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Soucie, Tanja, Nikol Radović, Renata Svedrec, and Helena Car. "Using Technology to Discover and Explore Linear Functions and Encourage Linear Modeling." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-80959.
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In our presentation we will show how technology enables us to improve the teaching and learning of linear functions at the middle school level. Through various classroom activities that involve technology such as dynamic geometry software, graphing calculators and Excel, students explore functions and discover basic facts about them on their own. Students then work with real life data and on real life problems to draw graphs and form linear models that correspond to given situations as well as draw inferences based on their models. Participants will receive complete classroom materials for the unit on linear functions.
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Massow, Mareike. "Linear extension graphs and linear extension diameter." Göttingen Cuvillier, 2009. http://d-nb.info/1000129489/04.
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Hernandez, Erika Lyn. "Parameter Estimation in Linear-Linear Segmented Regression." Diss., CLICK HERE for online access, 2010. http://contentdm.lib.byu.edu/ETD/image/etd3551.pdf.
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Dietz, Otto. "Linear and non-linear properties of light." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17474.
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Alle optischen Systeme haben den gleichen Zweck: Sie manipulieren Eigenschaften des Lichts, durch Interaktion mit Materie. In dieser Arbeit werden zwei wichtige Teilaspekte aus diesem Kontext untersucht, im linearen und im nicht-linearen Bereich. In Teil I werden die bekannten Bragg-Reflexionen in neuem Licht betrachtet. Bragg Reflexion findet statt, wenn Licht mit einem periodischen Medium interagiert. Die Bragg-Bedingung verknüpft den Gitterabstand in einem Kristall mit der Wellenlänge, die von ihm reflektiert wird. In dieser Arbeit werden die Bragg Reflexionen in gewellten Wellenleitern untersucht. Es wird gezeigt, dass die Bragg-Bedingung nicht ausreicht, um die Streuung in diesen Wellenleitern zu verstehen. Es wird numerisch und analytisch demonstriert, dass unebene Ränder eine neue Reflexionsbedingung schaffen, die über das einfache Bragg-Bild hinausgeht. Dieser Streueffekt, der Square Gradient Bragg-Mechanismus ist aus statistischen Streuansätzen bekannt. Er hängt mit der Krüummung des Randes zusammen und hat einen starken Einfluss auf die Wellenleitung in diesen Systemen. In dieser Arbeit wird die erste allgemeine Theorie für den Square Gradient Bragg Streumechanismus vorgestellt, die es ermöglicht, Voraussagen für einzelne Wellenleiter mit beliebig deformierten Rändern zu treffen. Eine weitere wichtige Eigenschaft des Lichts wird in Teil II dieser Arbeit untersucht: Die Verschränkung zwischen zwei Photonen. Verschränkung ist ein intuitiv nicht verständliches Phänomen, weil es in der uns umgebenden klassischen Welt kein Analogon hat. Insbesondere verletzt es unsere implizite Annahme eines lokalen Realismus, weil voneinander entfernte Teilchen scheinbar instantan miteinander wechselwirken können. In dieser Arbeit wird eine neue und verstimmbare Quelle für verschränkte Photonen entworfen. Die Photonenpaare werden in nicht-linearen Kristallen erzeugt, aber ihre Verschränkung wird rein geometrisch erzwungen. Dieser geometrische Ansatz erlaubt es, die Frequenz der Photonen einzustellen. Hier übertrifft diese neue Quelle ihre Vorgänger, die ausführlich besprochen werden. Die Verschränkung der erzeugten Photonen wird experimentell nachgewiesen.Any optical experiment, any optical technology is only about one thing: Manipulating the properties of light through interaction with matter. This thesis will address two important issues in this broad context, in the linear and in the non-linear regime. In Part I, the well-known Bragg reflection is revised. Bragg reflection takes place whenever light interacts with a periodic structure. The famous Bragg condition relates the lattice spacing in a crystal to the wavelength which is effectively reflected by that lattice. In this thesis the Bragg reflection in dielectric waveguides is investigated. It is shown that the Bragg condition is not sufficient to describe the scattering situation in waveguides with corrugated boundaries. It is demonstrated, analytically and numerically, that corrugated boundaries cause a new type of reflection condition, which goes beyond the Bragg picture. This scattering mechanism, the Square Gradient Bragg Scattering, is known from statistical scattering approaches. It is connected to the curvature of the boundary and has a strong influence on the wave propagation in these systems. Here the first general theory for Square Gradient Bragg Scattering is presented, which allows for making predictions for single corrugated waveguides with arbitrary boundaries. Another important property of light is investigated in Part II of this thesis: The entanglement of two photons. Entanglement is a counter-intuitive phenomenon, because it has no classical analogy. It especially violates our assumption of local realism, because distant particles seemingly act on each other instantaneously. In this thesis a new tunable and portable source of photon pairs is designed. The photon pairs are created in non-linear crystals, but their entanglement is enforced in a purely geometrical manner. This geometrical approach makes the setup tunable. This is where the new design supersedes its predecessor, which will be discussed in detail. The entanglement of the generated photons is demonstrated experimentally.
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Salgarella, Ester. "Aegean linear script(s) : rethinking the relationship between Linear A and Linear B." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/283184.
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When does a 'continuum' become a divide? My research investigates the genetic relationship between Linear A and Linear B (henceforth LA, LB), two Bronze Age scripts attested on Crete and Mainland Greece and understood to have developed one straight out of the other. By using an interdisciplinary methodology, I integrated linguistic, epigraphic, palaeographic and archaeological evidence, and placed the writing practice in its socio-historical setting. By challenging traditional views, my work has called into question widespread assumptions and interpretative schemes on this relationship. I carried out a systematic assessment of the structural characteristics underlying both systems and a palaeographic examination of their sign inventories. Built on these analyses, I put forward a more fluid model of script development, which takes LA and LB no longer as two separate scripts but as the very same one: the 'Aegean Linear Script'. Over time, this underwent only minimal adaptation when required to meet the needs of another language, arguably in view of the changing socio-political context. This new interpretation is in sharp contrast with the view traditionally held of a strong standardisation process having taken place, which sees LB as mere product of secondary script development. My conclusion has interesting implications not only for the history of the writing tradition on Crete, but also for our appreciation of the contemporary socio-historical context. This view, in turns, opens up new perspectives on the ideology associated with the retention of a script, matters of identity and how identity was negotiated at the very moment when Cretans and Greek-speaking Mainlanders came into closer contact in the Late Bronze Age. I have also noted that in this period the same scenario depicting soft adaptation of motives is witnessed on the side of material culture, displaying meaningful interplay and amalgamation of both Mainland and Cretan traditions.
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Edlund, Ove. "Solution of linear programming and non-linear regression problems using linear M-estimation methods /." Luleå, 1999. http://epubl.luth.se/1402-1544/1999/17/index.html.
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Persson, Jonas. "Linear models of non-linear power system components." Licentiate thesis, KTH, Electrical Systems, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-1415.
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Yesilyurt, Deniz. "Solving Linear Diophantine Equations And Linear Congruential Equations." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-19247.
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This report represents GCD, euclidean algorithm, linear diophantine equation and linear congruential equation. It investigates the methods for solving linear diophantine equations and linear congruential equations in several variables. There are many examples which illustrate the methods for solving equations.
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Milillo, Irene. "Linear and non-linear effects in structure formation." Thesis, University of Portsmouth, 2010. https://researchportal.port.ac.uk/portal/en/theses/linear-and-nonlinear-effects-in-structure-formation(a5115b9e-d7af-4255-83bd-ddb7913c1e31).html.
