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Dissertations / Theses on the topic 'Geometry Mathematical models'
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Liu, Yang, and 劉洋. "Optimization and differential geometry for geometric modeling." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40988077.
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Tucker, Gayle. "Mathematical modelling in neurophysiology : neuronal geometry in the construction of neuronal models." Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.414405.
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Chou, Chia-Peng. "A mathematical model of building daylighting based on first principles of astrometry, solid geometry and optical radiation transfer." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/82904.
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There is a growing recognition in design professions that lighting is a significant factor in energy consideration. This has generated an interest in daylighting; the bringing of direct and diffuse daylight into buildings to reduce the use of artificial lighting. Many methods exist for quantifying diffuse daylight distribution for use in the design of buildings, but the methods vary widely both in technique and capability. Moreover, no present method deals with direct daylight (sunshine) distribution. Additionally, none have taken advantage of improvements in computer technology that make feasible more complex mathematical computational models for dealing with direct and diffuse daylight together.
This dissertation describes the theoretical development and computer implementation of a new mathematical approach to analyzing the distribution of direct and diffuse daylight. This approach examines light transfer from extraterrestrial space to the inside of a room based on the principles of astrometry, solid geometry, and radiation transfer. This study discusses and analyzes certain aspects critical to develop a mathematical model for evaluating daylight performance and compares the results of the proposed model with 48 scale model studies to determine the validity of using this mathematical model to predict the daylight distribution of a room. Subsequent analysis revealed no significant variation between scale model studies and this computer simulation. Consequently, this mathematical model with the attendant computer program, has demonstrated the ability to predict direct and diffuse daylight distribution. Thus, this approach does indeed have the potential for allowing designers to predict the effect of daylight performance in the schematic design stage.
A microcomputer program has been developed to calculate the diffuse daylight distribution. The computation procedures of the program use the proposed mathematical model method. The program was developed with a menu-driven format, where the input data can be easily chosen, stored, and changed to determine the effects of different parameters. Results can be obtained through two formats. One data format provides complete material for analyzing the aperture size and location, glass transmission, reflectance factors, and room orientation. The other provides the graphic displays which represent the illuminance in plan, section, and 3-dimensional contour. The program not only offers a design tool for determining the effects of various daylighting options quickly and accurately in the early design stage, but also presents the daylight distribution with less explanation and with more rapid communication with the clients. The program is written in BASICA language and can be used with the IBM microcomputer system.<br>Ph. D.
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張麗霞 and Lai-ha Freda Cheung. "On envelopes and envelope theorem." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1991. http://hub.hku.hk/bib/B31976505.
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Koehl, Christian. "Geometry of supersymmetric sigma models and D-brane solitons." Thesis, Queen Mary, University of London, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325106.
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Tran, Tat Dat. "Information Geometry and the Wright-Fisher model of Mathematical Population Genetics." Doctoral thesis, Universitätsbibliothek Leipzig, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-90508.
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My thesis addresses a systematic approach to stochastic models in population genetics; in particular, the Wright-Fisher models affected only by the random genetic drift. I used various mathematical methods such as Probability, PDE, and Geometry to answer an important question: \"How do genetic change factors (random genetic drift, selection, mutation, migration, random environment, etc.) affect the behavior of gene frequencies or genotype frequencies in generations?”.
In a Hardy-Weinberg model, the Mendelian population model of a very large number of individuals without genetic change factors, the answer is simple by the Hardy-Weinberg principle: gene frequencies remain unchanged from generation to generation, and genotype frequencies from the second generation onward remain also unchanged from generation to generation.
With directional genetic change factors (selection, mutation, migration), we will have a deterministic dynamics of gene frequencies, which has been studied rather in detail. With non-directional genetic change factors (random genetic drift, random environment), we will have a stochastic dynamics of gene frequencies, which has been studied with much more interests. A combination of these factors has also been considered.
We consider a monoecious diploid population of fixed size N with n + 1 possible alleles at a given locus A, and assume that the evolution of population was only affected by the random genetic drift. The question is that what the behavior of the distribution of relative frequencies of alleles in time and its stochastic quantities are.
When N is large enough, we can approximate this discrete Markov chain to a continuous Markov with the same characteristics. In 1931, Kolmogorov first introduced a nice relation between a continuous Markov process and diffusion equations. These equations called the (backward/forward) Kolmogorov equations which have been first applied in population genetics in 1945 by Wright.
Note that these equations are singular parabolic equations (diffusion coefficients vanish on boundary). To solve them, we use generalized hypergeometric functions. To know more about what will happen after the first exit time, or more general, the behavior of whole process, in joint work with J. Hofrichter, we define the global solution by moment conditions; calculate the component solutions by boundary flux method and combinatorics method.
One interesting property is that some statistical quantities of interest are solutions of a singular elliptic second order linear equation with discontinuous (or incomplete) boundary values. A lot of papers, textbooks have used this property to find those quantities. However, the uniqueness of these problems has not been proved. Littler, in his PhD thesis in 1975, took up the uniqueness problem but his proof, in my view, is not rigorous. In joint work with J. Hofrichter, we showed two different ways to prove the uniqueness rigorously. The first way is the approximation method. The second way is the blow-up method which is conducted by J. Hofrichter.
By applying the Information Geometry, which was first introduced by Amari in 1985, we see that the local state space is an Einstein space, and also a dually flat manifold with the Fisher metric; the differential operator of the Kolmogorov equation is the affine Laplacian which can be represented in various coordinates and on various spaces. Dynamics on the whole state space explains some biological phenomena.
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Mazzetti, Caterina. "A mathematical model of the motor cortex." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/15002/.
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In this work we present a geometric model of motor cortex that generalizes an already existing model of visual cortex.
The thesis opens by recalling the notions of fiber bundles, principal bundles, Lie groups and sub-Riemannian geometry. In particular, we enunciate Chow’s theorem which ensures that if the Hörmander condition holds, the space connectivity property is satisfied.
Then we recall the visual cortex model proposed by Citti-Sarti, which describes the set of simple cells
as a Lie group with sub-Riemannian metric.
The original part of the thesis is the extension
to the motor cortex. Based on neural data, collected by Georgopoulos, we study the set of motor cortical cells and we describe them as a principal bundle. The fiber contains the movement direction and shapes the hypercolumnar structure measured. Finally we determine the intrinsic coordinates of the motor cortex, studying the cellular response to the motor impulse.
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Soderquist, Hans Lars. "Automatic geometric data migration throughout views of a model fidelity family /." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1184.pdf.
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Grudić, Gregory Z. "Iterative inverse kinematics with manipulator configuration control and proof of convergence." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/42018.
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A complete solution to the inverse kinematics problem for a large class of practical manipulators,
which includes manipulators with no closed form inverse kinematics equations, is presented in this
thesis. A complete solution to the inverse kinematics problem of a manipulator is defined as a method
for obtaining the required joint variable values to establish the desired endpoint position, endpoint
orientation, and manipulator configuration; the only requirement being that the desired solution
exists. For all manipulator geometries that satisfy a set of conditions (THEOREM I), an algorithm
is presented that is theoretically guaranteed to always converge to the desired solution (if it exists).
