrete beskrywing nie geldig is nie. Laastens word ’n formule vir die aantal elemente van die sentraliseerder van bB verskaf, indien R ’n UFG en R=hki eindig is.
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Liu, Fu Ph D. Massachusetts Institute of Technology. "Contributions to the theory of Ehrhart polynomials." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/34542.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.Includes bibliographical references (p. 89-91).
In this thesis, we study the Ehrhart polynomials of different polytopes. In the 1960's Eugene Ehrhart discovered that for any rational d-polytope P, the number of lattice points, i(P,m), in the mth dilated polytope mP is always a quasi-polynomial of degree d in m, whose period divides the least common multiple of the denominators of the coordinates of the vertices of P. In particular, if P is an integral polytope, i(P, m) is a polynomial. Thus, we call i(P, m) the Ehrhart (quasi-)polynomial of P. In the first part of my thesis, motivated by a conjecture given by De Loera, which gives a simple formula of the Ehrhart polynomial of an integral cyclic polytope, we define a more general family of polytopes, lattice-face polytopes, and show that these polytopes have the same simple form of Ehrhart polynomials. we also give a conjecture which connects our theorem to a well-known fact that the constant term of the Ehrhart polynomial of an integral polytope is 1. In the second part (joint work with Brian Osserman), we use Mochizuki's work in algebraic geometry to obtain identities for the number of lattice points in different polytopes. We also prove that Mochizuki's objects are counted by polynomials in the characteristic of the base field.
by Fu Liu.
Ph.D.
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Worthing, Rodney A. (Rodney Alan). "Contributions to the variational theory of convection." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/10577.
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Lee, Yoonweon. "Contributions to regularized determinants of elliptic operators /." The Ohio State University, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487864485229135.
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Lee, Doobum. "Contributions to rational homotopy theory of S¹-spaces /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487676847117724.
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Moher, Michael L. "Contributions to the theory of product-limit estimators." Thesis, University of Ottawa (Canada), 1989. http://hdl.handle.net/10393/5929.
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The product-limit estimator is shown to be a strongly uniformly consistent estimator of the distribution function of a renewal process which started long before the commencement of observation. This product-limit estimator is based on the censored data obtained from independent realizations of such a process in one of two scenarios: one observation per renewal process, and multiple observations per renewal process. In the former scenario a lower bound on the rate of convergence is obtained.
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Wong, Tityik 1962. "Contributions to the theory of stochastic orders." Diss., The University of Arizona, 1996. http://hdl.handle.net/10150/290627.
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This dissertation adds some new results to the theory of stochastic orders. Chapter 1 contains definitions and known results that are related to our study. In Chapter 2, we introduce two new stochastic orders based on ratios of Laplace transforms, and study various properties of the new orders. Among the many properties we discover, the most interesting ones are the relations between the new orders and some existing stochastic orders. In Chapter 3, we obtain various stochastic comparison results of random extrema, that is, the maxima and minima of samples with random sizes. Some results in Chapter 2 find their applications here. In Chapter 4, we study the preservation of various stochastic orders (including the new orders introduced in Chapter 2) under random mapping by point processes. Chapter 5 contains results concerning the preservation of multivariate stochastic orders under shock models. In Chapter 6 we study the preservation of multivariate stochastic orders under random mapping by point processes. Examples and applications of main theorems are presented throughout the dissertation.
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Remenyi, Norbert. "Contributions to Bayesian wavelet shrinkage." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/45898.
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This thesis provides contributions to research in Bayesian modeling and shrinkage in the wavelet domain. Wavelets are a powerful tool to describe phenomena rapidly changing in time, and wavelet-based modeling has become a standard technique in many areas of statistics, and more broadly, in sciences and engineering. Bayesian modeling and estimation in the wavelet domain have found useful applications in nonparametric regression, image denoising, and many other areas. In this thesis, we build on the existing
techniques and propose new methods for applications in nonparametric regression, image denoising, and partially linear models.
The thesis consists of an overview chapter and four main topics. In Chapter 1, we provide an overview of recent developments and the current status of Bayesian wavelet shrinkage research. The chapter contains an extensive literature review consisting of almost 100 references. The main focus of the overview chapter is on nonparametric regression, where the observations come from an unknown function contaminated with Gaussian noise. We present many methods which employ model-based and adaptive shrinkage of the wavelet coefficients through Bayes rules. These includes new developments such as dependence models, complex wavelets, and Markov chain Monte Carlo (MCMC) strategies. Some applications of Bayesian wavelet shrinkage, such as curve classification, are discussed.
In Chapter 2, we propose the Gibbs Sampling Wavelet Smoother (GSWS), an adaptive wavelet denoising methodology. We use the traditional mixture prior on the wavelet coefficients, but also formulate a fully Bayesian hierarchical model in the wavelet domain accounting for the uncertainty of the prior parameters by placing hyperpriors on them. Since a closed-form solution to the Bayes estimator does not exist, the procedure is computational, in which the posterior mean is computed via MCMC simulations. We show how to efficiently develop a Gibbs sampling algorithm for the proposed model. The developed procedure is fully Bayesian, is adaptive to the underlying signal, and provides good denoising performance compared to state-of-the-art methods. Application of the method is illustrated on a real data set arising from the analysis of metabolic pathways, where an iterative shrinkage procedure is developed to preserve the mass balance of the metabolites in the system. We also show how the methodology can be extended to complex wavelet bases.
In Chapter 3, we propose a wavelet-based denoising methodology based on a Bayesian hierarchical model using a double Weibull prior. The interesting feature is that in contrast to the mixture priors traditionally used by some state-of-the-art methods, the wavelet coefficients are modeled by a single density. Two estimators are developed, one based on the posterior mean and the other based on the larger posterior mode; and we show how to calculate these estimators efficiently. The methodology provides good denoising performance, comparable even to state-of-the-art methods that use a mixture prior and an empirical Bayes setting of hyperparameters; this is demonstrated by simulations on standard test functions. An application to a real-word data set is also considered.
In Chapter 4, we propose a wavelet shrinkage method based on a neighborhood of wavelet coefficients, which includes two neighboring coefficients and a parental coefficient. The methodology is called Lambda-neighborhood wavelet
shrinkage, motivated by the shape of the considered neighborhood. We propose a Bayesian hierarchical model using a contaminated exponential prior on the total mean energy in the Lambda-neighborhood. The hyperparameters in the model are estimated by the empirical Bayes method, and the posterior mean, median, and Bayes factor are obtained and used in the estimation of the total mean energy. Shrinkage of the neighboring coefficients is based on the ratio of the estimated and observed energy. The proposed methodology is comparable and often superior to several established wavelet denoising methods that utilize neighboring information, which is demonstrated by extensive simulations. An application to a real-world data set from inductance plethysmography is considered, and an extension to image denoising is discussed.
In Chapter 5, we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for nonparametric components with various degrees of smoothness. A hierarchical Bayes model is formulated on the parameters of this representation, where the estimation and variable selection is performed by a Gibbs sampling procedure. For both the parametric and nonparametric part of the model we are using point-mass-at-zero contamination priors with a double exponential spread distribution. In this sense we extend the model of Chapter 2 to partially linear models. Only a few papers in the area of partially linear wavelet models exist, and we show that the proposed methodology is often superior to the existing methods with respect to the task of estimating model parameters. Moreover, the method is able to perform Bayesian variable selection by a stochastic search for the parametric part of the model.
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Jang, Chang Young. "Contributions to the theory and applications of Hermite methods." Thesis, Southern Methodist University, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3725268.