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The subject matter of this thesis is the formation of large-scale structure in the universe. Most of the study has dealt with the non-linear evolution of cosmological uctuations, focusing on the scalar sector of perturbation theory. The period of transition between the radiation era and the matter era has been largely examined, extending the already known linear results to a nonstandard matter model and to a non-linear analysis. The obtained second order solutions for the matter uctuations variables have been used to find the skewness of the density and velocity distributions, an important statistical estimator measuring the level of non-Gaussianity of a distribution. In the context of cosmological perturbations, a complete Post-Newtonian (1PN) treatment is presented with the aim of obtaining a set of equations suitable in particular for the intermediate scales. The final result agrees with both the non linear Newtonian theory of small scales and the linear general relativistic theory of large scales. Analyzing the limiting cases of our approach to 1PN cosmology, we have clarified the link between the Newtonian theory of gravity and General Relativity. This work is the result of the agreement signed by the Department of Physics, University of Roma Tor Vergata and the Institute of Cosmology and Gravitation, University of Portsmouth, United Kingdom in the formal context of the co-tutela project. The chapters 5, 6 and 7 are the themes of two articles in preparation, that will be shortly submitted: "How the universe got its skewness" - M. Bruni, I.Milillo, K.Koyama; "Post-Newtonian Cosmology" - I. Milillo, D.Bertacca, M. Bruni
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Strandell, Gustaf. "Linear and Non-linear Deformations of Stochastic Processes." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributr], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3689.
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Koch, Frank. "Linear and non-linear measurements in optical fibres." Thesis, Imperial College London, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.399244.
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Marion, Christian. "Linear soundings : 26 fragments of the linear discourse." Thesis, Massachusetts Institute of Technology, 1986. http://hdl.handle.net/1721.1/78958.
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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Architecture; and, (M.C.P.)--Massachusetts Institute of Technology, Dept. of Urban Studies and Planning, February 1987.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ROTCH.
Includes bibliographical references (leaves 194-197).
This text is a follow-up study for a work that focused on squares that was published by the author as Piazza Pulita [Roma, Officina Edizione, 1983]. The purpose of both works is to comment on the production of sense of linear features of the environment. The multidimensional character of these features, which includes economic, sociological, political, psychological and aesthetic, or even exclusively, technical components, make it necessary to approach them heterogeneously. That is, a set of observations that must be used that imply multiple points of view: a plurality of pertinence. For heuristic purposes, these observations are organized from two points of view: -- A roughly chronological point of view according to which the evolution of lines is seen as a means of social organization and cultural expression. -- An experimental point of view that at temps to express the effects of linear features of primarily the built environment. The effects focused on are generally space and time effects. It is the very principle of this research upon the discourses of linearity (and of the text which represents it) that its figures cannot be classified: organized, hierarchized, arranged with a view to an end (a settlement): there are no first figures, no last figures. To let it be understood that there was no question here of a history of line (of a line story) and to discourage the temptation of uniform meaning, it was necessary to choose an absolute insignificant order. Hence, we have subjugated the series of figures (inevitable as any series is, since the text is by its very nature obliged progress) to to a pair of arbitrary factors: that of nomination and that of alphabet. Each of these arbitrary factors is, nonetheless, tempered: one by semantic necessity (among all the nouns in the dictionary, a figure can usually receive only two or three), the other by the age-old convention which decides the number of letters in our alphabet. Hence, we have avoided the wiles of pure chance, which might, indeed, have produced logical sequences; for we must not underestimate the power of chance to engender monsters; the monster in this case, would have emerged from a certain order of figures, a "philosophy of line" where we must look for no more than its affirmation. An approach towards the line rests on simple questions: What is it? What is its nature? Why does it exist? The focus of this research is to perceive explicitly the collective image of lines through its urbanistic production as well as its mode of production representation. An approach to the theme of linearity rather than to the actual street, channel or skyscraper, allows distance in analysis and constructive analogies. To learn means, here, to compare. When one compares an apple and a grapefruit, one learns about fruit. When one compares an apple and a bowling ball, one learns about symbol. When one compares an apple and a car, one learns about object. When one compares different phenomena that share a single characteristic, we learn about this common feature. We describe this world of similarities on the basis of paleological thought, where the line i s a street, the line is an elevator, the line is transportation, the line is time, the line is architecture. These-stories will teach us about the line as a phenomenon. THE SPEED AT WHICH LIFE IS LIVED IN THE PRESENT HISTORICAL POINT HAS CREATED A PERCEPTION OF THE LINEAR ENVIRONMENT, THAT IS PARTIAL AND LIMITED ONLY TO WHAT IS SEEN AT A GIVEN INSTANT. LINES ARE BEING INCREASINGLY EXPERIENCED NOT AS FEATURES OF STRUCTURES, NOT AS PARTS OF A WHOLE, BUT FOR THEIR OWN SAKE AND AS IF FROZEN IN A SINGLE MOMENT IN TIME. IN OTHER WORDS, BOTH APPROACHES LEAD TO THE SAME POINT: LINEARITY IS SUPPORT TO DISAGGREGATION OF SPACE BECAUSE OF THE USE OF ITS POTENTIAL EXTENSIVITY.
by Christian Marion.
M.C.P.
M.S.
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Lampietti, Dario Giovanni. "Foreign exchange markets linear vs. non-linear models /." [Zürich] : [Citibank], 1993. http://www.ub.unibe.ch/content/bibliotheken_sammlungen/sondersammlungen/dissen_bestellformular/index_ger.html.
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MILILLO, IRENE. "Linear and non-linear effects in structure formation." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2010. http://hdl.handle.net/2108/1246.
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La tesi riguarda la formazione di strutture a larga scala nell'universo, cioè l'origine degli addensamenti di materia che hanno portato alla formazione dei cluster di galassie. La maggior parte del lavoro ha riguardato aspetti non lineari della Teoria delle Perturbazioni Cosmologiche, trattando in particolare il periodo di transizione tra epoca della radiazione e epoca della materia. In questo contesto si è considerato un modello non-standard di materia, analizzando il ruolo dell'indice barotropico nell'evoluzione del contrasto di densità .
La nota approssimazione Meszaros è stata generalizzata ad una analisi non lineare che ha permesso di trovare la skewness della distribzione di materia, un importante indice di non-Gaussianità rilevabile dai dati osservativi.
Nel contesto delle perturbazioni cosmologiche è stata formulata la teoria Post-Newtoniana (1PN) con lo scopo di ottenere un set di equazioni valido per ogni range di distanze, in particolare per le scale intermedie. I risultati finali coincidono sia con la teoria lineare relativistica per grandi scale sia con la teoria non lineare Newtoniana per piccole scale; quest'ultima connessione fornisce una chiara visione della relazione fra Relatività Generale e teoria Newtoniana.The subject matter of this thesis is the formation of large-scale structure in the universe, describing the clustering of matter in galaxies and clusters of galax- ies. Most of the study has dealt with the non-linear evolution of cosmological fluctuations, focusing on the scalar sector of perturbation theory. The period of transition between the radiation era and the matter era has been largely examined, extending the already known linear results to a non-standard matter model and to a non-linear analysis. The obtained second order solutions for the matter fluctuations variables have been used to find the skewness of the density and velocity distributions, an important statistic estimator measuring the level of non-Gaussianity of a statistic ensamble. In the contest of cosmological perturbations a complete Post-Newtonian (1PN) treatment is presented with the aim of obtain a set of equations suitable in particular for the intermediate scales. The final result agrees with both the non linear Newtonian theory of small scales and the linear general relativistic theory of large scales. Analyzing the limit cases of our approach to 1PN cosmology, we have clarified the link between the Newtonian theory of gravity and General Relativity.
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Wilbanks, John W. (John Winston). "Linear Unification." Thesis, University of North Texas, 1989. https://digital.library.unt.edu/ark:/67531/metadc500971/.
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Efficient unification is considered within the context of logic programming. Unification is explained in terms of equivalence classes made up of terms, where there is a constraint that no equivalence class may contain more than one function term. It is demonstrated that several well-known "efficient" but nonlinear unification algorithms continually maintain the said constraint as a consequence of their choice of data structure for representing equivalence classes. The linearity of the Paterson-Wegman unification algorithm is shown largely to be a consequence of its use of unbounded lists of pointers for representing equivalences between terms, which allows it to avoid the nonlinearity of "union-find".