The algorithm is extensively tested on two complex 6 degree of freedom manipulators which have no
known closed form inverse kinematics equations. It is shown that the algorithm can be used in real
time manipulator control. Applications of the method to other 6 DOF manipulator geometries and to
redundant manipulators are discussed.<br>Applied Science, Faculty of<br>Electrical and Computer Engineering, Department of<br>Graduate
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Schuerg, Frank. "Fractal geometry of iso-surfaces of a passive scalar in a turbulent boundary layer." Thesis, Available online, Georgia Institute of Technology, 2004:, 2003. http://etd.gatech.edu/theses/available/etd-04082004-180358/unrestricted/schuerg%5ffrank%5f200312%5fms.pdf.
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Nespolo, Rodrigo Fernando. "Uma proposta de ensino de matemática para a educação básica." Universidade Tecnológica Federal do Paraná, 2014. http://repositorio.utfpr.edu.br/jspui/handle/1/1093.
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Neste trabalho apresenta-se uma proposta de ensino que tem como interesse a motivação dos alunos para aprenderem matemática. Foram pesquisadas diversas bibliografias que propõem a Modelagem Matemática como alternativa de ensino da matemática, ligando conhecimento escolar ao cotidiano do aluno. Na sequência, relatamos nossa proposta de ensino aplicada a uma turma do sexto ano do Ensino Fundamental na qual foram trabalhados os conteúdos de circunferência e seus elementos, os números irracionais e operações com números decimais, através da atividade que denominamos “Festa da Matemática”. Nesta proposta, ilustramos como estes conteúdos matemáticos estão presentes no cotidiano e podem ser trabalhado em uma série que não prevê em seu currículo tais temas, fugindo do aspecto linear presente na maioria dos programas curriculares. A metodologia adotada na pesquisa foi a qualitativa e os dados foram coletados em encontros semanais de ensino de matemática durante os meses de outubro e novembro no ano letivo de 2013. A partir do trabalho desenvolvido verificaram-se melhorias significativas no interesse dos alunos em aprender matemática, o que proporcionou, consequentemente, melhorias no rendimento individual de cada aluno e da turma como um todo. A principal característica observada nos alunos, durante a aplicação do trabalho com a Modelagem Matemática foi a motivação em aprender novos conteúdos matemáticos despertada por um conteúdo abordado de forma significativa e diferenciada.<br>This paper presents a school proposal for that has as interest the students' motivation to learn Mathematics. Several bibliographies that propose Mathematical Modeling as an alternative teaching Mathematics, connecting school knowledge to everyday studen were surveyed. Following, we describe our proposal of teaching applied to a class of sixth grade of elementary school in which the contents of a circle and its elements, irrational numbers and operations with decimals, through the activity we call "Feast of Mathematics" were worked. In this proposal, we illustrate how these math concepts are present in everyday life and can be worked into a series that does not include in the grade’s curriculum such subjects, fleeing the linear aspect present in most curricula programs. The methodology used in the research was qualitative and the data were collected at weekly meetings of teaching Mathematics during the months of October and November in the academic year of 2013. From the developed work, there were noticed significant improvements in students' interest in learning Math, which provided, consequently, improvements in individual performance of each student and in the class as a whole. The main feature observed in the students during the application work with Mathematical Modeling was the motivation to learn new mathematical content awakened by a significant content and approached in a different way.
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Morkel, Chantelle. "Non-interactive modeling tools and support environment for procedural geometry generation." Thesis, Rhodes University, 2006. http://eprints.ru.ac.za/242/.
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Lundholm, Douglas. "Zero-energy states in supersymmetric matrix models." Doctoral thesis, KTH, Matematik (Avd.), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-12846.
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The work of this Ph.D. thesis in mathematics concerns the problem of determining existence, uniqueness, and structure of zero-energy states in supersymmetric matrix models, which arise from a quantum mechanical description of the physics of relativistic membranes, reduced Yang-Mills gauge theory, and of nonperturbative features of string theory, respectively M-theory. Several new approaches to this problem are introduced and considered in the course of seven scientific papers, including: construction by recursive methods (Papers A and D), deformations and alternative models (Papers B and C), averaging with respect to symmetries (Paper E), and weighted supersymmetry and index theory (Papers F and G). The mathematical tools used and developed for these approaches include Clifford algebras and associated representation theory, structure of supersymmetric quantum mechanics, as well as spectral theory of (matrix-) Schrödinger operators.<br>QC20100629
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Geja, Nokuzola Hlaleleni. "Investigating a way of teaching transformation geometry in grade 9 applying van Hiele’s theory and Kilpatrick’s model : a case study." Thesis, Rhodes University, 2015. http://hdl.handle.net/10962/d1020601.
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Transformation geometry has been neglected in our schools because teachers are often not proficient enough to teach it, as it was not part of the syllabus during their training. The study investigates effective ways of teaching transformation geometry in grade 9, applying van Hiele’s theory (1986) of geometry teaching and learning and Kilpatrick’s model of mathematical proficiency. The teaching programme activities require consistent use of physical manipulatives by the teacher for effective teaching, learning and understanding of geometric concepts. The type of study is a case study. Data collection tools are: - baseline evaluation, teacher & learner interviews (pre & post programme intervention) and observation (pre & post) during the implementation of the teaching programme. Results were analysed both qualitatively and quantitatively. My research findings show some improvement of learner performance after the application of the programme. Baseline evaluation shows that some learners attained below and above 30%. Interviews showed that some learners had problems before the implementation of the programme and some problems were eliminated by the use of the programme activities and learning progression was evident. Learner performance showed that learners had acquired some knowledge and critical thinking and reasoning skills, reflection skills, communication through LOLT improved, commitment to activities of the programme and teaching practice had improved. Learner performance showed that a learner can be in two different levels at the same time. Consistent use of manipulatives resulted in effective teaching and learning of geometry in grade 9. The results of this research support other researchers’ views of teaching geometry using van Hiele’s theory (1986) and Kilpatrick et al. (2001). Shaw (2002) argues that teaching geometry with manipulatives enhances conceptual understanding by the learner. In my opinion, it also promotes immediate intervention by the teacher as soon as the learner picks an incorrect object. The project enhanced and improved levels of communication between the learner, teacher and others in the classroom.
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Whitmer, Kelly Joan. "Learning to see in the Pietist Orphanage : geometry, philanthropy and the science of perfection, 1695-1730." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/2427.
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This is a dissertation about the Halle method, or the visual pedagogies of the Pietist Orphanage as they were developed in the German university town of Halle from 1695 until 1730. A “Pietist” was someone who was affiliated with an evangelical reform movement first initiated by Philipp Jakob Spener in the 1670s. A long and deeply entrenched historiographical tradition has portrayed the Halle proponents of this movement—especially their leader August Hermann Francke—as zealous, yet practical, Lutheran reformers who were forced to directly confront the ideals of early Enlightenment in conjunction with the state-building mandate of Brandenburg-Prussia. This has led to a persistent tendency to see Halle Pietists as “others” who cultivated their collective identity in opposition to so-called Enlightenment intellectuals, like Christian Wolff, at the same time as they exerted a marked influence on these same persons. As a result of this dichotomous portrayal over the years, the impact of the Halle method on educational reform, and on the meanings eighteenth-century Europeans attached to philanthropy more generally, has been misunderstood. I argue that the Pietist Orphanage holds the key to remedying several problems that have impeded our ability to understand the significance of Pietist pedagogy and philanthropy. This was a site specifically designed to introduce children to the conciliatory knowledge-making strategies of the first Berlin Academy of Science members and their associates. These strategies championed the status of the heart as an assimilatory juncture point and were refined in the schools of the Pietist Orphanage, which itself functioned as a visual showplace that viewers could observe in order to edify and improve themselves. It was the material expression of Halle Pietists’ commitment to a “third way” and marked their attempt to assimilate experience and cognition, theology and philosophy, absolutism and voluntarism. The dissertation examines several personalities who had a direct bearing on this conciliatory project: namely E. W. von Tschirnhaus, Johann Christoph Sturm, Leonhard Christoph Sturm, Gottfried Wilhelm Leibniz and Christian Wolff. It also examines how the method was applied in the Halle Orphanage schools and extended elsewhere.