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An analysis of dispersion and dissipation properties of Hermite methods applied to linear hyperbolic equations in one and two dimensional space is discussed. We employed two approaches for this analysis. First, we derive a modified equation to approximate the leading order dissipation errors in the Hermite scheme. Second, we numerically compute the dispersion relation of discrete Fourier modes of the scheme by a modal analysis. Numerical results are presented to illustrate the resolution requirements of Hermite methods. We also discuss an implementation of Hermite methods on overlapping grids. Here we investigate the accuracy of the solution to linear acoustics in a two-dimensional disk. Numerical results show that Hermite methods accurately propagate waves without a need of artificial dissipation on overlapping regions. In support of large-scale computations of compressible flows, we study the stability of Hermite methods for hyperbolic-parabolic equations and also experiment with various methods for treating product of nonlinearities.
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McNeil, Weatha Gale. "Educational contributions of David Eugene Smith /." Access Digital Full Text version, 1986. http://pocketknowledge.tc.columbia.edu/home.php/bybib/1080979x.
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Reeve, Fiona Jane Helen. "Contributions to the theory of factorized groups." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/110622/.
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In chapter 1 we begin by describing certain group theoretical concepts which appear during the course of this thesis. We also supply a brief survey of results concerning factorized groups, relating them to our investigations. In chapter 2, section 2.2, we consider groups which possess a triple factorization. We show that if a Cernikov group is factorized by three nilpotent subgroups it is itself nilpotent. It is then possible to generalize this result to a wider class of infinite groups, denoted by Ǽ In section 2.3 we continue this theme by examining groups which have a triple factorization by three abelian subgroups. If such a group has finite abelian total rank then it must be nilpotent. In section 2.4 we investigate the circumstances under which a subgroup inherits the factorization of the group. We show that if a Cernikov group is factorized by two abelian subgroups, then its Fitting subgroup factorizes. Once again this result holds for the class Ǽ, furthermore we are able to show that the Hirsch-Plotkiu radical also factorizes. Chapter 3 examines this question in relation to the formation subgroups of a group. Let § denote a formation of finite soluble groups as defined in section 3.1. We begin by reviewing the existence and behaviour of the L§ -covering subgroups and L§ -normalizers of a periodic (LŊ)Ø-group. Then, by taking § to be the formation of finite nilpotent groups, we prove that, if such a group is factorized by two nilpotent subgroups, then there is an L§ -covering subgroup which also factorizes. By specializing to Cernikov groups we are able to show that the above holds for an arbitrary saturated formation §. In the final chapter of this thesis we consider the situation where the product of two abelian subgroups of a group G is not itself a group. We then examine a subgroup M of G which lies in the product set. By imposing extra conditions we are able to produce some bounds on the exponent of M in terms of those of the factors. Lastly we show that if the torsion-free nilpotent group G is generated by two infinite cyclic subgroups then a subgroup which lies in their product is abelian.
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Char, Shobha Gopinath. "Contributions to the study of continuous functors /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487262825076951.
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Zhu, Haolong. "Contributions to some areas in reliability theory." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185993.
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This work consists of some contributions to several areas in reliability theory. Chapter 1 is a short summary of the results obtained in this work with a brief overview of related areas. In Chapter 2, a model for k-out-of-n systems with n dependent components is studied. Sufficiency conditions on the conditional failure rate functions are given which imply that the first failure time of such a system is IFR (increasing failure rate). This result contains an earlier result of Esary and Proschan (1963) as a special case. Chapter 3 focuses on the block replacement policy, one of the most popular maintenance policies. Several new results which connect the properties of the block replacement policy with the properties of the corresponding renewal function and the excess lifetime are obtained. Some applications and relationships between these new results and some well known results are included. Chapter 4 deals with a model for discrete dependent maintenance reliability systems (DDMRS). We identify the conditions on the discrete conditional transition probabilities under which the two performance sequences associated with two DDMRS's are comparable in stochastic ordering. Further results and applications are discussed. In Chapter 5, several results on the properties of first failure times of some discrete dependent reliability systems (with or without maintenance) are presented.
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Li, Zhenkun Ph D. Massachusetts Institute of Technology. "Contributions to sutured monopole and sutured instanton Floer homology theories." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/126928.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 261-267).
In this thesis, we present the development of some aspects of sutured monopole and sutured instanton Floer homology theories. Sutured monopole and instanton Floer homologies were introduced by Kronheimer and Mrowka. They are the adaption of monopole and instanton Floer theories to the case of balanced sutured manifolds, which are compact oriented 3-manifolds together with some special data on the boundary called the suture. We construct the gluing and cobordism maps in these theories, construct gradings associated to properly embedded surfaces inside the balanced sutured manifolds, and use these tools to further construct minus versions of knot Floer homologies in monopole and instanton theories. These constructions contribute to laying down a solid basis in sutured monopole and sutured instanton Floer homology theories, upon which we could develop further applications.
by Zhenkun Li.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics
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Silva, Isabel Maria Marques da. "Contributions to the analysis of discrete-valued time series." Tese, Universidade do Porto. Reitoria, 2005. http://hdl.handle.net/10216/9742.
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Dissertação de Doutoramento em Matemática Aplicada apresentada à Faculdade de Ciências da Universidade do PortoSéries temporais de contagem, categóricas ou binárias são exemplos de séries temporaisde valor discreto que aparecem frequentemente na prática. No entanto, uma vezque estas séries apresentam valores que pertencem a conjuntos finitos ou infinitosnumeráveis, os métodos tradicionais utilizados na análise de séries temporais não sãoadequados.Vários modelos para processos estacionários com distribuição marginal discreta têmsido propostos. Um desses modelos, particularmente usado para séries de contagem,são os processos Auto-Regressivos de valor INteiro de ordem p, denotados por INAR(p).Na primeira parte desta tese, os processos INAR são estudados quer no contexto deuma única série temporal, quer de réplicas da mesma série temporal. As principaiscaracterísticas destes modelos são apresentadas e exploradas de modo a obter métodosde estimação mais robustos. Por exemplo, as estatísticas de ordem superior forneceminformação adicional sobre os processos INAR porque estes são processos não lineares.Assim, são propostos dois métodos de estimação baseados em momentos e cumulantesde terceira ordem. Por outro lado, a utilização do critério de Whittle como métodode estimação é justificada através da propriedade mixing dos processos INAR. Mais,o critério automático para selecção de ordem baseado na versão corrigida do Critériode Informação de Akaike (AICC) é estabelecido para processos INAR. Extensos estudosde simulação investigam e comparam o desempenho dos diferentes estimadorespropostos, assim como do critério de selecção de ordem.Dados reais de contagem (duas séries temporais associadas a aplicações médicas eum conjunto de réplicas relacionadas com a astronomia) são analisados considerandoa metodologia subjacente aos modelos INAR. Verifica-se que a classe dos modelosINAR é adequada para a descrição dos dados.Existem séries temporais que apresentam mudanças abruptas, formas descontínuasou cujos valores pertencem a um conjunto finito discreto. Nestes casos, ...
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Eriksson, Jonatan. "Emmy Noethers Contributions to Symmetries and Conservation Laws 2000." Thesis, Uppsala University, Department of Mathematics, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-122542.
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Soto, José Antonio Ph D. Massachusetts Institute of Technology. "Contributions on secretary problems, independent sets of rectangles and related problems." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/67819.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 187-198).