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Amaral, Estáquio. "Programação Linear." Master's thesis, Universidade de Aveiro, 2017. http://hdl.handle.net/10773/22201.
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Mestrado em Matemática e AplicaçõesA Programação Linear pode ser considerada uma técnica que permite otimizar funções lineares sujeitas a restrições igualmente lineares. A Programação Linear permite modelar problemas que ocorrem nos mais diversos setores de atividade, como o comércio, a indústria, a gestão de recursos humanos. A disciplina Programação Linear - breve introdução, integra o programa curricular do curso Ensino de Matemática, na Universidade Nacional Timor Lorosa’e, sendo importante para o professor um aprofundamento e uma ampliação do conhecimento matemático nesta área. Assim, o objetivo desta dissertação é fazer um estudo, de modo acessível, da Programação Linear. Neste trabalho são apresentados exemplos de problemas de Programação Linear, bem como explicada a sua resolução algébrica e gráfica. É estudado o método simplex, desenvolvido por Dantzig, para a resolução de problemas de Programação Linear e são referidos alguns aspetos geométricos que permitem dar uma interpretação a estes problemas e às suas soluções. Aborda-se a teoria da dualidade, a pós-otimização e o caso particular do problema de transporte.
Linear Programming can be considered a technique that optimizes a linear function over a feasible set defined by a set of linear constraints. Linear programming allows to model problems that arise in diverse sectors of activity, such as commerce, industry, human resources management. The course “A brief introduction to Linear Programming” is a curricular unit of the Teaching Mathematics degree at the National University of Timor Lorosa’e. It is crucial for the lecturers of this course to deepening and broadening their mathematical knowledge in this area. The objective of this dissertation is to make an accessible text of Linear Programming that can be used by those lectures in their classes. In this dissertation, examples of linear programming problems are presented as well as algebraic and graphical resolution of some of them. In addition, the simplex method developed by Danzig for solving linear programming problems is introduced, and some geometric aspects that allow an interpretation of this method and the corresponding solutions are explored. It is explored the theory of duality, including properties of dual problems, post-optimization, as well as the particular case of transportation problems.
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Campos, Luiz Guilherme Franco Pires de. "Otimização linear." reponame:Repositório Institucional da UFABC, 2016.
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Orientador: Prof. Dr. Jerônimo Cordoni PellegriniDissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2016.
O objetivo deste trabalho é apresentar alguns métodos para a resolução de problemas de programação linear. Iremos definir este tipo de problema e mostrar alguns casos onde pode-se obter uma solução ótima com a ajuda de gráficos. Outra preocupação é mostrar que existem várias aplicações para otimização linear, por esse motivo alguns problemas clássicos serão discutidos e modelados. Para uma melhor compreensão sobre restrições lineares e soluções viáveis, iremos definir conjunto convexo, poliedro e politopo. Algumas situações especiais que podem surgir em otimização serão discutidas, especificamente os casos de problemas inviáveis, ilimitados e degenerados. O Método Simplex, que percorre os vértices do poliedro determinado pelas restrições lineares, será apresentado juntamente com o método das duas fases e alguns exemplos. Para resolver problemas de programação linear inteira, que são aqueles onde restringimos as variáveis de decisão a valores inteiros, o método Branch-and-Bound e Planos de Corte serão apresentados. O caso de matriz totalmente unimodular também será discutido. Finalizando, uma sequência de problemas de programação linear será sugerida, onde professor e aluno do ensino médio terão a oportunidade de discutir, modelar e encontrar a solução ótima destes problemas contando com auxílio de recursos computacionais se necessário.
The aim of this work is to present some methods for solving linear programming problems. We will define this kind of problem and show some cases where you can obtain an optimal solution with the help of graphics. Another concern is to show that there are several applications for linear optimization, therefore some classic problems will be discussed and modeled. For a better understanding about linear constraints and feasible solutions, we will define convex set, polyhedron and polytope. Some special situations that may arise in optimization will be discussed, specifically the cases of unfeasible, unlimited and degenerate problems. The Simplex method, which runs through the vertices of the polyhedron determined by linear constraints, will be presented along with the method of the two phases and some examples. To solve integer programming problems, which are those that restrict the decision variables to integer values, the Branch-and-Bound and Cutting-Plane method will be presented. The case of totally unimodular matrix will also be discussed. Finally, a sequence of linear programming problems is suggested, where teacher and high school student will have the opportunity to discuss, model and find the optimal solution of these problems with help of computer resources if necessary.
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Randell, David. "Bayes linear variance learning for mixed linear temporal models." Thesis, Durham University, 2012. http://etheses.dur.ac.uk/3646/.
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Modelling of complex corroding industrial systems is ritical to effective inspection and maintenance for ssurance of system integrity. Wall thickness and corrosion rate are modelled for multiple dependent corroding omponents, given observations of minimum wall thickness per component. At each inspection, partial observations of the system are considered. A Bayes Linear approach is adopted simplifying parameter estimation and avoiding often unrealistic distributional assumptions. Key system variances are modelled, making exchangeability assumptions to facilitate analysis for sparse inspection time-series. A utility based criterion is used to assess quality of inspection design and aid decision making. The model is applied to inspection data from pipework networks on a full-scale offshore platform.
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Neff, Andrew. "Linear and non-linear control of a quadrotor UAV." Connect to this title online, 2007. http://etd.lib.clemson.edu/documents/1181251774/.
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Mwesigye, Feresiano. "Elementary equivalence of linear orders and coloured linear orders." Thesis, University of Leeds, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.496139.
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Hagan, Richard Peter. "Linear and Non-Linear Aspects of the Multifocal-Electroretinogram." Thesis, University of Liverpool, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.507506.
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Duque, Jose Gerivaldo dos Santos. "Magnetoimpedância gigante linear e não-linear em ligas amorfas." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/278277.
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Orientador: Marcelo KnobelTese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin
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Abstract: Not informed.
Doutorado
Física da Matéria Condensada
Doutor em Ciências
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Rettes, Julio Alberto Sibaja. "Robust algorithms for linear regression and locally linear embedding." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/22445.
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RETTES, Julio Alberto Sibaja. Robust algorithms for linear regression and locally linear embedding. 2017. 105 f. Dissertação (Mestrado em Ciência da Computação)- Universidade Federal do Ceará, Fortaleza, 2017.Submitted by Weslayne Nunes de Sales (weslaynesales@ufc.br) on 2017-03-30T13:15:27Z No. of bitstreams: 1 2017_dis_rettesjas.pdf: 3569500 bytes, checksum: 46cedc2d9f96d0f58bcdfe3e0d975d78 (MD5)
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Nowadays a very large quantity of data is flowing around our digital society. There is a growing interest in converting this large amount of data into valuable and useful information. Machine learning plays an essential role in the transformation of data into knowledge. However, the probability of outliers inside the data is too high to marginalize the importance of robust algorithms. To understand that, various models of outliers are studied. In this work, several robust estimators within the generalized linear model for regression framework are discussed and analyzed: namely, the M-Estimator, the S-Estimator, the MM-Estimator, the RANSAC and the Theil-Sen estimator. This choice is motivated by the necessity of examining algorithms with different working principles. In particular, the M-, S-, MM-Estimator are based on a modification of the least squares criterion, whereas the RANSAC is based on finding the smallest subset of points that guarantees a predefined model accuracy. The Theil Sen, on the other hand, uses the median of least square models to estimate. The performance of the estimators under a wide range of experimental conditions is compared and analyzed. In addition to the linear regression problem, the dimensionality reduction problem is considered. More specifically, the locally linear embedding, the principal component analysis and some robust approaches of them are treated. Motivated by giving some robustness to the LLE algorithm, the RALLE algorithm is proposed. Its main idea is to use different sizes of neighborhoods to construct the weights of the points; to achieve this, the RAPCA is executed in each set of neighbors and the risky points are discarded from the corresponding neighborhood. The performance of the LLE, the RLLE and the RALLE over some datasets is evaluated.
