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Tonner, Jaromír. "Overcomplete Mathematical Models with Applications". Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2010. http://www.nusl.cz/ntk/nusl-233893.
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Chen, Donoho a Saunders (1998) studují problematiku hledání řídké reprezentace vektorů (signálů) s použitím speciálních přeurčených systémů vektorů vyplňujících prostor signálu. Takovéto systémy (někdy jsou také nazývány frejmy) jsou typicky vytvořeny buď rozšířením existující báze, nebo sloučením různých bazí. Narozdíl od vektorů, které tvoří konečně rozměrné prostory, může být problém formulován i obecněji v rámci nekonečně rozměrných separabilních Hilbertových prostorů (Veselý, 2002b; Christensen, 2003). Tento funkcionální přístup nám umožňuje nacházet v těchto prostorech přesnější reprezentace objektů, které, na rozdíl od vektorů, nejsou diskrétní. V této disertační práci se zabývám hledáním řídkých representací v přeurčených modelech časových řad náhodných veličin s konečnými druhými momenty. Numerická studie zachycuje výhody a omezení tohoto přístupu aplikovaného na zobecněné lineární modely a na vícerozměrné ARMA modely. Analýzou mnoha numerických simulací i modelů reálných procesů můžeme říci, že tyto metody spolehlivě identifikují parametry blízké nule, a tak nám umožňují redukovat původně špatně podmíněný přeparametrizovaný model. Tímto významně redukují počet odhadovaných parametrů. V konečném důsledku se tak nemusíme starat o řády modelů, jejichž zjišťování je většinou předběžným krokem standardních technik. Pro kratší časové řady (100 a méně vzorků) řídké odhady dávají lepší predikce v porovnání s těmi, které jsou založené na standardních metodách (např. maximální věrohodnosti v MATLABu - MATLAB System Identification Toolbox (IDENT)). Pro delší časové řady (500 a více) obě techniky dávají v podstatě stejně přesné predikce. Na druhou stranu řešení těchto problémů je náročnější, a to i časově, nicméně výpočetní doba je stále přijatelná.
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Jones, Jennifer Grace. "A mathematical model of emphysema". Thesis, University of Bristol, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269229.
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Durfee, Lucille J. "BIO-MATHEMATICS: INTRODUCTION TO THE MATHEMATICAL MODEL OF THE HEPATITIS C VIRUS". CSUSB ScholarWorks, 2016. https://scholarworks.lib.csusb.edu/etd/428.
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In this thesis, we will study bio-mathematics. We will introduce differential equations, biological applications, and simulations with emphasis in molecular events. One of the first courses of action is to introduce and construct a mathematical model of our biological element. The biological element of study is the Hepatitis C virus. The idea in creating a mathematical model is to approach the biological element in small steps. We will first introduce a block (schematic) diagram of the element, create differential equations that define the diagram, convert the dimensional equations to non-dimensional equations, reduce the number of parameters, identify the important parameters, and analyze the results. These results will tell us which variables must be adjusted to prevent the Hepatitis C virus from becoming chronic.
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Di, Domenico Chiara. "A mathematical model for migraine aura". Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12350/.
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Nella tesi è descritto un modello matematico per l'aura emicranica e, più precisamente, per lo scotoma scintillante (schema di fortificazione) e per la Cortical Spreading Depression, il fenomeno neuropatofisiologico alla base dell'aura. In particolare è spiegato un modello cinematico per l'evoluzione della CSD nella corteccia visiva primaria, considerata un mezzo debolmente eccitabile, la mappa retino-corticale e il modello, tramite fibrato, dei Pinwheels di V1.
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Thorsen, Kjetil. "Mathematical Model of the Geomagnetic Field". Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2006. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9329.
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First comes a description of a mathematical model of the geomagnetic field. Then some discussion of the classical non-uniqueness results of Backus. Further we look at more recent results concerning reconstruction of the geomagnetic field from intensity and the normal component of the field. New stability estimate for this reconstruction is obtained.
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Cho, Jae Hyun. "Computer aids for mathematical model-building". Thesis, Imperial College London, 1997. http://hdl.handle.net/10044/1/8256.