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Calatroni, Luca. "New PDE models for imaging problems and applications." Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/256139.
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Variational methods and Partial Differential Equations (PDEs) have been extensively employed for the mathematical formulation of a myriad of problems describing physical phenomena such as heat propagation, thermodynamic transformations and many more. In imaging, PDEs following variational principles are often considered. In their general form these models combine a regularisation and a data fitting term, balancing one against the other appropriately. Total variation (TV) regularisation is often used due to its edgepreserving and smoothing properties. In this thesis, we focus on the design of TV-based models for several different applications. We start considering PDE models encoding higher-order derivatives to overcome wellknown TV reconstruction drawbacks. Due to their high differential order and nonlinear nature, the computation of the numerical solution of these equations is often challenging. In this thesis, we propose directional splitting techniques and use Newton-type methods that despite these numerical hurdles render reliable and efficient computational schemes. Next, we discuss the problem of choosing the appropriate data fitting term in the case when multiple noise statistics in the data are present due, for instance, to different acquisition and transmission problems. We propose a novel variational model which encodes appropriately and consistently the different noise distributions in this case. Balancing the effect of the regularisation against the data fitting is also crucial. For this sake, we consider a learning approach which estimates the optimal ratio between the two by using training sets of examples via bilevel optimisation. Numerically, we use a combination of SemiSmooth (SSN) and quasi-Newton methods to solve the problem efficiently. Finally, we consider TV-based models in the framework of graphs for image segmentation problems. Here, spectral properties combined with matrix completion techniques are needed to overcome the computational limitations due to the large amount of image data. Further, a semi-supervised technique for the measurement of the segmented region by means of the Hough transform is proposed.
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O'Neill, Finbarr Gerard. "Mathematical model of trawl cod-end geometry." Thesis, University of Aberdeen, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265381.
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To ensure that the conservation regulations which govern fishing gears are effective, they must be based on an understanding of the process by which fish are selected. The region where most fish selection is considered to take place is the cod-end, the aftmost part of a trawl net and the region where the catch accumulates. In recent years, it has become increasingly apparent that fish selection in the cod-end is dependent on a range of physical, environmental and fish behavioural parameters. Essential to a study of any of these parameters is a knowledge of the cod-end geometry which is determined by the interaction of the water flow, the catch size and the design and physical characteristics of the netting. In this thesis a continuum model of the deformation of a class of axisymmetric networks is developed where the mesh elements are reflection symmetric, the mesh bars are extensible and where arbitrary membrane forces act in the plane of the net, normal to the edges of the mesh elements. When applied to the fishing industry this provides a continuum model of the geometry of an axisymmetric trawl cod-end made from netting of a generalized mesh shape. It is shown how mesh shapes that are of interest to the fishing industry can be investigated, and the geometry of cod-ends made from diamond shaped mesh under the influence of various types of pressure loads is examined in detail. A qualitative description of the hydrodynamic forces that act on the cod-end catch is presented and it is shown that the predictions based on this description are consistent with experimental results from a series of wind tunnel trials. Using this description of the hydrodynamic forces the effect on cod-end geometry of mesh resistance to opening which arises as a result of twine flexural rigidity is examined.
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Franceschiello, Benedetta. "Cortical based mathematical models of geometric optical illusions." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066131/document.
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Cette thèse présente des modèles mathématiques pour la perception visuelle et s'occupe des phénomènes où on reconnait une brèche entre ce qui est représenté et ce qui est perçu. La complétion amodale consiste en percevoir un complètement d'un object qui est partiellement occlus, en opposition avec la complétion modale, dans laquelle on perçoit un object même si ses contours ne sont pas présents dans l'image [Gestalt, 99]. Ces contours, appelés illusoires, sont reconstruits par notre système visuelle et ils sont traités par les cortex visuels primaires (V1/V2) [93]. Des modèles géométriques de l'architecture fonctionnelle de V1 on le retrouve dans le travail de Hoffman [86]. Dans [139] Petitot propose un modèle pour le complètement de contours, équivalent neurale du modèle proposé par Mumford [125]. Dans cet environnement Citti et Sarti introduisent un modèle basé sur l'architecture fonctionnelle de la cortex visuel [28], qui justifie les illusions à un niveau neurale et envisage un modèle neuro-géometrique pour V1. Une autre classe sont les illusions d'optique géométriques (GOI), découvertes dans le XIX siècle [83, 190], qui apparaissent en présence d'une incompatibilité entre ce qui est présent dans l'espace object et le percept. L'idée fondamentale développée ici est que les GOIs se produisent suite à une polarisation de la connectivité de V1/V2, responsable de l'illusion. A partir de [28], où la connectivité qui construit les contours en V1 est modelée avec une métrique sub-Riemannian, on étend cela en disant que pour le GOIs la réponse corticale du stimule initial module la connectivité, en devenant un coefficient pour la métrique. GOIs seront testés avec ce modèle<br>This thesis presents mathematical models for visual perception and deals with such phenomena in which there is a visible gap between what is represented and what we perceive. A phenomenon which drew the interest most is amodal completion, consisting in perceiving a completion of a partially occluded object, in contrast with the modal completion, where we perceive an object even though its boundaries are not present [Gestalt theory, 99]. Such boundaries reconstructed by our visual system are called illusory contours, and their neural processing is performed by the primary visual cortices (V1/V2), [93]. Geometric models of the functional architecture of primary visual areas date back to Hoffman [86]. In [139] Petitot proposed a model of single boundaries completion through constraint minimization, neural counterpart of the model of Mumford [125]. In this setting Citti and Sarti introduced a cortical based model [28], which justifies the illusions at a neural level and provides a neurogeometrical model for V1. Another class of phenomena are Geometric optical illusions (GOIs), discovered in the XIX century [83, 190], arising in presence of a mismatch of geometrical properties between an item in object space and its associated percept. The fundamental idea developed here is these phenomena arise due to a polarization of the connectivity of V1/V2, responsible for the misperception. Starting from [28] in which the connectivity building contours in V1 is modeled as a sub-Riemannian metric, we extend it claiming that in GOIs the cortical response to the stimulus modulates the connectivity of the cortex, becoming a coefficient for the metric. GOIs will be tested through this model
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Dunn, Sara-Jane Nicole. "Towards a computational model of the colonic crypt with a realistic, deformable geometry." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:c3c9440a-52ac-4a3d-8e1c-5dc276b8eb6c.