Na atualidade um grande volume de dados é produzido na nossa sociedade digital. Existe um crescente interesse em converter esses dados em informação útil e o aprendizado de máquinas tem um papel central nessa transformação de dados em conhecimento. Por outro lado, a probabilidade dos dados conterem outliers é muito alta para ignorar a importância dos algoritmos robustos. Para se familiarizar com isso, são estudados vários modelos de outliers. Neste trabalho, discutimos e analisamos vários estimadores robustos dentro do contexto dos modelos de regressão linear generalizados: são eles o M-Estimator, o S-Estimator, o MM-Estimator, o RANSAC e o Theil-Senestimator. A escolha dos estimadores é motivada pelo principio de explorar algoritmos com distintos conceitos de funcionamento. Em particular os estimadores M, S e MM são baseados na modificação do critério de minimização dos mínimos quadrados, enquanto que o RANSAC se fundamenta em achar o menor subconjunto que permita garantir uma acurácia predefinida ao modelo. Por outro lado o Theil-Sen usa a mediana de modelos obtidos usando mínimos quadradosno processo de estimação. O desempenho dos estimadores em uma ampla gama de condições experimentais é comparado e analisado. Além do problema de regressão linear, considera-se o problema de redução da dimensionalidade. Especificamente, são tratados o Locally Linear Embedding, o Principal ComponentAnalysis e outras abordagens robustas destes. É proposto um método denominado RALLE com a motivação de prover de robustez ao algoritmo de LLE. A ideia principal é usar vizinhanças de tamanhos variáveis para construir os pesos dos pontos; para fazer isto possível, o RAPCA é executado em cada grupo de vizinhos e os pontos sob risco são descartados da vizinhança correspondente. É feita uma avaliação do desempenho do LLE, do RLLE e do RALLE sobre algumas bases de dados.
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Magalhães, Alex de Souza. "Álgebra linear no ensino médio." reponame:Repositório Institucional da UFC, 2014. http://www.repositorio.ufc.br/handle/riufc/10443.
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MAGALHÃES,Alex de Souza. Álgebra linear no ensino médio. 2014. 66 f. Dissertação (Mestrado em Matemática em Rede Nacional) - Centro de Ciências, Universidade Federal do Ceará, Juazeiro do Norte, 2014Submitted by Erivan Almeida (eneiro@bol.com.br) on 2015-01-12T17:27:15Z No. of bitstreams: 1 2014_dis_asmagalhaes.pdf: 1206195 bytes, checksum: 08cd182b635c0bad153b88d8e8448b83 (MD5)
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In this work, we will make a presentation of Linear Algebra in high school this alternative form. In this way, the introduction of the concepts of vector space and afine variety, which are introduced through the study of matrices and linear systems, will be proposed. Thus the arrays appear as elements of a vector space and the solution set of a linear system as an a ne variety. This text will not be addressed the idea of determinants,we believe this can be without much damage, withdrawal of the mathematical curriculum of basic education.
Neste trabalho, faremos uma apresentação da Álgebra Linear presente no ensino médio de forma alternativa. Nesta forma, será proposto a introdução dos conceitos de espaço vetorial e variedade afim, que serão exemplificados através do estudo das matrizes e dos sistemas lineares. Sendo assim as matrizes aparecem como elementos de um espaço vetorial e o conjunto solução de um sistema linear como uma variedade afim. Neste texto não será abordado a ideia de determinantes, acreditamos que esta pode ser, sem muitos prejuízos, retirada do currículo matemático da educação básica.
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Levorato, Gabriela Baptistella Peres [UNESP]. "Matrizes, determinantes e sistemas lineares: aplicações na Engenharia e Economia." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/151612.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
O presente trabalho mostra a importância da Álgebra Linear e em particular da Teoria de Matrizes, Determinantes e Sistemas Lineares para resolver problemas práticos e contextualizados. Mostramos aplicações em circuitos elétricos, no balanceamento de equações químicas, nos modelos aberto e fechado de Leontief, e no funcionamento do GPS. Ainda, foi aplicado um plano de aula para os alunos do segundo ano do Ensino Médio e apresentamos sugestões de exercícios de vestibulares sobre os tópicos estudados, para serem abordados em sala de aula.
The present work shows the importance of Linear Algebra and in particular of Matrix Theory, Determinants and Linear Systems to solve practical and contextualized problems. We show applications in electrical circuits, in the balancing of chemical equations, in the open and closed models of Leontief, and in the operation of GPS. Also, a lesson plan was applied to the students of the second year of high school and we presented suggestions of exercises of vestibular about the topics studied, to be approached in the classroom.
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Freitas, Mário Sérgio Teixeira de. "Dinâmica nao-linear e caos em osciladores lineares por partes." reponame:Repositório Institucional da UFPR, 2003. http://hdl.handle.net/1884/36662.
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Orientador : Ricardo Luiz VianaTese (doutorado) - Universidade Federal do Paraná
Resumo: Um oscilador linear por partes, carregado, amortecido e forçado é investigado numericamente. A não-linearidade é devida à rigidez assimétrica. A motivação física remete às ondulações de uma ponte pênsil, estimulada pelo fluxo lateral do vento. Um mapa de Poincaré bidimensional é obtido. Os parâmetros são introduzidos gradualmente, favorecendo uma abordagem fenomenológica. Retratos de fase revelam multi-estabilidade com estrutura de bacia muito intrincada, cujo expoente de incerteza resulta não-inteiro, apesar de argumentos geométricos demonstrarem que esta estrutura não é fractal. Um atrator caótico é destruído por uma crise de fronteira. Próximo ao parâmetro crítico, o tempo médio de transiente diminui com o amortecimento segundo uma lei de potência. Ocorre erosão da bacia de segurança quando é introduzido um limiar de ruptura para a mola unilateral. Atratores de períodos mais altos são destruídos pela adição de ruído. Movimento quasiperiódico, sincronização e caos são criados pelo acoplamento entre dois osciladores conectados por uma mola unilateral.
Abstract: A forced damped and preloaded piecewise-linear oscillator is numerically investigated. Nonlinearity is due to asymmetrical stiffness. Physical motivation alludes to the undulations of a suspension bridge, stimulated by transversal wind flow. A two-dimensional Poincare map is obtained. Parameters are gradually introduced, enhancing a phenomenological approach. Phase portraits reveal multistability with a highly entangled basin structure, which uncertainty exponent is non-integer, despite geometrical arguments demonstrate this structure is not fractal. A chaotic attractor is destroyed through boundary crisis. Close to critical parameter, average transient time decreases with damping as a power-law. Erosion of safe basin occurs as a rupture threshold for the one-sided spring is established. Periodic attractors with higher periods are destroyed by addition of noise. Quasiperiodic motion, synchronization and chaos are created by the coupling between two oscillators connected by a one-sided spring.
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Nzabanita, Joseph. "Estimation in Multivariate Linear Models with Linearly Structured Covariance Matrices." Licentiate thesis, Linköpings universitet, Matematiska institutionen, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-78845.