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Darabi, Pirooz. "A mathematical model for cement kilns". Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/32346.
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Rotary kilns have numerous industrial applications including cement production. Frequent operational
problems such as low thermal efficiency, refractory failure, and poor product quality have prompted
extensive efforts to improve and optimize their design. Mathematical modeling and Computational Fluid
Dynamics constitute effective tools recently used for these purposes.
A cement kiln consists of three major parts: the hot flow, the bed, and the wall. A CFD code which had
the capability of simulating the hot gas was developed further to simulate the kiln. In the present work,
two 1-D mathematical models are proposed and implemented in the existing CFD code. The first model
consists of the steady-state solution for the material and temperature evolution within the bed. The second
one simulates tire combustion in the kiln. The tire burning model assumes that tire combustion occurs in
two major successive steps, devolatization and char combustion. For the devolatization model, external
heat and mass transfer, three parallel reactions, and enthalpy effects are considered the dominant
phenomena. The char combustion model considers the enthalpy effect and the external mass transfer.
With the aid of the developed model, full-scale industrial cement kilns under steady-state and realistic
operational conditions are simulated. In addition, cement kilns with combustion of full scrap tires in the
middle of them are mathematically modeled. The limits and feasibility of tire combustion are further
explored by running numerical simulations with different tire flow rates and different injector locations.
The flow field, temperature distribution and species distribution are presented. Analysis of the results
indicates that, with the help of the proposed model, a better understanding of the important processes
within cement kilns can be obtained. The model can be used for addressing operational problems and
optimizing designs. It is also concluded that successful firing of tires can lead to a cheaper, longer lasting,
and less polluting kiln.Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate
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She, Chunfeng. "A mathematical model for power derivatives". [Bloomington, Ind.] : Indiana University, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3297110.
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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2007.Title from dissertation home page (viewed Sept. 29, 2008). Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1045. Adviser: Victor W. Goodman.
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Roose, T. "Mathematical model of plant nutrient uptake". Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365790.
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This thesis deals with the mathematical modelling of nutrient uptake by plant roots. It starts with the Nye-Tinker-Barber model for nutrient uptake by a single bare cylindrical root. The model is treated using matched asymptotic expansion and an analytic formula for the rate of nutrient uptake is derived for the first time. The basic model is then extended to include root hairs and mycorrhizae, which have been found experimentally to be very important for the uptake of immobile nutrients. Again, analytic expressions for nutrient uptake are derived. The simplicity and clarity of the analytical formulae for the solution of the single root models allows the extension of these models to more realistic branched roots. These models clearly show that the `volume averaging of branching structure' technique commonly used to extend the Nye-Tinker-Barber with experiments can lead to large errors. The same models also indicate that in the absence of large-scale water movement, due to rainfall, fertiliser fails to penetrate into the soil. This motivates us to build a model for water movement and uptake by branched root structures. This model considers the simultaneous flow of water in the soil, uptake by the roots, and flow within the root branching network to the stems of the plant. The water uptake model shows that the water saturation can develop pseudo-steady-state wet and dry zones in the rooting region of the soil. The dry zone is shown to stop the movement of nutrient from the top of the soil to the groundwater. Finally we present a model for the simultaneous movement and uptake of both nutrients and water. This is discussed as a new tool for interpreting available experimental results and designing future experiments. The parallels between evolution and mathematical optimisation are also discussed.
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Kelly, R. J. "Mathematical model of multi-phase snowmelt". Thesis, University of East Anglia, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.377740.
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Chew, Elaine 1970. "Towards a mathematical model of tonality". Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/9139.
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Thesis (Ph.D.)--Massachusetts Institute of Technology, Sloan School of Management, 2000.Includes bibliographical references (p. 163-166).