We study three problems arising from different areas of combinatorial optimization. We first study the matroid secretary problem, which is a generalization proposed by Babaioff, Immorlica and Kleinberg of the classical secretary problem. In this problem, the elements of a given matroid are revealed one by one. When an element is revealed, we learn information about its weight and decide to accept it or not, while keeping the accepted set independent in the matroid. The goal is to maximize the expected weight of our solution. We study different variants for this problem depending on how the elements are presented and on how the weights are assigned to the elements. Our main result is the first constant competitive algorithm for the random-assignment random-order model. In this model, a list of hidden nonnegative weights is randomly assigned to the elements of the matroid, which are later presented to us in uniform random order, independent of the assignment. The second problem studied is the jump number problem. Consider a linear extension L of a poset P. A jump is a pair of consecutive elements in L that are not comparable in P. Finding a linear extension minimizing the number of jumps is NP-hard even for chordal bipartite posets. For the class of posets having two directional orthogonal ray comparability graphs, we show that this problem is equivalent to finding a maximum independent set of a well-behaved family of rectangles. Using this, we devise combinatorial and LP-based algorithms for the jump number problem, extending the class of bipartite posets for which this problem is polynomially solvable and improving on the running time of existing algorithms for certain subclasses. The last problem studied is the one of finding nonempty minimizers of a symmetric submodular function over any family of sets closed under inclusion. We give an efficient O(ns)-time algorithm for this task, based on Queyranne's pendant pair technique for minimizing unconstrained symmetric submodular functions. We extend this algorithm to report all inclusion-wise nonempty minimal minimizers under hereditary constraints of slightly more general functions.
by José Antonio Soto.
Ph.D.
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Lewis, Owen Leslie. "Mathematical Investigation of Hydrodynamic Contributions to Amoeboid Cell Motility in Physarum polycephalum." Thesis, University of California, Davis, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3685252.
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In this work, we investigate the role of intracellular fluid flow in the migration of Physarum polycephalum. We develop two distinct models. Initially, we model the intracellular space of a physarum plasmodium as a peristaltic chamber. We derive a PDE relating the deformation of the chamber boundary and the flux of fluid along the chamber center line. We then solve this PDE for two distinct boundary deformations and evaluate the characteristic stress associated with the peristaltic flow. We compare the derived stress, as well as the relative phase of the deformation and flow waves, with values seen in experiments. Second, we develop a poro-elastic model of the interior of physarum that accounts for cytoskeletal structure, as well as adhesive interactions with the substrate. We develop this model within a framework similar to the Immersed Boundary method, which readily allows for computer simulation. We then use this model to simulate cell crawling across a range of parameters that characterize the coordination of adhesion to the substrate. We identify a spatio-temporal form of adhesion coordination that is consistent with experiments. We also show that this form is both efficient and robust, when compared to similar forms of adhesion coordination.
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Lantuéjoul, Christian. "Morphologie mathématique, géostatistique et stéréologie : contributions à l'élaboration de modèles." Habilitation à diriger des recherches, Université Paris Sud - Paris XI, 2008. http://tel.archives-ouvertes.fr/tel-00430389.
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Le présent document donne un aperçu des sujets sur lesquels j'ai travaillé pendant un peu plus de trente ans à l'Ecole des Mines, dans les domaines de la morphologie mathématique et de la géostatistique. Issus tous deux de la nécessité d'examiner des jeux de données à des échelles différentes, ces deux domaines ont ensuite évolué dans des directions assez différentes, l'un vers l'analyse d'image l'autre vers les statistiques spatiales. Mon séjour en morphologie mathématique de 1972 à 1984 fut pour moi l'occasion de participer à l'essor d'une discipline nouvelle, dans laquelle tout était ouvert. J'espère que l'application du chapitre 1 rend compte de cet état d'esprit. En 1985, mon passage en géostatistique m'a ouvert de nouveaux horizons. Initiée en Afrique du Sud par les travaux précurseurs de H. Sichel et D. Krige, cette discipline a été complètement reformalisée par G. Matheron. De vocation au départ minière, elle s'est progressivement enrichie au contact d'applications nouvelles (pétrole, environnement, génie forestier, météo, halieutique, épidémiologie, science des matériaux...), faisant à leur tour surgir des problématiques nouvelles. Les chapitres 3 et 4 témoignent de cette évolution avec la construction de modèles stochastiques spatiaux et la conception d'algorithmes de simulation conditionnelle. A la charnière des deux domaines gure la stéréologie. Elle s'avère incontournable dans la mesure où les données morphologiques ou géostatistiques sont souvent disponibles dans un espace de dimension inférieure à l'espace de travail (lames minces ou sections polies pour des images microscopiques, forages dans un réservoir pétrolier...). Quelques travaux de stéréologie sont présentés au chapitre 2. Finalement une liste de quelques problèmes sur lesquels il conviendrait de faire porter nos efforts fait l'objet du dernier chapitre.
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Silva, Isabel Maria Marques da. "Contributions to the analysis of discrete-valued time series." Doctoral thesis, Universidade do Porto. Reitoria, 2005. http://hdl.handle.net/10216/9742.
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Dissertação de Doutoramento em Matemática Aplicada apresentada à Faculdade de Ciências da Universidade do PortoSéries temporais de contagem, categóricas ou binárias são exemplos de séries temporaisde valor discreto que aparecem frequentemente na prática. No entanto, uma vezque estas séries apresentam valores que pertencem a conjuntos finitos ou infinitosnumeráveis, os métodos tradicionais utilizados na análise de séries temporais não sãoadequados.Vários modelos para processos estacionários com distribuição marginal discreta têmsido propostos. Um desses modelos, particularmente usado para séries de contagem,são os processos Auto-Regressivos de valor INteiro de ordem p, denotados por INAR(p).Na primeira parte desta tese, os processos INAR são estudados quer no contexto deuma única série temporal, quer de réplicas da mesma série temporal. As principaiscaracterísticas destes modelos são apresentadas e exploradas de modo a obter métodosde estimação mais robustos. Por exemplo, as estatísticas de ordem superior forneceminformação adicional sobre os processos INAR porque estes são processos não lineares.Assim, são propostos dois métodos de estimação baseados em momentos e cumulantesde terceira ordem. Por outro lado, a utilização do critério de Whittle como métodode estimação é justificada através da propriedade mixing dos processos INAR. Mais,o critério automático para selecção de ordem baseado na versão corrigida do Critériode Informação de Akaike (AICC) é estabelecido para processos INAR. Extensos estudosde simulação investigam e comparam o desempenho dos diferentes estimadorespropostos, assim como do critério de selecção de ordem.Dados reais de contagem (duas séries temporais associadas a aplicações médicas eum conjunto de réplicas relacionadas com a astronomia) são analisados considerandoa metodologia subjacente aos modelos INAR. Verifica-se que a classe dos modelosINAR é adequada para a descrição dos dados.Existem séries temporais que apresentam mudanças abruptas, formas descontínuasou cujos valores pertencem a um conjunto finito discreto. Nestes casos, ...
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Silva, Isabel Maria Marques da. "Contributions to the analysis of discrete-valued time series." Doctoral thesis, Universidade do Porto. Reitoria, 2005. https://repositorio-aberto.up.pt/handle/10216/91963.