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This thesis focuses on the problem of estimating parameters in multivariate linear models where particularly the mean has a bilinear structure and the covariance matrix has a linear structure. Most of techniques in statistical modeling rely on the assumption that data were generated from the normal distribution. Whereas real data may not be exactly normal, the normal distributions serve as a useful approximation to the true distribution. The modeling of normally distributed data relies heavily on the estimation of the mean and the covariance matrix. The interest of considering various structures for the covariance matrices in different statistical models is partly driven by the idea that altering the covariance structure of a parametric model alters the variances of the model’s estimated mean parameters. The extended growth curve model with two terms and a linearly structured covariance matrix is considered. In general there is no problem to estimate the covariance matrix when it is completely unknown. However, problems arise when one has to take into account that there exists a structure generated by a few number of parameters. An estimation procedure that handles linear structured covariance matrices is proposed. The idea is first to estimate the covariance matrix when it should be used to define an inner product in a regression space and thereafter reestimate it when it should be interpreted as a dispersion matrix. This idea is exploited by decomposing the residual space, the orthogonal complement to the design space, into three orthogonal subspaces. Studying residuals obtained from projections of observations on these subspaces yields explicit consistent estimators of the covariance matrix. An explicit consistent estimator of the mean is also proposed and numerical examples are given. The models based on normally distributed random matrix are also studied in this thesis. For these models, the dispersion matrix has the so called Kronecker product structure and they can be used for example to model data with spatio-temporal relationships. The aim is to estimate the parameters of the model when, in addition, one covariance matrix is assumed to be linearly structured. On the basis of n independent observations from a matrix normal distribution, estimation equations in a flip-flop relation are presented and numerical examples are given.
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Chen, Hua, Wei-Xi Li, and Chao-Jiang Xu. "Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations." Universität Potsdam, 2007. http://opus.kobv.de/ubp/volltexte/2009/3028/.
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Häggström, Lundevaller Erling. "Tests of random effects in linear and non-linear models." Doctoral thesis, Umeå universitet, Statistik, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-15.
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Andreotti, Sandro [Verfasser]. "Linear Programming and Integer Linear Programming in Bioinformatics / Sandro Andreotti." Berlin : Freie Universität Berlin, 2015. http://d-nb.info/1066645213/34.
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Häggström, Lundevaller Erling. "Tests of random effects in linear and non-linear models /." Umeå : Department of Statistics, University of Umeå, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-15.
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Miao, Quan. "Nuclear Dynamics in Linear and Non-linear X-ray Processes." Doctoral thesis, KTH, Teoretisk kemi och biologi, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-133432.
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New generations of brilliant synchrotron radiation sources and intense X-ray and optical lasers have opened unprecedent opportunities in linear and non-linear spectroscopies of molecules. This together with new instrumentation calls for further development of theory to explain observations and suggest new experiments. These two goals are the main objectives of the present thesis. In the first part of the thesis we study resonant inelastic X-ray scattering of the oxygen molecule. Recent experimental data of O2 show the dependence of the vibrational profile on the polarization of the X-rays. This vibrational scattering anisotropy is explained by the interference of the resonant and nonresonant inelastic scattering channels in O2. The second part of the thesis explores X-ray lasing caused by ultrafast dissociation of the HCl molecule in a repulsive core-excited state pumped by an X-ray free-electron laser. We show that the lasing efficiency is drastically enhanced due to the self-trapping of the amplified pulse into the ridge of the gain. The third part of the thesis is devoted to another non-linear phenomenon - optical limiting. Our time-dependent simulations are in agreement with the experimental data and show that phthalocyanines with heavy central metals exhibit good optical limiting properties for nanosecond pulses. Symmetry and the symmetry breaking are important fundamental concepts in physics, chemistry and biology. In the next part of the thesis we study theoretically the novel symmetry breaking mechanism in resonant Auger scattering. Both theory and electron-ion coincidence measurements for the oxygen molecule evidence the symmetry breaking of the oxygen cation caused by momentum exchange between the fast Auger electron and counter propagating dissociating oxygen atoms. The last part of the thesis is devoted to the role of the rotational degrees of freedom in X- ray ionization of molecules. We present here new results related to the rotational Doppler and angular recoil effects in X-ray ionization using the N2 and HCl molecules as illustrating examples. The dependence of the ionization cross section on the direction of ejection of fast electrons explains the sensitivity of the rotational broadening to the final state and to the polarization of X-rays observed recently for the N2 molecule. The theory reveals the novel effect of site-selectivity of X-ray valence ionization caused by the excitation of the rotational degrees of freedom which is different for different ionization sites. Large recoil angular momentum related to the ejection of an electron from the light hydrogen atom results in a red shifted broad pedestal in the X-ray photoelectron spectrum of HCl.QC 20131108
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Tomas, Helena. "Understanding the transcription from Linear A to Linear B script." Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.397466.
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Pechev, Alexandre Nikolov. "Robust linear and non-linear control of magnetically levitated systems." Thesis, Cardiff University, 2004. http://orca.cf.ac.uk/55944/.
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The two most advanced applications of contactless magnetic levitation are high-speed magnetic bearings and magnetically levitated vehicles (Maglev) for ground transportation using superconducting magnets and controlled d.c. electromagnets. The repulsion force from superconducting magnets provide stable levitation with low damping, while the suspension force generated by electromagnets is inherently unstable. This instability, due to the in verse force-distance relationship, requires the addition of feedback controllers to sustain stable suspension. The problem of controlling magnetically levitated systems using d.c. electromagnets under different operating conditions has been studied in this thesis with a design process primarily driven by experimental results from a representative single-magnet test rig and a multi-magnet vehicle. The controller-design stages are presented in detail and close relationships have been constructed between selection of performance criteria for the derivation process and desired suspension characteristics. Both linear and nonlinear stabilising compensators have been developed. Simulation and experimental results have been studied in parallel to assess operational stability and the main emphasis has been given to assessing performance under different operational conditions. For the experimental work, a new digital signal processor-based hardware platform has been designed, built with interface to Matlab/Simulink. The controller design methods and algorithmic work presented in this thesis can be divided into: non-adaptive, adaptive, optimal linear and nonlinear. Adaptive algorithms based on model reference control have been developed to improve the performance of the suspension system in the presence of considerable variations in external payload and force disturbances. New design methods for Maglev suspension have been developed using robust control theory (%oo and fi synthesis). Single- and multi-magnet control problems have been treated using the same framework. A solution to the Hoo controller-optimisation problem has been derived and applied to Maglev control. The sensitivity to robustness has been discussed and tools for assessing the robustness of the closed-loop system in terms of sustaining stability and performance in the presence of uncertainties in the suspension model have been presented. Multivariable controllers based on %00 and /i synthesis have been developed for a laboratory scale experimental vehicle weighing 88 kg with four suspension magnets, and experimental results have been derived to show superiority of the proposed design methods in terms of ability to deal with external disturbances. The concept of Hoo control has been extended to the nonlinear setting using the concepts of energy and dissipativity, and nonlinear state-feedback and out put-feed back controllers for Maglev have been developed and reported. Simulation and experimental results have been presented to show the improved performance of these controllers to attenuate guideway-induced disturbances while maintaining acceptable suspension qualities and larger operational bandwidth.
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Rahimzadeh, Behzad. "Linear and non-linear viscoelastic behaviour of binders and asphalts." Thesis, University of Nottingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.246403.
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Womersley, Martin Nigel. "Linear and non-linear optical properties of electro-optic crystals." Thesis, University of Warwick, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263787.
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Wilcox, Samuel L. "Constructing quasi-linear oxygen uptake responses from non-linear parameters." Thesis, Kansas State University, 2014. http://hdl.handle.net/2097/18706.