This dissertation addresses the question of how musical pitches generate a tonal center. Being able to characterize the relationships that generate a tonal center is crucial to the computer analysis and the generating of western tonal music. It also can inform issues of compositional styles, structural boundaries, and performance decisions. The proposed Spiral Array model offers a parsimonious description of the inter-relations among tonal elements, and suggests new ways to re-conceptualize and reorganize musical information. The Spiral Array generates representations for pitches, intervals, chords and keys within a single spatial framework, allowing comparisons among elements from different hierarchical levels. Structurally, this spatial representation is a helical realization of the harmonic network (tonnetz). The basic idea behind the Spiral Array is the representation of higher level tonal elements as composites of their lower level parts. The Spiral Array assigns greatest prominence to perfect fifth and major /minor third interval relations, placing elements related by these intervals in proximity to each other. As a result, distances between tonal entities as represented spatially in the model correspond to perceived distances among sounding entities. The parameter values that affect proximity relations are prescribed based on a few perceived relations among pitches, intervals, chords and keys. This process of interfacing between the model and actual perception creates the opportunity to research some basic, but till now unanswered questions about the relationships that generate tonality. A generative model, the Spiral Array case; provides a framework on which to design viable and efficient algorithms for problems in music cognition. I demonstrate its versatility by applying the model to three different problems: I develop an algorithm to determine the key of musical passages that, on average, performs better than existing ones when applied to the 24 fugue subjects in Book I of Bach's WTC; I propose the first computationally viable method for determining modulations (the change of key); and, I design a basic algorithm for finding the roots of chords, comparing its results to those of algorithms by other researchers. All three algorithms were implemented in Matlab.
by Elaine Chew.
Ph.D.
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Jones, Charles H. "A Mathematical Model for Instrumentation Configuration". International Foundation for Telemetering, 2010. http://hdl.handle.net/10150/604273.
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ITC/USA 2010 Conference Proceedings / The Forty-Sixth Annual International Telemetering Conference and Technical Exhibition / October 25-28, 2010 / Town and Country Resort & Convention Center, San Diego, CaliforniaThis paper describes a model of how to configure settings on instrumentation. For any given instrument there may be 100s of settings that can be set to various values. However, randomly selecting values for each setting is not likely to produce a valid configuration. By "valid" we mean a set of setting values that can be implemented by each instrument. The valid configurations must satisfy a set of dependency rules between the settings and other constraints. The formalization provided allows for identification of different sets of configurations settings under control by different systems and organizations. Similarly, different rule sets are identified. A primary application of this model is in the context of a multi-vendor system especially when including vendors that maintain proprietary rules governing their systems. This thus leads to a discussion of an application user interface (API) between different systems with different rules and settings.
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Nguyen, An. "Mathematical model of competence regulation circuit". Thesis, University of Southampton, 2014. https://eprints.soton.ac.uk/374173/.
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Gene expression regulatory networks are molecular networks which describe interactions among gene products in terms of biochemical reactions. This helps us understand the molecular mechanisms underlying important biological processes as well as cell functioning as a whole. For instance, the phenomenon of bacterial competence, whereby a bacterium enters a transiently differentiated state, incorporating DNA fragments from its environment into its genome, has been studied with the help of such gene regulatory circuits (Suel et al., 2006; Maamar and Dubnau, 2005). As a result, a genetic circuit has been taken into account in order to describe the transition from a vegetative state to a transient state of competence and vice versa. In this work, we are going to study a genetic circuit presented by Suel et al. (2007) to describe this dynamical behaviour. The authors introduce model reduction techniques to study the behaviour of stochastic chemical system of X species by means of an adiabatic two dimensional model. While the adiabatic model helps us understand about the dynamics near the steady state, it gives an incorrect description of the time-scales of the competent state. For this reason, it is necessary to build up a model which better describes the system realistically. In the thesis, I propose an approximate two-dimensional model of the full high-dimensional system and from that, the dynamics of the system can be simulated more accurately compared to that of Suel et al. (2007). I then show how to put the noise back into the approximate model to be able come up with a stochastic model which can mathematically describe the dynamical behaviour of the original high dimensional system. I also found out that the evolution of the system is not well approximated by a Langevin process. This leads to a gap between the real behavior which is described by Gillespie's stochastic simulation and the Langevin approximation. To overcome this, I have fixed the stochastic Langevin model by incorporating empirically tunable noise into the model so as to obtain a similar behaviour as observed in the original system. I also introduce the chemical Fokker-Planck equation aimed to estimate the probability density function of species concentrations which are involved in the biochemical system.