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Colorectal cancer (CRC) is one of the most prevalent and deadly forms of cancer. Its high mortality rate is associated with difficulties in early detection, which is crucial to survival. The onset of CRC is marked by macroscopic changes in intestinal tissue, originating from a deviation in the healthy cell dynamics of glands known as the crypts of Lieberkuhn. It is believed that accumulated genetic alterations confer on mutated cells the ability to persist in the crypts, which can lead to the formation of a benign tumour through localised proliferation. Stress on the crypt walls can lead to buckling, or crypt fission, and the further spread of mutant cells. Elucidating the initial perturbations in crypt dynamics is not possible experimentally, but such investigations could be made using a predictive, computational model. This thesis proposes a new discrete crypt model, which focuses on the interaction between cell- and tissue-level behaviour, while incorporating key subcellular components. The model contains a novel description of the role of the surrounding tissue and musculature, which allows the shape of the crypt to evolve and deform. A two-dimensional (2D) cross-sectional geometry is considered. Simulation results reveal how the shape of the crypt base may contribute mechanically to the asymmetric division events typically associated with the stem cells in this region. The model predicts that epithelial cell migration may arise due to feedback between cell loss at the crypt collar and density-dependent cell division, an hypothesis which can be investigated in a wet lab. Further, in silico experiments illustrate how this framework can be used to investigate the spread of mutations, and conclude that a reduction in cell migration is key to confer persistence on mutant cell populations. A three-dimensional (3D) model is proposed to remove the spatial restrictions imposed on cell migration in 2D, and preliminary simulation results agree with the hypotheses generated in 2D. Computational limitations that currently restrict extension to a realistic 3D geometry are discussed. These models enable investigation of the role that mechanical forces play in regulating tissue homeostasis, and make a significant contribution to the theoretical study of the onset of crypt deformation under pre-cancerous conditions.
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Sanfelice, Paulo Cesar. "Embalando e despachando: a relação mútua entre modelos geométricos e a aprendizagem escolar." Universidade Tecnológica Federal do Paraná, 2017. http://repositorio.utfpr.edu.br/jspui/handle/1/2734.
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Este trabalho apresenta uma proposta de abordagem de modelação matemática voltada principalmente aos últimos anos da educação básica. Com base nos pressupostos da resolução de problemas, explora-se diversos conteúdos com significação. O fenômeno social a ser modelado consiste no formato e variações nas dimensões de embalagens a serem despachadas pelos Correios. As representações geométrica, gráfica e algébrica serão valorizadas no decorrer do desenvolvimento das atividades. A título de aprofundamento dos estudos, serão sugeridas algumas articulações possíveis entre conteúdos da educação básica e da graduação, como por exemplo, entre a função quadrática e estudo de máximos e mínimos, limites e derivadas.<br>This work presents a proposal for a mathematical modeling approach focused mainly on the last years of basic education. Based on the assumptions of solving problem, it explores several meaningful content. The social problem to be modeled consists of the format and variations in the dimensions of packages to be despatched by the Correios. The geometric, graphic and algebraic representations will be valued during the development of activities. In order to deepen the studies, it will be suggested some possible articulations between contents of basic and undergraduate education, for example, between the quadratic function and study of maximum and minimum, limits and derivatives.
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Safuanov, Ildar S., and Valery A. Gusev. "Creative mathematical activity of the students in the model of differentiated teaching in Russian Federation." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-80882.
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In this paper, creative mathematical activities of school pupils in conditions of the differentiated teaching in Russian Federation are described. Various forms of differentiated teaching (internal – level, external – profile) are characterized. Ways of using entertaining problems for detecting and fostering mathematical abilities are revealed. New course of geometry for differentiated teaching is introduced.
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Björnberg, Jakob Erik. "Graphical representations of Ising and Potts models : stochastic geometry of the quantum Ising model and the space-time Potts model." Thesis, University of Cambridge, 2010. https://www.repository.cam.ac.uk/handle/1810/224774.
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Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as external conditions are varied. Two models in particular are of great interest to mathematicians, namely the Ising model of a magnet and the percolation model of a porous solid. These models in turn are part of the unifying framework of the random-cluster representation, a model for random graphs which was first studied by Fortuin and Kasteleyn in the 1970's. The random-cluster representation has proved extremely useful in proving important facts about the Ising model and similar models. In this work we study the corresponding graphical framework for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960's. The second model is the space-time percolation process, which is closely related to the contact model for the spread of disease. In Chapter 2 we define the appropriate 'space-time' random-cluster model and explore a range of useful probabilistic techniques for studying it. The space-time Potts model emerges as a natural generalization of the quantum Ising model. The basic properties of the phase transitions in these models are treated in this chapter, such as the fact that there is at most one unbounded fk-cluster, and the resulting lower bound on the critical value in Z. In Chapter 3 we develop an alternative graphical representation of the quantum Ising model, called the random-parity representation. This representation is based on the random-current representation of the classical Ising model, and allows us to study in much greater detail the phase transition and critical behaviour. A major aim of this chapter is to prove sharpness of the phase transition in the quantum Ising model - a central issue in the theory - and to establish bounds on some critical exponents. We address these issues by using the random-parity representation to establish certain differential inequalities, integration of which give the results. In Chapter 4 we explore some consequences and possible extensions of the results established in Chapters 2 and 3. For example, we determine the critical point for the quantum Ising model in Z and in 'star-like' geometries.
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Passaro, Davide. "Model building on gCICYs." Thesis, Uppsala universitet, Institutionen för fysik och astronomi, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-411813.
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Prompted by the success of heterotic line bundle model building on Complete Intersection Calabi Yau (CICY) manifolds and the new developments regarding a generalization thereof, I analyze the possibility of model building on generalized CICY (gCICY) manifolds. Ultimately this is realized on two examples of gCICYs, one of which topologically equivalent to a CICY and one inequivalent to any previously studied examples. The first chapter is dedicated to reporting background information on CICYs and gCICYs. The mathematical machinery of CICYs and their generalizations are introduced alongside explicit constructions of two examples. The second chapter introduces the reader to heterotic line bundle model building on CICYs and gCICYs. In the setting of gCICYs, similar to regular CICYs, model building is accomplished in two steps: first the larger $E_{8}$ gauge group is broken to an $SU( 5 )$ grand unified theory through a line bundle model. Then the GUT is broken using Wilson line symmetry breaking, for which the presence of a freely acting discrete symmetry must be established. To that end, I proceed to show that the two previous examples benefit from a $\mathbb{Z}_{2}$ freely acting discrete symmetry. Utilizing this symmetry I construct 20 and 11 explicit models for the two gCICY examples respectively, by scanning over a finite range of line bundle charges.<br>Ett av de största problemen i modern teoretisk fysik är att hitta en teori för kvantgravitation.För en konsekvent kvantteori gravitation skulle vara en väsentlig del i fysikens pussel, och koppla samman gravitationsfysiken för planeter och galaxer, som beskrivs av allmänna relativitetsteorin, till fysiken för partiklar, beskrivet av kvantfältteori.Bland de mest lovande teorierna finns strängteorin som föreslår att ersätta partiklar med strängar som materiens grundläggande beståndsdel.Förutom att lösa kvantgravitationproblemet hoppas teoretiska fysiker genom strängteorin att förenkla beskrivningen av partikelfysik.Detta skulle ske genom att ersätta hela partikelzoo med ett enda objekt: strängen.Olika vibrationer i strängen skulle motsvara olika partiklar och interaktioner mellan strängar skulle motsvara interaktioner mellan partiklar.För att vara motsägelsefri kräver dock strängteori att det finns minst sex fler dimensioner än de vi kan uppleva.En av strategierna som för närvarande studeras för att förlika extra dimensioner med och moderna experiment kallas ``kompaktifiering'' eller ``compactification'' på engelska.Strategin föreslår att dessa extra dimensioner ska vara kompakta och så små att de är osynliga för observationer.Interesant nog påverkar geometrin i det sexdimensionella kompakta rummet i stor utsträckning fysiken som strängteorin producerar: olika rum skulle producera olika partiklar och olika grundläggande naturkrafter.I den här uppsatsen studerar jag två exempel på sådana sexdimensionella rum som kommer från en uppsättning av rum som kallas `` generaliserade CICYs'' som nyligen har upptäckts.Med hjälp av de tekniker som liknar de som har utvecklats för andra liknade rum, visar jag att vissa aspekter av en strängteori kompaktifierad på generaliserade CICY återspeglar de som mäts genom moderna partikelfysikexperiment.