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Master of ScienceDepartment of Kinesiology
Thomas J. Barstow
Purpose: Oxygen uptake (VO2) has been shown to be controlled by a nonlinear system, yet the VO2 response to ramp style exercise appears linear. We tested the hypothesis that an integrative model incorporating nonlinear parameter values could accurately estimate actual VO2 responses to ramp style exercise. Methods: Six healthy, men completed three bouts of varying ramp rate exercise (slow ramp (SR): 15 W/min, regular ramp (RR) 30 W/min, fast ramp (FR) 60W/min) and four bouts of extended-step incremental exercise, where each step lasted 5-15 min or until volitional fatigue on a cycle ergometer on separate days. The step-responses were then fit with a simple monoexponential starting at time zero (MONO) or allowing a time delay and using only the first 5 min of data (5TD). The resulting VO2 parameters from the step protocol were incorporated into an integrative model for the estimation of the VO2 response to each of the rates of ramp incremental exercise. The parameters from the actual and model ramp protocols were compared with 2 way repeated-measures ANOVAs. Results: Both Gain (G) and Mean Response Time (MRT) (or time constant) values increased significantly across work rate transitions (mean±SD; Gain:10.0±0.9, 11.6±1.1, 13.1±1.3, 17.6±3.3 ml O2/min/W; MRT:39.4±7.7, 54.0±5.4, 79.6±15.0, 180.1±56.2 s). Up to maximalVO2 the models over-estimated the actual VO2 response for FR (Gain: ACT 8.7±1.0, MONO 9.9±0.4, 5TD 10.3±0.3 ml O2/min/W). Up to 80% maximal VO2 the models accurately predicted the actual VO2 response across all ramp rates (Gain: ACT 10.7±1.1, 10.2±0.5, 9.2±1.0; MONO 11.0±0.8, 10.3±0.6, 9.2±0.5; 5TD 10.4±0.4, 10.2±0.3, 9.8±0.2 ml O2/min/W, values are listed SR,RR,FR). Conclusions: When variable parameter values (G and either MRT or time constant and time delay) were utilized by an integrative model, accurate estimations of the VO2 response to ramp incremental exercise were possible regardless of ramp rate (up to 80% maximal VO2). The increases in both G and MRT (or time constant) appear to balance each other to produce the quasi-linear VO2 responses.
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Escobar-Ruiz, Edwill Alejandro. "Linear and non-linear ultrasonic NDE of titanium diffusion bonds." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/28681.
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Diffusion bonding is an attractive solid-state welding technique that promises weight reduction and improved performance in the aerospace industry. However, its adoption in fracture critical titanium components has been limited by the complications that macroscopic anisotropy introduces to typical ultrasonic NDE. Two strands of ultrasonic NDE, linear and non-linear acoustics, have been studied with the aim of overcoming these complications. A promising linear technique that uses the phase of reflected diffusion-bond signals to extract otherwise hidden interface information was selected for further development. The principal parameters that affect the phase analysis of ultrasonic signals were investigated and their optimisation resulted in up to an order of magnitude improvement in phase measurement reliability, even at low signal-to-noise ratios. The application of these optimised parameters without a priori knowledge of the signal arrival time was illustrated, and the sensitivity of the approach to ambient temperature and annealing effects was also explored. The original technique was susceptible to measurement error and proved impractical for typical aerospace component geometries, but these shortcomings have been overcome by the improvements and adaptations proposed here. However, it was shown that the efficacy of the technique depends on the relative acoustic impedances of the bonded media and, coupled with the sensitivity limit intrinsic to linear acoustic methods, this dependence acted to curtail the benefits of the approach and prompted the exploration of alternative techniques. Non-linear ultrasonic methods are significantly more sensitive than their linear counterparts to the imperfections likely to be present at diffusion-bonded interfaces, but suppressing extraneous contributions to the non-linear response of the interface is not trivial. An approach that succeeds in suppressing such contributions was studied and developed here. The technique, which is based on the non-collinear mixing of ultrasonic waves to generate a spectrally, modally and spatially dissociable third wave, was used to reliably characterise a set of samples whose bond quality was indeterminable using linear ultrasonic methods. Application of the technique to diffusion-bonded titanium aerospace components has been demonstrated and a significant improvement in ultrasonic NDE capability was achieved.
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Freire, António Manuel Simões. "Análise pseudo-linear e não-linear de pontes atirantadas metálicas." Master's thesis, Departamento de Engenharia Civil, 2002. http://hdl.handle.net/10316/15741.
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Croft, Lance Calloway. "Interpolating Beach Profile Data Using Linear and Non-linear Functions." Scholar Commons, 2014. https://scholarcommons.usf.edu/etd/5206.
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ABSTRACT
Beach and nearshore surveys are conducted in a variety of ways, the most commonly used being the level-and-transit method; because it is inexpensive, time conducive and highly accurate. Specifically, beach surveys are conducted to better understand cross-shore, long-shore sediment transport processes, as well as to quantify volume changes, which are used to evaluate beach performance. In this study, a section of the beach on Sand Key, FL was surveyed using rod-and-transit. In addition to the commonly used linear data analysis, a non-linear analysis was conducted using NURBS (Non-Uniform Rational B-Splines).
Survey data was collected within a short time window to ensure minimal environmental changes associated with waves and anthropological factors. Beach profiles were surveyed using two spatial resolutions, including 1) a typical variable resolution determined by the rodman based on observed morphology changes, and 2) a uniform, high resolution of 25 centimeters per point. The results indicate that variable resolution survey with careful observation by the rodman provided adequate accuracy as compared to the very high-resolution survey.
The goal of this study is to create a realistic surface between the beach profiles that are spaced relatively far apart. The commonly used contouring method (a linear method) may create mismatch among major morphology units, .e.g., bar crest, if they have different elevations alongshore. Here a non-linear method is developed by 1) identifying major morphological units, in this case dune top, berm crest, trough bottom, and bar crest 2) linking the units using a cubic spline, and 3) generating a surface using a NURBS sweep2 function. Bisector profiles are sliced from the surface generated using linear and non-linear methods, and compared with surveyed profiles at the same location. The profiles generated using the non-linear method matched more closely to the measured profile than that from the linear method. The non-linear NURBS surface resulted in a consistently greater beach volume between the surveyed profiles than the linear method of volume calculation.
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Mancinelli, Mattia. "Linear and non linear coupling effects in sequence of microresonators." Doctoral thesis, Università degli studi di Trento, 2013. https://hdl.handle.net/11572/369276.
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My work was carried out with the aim of devising and characterize novel integrated devices for signal routing in optical networks on chip. Several type of optical microresonators, both in a single and coupled configuration (CROW, SCISSOR), are discussed starting from the fundamental theory till dealing with novel configurations. The coupling between a Mach-Zehnder interferometer and such configuration of microresonators is also investigated. Since the used material platform is the silicon on insulator (SOI), an in depth study of the microresonators behaviour has demanded an investigation in both in the linear and non-linear regime.
All devices were fabricated through a standard CMOS facility by using deep UV lithography in order to verify the reliability of resolution and throughput similar to those required for commercial applications. Particular attention has been paid in the study of structures robust with respect to manufacturing defects.
All the steps necessary to develop a device for integrated optics are studied in deep: device conception, device simulations through analytic and FEM simulations, GDS mask design, experimental characterizations.
All the devices parameters are carefully reported to allow the reproduction of the experimental results. Where it was possible, suggestions on how to improve the fabricated devices performance were given.
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Mancinelli, Mattia Mancinelli. "Linear and non linear coupling effects in sequence of microresonators." Doctoral thesis, University of Trento, 2013. http://eprints-phd.biblio.unitn.it/1050/1/Doctoral_thesis_Mattia_Mancinelli_2013.pdf.
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My work was carried out with the aim of devising and characterize novel integrated devices for signal routing in optical networks on chip. Several type of optical microresonators, both in a single and coupled configuration (CROW, SCISSOR), are discussed starting from the fundamental theory till dealing with novel configurations. The coupling between a Mach-Zehnder interferometer and such configuration of microresonators is also investigated. Since the used material platform is the silicon on insulator (SOI), an in depth study of the microresonators behaviour has demanded an investigation in both in the linear and non-linear regime.
All devices were fabricated through a standard CMOS facility by using deep UV lithography in order to verify the reliability of resolution and throughput similar to those required for commercial applications. Particular attention has been paid in the study of structures robust with respect to manufacturing defects.
All the steps necessary to develop a device for integrated optics are studied in deep: device conception, device simulations through analytic and FEM simulations, GDS mask design, experimental characterizations.
All the devices parameters are carefully reported to allow the reproduction of the experimental results. Where it was possible, suggestions on how to improve the fabricated devices performance were given.