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KOPAYGORODSKY, EUGENE M. "MATHEMATICAL MODEL OF ULTRA-RAPID PSA". University of Cincinnati / OhioLINK, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1002135981.
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Nixdorf, Timothy Allen. "A Mathematical Model for Carbon Nanoscrolls". University of Akron / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1406060123.
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Anderson, Kerri-Ann. "A Mathematical Model of Cytokinetic Morphogenesis". The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429607984.
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Rhoads, Daniel Joseph. "A Mathematical Model of Graphene Nanostructures". University of Akron / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=akron1438978423.
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Bathena, Karthik. "A mathematical model of cutaneous leishmaniasis /". Online version of thesis, 2009. http://hdl.handle.net/1850/10824.
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O'Brien, Colleen S. "A Mathematical Model for Colloidal Aggregation". [Tampa, Fla.] : University of South Florida, 2003. http://purl.fcla.edu/fcla/etd/SFE0000161.
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Behzadi, Mahsa. "A mathematical model of Phospholipid Biosynthesis". Phd thesis, Ecole Polytechnique X, 2011. http://pastel.archives-ouvertes.fr/pastel-00674401.
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A l'heure de l'acquisition de donn'ees 'a haut d'ebit concernant le m'etabolisme cellulaire et son 'evolution, il est absolument n'ecessaire de disposer de mod'eles permettant d'int'egrer ces donn'ees en un ensemble coh'erent, d'en interpr'eter les variations m'etaboliques r'ev'elatrice, les 'etapes clefs o'u peuvent s'exercer des r'egulations, voire mˆeme d'en r'ev'eler des contradictions apparentes met- tant en cause les bases sur lesquelles le mod'ele lui-mˆeme est construit. C'est ce type de travail que j'ai entrepris 'a propos de donn'ees exp'erimentales obtenues dans le laboratoire biologique sur le m'etabolisme de cellules tu- morales en r'eponse 'a un traitement anti-canc'ereux. Je me suis attach'ee 'a la mod'elisation d'un point particulier de ce m'etabolisme. Il concerne le m'etabolisme des glyc'erophospholipides qui sont de bons marqueurs de la prolif'eration cellulaire. Les phospholipides constituent l'essentiel des mem- branes d'une cellule et l''etude de leur synth'ese (en particulier chez les cellules de mammif'eres) est de ce fait un sujet important. Ici, nous avons pris le parti de mettre en place un mod'ele math'ematique par 'equations diff'erentielles ordinaires, qui est essentiellement bas'e sur des 'equations hyperboliques (Michaelis-Menten), mais aussi sur des cin'etiques type loi d'action de masse et diffusion. Le mod'ele, compos'e de 8 'equations diff'erentielles, donc de 8 substrats d'int'erˆet, comporte naturellementdes param'etres inconnus in vivo, et certains d'ependents des conditions cellulaires (diff'erentiations de cellules, pathologies, . . .). Le mod'ele s'epare la structure du r'eseau m'etabolique, l''ecriture de la matrice de stoechiom'etrie, celles des 'equations de vitesse et enfin des 'equations diff'erentielles. Le mod'ele choisi est le mod'ele murin (souris/rat), parce qu'il est lui-mˆeme un mod'ele de l'homme. Plusieurs con- ditions sont successivement consid'er'ees pour l'identification des param'etres, afin d''etudier les liens entre la synth'ese de phospholipides et le cancer : - le foie sain du rat, - le m'elanome B16 et le carcinome de la lign'ee 3LL chez la souris, respectivement sans traitement, en cours de traitement 'a la Chloro'ethyl-nitrosour'ee et apr'es traitement, - enfin le m'elanome B16 chez la souris sous stress de privation de m'ethionine. En r'esum'e, ce tra- vail fourni une interpr'etation nouvelle des donn'ees exprimentales en mon- trant le rˆole essentiel de la PEMT et la nature superstable de l''etat sta- tionnaire de fonctionnement du r'eseau m'etabolique des phospholipides lors de la canc'erog'en'ese et du traitement des cancers. Il montre bien l'avantage de l'utilisation d'un mod'ele math'ematique dans l'interpr'etation de donn'ees m'etaboliques complexes.