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Séries temporais de contagem, categóricas ou binárias são exemplos de séries temporais de valor discreto que aparecem frequentemente na prática. No entanto, uma vez que estas séries apresentam valores que pertencem a conjuntos finitos ou infinitos numeráveis, os métodos tradicionais utilizados na análise de séries temporais não são adequados.Vários modelos para processos estacionários com distribuição marginal discreta têm sido propostos. Um desses modelos, particularmente usado para séries de contagem, são os processos Auto-Regressivos de valor INteiro de ordem p, denotados por INAR(p). Na primeira parte desta tese, os processos INAR são estudados quer no contexto de uma única série temporal, quer de réplicas da mesma série temporal. As principais características destes modelos são apresentadas e exploradas de modo a obter métodos de estimação mais robustos. Por exemplo, as estatísticas de ordem superior fornecem informação adicional sobre os processos INAR porque estes são processos não lineares. Assim, são propostos dois métodos de estimação baseados em momentos e cumulantes de terceira ordem. Por outro lado, a utilização do critério de Whittle como método de estimação é justificada através da propriedade mixing dos processos INAR. Mais, o critério automático para selecção de ordem baseado na versão corrigida do Critério de Informação de Akaike (AICC) é estabelecido para processos INAR. Extensos estudos de simulação investigam e comparam o desempenho dos diferentes estimadores propostos, assim como do critério de selecção de ordem.Dados reais de contagem (duas séries temporais associadas a aplicações médicas e um conjunto de réplicas relacionadas com a astronomia) são analisados considerando a metodologia subjacente aos modelos INAR. Verifica-se que a classe dos modelos INAR é adequada para a descrição dos dados.Existem séries temporais que apresentam mudanças abruptas, formas descontínuas ou cujos valores pertencem a um conjunto finito discreto. Nestes casos, faz mais sentido (estatístico) aplicar a análise espectral de Walsh-Fourier para caracterizar os dados através das funções de Walsh (ondas quadradas). É um procedimento análogo à análise de Fourier, que caracteriza a variação periódica de séries temporais contínuas.Considerando que durante uma intervenção cirúrgica um paciente passa por vários níveis de relaxamento muscular, na segunda parte desta tese investiga-se em que medida a análise de Walsh-Fourier pode contribuir para melhorar a construção de um sistema de controlo adaptativo, em tempo real, para o bloqueio neuromuscular. Verifica-se que a análise espectral de Walsh-Fourier caracteriza a resposta induzida por um bolus administrado no início da anestesia. Esta caracterização conduz à estimação robusta dos parâmetros do controlador e é adequada para uso em ambiente clínico.Discrete-valued time series are common in practice, yet methods for their analysis have been developed only recently. The fact that the variables take values on a finite or countably infinite set renders the traditional representations of dependence either impossible or impractical.Several models for stationary processes with discrete marginal distributions have been proposed. The first part of this thesis is concerned with the INteger-valued AutoRegressive, INAR(p), process, both in the context of a single and of replicated time series. The principal characteristics of the INAR(p) processes are reviewed and explored in order to improve the analysis of this process by providing new and powerful estimation methods for the parameters. For instance, since the INAR(p) process is not linear, high-order statistics provide additional information for the process. Thus, two estimation methods based on third-order moments and cumulants are proposed. On the other hand, the Whittle estimation is justified by the mixing property satisfied by the INAR(p) process. Furthermore, an automatic criterion for order selection, based on the corrected version of the Akaike Information Criterion (AICC), is established in the INAR framework. The small sample properties of the criterion for order selection as well as of the estimators proposed are comprehensively analyzed using simulation.INAR processes are fitted to three data sets: two single time series concerning with medical applications and a set of two replicates of astronomical time series. It is found that the class of INAR models is suitable for the description of the data.Walsh-Fourier spectral analysis (WFA) is a procedure used to analyze time series, specially when sharp discontinuities and changes of level occur in the data. The procedure is similar to the well known Fourier analysis, that characterizes the periodic variation in a continuous signal. Considering that during the surgical intervention a patient attains different levels of neuromuscular blockade, in the second part of the thesis the contribution of WFA to the design of an on-line adaptive control system for neuromuscular blockade is investigated.WFA provides a characterization of the neuromuscular blockade response induced by an initial bolus given at the beginning of anaesthesia, leading to robust controller parameter estimation suitable for use in a clinical environment.
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Bucicovschi, Bogdan. "Contributions to the complex powers and zeta function of Elliptic Pseudodifferntial Operators /." The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488187763847262.
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Hedin, Anton. "Contributions to Pointfree Topology and Apartness Spaces." Doctoral thesis, Uppsala universitet, Algebra, geometri och logik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-152068.
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The work in this thesis contains some contributions to constructive point-free topology and the theory of apartness spaces. The first two papers deal with constructive domain theory using formal topology. In Paper I we focus on the notion of a domain representation of a formal space as a way to introduce generalized points of the represented space, whereas we in Paper II give a constructive and point-free treatment of the domain theoretic approach to differential calculus. The last two papers are of a slightly different nature but still concern constructive topology. In paper III we consider a measure theoretic covering theorem from various constructive angles in both point-set and point-free topology. We prove a point-free version of the theorem. In Paper IV we deal with issues of impredicativity in the theory of apartness spaces. We introduce a notion of set-presented apartness relation which enables a predicative treatment of basic constructions of point-set apartness spaces.
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Leeves, Alastair. "Contributions to the theory of subnormal subgroups and factorized groups." Thesis, University of Warwick, 1991. http://wrap.warwick.ac.uk/108583/.
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The purpose of this thesis is to investigate some problems concerning products of groups, that is given a group G with subgroups H and K. We investigate what effect the structures of H and K have on the the structure of the product HK. In chapters 2 and 3 we consider the case where the product is itself a group and in chapter 4 we consider the case where the product need not be a group.
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Schuerger, Houston S. "Contributions to Geometry and Graph Theory." Thesis, University of North Texas, 2020. https://digital.library.unt.edu/ark:/67531/metadc1707341/.
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In geometry we will consider n-dimensional generalizations of the Power of a Point Theorem and of Pascal's Hexagon Theorem. In generalizing the Power of a Point Theorem, we will consider collections of cones determined by the intersections of an (n-1)-sphere and a pair of hyperplanes. We will then use these constructions to produce an n-dimensional generalization of Pascal's Hexagon Theorem, a classical plane geometry result which states that "Given a hexagon inscribed in a conic section, the three pairs of continuations of opposite sides meet on a straight line." Our generalization of this theorem will consider a pair of n-simplices intersecting an (n-1)-sphere, and will conclude with the intersections of corresponding faces lying in a hyperplane. In graph theory we will explore the interaction between zero forcing and cut-sets. The color change rule which lies at the center of zero forcing says "Suppose that each of the vertices of a graph are colored either blue or white. If u is a blue vertex and v is its only white neighbor, then u can force v to change to blue." The concept of zero forcing was introduced by the AIM Minimum Rank - Special Graphs Work Group in 2007 as a way of determining bounds on the minimum rank of graphs. Later, Darren Row established results concerning the zero forcing numbers of graphs with a cut-vertex. We will extend his work by considering graphs with arbitrarily large cut-sets, and the collections of components they yield, to determine results for the zero forcing numbers of these graphs.
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Navarrete, Ulloa Jairo Alfredo. "Algebraic models of conceptual metaphor: contributions to the understanding of mathematics learning processes." Tesis, Universidad de Chile, 2013. http://www.repositorio.uchile.cl/handle/2250/113481.