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Osta, Iman M. "From Physical Model To Proof For Understanding Via DGS: Interplay Among Environments." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-80806.
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The widespread use of Dynamic Geometry Software (DGS) is raising many interesting questions and discussions as to the necessity, usefulness and meaning of proof in school mathematics. With these questions in mind, a didactical sequence on the topic “Conics” was developed in a teacher education course tailored for pre-service secondary math methods course. The idea of the didactical sequence is to introduce “Conics” using a concrete manipulative approach (paper folding) then an explorative DGS-based construction activity embedding the need for a proof. For that purpose, the DGS software serves as an intermediary tool, used to bridge the gap between the
physical model and the formal symbolic system of proof. The paper will present an analysis of participants’ geometric thinking strategies, featuring proof as an embedded process in geometric construction situations.
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Roberts, Gwendolyn Rose 1963. "A comparison of multiple univariate and multivariate geometric moving average control charts." Thesis, The University of Arizona, 1988. http://hdl.handle.net/10150/276779.
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This study utilizes a Monte Carlo simulation to examine the performance of multivariate geometric moving average control chart schemes for controlling the mean of a multivariate normal process. The study compares the performance of the proposed method with a multivariate Shewhart chart, a multiple univariate cumulative sum (CUSUM) control chart, a multivariate CUSUM control chart and a multiple univariate geometric moving average control chart.
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Harvey, Emily Paige. "Analysing mathematical models of intracellular calcium dynamics using geometric singular perturbation techniques." Thesis, University of Auckland, 2011. http://hdl.handle.net/2292/10814.
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Oscillations in free intracellular calcium (Ca2+) concentration are known to act as signals in almost all cell types, transmitting messages which control cellular processes including muscle contraction, cellular secretion and neuronal firing. Due to the universal nature of calcium oscillations, understanding the physiological mechanisms that underlie them is of great importance. A key feature of intracellular calcium dynamics that has been found experimentally is that some physiological processes occur much faster than others. This leads to models with variables evolving on very different time scales. In this thesis we survey a range of representative models of intracellular calcium dynamics, using geometric singular perturbation techniques with the aim of determining the usefulness of these techniques and what their limitations are. We find that the number of distinct time scales and the number of variables evolving on each time scale varies between models, but that in all cases there are at least two time scales, with at least two slower variables. Using geometric singular perturbation techniques we identify parameter regimes in which relaxation oscillations are seen and those where canard induced mixed mode oscillations are present. We find that in some cases these techniques are very useful and explain the observed dynamics well, but that the theory is limited in its ability to explain the dynamics when there are three or more distinct time scales in a model. It has been proposed that a simple experiment, whereby a pulse of inositol (1,4,5)- trisphosphate (IP3) is applied to a cell, can be used to distinguish between two competing mechanisms which lead to calcium oscillations [53]. However, detailed mathematical investigation of models has identified an anomalous delay in the pulse responses of some models, making interpretation of the experimental data difficult [14]. In this thesis we find that the response of models to a pulse of IP3 can be understood in part by using geometric singular perturbation techniques. Using recently developed theory for systems with three or more slow variables, we find that the anomalous delay can be due to the presence of folded nodes and their corresponding canard solutions or due to the presence of a curve of folded saddles. This delay due to a curve of folded saddles is a novel delay mechanism that can occur in systems with three or more slow variables. Importantly, we find that in some models the response to a pulse of IP3 is contrary to predictions for all bifurcation parameter values, which invalidates the proposed experimental protocol.
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Londani, Mukhethwa. "Numerical Methods for Mathematical Models on Warrant Pricing." University of the Western Cape, 2010. http://hdl.handle.net/11394/8210.
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>Magister Scientiae - MSc<br>Warrant pricing has become very crucial in the present market scenario. See, for example, M. Hanke and K. Potzelberger, Consistent pricing of warrants and traded options, Review Financial Economics 11(1) (2002) 63-77 where the authors indicate that warrants issuance affects the stock price process of the issuing company. This change in the stock price process leads to subsequent changes in the prices of options written on the issuing company's stocks. Another notable work is W.G. Zhang, W.L. Xiao and C.X. He, Equity warrant pricing model under Fractional Brownian motion and an empirical study, Expert System with Applications 36(2) (2009) 3056-3065 where the authors
construct equity warrants pricing model under Fractional Brownian motion and deduce the European options pricing formula with a simple method. We study this paper in details in this mini-thesis. We also study some of the mathematical models on warrant pricing using the Black-Scholes framework. The relationship between the price of the warrants and the price of the call accounts for the dilution effect is also studied mathematically. Finally we do some numerical simulations to derive the value of warrants.
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Osta, Iman M. "From Physical Model To Proof For Understanding Via DGS:Interplay Among Environments." Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 464 - 468, 2012. https://slub.qucosa.de/id/qucosa%3A1798.
Full textAbstract:
The widespread use of Dynamic Geometry Software (DGS) is raising many interesting questions and discussions as to the necessity, usefulness and meaning of proof in school mathematics. With these questions in mind, a didactical sequence on the topic “Conics” was developed in a teacher education course tailored for pre-service secondary math methods course. The idea of the didactical sequence is to introduce “Conics” using a concrete manipulative approach (paper folding) then an explorative DGS-based construction activity embedding the need for a proof. For that purpose, the DGS software serves as an intermediary tool, used to bridge the gap between the
physical model and the formal symbolic system of proof. The paper will present an analysis of participants’ geometric thinking strategies, featuring proof as an embedded process in geometric construction situations.
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Skoczelas, Brenda M. "A mathematical model for calculating the effect of toroidal geometry on the measured magnetic field." Muncie, Ind. : Ball State University, 2009. http://cardinalscholar.bsu.edu/714.
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Steyn, Catherina. "An investigation of the link between the typical geometry errors and the Van Hiele levels of geometric thought of grade 9 learners." Thesis, Nelson Mandela Metropolitan University, 2017. http://hdl.handle.net/10948/12152.
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South African learners perform poorly in the geometry sections of both national and international assessments. Numerous assessment reports mention multiple errors that keep re-occurring and play a big role in the learners’ poor performance. For this research, the link between the grade 9 learners Van Hiele levels of thought and the typical errors that they made were investigated. In this mixed method study, 194 grade 9 learners in two schools in Port Elizabeth, South Africa were tested using a Van Hiele based test. A test was set up containing multiple-choice and open-ended questions and was used to determine firstly, the predominant level of geometric reasoning of the learners and secondly, to determine their typical errors. Semi-structured interviews were held with six learners to gain more insight into some of the typical errors uncovered in the tests. The quantitative data revealed that the learners’ predominant levels of geometric thought were low. Furthermore, the qualitative data revealed typical error patterns concerning angles and sides, parallel lines, hierarchy of quadrilaterals and incorrect reasons in the proofs. The quantitative and qualitative data was merged to determine if the errors could be linked to the Van Hiele levels. From the findings, it was concluded that most of their typical errors could be linked to the Van Hiele levels of the learners.