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Behzadi, Mahsa. "A Mathematical Model of Phospholipid Biosynthesis". Phd thesis, Palaiseau, Ecole polytechnique, 2011. https://theses.hal.science/docs/00/65/03/99/PDF/BehzadiPhD.pdf.
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A l'heure de l'acquisition de données à haut débit concernant le métabolisme cellulaire et son évolution, il est absolument nécessaire de disposer de modèles permettant d'intégrer ces données en un ensemble cohérent, d'en interpréter les variations métaboliques révélatrice, les étapes clefs où peuvent s'exercer des régulations, voire même d'en révéler des contradictions apparentes mettant en cause les bases sur lesquelles le modèle lui-même est construit. C'est ce type de travail que j'ai entrepris à propos de données expérimentales obtenues dans le laboratoire biologique sur le métabolisme de cellules tumorales en réponse à un traitement anti-cancéreux. Je me suis attachée à la modélisation d'un point particulier de ce métabolisme. Il concerne le métabolisme des glycérophospholipides qui sont de bons marqueurs de la prolifération cellulaire. Les phospholipides constituent l'essentiel des membranes d'une cellule et l'étude de leur synthèse (en particulier chez les cellules de mammifères) est de ce fait un sujet important. Ici, nous avons pris le parti de mettre en place un modèle mathématique par équations différentielles ordinaires, qui est essentiellement basé sur des équations hyperboliques (Michaelis-Menten), mais aussi sur des cinétiques type loi d'action de masse et diffusion. Le modèle, composé de 8 équations différentielles, donc de 8 substrats d'intérêt, comporte naturellement des paramètres inconnus in vivo, et certains dépendents des conditions cellulaires (différentiations de cellules, pathologies,. . . ). Le modèle sépare la structure du réseau métabolique, l' ́écriture de la matrice de stoechiométrie, celles des équations de vitesse et enfin des équations différentielles. Le modèle choisi est le modèle murin (souris/rat), parce qu'il est lui-même un modèle de l'homme. Plusieurs conditions sont successivement considérées pour l'identification des paramètres, afin d'étudier les liens entre la synthèse de phospholipides et le cancer : - le foie sain du rat, - le mélanome B16 et le carcinome de la lign ́ee 3LL chez la souris, respectivement sans traitement, en cours de traitement 'a la Chloroéthyl-nitrosourée et après traitement, - enfin le mélanome B16 chez la souris sous stress de privation de méthionine. En résumé, ce travail fourni une interprétation nouvelle des données expérimentales en montrant le rôle essentiel de la PEMT et la nature superstable de l'état sta- tionnaire de fonctionnement du réseau métabolique des phospholipides lors de la cancérogènèse et du traitement des cancers. Il montre bien l'avantage de l'utilisation d'un modèle mathématique dans l'interprétation de données métaboliques complexesWhen measuring high-throughput data of cellular metabolism and its evolution, it is imperative to use appropriate models. These models allow the incorporation of these data into a coherent set. They also allow inter- pretation of the relevant metabolic variations and the key regulatory steps. Finally, they make contradictions apparent that question the basis on which the model itself is constructed. I use the experimental data of the metabolism of tumor cells in response to an anti-cancer treatment obtained in the biological laboratory. I focus on the modeling of a particular point: the metabolism of glyc- erophospholipids, which are good markers of cell proliferation. Phospho- lipids are essential parts of cell membranes and the study of their synthe- sis (especially mammalian cells) is therefore an important issue. In this work, our choice is to use a mathematical model by ordinary differential equations. This model relies essentially on hyperbolic equations (Michaelis- Menten) but also on kinetics, based on the law of mass action or on the diffusion. The model consists of 8 differential equations thus providing 8 substrates of interest. It has naturally some parameters which are unknown in vivo. Moreover some of them depend on the cellular conditions (cellular differentiation, pathologies). The model is a collection of the structure of the metabolic network, the writing of the stoichiometry matrix, generating the rate equations and finally differential equations. The chosen model is the mouse model (mouse / rat), because it is it- self a model of human. To study the relationship between the synthesis of phospholipids and cancer, several conditions are successively considered for the identification of parameters: - The healthy liver of the rat - The B16 melanoma and 3LL carcinoma line in mice, respectively, without treatment, during treatment with chloroethyl-nitrosourea and after treatment - Finally, the B16 melanoma in mice under methionine deprivation stress. In summary, my work provides a new interpretation of experimental data showing the essential role of PEMT enzyme and the superstable nature of 9 phospholipids metabolic network in carcinogenesis and cancer treatment. It shows the advantage of using a mathematical model in the interpretation of complex metabolic data
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Sak, Ugur. "Mđ: THE THREE-MATHEMATICAL MINDS MODEL FOR THE IDENTIFICATION OF MATHEMATICALLY GIFTED STUDENTS". Tucson, Arizona : University of Arizona, 2005. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu%5Fetd%5F1032%5F1%5Fm.pdf&type=application/pdf.