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Doctor en Ciencias de la Ingeniería, Mención Modelación MatemáticaThis thesis studies a human cognitive phenomenon called Conceptual Metaphor in the context of mathematics learning and reasoning. Metaphor enables the understanding of an abstract concept called target, e.g. numbers, in terms of a more concrete concept called source, e.g. piles of can-dies. Often, inferences from the source are carried to the target and applied there yielding some conclusions about the target. This is known as reasoning by analogy. Empirical evidence indicates that metaphor enhances learning. Converging evidence is pro-vided by working scientists who report the use of analogies while developing their theories. On the other hand, some people advise against its usage in education. They argue that politicians and communicators often lead people into erroneous conclusions by using metaphor, and then, analo-gies undermine objective reasoning. This discussion highlights the need for research to shed light into the learning mechanics underlying metaphor in order to understand its scope and limitations. This work presents a formal model of metaphor which can be used as a framework to study learning by analogy. Since the model is abstract, we use Chapter 1 to make ideas more concrete: we use our formalism for analize deeply a well known example. Along these lines, Chapter 5 presents formalizations of other metaphors frequently encountered in mathematics teaching. The model is built in Chapter 4 where the source and the target of a metaphor are formalized by a key concept named domain. Some results of this chapter are accompanied by cognitive in-terpretations, as for example, Theorems 40, 41, 42, and Proposition 26 can be seen as descriptions of how an analogy carries reasonings from its source to its target. Also, Theorems 30 and 31 sug-gest models for the process of learning by analogy. Finally, Chapter 4 presents some theoretical constructions such as products and coproducts of domains. Our metaphor model relates two domains, each one defined as a mixture of language and semantics. Most results of Chapter 4 need the premise that the two involved languages are compatible . Mathematically, they need a map able to preserve the structure determined by a syntactical operation called substitution. This compatibility notion is characterized for the case of language terms in Chapter 2 by applying unification theory and graph theory. And in Chapter 3, this compatibilitynotion is characterized for the case of the language formulas by adapting the methods of Chapter 2. Finally, one Appendix (Relational Spaces) presents another approach to study metaphor. There, domains are defined with semantics only, leaving language aside. Most of the results emphasized above are lost or at least weakened suggesting that the abstract information provided by symbols and the recursion provided by the grammar of the language are necessary to mimic metaphor s behavior. This observation, together with other results of this thesis, might point to a relation between the recursion property of human languages1 and the ability of learning by analogy. 1 The linguist Noam Chomsky claims that recursion is the only human component of the faculty of language [49].
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Jaume, Mathieu. "Contributions à la sémantique de la programmation logique." Phd thesis, Ecole des Ponts ParisTech, 1999. http://tel.archives-ouvertes.fr/tel-00005594.
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La notion de preuves en programmation logique est examinée à deux niveaux différents. D'un point de vue externe, la "théorie classique" de la programmation logique est complètement formalisée dans le calcul des constructions inductives. Après avoir envisagé le problème de la définition de fonctions partielles dans un système dans lequel seules les fonctions totales sont représentables, l'unification est obtenue en réutilisant une preuve formelle existante portant sur un sur-ensemble des termes. Les propriétés fondamentales des SLD-résolution sont alors formalisées. Le niveau de détail imposé par la mécanisation des preuves considérées a mis en relief la complexité cachée de certaines preuves: le mécanisme de renommage est traité de manière explicite, transformant ainsi certaines certitudes théoriques en réalités. D'un point de vue interne, les preuves SLD,finies ou infinies, sont comparées à celles que l'on peut obtenir, par induction ou par co-induction, à partir des clauses d'un programme logique vues comme des règles d'inférence. Dans le cas fini la correspondance est complète ("ce que calcule un programme est prouvable") tandis que dans le cas infini, certains objets non calculables sont toutefois prouvables. Les propriétés classiques des définitions co-inductives et la comparaison de certaines dérivations infinies à des termes de preuve d'un type co-inductif, se révèlent utiles tant pour expliquer les résultats d'incomplétude d'approches existantes que pour définir une sémantique valide et complète pour une classe de dérivations infinies (précisement celles qui ne construisent pas de termes infinis).(résumé de l'auteur)
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Besse, Ian Matthew. "Modeling caveolar sodium current contributions to cardiac electrophysiology and arrhythmogenesis." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/463.
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Proper heart function results from the periodic execution of a series of coordinated interdependent mechanical, chemical, and electrical processes within the cardiac tissue. Central to these processes is the action potential - the electrochemical event that initiates contraction of the individual cardiac myocytes. Many models of the cardiac action potential exist with varying levels of complexity, but none account for the electrophysiological role played by caveolae - small invaginations of the cardiac cell plasma membrane. Recent electrophysiological studies regarding these microdomains reveal that cardiac caveolae function as reservoirs of 'recruitable' sodium ion channels. As such, caveolar channels constitute a substantial and previously unrecognized source of sodium current that can significantly influence action potential morphology. In this thesis, I formulate and analyze new models of cardiac action potential which account for these caveolar sodium currents and provide a computational venue in which to develop and test new hypotheses. My results provide insight into the role played by caveolar ionic currents in regulating the electrodynamics of cardiac myocytes and suggest that in certain pathological cases, caveolae may play an arrhythmogenic role.
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Du, Dong. "Contributions to Persistence Theory." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1338304358.
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Gravejat, Philippe. "Quelques contributions à l'analyse mathématique de l'équation de Gross-Pitaevskii et du modèle de Bogoliubov-Dirac-Fock." Habilitation à diriger des recherches, Université Paris Dauphine - Paris IX, 2011. http://tel.archives-ouvertes.fr/tel-00706916.
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Ce mémoire présente plusieurs contributions quant à l'analyse mathématique de l'équation de Gross-Pitaevskii et du modèle de Bogoliubov-Dirac-Fock. Au sujet de l'équation de Gross-Pitaevskii, l'analyse commence par la construction variationnelle des ondes progressives minimisantes. La preuve de la stabilité orbitale du soliton noir en dimension un, et la description de la limite transsonique des ondes progressives minimisantes vers les états fondamentaux de l'équation de Kadomtsev-Petviashvili en dimension deux, viennent compléter cette construction. L'analyse s'achève par la dérivation rigoureuse du régime ondes longues vers l'équation de Korteweg-de Vries en dimension un. Quant au modèle de Bogoliubov-Dirac-Fock, il s'agit de construire les états fondamentaux du modèle réduit, puis de préciser le processus de renormalisation de leur charge, lequel autorise le calcul d'un développement asymptotique de la densité de charges du vide polarisé, qui est cohérent avec les développements perturbatifs de l'électrodynamique quantique.
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bellaassali, said. "Contributions à l'optimisation multicritère." Phd thesis, Université de Bourgogne, 2003. http://tel.archives-ouvertes.fr/tel-00004337.
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Le thème central de cette thèse est l'étude des problèmes d'optimisation multicritère avec ou sans dynamique ainsi que le problème général de Bolza et ses applications. Après avoir rappelé quelques concepts d'analyse non lisse, on étudie dans la première partie de cette thèse l'existence des multiplicateurs de Lagrange pour des problèmes d'optimisation multicritère en dimension infinie en termes d'une préférence générale. En introduisant la notion de la régularité d'une préférence et en utilisant la condition de qualification calme, on établit l'existence des multiplicateurs de Karush-Kuhn-Tucker. Ceci nous permet d'exhiber des multiplicateurs de Fritz-John en termes du sous-différentiel approché au sens de Ioffe. En conséquence on obtient des résultats similaires pour le cas d'une préférence définie par un cône convexe ou bien par une fonction d'utilité. On établit dans la deuxième partie des conditions nécessaires d'optimalité pour le problème général de Bolza en termes du sous différentiel Fréchet limite sans aucune hypothèse de convexité. Ce résultat nous permet de retrouver les résultats de Vinter-Zheng, Ioffe-Rockafellar et d'établir le principe du maximum avec une nouvelle inclusion d'Euler-Lagrange. On applique ce dernier aux problèmes isopérimetriques, au modèle général de croissance économique de Ramsey et à un problème de génie chimique. En utilisant la notion de préférence de la première partie et les résultats de la deuxième, on établit dans la troisième partie des conditions nécessaires d'optimalité et des conditions Hamiltoniennes d'un problème d'optimisation multicritère dynamique. Enfin on donne des résultats similaires pour le cas d'une préférence définie par un cône convexe ou une fonction d'utilité.