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Barcenas, Carolina. "Geometric tolerance verification using superquadrics." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/25603.
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El-Berry, S. E. M. "Some geometric and negative binomial time series models." Thesis, University of Strathclyde, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381119.
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Björnberg, Jakob Erik. "Graphical representations of Ising and Potts models : Stochastic geometry of the quantum Ising model and the space-time Potts model." Doctoral thesis, KTH, Matematik (Inst.), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11267.
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HTML clipboard Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as external conditions are varied. Two models in particular are of great interest to mathematicians, namely the Ising model of a magnet and the percolation model of a porous solid. These models in turn are part of the unifying framework of the random-cluster representation, a model for random graphs which was first studied by Fortuin and Kasteleyn in the 1970’s. The random-cluster representation has proved extremely useful in proving important facts about the Ising model and similar models. In this work we study the corresponding graphical framework for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960’s. The second model is the space–time percolation process, which is closely related to the contact model for the spread of disease. In Chapter 2 we define the appropriate space–time random-cluster model and explore a range of useful probabilistic techniques for studying it. The space– time Potts model emerges as a natural generalization of the quantum Ising model. The basic properties of the phase transitions in these models are treated in this chapter, such as the fact that there is at most one unbounded fk-cluster, and the resulting lower bound on the critical value in <img src="http://upload.wikimedia.org/math/a/b/8/ab820da891078a8245d7f4f3252aee4f.png" />. In Chapter 3 we develop an alternative graphical representation of the quantum Ising model, called the random-parity representation. This representation is based on the random-current representation of the classical Ising model, and allows us to study in much greater detail the phase transition and critical behaviour. A major aim of this chapter is to prove sharpness of the phase transition in the quantum Ising model—a central issue in the theory— and to establish bounds on some critical exponents. We address these issues by using the random-parity representation to establish certain differential inequalities, integration of which gives the results. In Chapter 4 we explore some consequences and possible extensions of the results established in Chapters 2 and 3. For example, we determine the critical point for the quantum Ising model in <img src="http://upload.wikimedia.org/math/a/b/8/ab820da891078a8245d7f4f3252aee4f.png" /> and in ‘star-like’ geometries.<br>HTML clipboard Statistisk fysik syftar till att förklara ett materials makroskopiska egenskaper i termer av dess mikroskopiska struktur. En särskilt intressant egenskap är är fenomenet fasövergång, det vill säga en plötslig förändring i de makroskopiska egenskaperna när externa förutsättningar varieras. Två modeller är särskilt intressanta för en matematiker, nämligen Ising-modellen av en magnet och perkolationsmodellen av ett poröst material. Dessa två modeller sammanförs av den så-kallade fk-modellen, en slumpgrafsmodell som först studerades av Fortuin och Kasteleyn på 1970-talet. fk-modellen har sedermera visat sig vara extremt användbar för att bevisa viktiga resultat om Ising-modellen och liknande modeller. I den här avhandlingen studeras den motsvarande grafiska strukturen hos två näraliggande modeller. Den första av dessa är den kvantteoretiska Isingmodellen med transverst fält, vilken är en utveckling av den klassiska Isingmodellen och först studerades av Lieb, Schultz och Mattis på 1960-talet. Den andra modellen är rumtid-perkolation, som är nära besläktad med kontaktmodellen av infektionsspridning. I Kapitel 2 definieras rumtid-fk-modellen, och flera probabilistiska verktyg utforskas för att studera dess grundläggande egenskaper. Vi möter rumtid-Potts-modellen, som uppenbarar sig som en naturlig generalisering av den kvantteoretiska Ising-modellen. De viktigaste egenskaperna hos fasövergången i dessa modeller behandlas i detta kapitel, exempelvis det faktum att det i fk-modellen finns högst en obegränsad komponent, samt den undre gräns för det kritiska värdet som detta innebär. I Kapitel 3 utvecklas en alternativ grafisk framställning av den kvantteoretiska Ising-modellen, den så-kallade slumpparitetsframställningen. Denna är baserad på slumpflödesframställningen av den klassiska Ising-modellen, och är ett verktyg som låter oss studera fasövergången och gränsbeteendet mycket närmare. Huvudsyftet med detta kapitel är att bevisa att fasövergången är skarp—en central egenskap—samt att fastslå olikheter för vissa kritiska exponenter. Metoden består i att använda slumpparitetsframställningen för att härleda vissa differentialolikheter, vilka sedan kan integreras för att lägga fast att gränsen är skarp. I Kapitel 4 utforskas några konsekvenser, samt möjliga vidareutvecklingar, av resultaten i de tidigare kapitlen. Exempelvis bestäms det kritiska värdet hos den kvantteoretiska Ising-modellen på <img src="http://upload.wikimedia.org/math/a/b/8/ab820da891078a8245d7f4f3252aee4f.png" /> , samt i ‘stjärnliknankde’ geometrier.<br>QC 20100705
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Cordner, Nathan James. "Isomorphisms of Landau-Ginzburg B-Models." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/5882.
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Landau-Ginzburg mirror symmetry predicts isomorphisms between graded Frobenius algebras (denoted A and B) that are constructed from a nondegenerate quasihomogeneous polynomial W and a related group of symmetries G. In 2013, Tay proved that given two polynomials W1, W2 with the same quasihomogeneous weights and same group G, the corresponding A-models built with (W1, G) and (W2, G) are isomorphic. An analogous theorem for isomorphisms between orbifolded B-models remains to be found. This thesis investigates isomorphisms between B-models using polynomials in two variables in search of such a theorem. In particular, several examples are given showing the relationship between continuous deformation on the B-side and isomorphisms that stem as a corollary to Tay's theorem via mirror symmetry. Results on extending known isomorphisms between unorbifolded B-models to the orbifolded case are exhibited. A general pattern for B-model isomorphisms, relating mirror symmetry and continuous deformation together, is also observed.
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Solus, Liam. "Polyhedral Problems in Combinatorial Convex Geometry." UKnowledge, 2015. http://uknowledge.uky.edu/math_etds/32.
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In this dissertation, we exhibit two instances of polyhedra in combinatorial convex geometry. The first instance arises in the context of Ehrhart theory, and the polyhedra are the central objects of study. The second instance arises in algebraic statistics, and the polyhedra act as a conduit through which we study a nonpolyhedral problem.
In the first case, we examine combinatorial and algebraic properties of the Ehrhart h*-polynomial of the r-stable (n,k)-hypersimplices. These are a family of polytopes which form a nested chain of subpolytopes within the (n,k)-hypersimplex. We show that a well-studied unimodular triangulation of the (n,k)-hypersimplex restricts to a triangulation of each r-stable (n,k)-hypersimplex within. We then use this triangulation to compute the facet-defining inequalities of these polytopes. In the k=2 case, we use shelling techniques to devise a combinatorial interpretation of the coefficients of the h*-polynomials in terms of independent sets of certain graphs. From this, we then extract some results on unimodality. We also characterize the Gorenstein r-stable (n,k)-hypersimplices, and we conclude that these also have unimodal h*-polynomials.
In the second case, for a graph G on p vertices we consider the closure of the cone of concentration matrices of G. The extreme rays of this cone, and their associated ranks, have applications in maximum likelihood estimation for the undirected Gaussian graphical model associated to G. Consequently, the extreme ranks of this cone have been well-studied. Yet, there are few graph classes for which all the possible extreme ranks are known. We show that the facet-normals of the cut polytope of G can serve to identify extreme rays of this nonpolyhedral cone. We see that for graphs without K5 minors each facet-normal of the cut polytope identifies an extreme ray in the cone, and we determine the rank of this extreme ray. When the graph is also series-parallel, we find that all possible extreme ranks arise in this fashion, thereby extending the collection of graph classes for which all the possible extreme ranks are known.