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Sak, Ugur. "M3: The Three-Mathematical Minds Model for the Identification of Mathematically Gifted Students". Diss., The University of Arizona, 2005. http://hdl.handle.net/10150/194533.
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Views of giftedness have evolved from unilateral notions to multilateral conceptions. The primary purpose of this study was to investigate the psychological validity of the three-mathematical minds model (M3) developed by the author. The M3 is based on multilateral conceptions of giftedness to identify mathematically gifted students. Teachings of Poincare and Polya about mathematical ability as well as the theory of successful intelligence proposed by Sternberg (1997) provided the initial framework in the development of the M3. A secondary purpose was to examine the psychological validity of the three-level cognitive complexity model (C3) developed by the author. The C3 is based on studies about expertise to differentiate among gifted, above-average and average-below-average students at three levels.The author developed a test of mathematical ability based on the M3 and C3 with the collaboration of mathematicians. The test was administered to 291 middle school students from four different schools. The reliability analysis indicated that the M3 had a .72 coefficient as a consistency of scores. Exploratory factor analysis yielded three separate components explaining 55% of the total variance. The convergent validity analysis showed that the M3 had medium to high-medium correlations with teachers' ratings of students' mathematical ability (r = .45) and students' ratings of their own ability (r = .36) and their liking of mathematics (r = .35). Item-subtest-total score correlations ranged from low to high. Some M3 items were found to be homogenous measuring only one aspect of mathematical ability, such as creative mathematical ability, whereas some items were found to be good measures of more than one facet of mathematical ability.The C3 accounted for 41% of variance in item difficulty (R square = .408, p < .001). Item difficulty ranged from .02 to .93 with a mean of .29. The analysis of the discrimination power of the three levels of the C3 revealed that level-two and level-three problems differentiated significantly among three ability levels, but level-one problems did not differentiate between gifted and above average students. The findings provide partial evidence for the psychological validity of both the M3 and C3 for the identification of mathematically gifted students.
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Cox, Raymond Taylor. "Mathematical Modeling of Minecraft – Using Mathematics to Model the Gameplay of Video Games". The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1431009469.
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Durney, Clinton H. "A Two-Component Model For Bacterial Chemotaxis". The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366312981.
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Mohd, Jaffar Mai. "Mathematical models of hyphal tip growth". Thesis, University of Dundee, 2012. https://discovery.dundee.ac.uk/en/studentTheses/140f9a81-12ca-4337-a311-2f82441f1ea6.