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De, Lucca Brenno Jason Sanzio Peter. "Linear irreversible thermodynamics." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20975/.
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In questa tesi tratteremo il problema di costruire una teoria termodinamica per trasformazioni su un sistema passante per stati di non-equilibrio. Cercando di generalizzare a sistemi che non sono all’equilibrio, rilasseremo la richiesta che siano in equilibrio globalmente. Lo stato termodinamico sarà univocamente determinato da un insieme di parametri termodinamici definiti localmente, della stessa natura e significato fisico dei parametri usati nella termodinamica classica. Le molteplici assunzioni necessarie al fine di avere una teoria mesoscopica comunque predittiva verranno giustificate a posteriori, quando possibile, in base alle predizioni che da tale modello nasceranno. In particolare ci concentreremo sugli effetti termoelettrici di Thompson, Seebeck e Peltier, esempi storici di grande rilevanza nel campo della termodinamica del non-equilibrio.
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Sarrabezolles, Pauline. "Colourful linear programming." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1033/document.
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Le théorème de Carathéodory coloré, prouvé en 1982 par Bárány, énonce le résultat suivant. Etant donnés d Å1 ensembles de points S1,SdÅ1 dans Rd , si chaque Si contient 0 dans son enveloppe convexe, alors il existe un sous-ensemble arc-en-ciel T µ SdÅ1 iÆ1 Si contenant 0 dans son enveloppe convexe, i.e. un sous-ensemble T tel que jT \Si j • 1 pour tout i et tel que 0 2 conv(T ). Ce théorème a donné naissance à de nombreuses questions, certaines algorithmiques et d’autres plus combinatoires. Dans ce manuscrit, nous nous intéressons à ces deux aspects. En 1997, Bárány et Onn ont défini la programmation linéaire colorée comme l’ensemble des questions algorithmiques liées au théorème de Carathéodory coloré. Parmi ces questions, deux ont particulièrement retenu notre attention. La première concerne la complexité du calcul d’un sous-ensemble arc-en-ciel comme dans l’énoncé du théorème. La seconde, en un sens plus générale, concerne la complexité du problème de décision suivant. Etant donnés des ensembles de points dans Rd , correspondant aux couleurs, il s’agit de décider s’il existe un sous-ensemble arc-en-ciel contenant 0 dans son enveloppe convexe, et ce en dehors des conditions du théorème de Carathéodory coloré. L’objectif de cette thèse est de mieux délimiter les cas polynomiaux et les cas “difficiles” de la programmation linéaire colorée. Nous présentons de nouveaux résultats de complexités permettant effectivement de réduire l’ensemble des cas encore incertains. En particulier, des versions combinatoires du théorème de Carathéodory coloré sont présentées d’un point de vue algorithmique. D’autre part, nous montrons que le problème de calcul d’un équilibre de Nash dans un jeu bimatriciel peut être réduit polynomialement à la programmation linéaire coloré. En prouvant ce dernier résultat, nous montrons aussi comment l’appartenance des problèmes de complémentarité à la classe PPAD peut être obtenue à l’aide du lemme de Sperner. Enfin, nous proposons une variante de l’algorithme de Bárány et Onn, calculant un sous ensemble arc-en-ciel contenant 0 dans son enveloppe convexe sous les conditions du théorème de Carathéodory coloré. Notre algorithme est clairement relié à l’algorithme du simplexe. Après une légère modification, il coïncide également avec l’algorithme de Lemke, calculant un équilibre de Nash dans un jeu bimatriciel. La question combinatoire posée par le théorème de Carathéodory coloré concerne le nombre de sous-ensemble arc-en-ciel contenant 0 dans leurs enveloppes convexes. Deza, Huang, Stephen et Terlaky (Colourful simplicial depth, Discrete Comput. Geom., 35, 597–604 (2006)) ont formulé la conjecture suivante. Si jSi j Æ d Å1 pour tout i 2 {1, . . . ,d Å1}, alors il y a au moins d2Å1 sous-ensemble arc-en-ciel contenant 0 dans leurs enveloppes convexes. Nous prouvons cette conjecture à l’aide d’objets combinatoires, connus sous le nom de systèmes octaédriques, dont nous présentons une étude plus approfondieThe colorful Carathéodory theorem, proved by Bárány in 1982, states the following. Given d Å1 sets of points S1, . . . ,SdÅ1 µ Rd , each of them containing 0 in its convex hull, there exists a colorful set T containing 0 in its convex hull, i.e. a set T µ SdÅ1 iÆ1 Si such that jT \Si j • 1 for all i and such that 0 2 conv(T ). This result gave birth to several questions, some algorithmic and some more combinatorial. This thesis provides answers on both aspects. The algorithmic questions raised by the colorful Carathéodory theorem concern, among other things, the complexity of finding a colorful set under the condition of the theorem, and more generally of deciding whether there exists such a colorful set when the condition is not satisfied. In 1997, Bárány and Onn defined colorful linear programming as algorithmic questions related to the colorful Carathéodory theorem. The two questions we just mentioned come under colorful linear programming. This thesis aims at determining which are the polynomial cases of colorful linear programming and which are the harder ones. New complexity results are obtained, refining the sets of undetermined cases. In particular, we discuss some combinatorial versions of the colorful Carathéodory theorem from an algorithmic point of view. Furthermore, we show that computing a Nash equilibrium in a bimatrix game is polynomially reducible to a colorful linear programming problem. On our track, we found a new way to prove that a complementarity problem belongs to the PPAD class with the help of Sperner’s lemma. Finally, we present a variant of the “Bárány-Onn” algorithm, which is an algorithmcomputing a colorful set T containing 0 in its convex hull whose existence is ensured by the colorful Carathéodory theorem. Our algorithm makes a clear connection with the simplex algorithm. After a slight modification, it also coincides with the Lemke method, which computes a Nash equilibriumin a bimatrix game. The combinatorial question raised by the colorful Carathéodory theorem concerns the number of positively dependent colorful sets. Deza, Huang, Stephen, and Terlaky (Colourful simplicial depth, Discrete Comput. Geom., 35, 597–604 (2006)) conjectured that, when jSi j Æ d Å1 for all i 2 {1, . . . ,d Å1}, there are always at least d2Å1 colourful sets containing 0 in their convex hulls. We prove this conjecture with the help of combinatorial objects, known as the octahedral systems. Moreover, we provide a thorough study of these objects
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Rossi, Rosângela de Lourdes. "Interpolação linear logaritmica." Universidade Federal de São Carlos, 2015. https://repositorio.ufscar.br/handle/ufscar/7318.
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Não recebi financiamento
This dissertation project aims at the Teaching of Linear Interpolation logarithmic, with the target group students from High school and their teachers to facilitate the meeting of the logarithms of values without the use of board existing common logarithms or the calculating machines. The concepts, the properties of logarithms and interpolations inserted in activities based on the Didactic Engineering are the brand and the engine of development of this work. The materials handling, visualization of results and activities developed by high school students from public schools ensured the originality of the teaching relationship / learning of mathematics, especially in the Linear Interpolation logarithmic, circumscribing on purpose that objective.
Este projeto de dissertação tem por objetivo o Ensino da Interpolação Linear Logarítmica, tendo como público-alvo estudantes do Ensino médio bem como seus educadores visando facilitar o encontro dos valores de logaritmos sem o uso da tábua de logaritmos decimais existentes nem das máquinas de calcular. Os conceitos, as propriedades dos logaritmos e as interpolações inseridas nas atividades baseadas na Engenharia Didática são a marca e o propulsor do desenvolvimento desta dissertação. A manipulação de materiais, a visualização dos resultados e as atividades desenvolvidas pelos alunos do Ensino Médio da escola pública garantiu a originalidade da relação ensino/aprendizagem da Matemática, em especial na Interpolação Linear Logarítmica, circunscrevendo de forma proposital o referido objetivo.