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Calin, Ovidiu, and Chang Der-Chen. "The geometry on a step 3 Grushin model." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2672/.
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In this article we study the geometry associated with the sub-elliptic operator ½ (X²1 +X²2), where X1 = ∂x and X2 = x²/2 ∂y are vector fields on R². We show that any point can be connected with the origin by at least one geodesic and we provide an approximate formula for the number of the geodesics between the origin and the points situated outside of the y-axis. We show there are in¯nitely many geodesics between the origin and the points on the y-axis.
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Nollett, William R. "Phase transitions and the random-cluster representation for Delaunay Potts models with geometry-dependent interactions." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/60465/.
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We investigate the existence of phase transitions for a class of continuum multi-type particle systems. The interactions act on hyperedges between the particles, allowing us to define a class of models with geometry-dependent interactions. We establish the existence of stationary Gibbsian point processes for this class of models. A phase transition is defined with respect to the existence of multiple Gibbs measures, and we establish the existence of phase transitions in our models by proving that multiple Gibbs measures exist. Our approach involves introducing a random-cluster representation for continuum particle systems with geometry-dependent interactions. We then argue that percolation in the random-cluster model corresponds to the existence of a phase transition. The originality in this research is defining a random-cluster representation for continuum models with hyperedge interactions, and applying this representation in order to show the existence of a phase transition. We mainly focus on models where the interaction is defined in terms of the Delaunay hypergraph. We find that phase transitions exist for a class of models where the interaction between particles is via Delaunay edges or Delaunay triangles.
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Van, Putten Sonja. "Levels of thought in geometry of pre-service mathematics educators according to the van Hiele model." Diss., University of Pretoria, 2008. http://hdl.handle.net/2263/24834.
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This study aimed to investigate the level of understanding of Euclidian geometry, in terms of theoretical knowledge as well as its problem-solving application, in pre-service mathematics education (PME) students at the University of Pretoria. In order to do so, a one group pre-test/ post-test procedure was conducted around an intensive geometry module, and a representational group of students was interviewed before and after the module to discuss their high school experiences of learning geometry and to analyse their attitudes towards the subject. The van Hiele Theory of Levels of Thought in Geometry was used as the theoretical framework for this study. The PME students in this study, prior to their completion of the geometry module, lacked the content knowledge, skills and insight in Euclidian geometry that is expected at matric level (Level 3). The pre-test results revealed that half the group could only be classified as being on Level 0. By the time the post-test was written, 60% of the group had moved onto Level 1 as their maximum competence level. This implies that these students were all brought to greater insight by the teaching they received during the geometry module. However, the overall improvement in the group as revealed in the post-test results, consisted of an upward movement of only one level. Therefore, the geometry module offered did not bring about sufficient improvement for these students to be able to teach geometry adequately (Level 3 is required). The students who were interviewed for this study uniformly expressed their dislike or fear of Euclidian geometry in general, but described the positive change in their attitude during the course of the module because of the way it was presented. Training of students for a career as mathematics educators which includes an in-depth van Hiele-based geometry module would facilitate the acquisition of insight and relational understanding.<br>Dissertation (MEd)--University of Pretoria, 2008.<br>Curriculum Studies<br>MEd<br>unrestricted
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Delbem, Nilton Flávio. "Introdução matemática aos modelos cosmológicos /." Rio Claro : [s.n.], 2010. http://hdl.handle.net/11449/94340.
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Orientador: Wladimir Seixas<br>Banca: Manoel Borges Ferreira Neto<br>Banca: Henrique Lazari<br>Resumo: Esta dissertação tem a proposta de organizar, discutir e apresentar de maneira precisa os conceitos matemáticos de variedade diferenciável e de tensores envolvidos no estudo da Cosmologia sob o ponto de vista da Teoria da Relatividade Geral para o modelo de Friedmann-Lemaître-Robertson-Walker. Busca-se assim apresentar um texto didático que possa ser utilizado tanto nos cursos de graduação em Matemática como de Física para uma disciplina optativa de Introdução Matemática à Cosmologia<br>Abstract: The goal of this dissertation is to organize and discuss in a rigorous way the mathematical concepts of manifolds and tensors needed to the study of Cosmology and the Friedmann-Lemaître-Robertson-Walker model under the point of view of the General Relativity. In this way, this dissertation was written as textbook that could be used in an undergraduate course of Physics and Mathematics<br>Mestre
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Delbem, Nilton Flávio [UNESP]. "Introdução matemática aos modelos cosmológicos." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/94340.
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delbem_nf_me_rcla.pdf: 885461 bytes, checksum: 9ba35dff1d53b0378c1e134087c575b7 (MD5)<br>Universidade Estadual Paulista (UNESP)<br>Esta dissertação tem a proposta de organizar, discutir e apresentar de maneira precisa os conceitos matemáticos de variedade diferenciável e de tensores envolvidos no estudo da Cosmologia sob o ponto de vista da Teoria da Relatividade Geral para o modelo de Friedmann-Lemaître-Robertson-Walker. Busca-se assim apresentar um texto didático que possa ser utilizado tanto nos cursos de graduação em Matemática como de Física para uma disciplina optativa de Introdução Matemática à Cosmologia<br>The goal of this dissertation is to organize and discuss in a rigorous way the mathematical concepts of manifolds and tensors needed to the study of Cosmology and the Friedmann-Lemaître-Robertson-Walker model under the point of view of the General Relativity. In this way, this dissertation was written as textbook that could be used in an undergraduate course of Physics and Mathematics
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Herrera-Valdez, Marco Arieli. "Geometry and nonlinear dynamics underlying excitability phenotypes in biophysical models of membrane potential." Diss., The University of Arizona, 2014. http://hdl.handle.net/10150/312741.
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The main goal of this dissertation was to study the bifurcation structure underlying families of low dimensional dynamical systems that model cellular excitability. One of the main contributions of this work is a mathematical characterization of profiles of electrophysiological activity in excitable cells of the same identified type, and across cell types, as a function of the relative levels of expression of ion channels coded by specific genes. In doing so, a generic formulation for transmembrane transport was derived from first principles in two different ways, expanding previous work by other researchers. The relationship between the expression of specific membrane proteins mediating transmembrane transport and the electrophysiological profile of excitable cells is well reproduced by electrodiffusion models of membrane potential involving as few as 2 state variables and as little as 2 transmembrane currents. Different forms of the generic electrodiffusion model presented here can be used to study the geometry underlying different forms of excitability in cardiocytes, neurons, and other excitable cells, and to simulate different patterns of response to constant, time-dependent, and (stochastic) time- and voltage-dependent stimuli. In all cases, an initial analysis performed on a deterministic, autonoumous version of the system of interest is presented to develop basic intuition that can be used to guide analyses of non-autonomous or stochastic versions of the model. Modifications of the biophysical models presented here can be used to study complex physiological systems involving single cells with specific membrane proteins, possibly linking different levels of biological organization and spatio-temporal scales.
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Francis, Benjamin Lane. "Information Geometry and Model Reduction in Oscillatory and Networked Systems." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8512.