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Filamentous fungi are important in an enormous variety of ways to our life, with examples ranging from bioremediation, through the food and drinks industry to human health. These organisms can form huge networks stretching metres and even kilometres. However, their mode of growth is by the extension of individual hyphal tips only a few microns in diameter. Tip growth is mediated by the incorporation of new wall building materials at the soft apex. Just how this process is controlled (in fungi and in cell elongation in other organisms) has been the subject of intense study over many years and has attracted considerable attention from mathematical modellers. In this thesis, we consider mathematical models of fungal tip growth that can be classified as either geometrical or biomechanical. In every model we examine, a 2-D axisymmetric semihemisphere-like curve represents half the medial section of fungal tip geometry. A geometrical model for the role of the Spitzenkorper in the tip growth was proposed by Bartnicki-Garcia et al (1989), where a number of problems with the mathematical derivation were pointed out by Koch (2001). A suggestion is given as an attempt to revise the derivation by introducing a relationship between arc length of a growing tip, deposition of wall-building materials and tip curvature. We also consider two types of geometrical models as proposed by Goriely et al (2005). The first type considers a relationship between the longitudinal curvature and the function used to model deposition of wall-building materials. For these types of models, a generalized formulae for the tip shape is introduced, which allows localization of deposition of wall-building materials to be examined. The second type considers a relationship between longitudinal and latitudinal curvatures and the function used to model deposition of wall-building materials. For these types of models, a new formulation of the function used to model deposition of wall-building materials is introduced. Finally, a biomechanical model as proposed by Goriely et al (2010). Varying arc length of the stretchable region on the tip suggests differences in geometry of tip shape and the effective pressure profile. The hypothesis of orthogonal growth is done by focusing only on the apex of a "germ tube". Following that, it suggests that material points on the tip appear to move in a direction perpendicular to the tip either when surface friction is increased or decreased.
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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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Ohlsson, Henrik. "Mathematical Analysis of a Biological Clock Model". Thesis, Linköping University, Department of Electrical Engineering, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-6750.
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Have you thought of why you get tired or why you get hungry? Something in your body keeps track of time. It is almost like you have a clock that tells you all those things.
And indeed, in the suparachiasmatic region of our hypothalamus reside cells which each act like an oscillator, and together form a coherent circadian rhythm to help our body keep track of time. In fact, such circadian clocks are not limited to mammals but can be found in many organisms including single-cell, reptiles and birds. The study of such rhythms constitutes a field of biology, chronobiology, and forms the background for my research and this thesis.
Pioneers of chronobiology, Pittendrigh and Aschoff, studied biological clocks from an input-output view, across a range of organisms by observing and analyzing their overt activity in response to stimulus such as light. Their study was made without recourse to knowledge of the biological underpinnings of the circadian pacemaker. The advent of the new biology has now made it possible to "break open the box" and identify biological feedback systems comprised of gene transcription and protein translation as the core mechanism of a biological clock.
My research has focused on a simple transcription-translation clock model which nevertheless possesses many of the features of a circadian pacemaker including its entrainability by light. This model consists of two nonlinear coupled and delayed differential equations. Light pulses can reset the phase of this clock, whereas constant light of different intensity can speed it up or slow it down. This latter property is a signature property of circadian clocks and is referred to in chronobiology as "Aschoff's rule". The discussion in this thesis focus on develop a connection and also a understanding of how constant light effect this clock model.
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Kyllo, Andrew Kevin. "A mathematical model of the nickel converter". Thesis, University of British Columbia, 1989. http://hdl.handle.net/2429/27897.
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A mathematical model of the nickel converter has been developed based on the assumption that the converting reactions pass through a finite series of equilibrium steps. The model predicts the bath temperature and the composition of the three phases present. Detailed data collected during in-plant trials are used to test the validity of the model predictions.
The model is found to give relatively accurate predictions for the first blows of a converting charge, but overpredicts both temperature and iron removal during the last blows. The errors in the last blows are expected to be caused by the converting reactions coming under liquid phase mass transport control. An analysis of some of the more important variables in a converter operation indicates that, according to the assumption of equilibrium, there is very little that can be done to chemically improve the converting process.Applied Science, Faculty of
Materials Engineering, Department of
Graduate
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Murphy, Stephen D. "Mathematical model of the sprint relay race". Thesis, University of Ottawa (Canada), 1992. http://hdl.handle.net/10393/7745.
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The purpose of this investigation was to develop and validate mathematical models of the sprint relay race. Two approaches, a classical exponential approach and a "new" polynomial approach, were chosen for implementation. Archival film of a 100 m sprint was used to gather displacement data for the first 60 m of the race. Filming had been performed with a single highspeed 16 mm cine camera (LOCAM) at 50 fps. The coordinates were digitized, scaled and filtered using a low pass, critically damped, 4$\sp{\rm th}$ order, zero-lag Butterworth digital filter with a 1 Hz cutoff frequency. Linear velocities were calculated using finite differences. A sprinter was modelled in two ways. The first was an Exponential Model which required as input a personal best time for the 100 m race and the sprinter's maximum constant velocity. The second was a Polynomial Model which required as input the parameters mentioned in the Exponential Model and, additionally, the displacement coefficients for the first 60 m of the 100 m sprint. Relay software was developed to piece the sprint relay together using the corresponding exponential or polynomial approach. The results indicated that the relay software reasonably simulated the kinematic and temporal quantities of a 4 x 100 m relay and can be used by coaches to gain insight into the sprint relay without risking injury to their athletes. Furthermore, the Exponential Model, using less information, described the sprinter's kinematics better than the Polynomial Model.