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Taron, Maxime. "Recalage & Modélisation de Formes avec Incertitudes Contributions et Applications à la Segmentation avec a priori Statistique." Phd thesis, Ecole des Ponts ParisTech, 2007. http://pastel.archives-ouvertes.fr/pastel-00004044.
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Nous avons pu observer récemment d'importants progrès dans les techniques d'imageries médicales qui ont été accompagnés par le développement d'outils informatiques de prévisualisation et d'aide automatique au diagnostic. La réalisation de tels outils nécessite généralement la création d'un modèle mathématique capable de représenter les organes et dont la construction est divisée en trois étapes : (i) choisir et extraire les structures à étudier, (ii) choisir un modèle mathématique adapté à la représentation de ces structures particulières, (iii) estimer les variations des paramètres du modèle ainsi choisi. Cette thèse aborde donc chacune de ces taches de fac¸on originale. La modélisation des organes est décrite au travers de déformations et nécessite une étape préalable de recalage de forme. Ceci implique la définition d'une forme de référence ainsi que d'un ensemble de déformations. Cette thèse introduit l'utilisation d'incertitudes sur le recalage de formes : définies a l'aide d'une matrice de covariance dans l'espace des déformations, elles indiquent localement la fiabilité du recalage obtenu. Ensuite vient la modélisation des variations de formes, obtenue à partir d'un ensemble d'apprentissage représentant différentes instances de l'organe étudié. Cette thèse apporte à la phase de modélisation des déformations, les informations sur les erreurs de recalage au travers de la propagation des incertitudes. La contribution finale de la thèse touche à la segmentation de ces structures par un modèle déformable, guidé par le modèle de forme sur lequel les incertitudes dues au modèle sont évaluées. La segmentation cardiaque du ventricule gauche en imagerie scanner, ainsi que le corps calleux en imagerie à résonance magnétique ont été considérés pour démontrer les performances de cette approche.
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Velasco-Forero, Santiago. "Contributions en morphologie mathématique pour l'analyse d'images multivariées." Phd thesis, Ecole Nationale Supérieure des Mines de Paris, 2012. http://pastel.archives-ouvertes.fr/pastel-00820581.
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Cette thèse contribue au domaine de la morphologie mathématique et illustre comment la statistique multivariée et les techniques d'apprentissage numérique peuvent être exploitées pour concevoir un ordre dans l'espace des vecteurs et pour inclure les résultats d'opérateurs morphologiques au processus d'analyse d'images multivariées. En particulier, nous utilisons l'apprentissage supervisé, les projections aléatoires, les représentations tensorielles et les transformations conditionnelles pour concevoir de nouveaux types d'ordres multivariés et de nouveaux filtres morphologiques pour les images multi/hyperspectrales. Nos contributions clés incluent les points suivants :* Exploration et analyse d'ordre supervisé, basé sur les méthodes à noyaux.* Proposition d'un ordre nonsupervisé, basé sur la fonction de profondeur statistique calculée par projections aléatoires. Nous commençons par explorer les propriétés nécessaires à une image pour assurer que l'ordre ainsi que les opérateurs morphologiques associés, puissent être interprétés de manière similaire au cas d'images en niveaux de gris. Cela nous amènera à la notion de décomposition en arrière plan. De plus, les propriétés d'invariance sont analysées et la convergence théorique est démontrée.* Analyse de l'ordre supervisé dans les problèmes de correspondance morphologique de patrons, qui correspond à l'extension de l'opérateur tout-ou-rien aux images multivariées grâce à l'utilisation de l'ordre supervisé.* Discussion sur différentes stratégies pour la décomposition morphologique d'images. Notamment, la décomposition morphologique additive est introduite comme alternative pour l'analyse d'images de télédétection, en particulier pour les tâches de réduction de dimension et de classification supervisée d'images hyperspectrales de télédétection.* Proposition d'un cadre unifié basé sur des opérateurs morphologiques, pour l'amélioration de contraste et pour le filtrage du bruit poivre-et-sel.* Introduction d'un nouveau cadre de modèles Booléens multivariés en utilisant une formulation en treillis complets. Cette contribution théorique est utile pour la caractérisation et la simulation de textures multivariées.
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Saven, Jessica Lynn. "Do dollars matter beyond demographics? District contributions to reading and mathematics growth for students with disabilities." Thesis, University of Oregon, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3717466.
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Growth modeling in education has focused on student characteristics in multilevel growth accountability models and has rarely included financial variables. In this dissertation, relations of several demographic and financial characteristics of Oregon school districts to the reading and mathematics growth of students receiving special education services in Grades 3-8 were explored after accounting for student level demographic characteristics. Previous research indicated that three variables were potentially related to student growth: district level aggregated student demographics, district geography (e.g., location in a remote area), and district funding. Three sources of data were used to investigate these relationships: institutional data reported by the Oregon Department of Education, the Common Core of Data gathered by the National Center for Education Statistics, and Oregon Assessment of Knowledge and Skills test data collected as part of the National Center on Assessment and Accountability in Special Education.
Multi-level models of student growth across Grades 3-8 were constructed for reading and mathematics, with time (level-1) nested within students (level-2) and districts (level-3). Results demonstrated that although student-level demographic factors account for the majority of meaningful differences in student growth, both district demographic characteristics and financial investment in students were related to growth for students who received special education services.
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Saven, Jessica. "Do Dollars Matter Beyond Demographics? District Contributions to Reading and Mathematics Growth for Students with Disabilities." Thesis, University of Oregon, 2015. http://hdl.handle.net/1794/19306.
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Growth modeling in education has focused on student characteristics in multilevel growth accountability models and has rarely included financial variables. In this dissertation, relations of several demographic and financial characteristics of Oregon school districts to the reading and mathematics growth of students receiving special education services in Grades 3-8 were explored after accounting for student level demographic characteristics. Previous research indicated that three variables were potentially related to student growth: district level aggregated student demographics, district geography (e.g., location in a remote area), and district funding. Three sources of data were used to investigate these relationships: institutional data reported by the Oregon Department of Education, the Common Core of Data gathered by the National Center for Education Statistics, and Oregon Assessment of Knowledge and Skills test data collected as part of the National Center on Assessment and Accountability in Special Education.
Multi-level models of student growth across Grades 3-8 were constructed for reading and mathematics, with time (level-1) nested within students (level-2) and districts (level-3). Results demonstrated that although student-level demographic factors account for the majority of meaningful differences in student growth, both district demographic characteristics and financial investment in students were related to growth for students who received special education services.
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Bouvier, Patrick. "Contributions à l'étude de l'effet Hawking pour des modèles en interaction." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00937087.
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L'effet Hawking prédit, dans un espace-temps décrivant l'effondrement d'une étoile à symétrie sphérique vers un trou noir de Schwarzschild, qu'un observateur statique, situé à l'infini, observera un flux thermal de particules quantiques à la température de Hawking. La première démonstration mathématique de l'effet Hawking pour des champs quantiques libres est due à Bachelot, dont le travail sur les champs de Klein-Gordon a été ensuite étendu aux champs de Dirac, d'abord par Bachelot lui-même, puis par Melnyk. Ces travaux, placés dans le cadre d'une symétrie sphérique, ont été complétés par Häfner, qui donna une démonstration rigoureuse de l'effet Hawking pour des champs de Dirac, autour d'une étoile s'effondrant vers un trou noir de Kerr. Le but de cette thèse est d'étudier l'effet Hawking non plus dans un modèle de champs quantiques libres, où les problèmes posés se ramènent à l'étude d'équations aux dérivées partielles linéaires, mais dans un modèle de champs de Dirac en interaction. L'interaction est supposée à support compact, statique, et localisée à l'extérieur de l'étoile. Nous choisissons de traiter le cas d'un modèle jouet, dans un espace-temps de dimension 1+1, situation à laquelle on peut se ramener, au moins dans le cas libre, en utilisant la symétrie sphérique du problème. Nous étudions le comportement de champs de fermions de Dirac dans différentes situations : d'abord, pour une observable suivant l'effondrement de l'étoile ; puis pour une observable stationnaire ; enfin, pour une interaction dépendante du temps, localisée près de la surface de l'étoile. Dans chacun de ces cas, nous montrons l'existence de l'effet Hawking et donnons l'état limite correspondant.