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In this dissertation, I consider the problem of model reduction in both oscillatory and networked systems. Previously, the Manifold Boundary Approximation Method (MBAM) has been demonstrated as a data-driven tool for reducing the parametric complexity of so-called sloppy models. To be effective, MBAM requires the model manifold to have low curvature. I show that oscillatory models are characterized by model manifolds with high curvature in one or more directions. I propose methods for transforming the model manifolds of these models into ones with low curvature and demonstrate on a couple of test systems. I demonstrate MBAM as a tool for data-driven network reduction on a small model from power systems. I derive multiple effective networks for the model, each tailored to a specific choice of system observations. I find several important types of parameter reductions, including network reductions, which can be used in large power systems models. Finally, I consider the problem of piecemeal reduction of large systems. When a large system is split into pieces that are to be reduced separately using MBAM, there is no guarantee that the reduced pieces will be compatible for reassembly. I propose a strategy for reducing a system piecemeal while guaranteeing that the reduced pieces will be compatible. I demonstrate the reduction strategy on a small resistor network.
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Schmidtt, David Marmolejo. "Aspectos geométricos dos modelos de Toda /." São Paulo, 2005. http://hdl.handle.net/11449/132694.
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Orientador: José Francisco Gomes<br>Banca: Abraham Hirsz Zimerman<br>Banca: Eliezer Batista<br>Resumo: Nesta dissertação estudamos as estruturas geométricas e algébricas subjacentes aos modelos de Toda. Primeiramente, vemos como as equações de Toda são consequência da condição de curvatura nula de um certo fibrado principal holomórfico e posteriormente, introduzimos a formulação Lagrangiana dos mesmos, como perturbações integráveis de um modelo de WZW calibrado num espaço quociente. Terminamos com um estudo da dualidade própria destas teorias<br>Abstract: In this work we study the differential geometry formulation of Toda models. Firstly showing how the Toda equations are consequence of the zero curvature condition of a given holomorfic principal bundle and later introducing the Lagrangian formulation of the Toda models as integrable perturbations of a gauged WZW model in a special coset. We end up with a study of the duality properties of such class of theories<br>Mestre
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Henninger, Helen Clare. "The symmetry group of a model of hyperbolic plane geometry and some associated invariant optimal control problems." Thesis, Rhodes University, 2012. http://hdl.handle.net/10962/d1018232.
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In this thesis we study left-invariant control offine systems on the symmetry group of a. model of hyperbolic plane geometry, the matrix Lie group SO(1, 2)₀. We determine that there are 10 distinct classes of such control systems and for typical elements of two of these classes we provide solutions of the left-invariant optimal wntrol problem with quauratic costs. Under the identification of the Lie allgebra .so(l, 2) with Minkowski spacetime R¹̕'², we construct a controllabilility criterion for all left-invariant control affine systems on 50(1. 2)₀ which in the inhomogeneous case depends only on the presence or absence of an element in the image of the system's trace in R¹̕ ²which is identifiable using the inner product. For the solutions of both the optimal control problems, we provide explicit expressions in terms of Jacobi elliptic functions for the solutions of the reduced extremal equations and determine the nonlinear stability of the equilibrium points.
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Brown, Matthew Robert. "Construction and Isomorphism of Landau-Ginzburg B-Model Frobenius Algebras." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/5652.
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Landau-Ginzburg Mirror Symmetry provides for the construction of two algebraic objects, called the A- and B-models. Special cases of these models–constructed using invertible polynomials and abelian symmetry groups–are well understood. In this thesis, we consider generalizations of the B-model, and specifically address the associativity of the multiplication in these models. We also prove an explicit B-model isomorphism for a class of polynomials in three variables.
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Kekana, Grace Ramatsimele. "Using GeoGebra in transformation geometry : an investigation based on the Van Hiele model." Diss., University of Pretoria, 2016. http://hdl.handle.net/2263/60947.
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This study investigated the use of an advanced technological development (free GeoGebra software) within the secondary educational setting in four relatively under-resourced schools in the Gauteng Province of South Africa. This advancement is viewed as having the potential to promote the teaching and learning of complex ideas in mathematics, even within traditionally deprived communities. The focus in this study was on the teaching and learning of transformation geometry at Grade 9 and attainment was reflected in terms of the van Hieles' levels of geometrical thinking. A mixed methods approach was followed, where data was collected through lesson observations, written tests and semi-structured interviews. Four Grade 9 teachers from four schools were purposively selected, while twenty-four mathematics learners (six from each school) in the Tshwane metropolitan region were randomly selected. The teachers' lesson observations and interview outcomes were coded and categorised into themes, and the learners' test scripts were marked and captured. The analysis of test scores was structured according to the van Hieles' levels of geometric thought development. As far as the use of GeoGebra is concerned, it was found that teachers used the program in preparation for, as well as during lessons; learners who had access to computers or android technology, used GeoGebra to help them with practice and exercises. As far as the effect of the use of GeoGebra is concerned, improved performance in transformation geometry was demonstrated.<br>Dissertation (MEd)--University of Pretoria, 2016.<br>Science, Mathematics and Technology Education<br>MEd<br>Unrestricted
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Ong, Jin Boon. "Geometric modeling of manufacturing processes variations for model-based tolerance analysis." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-05042006-164537/.
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Hernandez, Gabriel. "Platform design for customizable products as a problem of access in a geometric space." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/16760.
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Tran, Tat Dat [Verfasser], Jürgen [Akademischer Betreuer] Jost, Jürgen [Gutachter] Jost, and Shun-ichi [Gutachter] Amari. "Information Geometry and the Wright-Fisher model of Mathematical Population Genetics / Tat Dat Tran ; Gutachter: Jürgen Jost, Shun-ichi Amari ; Betreuer: Jürgen Jost." Leipzig : Universitätsbibliothek Leipzig, 2012. http://d-nb.info/1238077277/34.
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Goodrich, David Charles. "Geometric simplification of a distributed rainfall-runoff model over a range of basin scales." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/185051.
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Distributed rainfall-runoff models are gaining widespread acceptance; yet, a fundamental issue that must be addressed by all users of these models is definition of an acceptable level of watershed discretization (geometric model complexity). The level of geometric model complexity is a function of basin and climatic scales as well as the availability of input and verification data. Equilibrium discharge storage is employed to develop a quantitative methodology to define a level of geometric model complexity commensurate with a specified level of model performance. Equilibrium storage ratios are used to define the transition from overland to channel-dominated flow response. The methodology is tested on four subcatchments in the USDA-ARS Walnut Gulch Experimental Watershed in southeastern Arizona. The catchments cover a range of basins scales of over three orders of magnitude. This enabled a unique assessment of watershed response behavior as a function of basin scale. High quality, distributed, rainfall-runoff data were used to verify the model (KINEROSR). Excellent calibration and verification results provided confidence in subsequent model interpretations regarding watershed response behavior. An average elementary channel support area of roughly 15% of the total basin area is shown to provide a watershed discretization level that maintains model performance for basins ranging in size from 1.5 to 631 hectares. Detailed examination of infiltration, including the role and impacts of incorporating small-scale infiltration variability in a distribution sense, into KINEROSR, over a range of soils and climatic scales was also addressed. The impacts of infiltration and channel losses on runoff response increase with increasing watershed scale as the relative influence of storms is diminished in a semi-arid environment such as Walnut Gulch. In this semi-arid environment, characterized by ephemeral streams, watershed runoff response does not become more linear with increasing watershed scale but appears to become more nonlinear.