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Roth, Simon. "Customising Linear-TV." Thesis, KTH, Skolan för datavetenskap och kommunikation (CSC), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-192691.
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The purpose of this thesis was to explore whether we can customise and personalise linear TV. The approach from the author was first to do an exten- sive research into the available literature and statistics, ex- amining the current technology and reasons and behaviour behind media consumption. Thereafter, the author interviewed ten individuals about their media habits, and got insight into how modern young professionals consume their media content. Finally, the author conducted an reverse engineering ex- periment on current SVOD services, to get a better under- standing of how refined the current recommendation sys- tems are. After analysing the resulting data and discussing it, the author concludes that although one can customise a linear TV service, doing so would not be beneficial to media com- panies with current technology and the media habits of the target group.Syftet med denna avhandling var att undersöka om vi kan användaranpassa linjär-TV. Tillvägagångssättet från författaren var först att göra en omfattande forskning om tillgänglig litteratur och statistik, att undersöka den nuvarande tekniken och motiv och bete- ende bakom media konsumtion. Därefter intervjuade författaren tio personer om deras me- dievanor, och fick inblick i hur moderna unga yrkesverk- samma konsumerar sitt medieinnehåll . Slutligen har författaren genomfört ett reverse engineering experiment på nuvarande SVOD tjänster för att få en bättre förståelse för hur förfinade nuvarande rekommendationssy- stem är. Efter att ha analyserat resulterande data och diskuterat det, drar författaren slutsatsen att även om man kan an- passa en linjär-TV-tjänst, så skulle detta inte vara fördel- aktigt för medieföretagen att genomföra detta med dagens teknik och målgruppens konsumtionsmönster.
Research and most of the writing done in 2014. Finnished in 2016.
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Bai, Xue. "Robust linear regression." Kansas State University, 2012. http://hdl.handle.net/2097/14977.
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Master of ScienceDepartment of Statistics
Weixin Yao
In practice, when applying a statistical method it often occurs that some observations deviate from the usual model assumptions. Least-squares (LS) estimators are very sensitive to outliers. Even one single atypical value may have a large effect on the regression parameter estimates. The goal of robust regression is to develop methods that are resistant to the possibility that one or several unknown outliers may occur anywhere in the data. In this paper, we review various robust regression methods including: M-estimate, LMS estimate, LTS estimate, S-estimate, [tau]-estimate, MM-estimate, GM-estimate, and REWLS estimate. Finally, we compare these robust estimates based on their robustness and efficiency through a simulation study. A real data set application is also provided to compare the robust estimates with traditional least squares estimator.
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Figueiredo, Cléber da Costa. "Calibração linear assimétrica." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-08032013-141153/.
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A presente tese aborda aspectos teóricos e aplicados da estimação dos parâmetros do modelo de calibração linear com erros distribuídos conforme a distribuição normal-assimétrica (Azzalini, 1985) e t-normal-assimétrica (Gómez, Venegas e Bolfarine, 2007). Aplicando um modelo assimétrico, não é necessário transformar as variáveis a fim de obter erros simétricos. A estimação dos parâmetros e das variâncias dos estimadores do modelo de calibração foram estudadas através da visão freqüentista e bayesiana, desenvolvendo algoritmos tipo EM e amostradores de Gibbs, respectivamente. Um dos pontos relevantes do trabalho, na óptica freqüentista, é a apresentação de uma reparametrização para evitar a singularidade da matriz de informação de Fisher sob o modelo de calibração normal-assimétrico na vizinhança de lambda = 0. Outro interessante aspecto é que a reparametrização não modifica o parâmetro de interesse. Já na óptica bayesiana, o ponto forte do trabalho está no desenvolvimento de medidas para verificar a qualidade do ajuste e que levam em consideração a assimetria do conjunto de dados. São propostas duas medidas para medir a qualidade do ajuste: o ADIC (Asymmetric Deviance Information Criterion) e o EDIC (Evident Deviance Information Criterion), que são extensões da ideia de Spiegelhalter et al. (2002) que propôs o DIC ordinário que só deve ser usado em modelos simétricos.This thesis focuses on theoretical and applied estimation aspects of the linear calibration model with skew-normal (Azzalini, 1985) and skew-t-normal (Gómez, Venegas e Bolfarine, 2007) error distributions. Applying the asymmetrical distributed error methodology, it is not necessary to transform the variables in order to have symmetrical errors. The frequentist and the Bayesian solution are presented. The parameter estimation and its variance estimation were studied using the EM algorithm and the Gibbs sampler, respectively, in each approach. The main point, in the frequentist approach, is the presentation of a new parameterization to avoid singularity of the information matrix under the skew-normal calibration model in a neighborhood of lambda = 0. Another interesting aspect is that the reparameterization developed to make the information matrix nonsingular, when the skewness parameter is near to zero, leaves the parameter of interest unchanged. The main point, in the Bayesian framework, is the presentation of two measures of goodness-of-fit: ADIC (Asymmetric Deviance Information Criterion) and EDIC (Evident Deviance Information Criterion ). They are natural extensions of the ordinary DIC developed by Spiegelhalter et al. (2002).
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Correia, José Vitor de Almeida Florentino. "Perpectiva linear paramétrica." Doctoral thesis, Universidade de Lisboa. Faculdade de Arquitetura, 2015. http://hdl.handle.net/10400.5/11733.
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Tese de Doutoramento em Arquitetura, com a especialização em Comunicação Visual, apresentada na Faculdade de Arquitetura da Universidade de Lisboa, para obtenção do grau de Doutor.O presente trabalho propõe e fundamenta um novo sistema de representação perspéctica, denominado Perspectiva Linear Paramétrica, que resulta de uma abordagem sistemática à ciência da perspectiva, sustentada na experiência didáctica de Desenho e Geometria Descritiva. Este sistema visa constituir-se como um sistema de perspectiva unificado, ao reunir e articular os actuais sistemas autónomos, referenciais na sua formulação: perspectiva planar, cilíndrica e esférica. O seu quadro conceptual é definido por três princípios: 1º dissociação entre superfície de representação e superfície de projecção; 2º mutabilidade da superfície de projecção; 3º adaptabilidade dos métodos de transferência da superfície de projecção para a superfície de representação. A sua operatividade assenta na utilização de uma superfície de projecção esferoidal, cuja identidade geométrica varia em função da concretização de dois parâmetros: Raio e Excentricidade. Os seus resultados gráficos reproduzem os sistemas referenciais mas acrescentam um número ilimitado de estados perspécticos intermédios (híbridos), enriquecendo assim, de forma inclusiva, o papel da perspectiva como código estruturante do desenho descritivo.
ABSTRACT: The present thesis proposes and sustains a new system of perspective representation, named Parametric Linear Perspective, which is the result of a systematic approach to the science of perspective, backgrounded by the didactical experience in Drawing and Descriptive Geometry disciplines. The Parametric Linear Perspective aims to be an unified perspective system, as it gathers and articulates the current independent systems that are referential to its formulation: planar perspective, cylindrical perspective and spherical perspective. Its conceptual framework is defined by three principles: 1st dissociation of representation surface and projection surface; 2nd mutability of the projection surface; 3rd adaptability of the method for transferring the information from the projection surface to the representation surface. The operativeness of the Parametric Linear Perspective is based on a spheroidal projection surface, which geometrical identity changes upon the definition of two parameters: Radius and Eccentricity. The graphic outputs can be similar to those of the referential systems, but also an unlimited number of intermediate (hybrid) perspective depictions, this way enlarging in an inclusive manner the role of linear perspective as a structuring code for descriptive drawing.
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Winerip, Jason. "Graph Linear Complexity." Scholarship @ Claremont, 2008. https://scholarship.claremont.edu/hmc_theses/216.
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This thesis expands on the notion of linear complexity for a graph as defined by Michael Orrison and David Neel in their paper "The Linear Complexity of a Graph." It considers additional classes of graphs and provides upper bounds for additional types of graphs and graph operations.