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Rivoirard, Jacques. "De l'analyse structurale à la modélisation des ressources naturelles : contributions géostatistiques." Habilitation à diriger des recherches, Université Pierre et Marie Curie - Paris VI, 2012. http://tel.archives-ouvertes.fr/tel-00664238.
Full textAbstract:
Mes travaux de recherche s'inscrivent dans le développement d'outils géostatistiques pour mieux décrire, comprendre et modéliser la distribution spatiale de ressources naturelles : ressources minières, pétrolières, halieutiques. J'ai parcouru, chemin faisant, les grands secteurs de la géostatistique que sont l'analyse structurale, l'estimation linéaire par krigeage ou cokrigeage, les méthodes non-linéaires, et enfin les simulations. Toute étude géostatistique commence par l'analyse structurale, dans laquelle on cherche à mettre en évidence la structure spatiale des variables en jeu, à l'aide d'outils structuraux tel le variogramme. J'ai étudié de façon empirique l'influence déterminante que pouvait avoir le choix du support de travail (surface ou volume élémentaire sur lequel est mesurée la variable), ainsi que l'émergence difficile d'une structure variographique. En halieutique, l'approche transitive (basée sur un échantillonnage à maille régulière ignorant les frontières), et certaines statistiques apparentées, se révèlent appropriées pour décrire des populations spatiales possédant quelques valeurs très fortes et des frontières diffuses. L'analyse structurale est naturellement cruciale lorsqu'il s'agit de mettre en évidence des liens structuraux entre variables, notamment hiérarchiques. Ainsi la taille des harengs plutôt que leur age, au Nord de l'Ecosse, ou la proportion de minerai plutôt que le métal, dans un gisement d'uranium en petites veines, apparaissent-elles comme pré-éminentes. Le croisement de variables, et les méthodes d'estimation associées (cokrigeage, analyse krigeante), se révèlent particulièrement adaptés pour filtrer des séries de données, sismiques par exemple. Les techniques de cartographie que sont krigeage et cokrigeage posent en pratique un problème majeur, celui du choix du voisinage utilisé pour faire l'estimation, c'est-à-dire le sous-ensemble des données qui est utilisé pour estimer la valeur inconnue en un point. Un voisinage trop petit dans l'estimation de blocs miniers s'accompagne d'un biais conditionnel, responsable d'une surestimation des blocs considérés comme riches. J'ai proposé des outils permettant de mieux choisir le voisinage. Par ailleurs, l'utilisation d'un voisinage glissant peut générer des discontinuités indésirables : une solution générale a été proposée. Enfin je me suis intéressé aux conditions dans lesquelles certaines versions simplifiées de cokrigeage, par exemple le cokrigeage collocalisé, ne s'accompagnent pas de perte d'information. Les problèmes de dépassement de seuils nécessitent, pour le moins, le recours à la géostatistique non-linéaire, basée sur des transformations de la variable en gaussienne ou indicatrices, par exemple. Dans certaines circonstances, le cokrigeage d'indicatrices s'obtient par krigeage de résidus d'indicatrices. Un modèle d'écrêtage permet une estimation adaptée à la présence de valeurs extrêmes, comme dans les gisements d'or. Par ailleurs, une méthode d'ajustement d'histogramme a été développée, permettant en particulier de combler de manière controlée les queues de distribution insuffisamment informées. En mine, la technique dite de conditionnement uniforme permet de prédire la distribution des valeurs de blocs à l'intérieur d'un panneau minier à partir de la seule teneur de ce panneau : la méthode a été étendue au cas multivariable. Les simulations géostatistiques permettent de représenter des phénomènes dans leur variabilité spatiale, et donc d'estimer des quantités complexes. Ainsi a-t-on pu évaluer les ressources récupérables en nodules polymétalliques dans le pacifique Nord, compte tenu de contraintes de pente. De même, l'incertitude sur l'estimation de l'abondance du hareng au Nord de l'Ecosse a pu être chiffrée en combinant différentes sources d'incertitude. Il a fallu pour cela adapter la lassique méthode de simulation transformée gaussienne aux problèmes de valeurs nulles en grand nombre. Quant au modèle résultant du seuillage d'une gaussienne, il permet la simulation de faciès de réservoirs hétérogènes, conditionnée par des données de faciès aux puits. Une technique a été imaginée afin de rendre une telle simulation cohérente avec les fluides observés aux puits. Avec le modèle booléen, les corps sableux sont considérés comme des objets implantés aléatoirement et indépendamment : contraignant dans le cas stationnaire, le modèle est beaucoup plus souple en présence de non-stationnarités, comme c'est généralement le cas des réservoirs hétérogènes. Cependant les simulations génétiques, simulant la genèse des formations géologiques, sont plus adaptées lorsqu'on cherche à reproduire par exemple la géométrie et l'agencement des corps sédimentaires complexes liés aux réservoirs chenalisés méandriformes. Des méthodes de conditionnement ad hoc et l'usage de formules heuristiques s'avèrent alors fort utiles.
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Sriananthakumar, Sivagowry 1968. "Contributions to the theory and practice of hypothesis testing." Monash University, Dept. of Econometrics and Business Statistics, 2000. http://arrow.monash.edu.au/hdl/1959.1/8836.
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Wang, Dongmei. "Some Contributions in Statistical Discrimination of Different Pathogens Using Observations through FTIR." Digital Archive @ GSU, 2009. http://digitalarchive.gsu.edu/math_theses/78.
Full textAbstract:
Fourier Transform Infrared (FTIR) has been use to discriminate different pathogens by signals from cells infected with these versus normal cells as references. To do the statistical analysis, Partial Least Square Regression (PLSR) was utilized to distinguish any two kinds of virus‐infected cells and normal cells. Validation using Bootstrap method and Cross‐validations were employed to calculate the shrinkages of Area Under the ROC Curve (AUC) and specificities corresponding to 80%, 90%, and 95% sensitivities. The result shows that our procedure can significantly discriminate these pathogens when we compare infected cells with the normal cells. On the height of this success, PLSR was applied again to simultaneously compare two kinds of virus‐infected cells and the normal cells. The shrinkage of Volume Under the Surface (VUS) was calculated to do the evaluation of model diagnostic performance. The high value of VUS demonstrates that our method can effectively differentiate virus‐infected cells and normal cells.
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Churchill, Indu Rasika U. "Contributions to Quandle Theory: A Study of f-Quandles, Extensions, and Cohomology." Scholar Commons, 2017. http://scholarcommons.usf.edu/etd/6814.
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Quandles are distributive algebraic structures that were introduced by David Joyce [24] in his Ph.D. dissertation in 1979 and at the same time in separate work by Matveev [34]. Quandles can be used to construct invariants of the knots in the 3-dimensional space and knotted surfaces in 4-dimensional space. Quandles can also be studied on their own right as any non-associative algebraic structures.
In this dissertation, we introduce f-quandles which are a generalization of usual quandles. In the first part of this dissertation, we present the definitions of f-quandles together with examples, and properties. Also, we provide a method of producing a new f-quandle from a given f-quandle together with a given homomorphism. Extensions of f-quandles with both dynamical and constant cocycles theory are discussed. In Chapter 4, we provide cohomology theory of f-quandles in Theorem 4.1.1 and briefly discuss the relationship between Knot Theory and f-quandles.
In the second part of this dissertation, we provide generalized 2,3, and 4- cocycles for Alexander f-quandles with a few examples.
Considering “Hom-algebraic Structures” as our nutrient enriched soil, we planted “quandle” seeds to get f-quandles. Over the last couple of years, this f- quandle plant grew into a tree. We believe this tree will continue to grow into a larger tree that will provide future fruit and contributions.
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Faugeras, Olivier P. "Contributions à la prévision statistique." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2008. http://tel.archives-ouvertes.fr/tel-00370418.
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Dans une première partie, on s'intéresse à la prévision d'une valeur future, non observée, d'un processus stochastique dont la loi est indexée par un paramètre inconnu, à partir des données passées de sa trajectoire. Plus précisément, on montre sur un modèle additif de régression comment on peut découpler, par un dispositif de séparation temporelle, le problème d'estimation du paramètre inconnu de celui du calcul du prédicteur probabiliste, pour obtenir un prédicteur statistique dont on étudie les propriétés de convergence asymptotiques.Dans une seconde partie, on cherche à prédire, au sens d'expliquer, une variable Y par une variable X. Pour cela, on s'intéresse à l'estimation de la densité conditionnelle de Y sachant X = x, à partir d'un n-échantillon de couples de variables (X_i; Y_i). On propose un nouvel estimateur de forme produit, basé sur la transformation de quantile et la fonction de copule, dont on étudie les propriétés de convergence et de normalité asymptotiques. On compare l'estimateur proposé aux estimateurs concurrents de forme quotient et on en propose des modifications et des extensions. Enfin, on étudie les propriétés des prédicteurs associés à cet estimateur, à savoir le mode, la moyenne et les ensembles de niveau conditionnels. Des applications, liens et perspectives sont aussi esquissées.
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Rodgerson, Joanne Kelly. "Contributions to the study of a class of optimal control problems on the matrix lie group SO(3)." Thesis, Rhodes University, 2009. http://hdl.handle.net/10962/d1007199.
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The purpose of this thesis is to investigate a class of four left-invariant optimal control problems on the special orthogonal group SO(3). The set of all control-affine left-invariant control systems on SO(3) can, without loss, be reduced to a class of four typical controllable left-invariant control systems on SO(3) . The left-invariant optimal control problem on SO(3) involves finding a trajectory-control pair on SO (3), which minimizes a cost functional, and satisfies the given dynamical constraints and boundary conditions in a fixed time. The problem is lifted to the cotangent bundle T*SO(3) = SO(3) x so (3)* using the optimal Hamiltonian on so(3)*, where the maximum principle yields the optimal control. In a contribution to the study of this class of optimal control problems on SO(3), the extremal equations on so(3)* (ident ified with JR3) are integrated via elliptic functions to obtain explicit expressions for the solution curves in each typical case. The energy-Casimir method is used to give sufficient conditions for non-linear stability of the equilibrium states.KMBT_363
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Grammont, Laurence. "CONTRIBUTIONS A L'APPROXIMATION NUMERIQUE D'OPERATEURS ET DE LEURS SPECTRES." Habilitation à diriger des recherches, Université Jean Monnet - Saint-Etienne, 2012. http://tel.archives-ouvertes.fr/tel-00867034.
Full textAbstract:
Mes travaux peuvent se diviser en deux thèmes : L'algèbre linéaire numérique. La théorie des opérateurs intégraux. L'algèbre linéaire numérique fut le cadre de ma thèse de doctorat, dédiée aux propriétés spectrales des opérateurs de Sylvester, endomorphismes d'espaces matriciels. J'ai tout naturellement utilisé mes connaissances, mes compétences et mon savoir faire, développés pendant ces années de formation par la recherche, pour attaquer un nouveau problème li e a une notion apparue dans les années 1990 et qui a connu un grand succès dans la communauté de l'algèbre linéaire numérique. Cette notion est celle des pseudospectres qui généralise celle des spectres dans le cadre de la théorie des perturbations. A cette notion est liée celle de rayon de stabilité. Suite a ces travaux sur les pseudospectres et ayant constat e que pour certaines matrices pathologiques, la détermination du pseudospectre était couteuse et entachées d'erreurs importantes, nous avons cherché si l'on ne pouvait pas définir d'autres généralisations du spectre plus facilement calculables. Nous avons étudié un ensemble du plan complexe, contenant les valeurs propres d'une matrice, défini comme un -voisinage des racines du polynome caractéristique. Je me suis ensuite tout naturellement tournée vers un nouveau chalenge, celui du problème polynomial de valeurs propres. Ce sujet s'est développé très récemment. Il y a des questions propres aux problèmes polynomiaux de valeurs propres qui n'ont ete posées qu' a partir des années 2000 et qui n'ont trouvées de premières réponses que cinq ans plus tard. Le domaine des problèmes polynomiaux de valeurs propres est en pleine expansion et beaucoup de problèmes restent a résoudre dans l'avenir. Parallèlement et plus directement li e aux équations matricielles, je me suis intéressée a la notion de stabilité de Lyapunov, tr es utile dans la communauté de la théorie du contrôle. Mon autre domaine de recherche concerne les équations intégrales du point de vue de l'approximation. Des méthodes de discrétisation conduisant a des matrices diagonales sont intéressantes. Ces considérations m'ont conduite à étudier l'approximation d'un équation d'opérateur intégral par une méthode d'ondelettes-vaguelettes. La difficulté de la mise en œuvre numérique m'a dirigée vers l' étude d'autres méthodes.
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Barty, Kengy. "Contributions à la discretisation des contraintes de mesurabilité pour les problèmes d'optimisation stochastique." Phd thesis, Ecole des Ponts ParisTech, 2004. http://tel.archives-ouvertes.fr/tel-00008867.
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Nous nous sommes penchés sur différents aspects des problèmesd'optimisation stochastique qui, à notre connaissance, ont été peu
étudiés. Ainsi, nous nous sommes intéressés au problème de l'effet dual,
puis à la discrétisation des contraintes de mesurabilité, à la
résolution numérique de problèmes avec contraintes en information statique et enfin,
nous avons étudié les conditions d'optimalité d'un problème
d'optimisation stochastique, le but recherché étant de mieux
comprendre comment intervient la contrainte de mesurabilité dans la
caractérisation de la (ou des) solution(s) optimale(s). Notre approche
numérique du problème est originale de deux points de vue :
Elle utilise les topologies sur l'espace des sigma-algèbres
pour mesurer la perte d'information due à la discrétisation de la
contrainte de mesurabilité. L'étude de cet espace nous a permis entre
autres d'apporter de nouveaux résultats qui constituent des éléments
essentiels dans notre étude~;
Nous montrons que l'erreur de discrétisation provient de la
contribution de deux termes d'erreur : une erreur issue de la
discrétisation de la contrainte de mesurabilité et une autre erreur
issue de l'approximation de l'espérance.
Nous donnons dans ce mémoire des résultats asymptotiques de
convergence d'une suite de problèmes discrets vers le problème
d'origine. Nous avons également, sur des problèmes particuliers, des
résultats de type Lipschitz sur la fonction valeur. Par ailleurs,
l'étude des conditions d'optimalité nous a permis d'obtenir deux
possibilités différentes d'approche d'un problème de commande optimale
stochastique.