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Sapp, M. Catherine. "A mathematical model to describe aortic dissections". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape16/PQDD_0019/MQ28655.pdf.
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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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Henderson, Peter C. "A mathematical model of a storage heater". Thesis, University of Ulster, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390066.
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Tereshchuk. "GAME OF LIFE AS A MATHEMATICAL MODEL". Thesis, Київ 2018, 2018. http://er.nau.edu.ua/handle/NAU/33916.
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Tereshchuk. "GAME OF LIFE AS A MATHEMATICAL MODEL". Thesis, Київ 2018, 2018. http://er.nau.edu.ua/handle/NAU/33715.
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PANDE, PARAG M. "MATHEMATICAL MODEL OF ETHANOL METABOLISM IN LIVER". Cleveland State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=csu1198775130.
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Frank, Kyle. "A Mathematical Model of Leishmania in Macrophages". The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1337872325.
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Natchimuthu, Chinnaraj Anand. "THERMAL CONDUCTIVITY ENHANCEMENT IN NANOFLUIDS -MATHEMATICAL MODEL". OpenSIUC, 2011. https://opensiuc.lib.siu.edu/theses/758.
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The study on developing a mathematical model for thermal conductivity enhancement in nanofluids was based on formation of nanoparticles into nanoclusters, nanolayer thickness, Brownian motion and volume fraction of nanoclusters. An equation for the thermal conductivity of nanofluids was developed. The expression developed successfully explained the enhanced thermal conductivity of nanofluids and led to some important conclusions. It was found that in this study the nanoparticles tend to form nanoclusters and the volume fraction of the nanoclusters and the trapped fluid in the nanocluster was contributing to the overall thermal conductivity enhancement. Various types of cluster formation was analyzed and it was understood that the nanoparticles forming a spherical nanoclusters are more effective in thermal conductivity enhancement. The contribution of Brownian motion of nanoparticles to the overall thermal conductivity of nanofluids was found to be very small. The study investigated the size distribution of nanoparticles which has been suggested to be an important factor and it gave satisfactory results. The values of the thermal conductivity for different nanofluid combinations were calculated using the expression developed from this study and they agreed with published experimental data. The present model was tested against several nanofluid combinations. To understand the properties that influence the thermal conductivity of nanofluids, parametric studies of a number of nanofluids were carried out. The parameters that were scrutinized to understand themal conductivity enhancement were nanoparticle diameter, nanolayer thickness and brownian motion. From the study, it was observed that Brownian motion is significant only when the particle diameter is less than 10 nm. From the parametric studies the mathematical model derived in this study was validated. The major factor for the thermal conductivity enhancement in nanofluids is the formations of nanoclusters. The combination of the base fluid and nanoparticles to from nanoclusters will provide better cooling solution than the convention cooling fluids.
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Ogutu, Benjamin Keroboto Za'Ngoti. "Energy balance mathematical model on climate change". Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066224/document.
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Dans cet étude, un modèle de complexité réduite des interactions et rétroactions du système couplé climat-économie-biosphère est construit avec le minimum de variables et d'équations nécessaires. Le Coupled Climate-Economy-Biosphere (CoCEB) est un modèle d’évaluation intégrée (IAM pour Integrated assessment model) du changement globale. Alors que beaucoup IAM traitent les coûts de réduction des émissions (abattement) simplement comme une perte non productive de revenu, cet étude considère également les activités d’abattement comme un investissement dans l'efficacité énergétique globale de l'économie et dans la diminution de l’ « intensité carbone » du système énergétique. L’étude montre que ces efforts aident à l’abattement du changement climatique et ont un effet positif sur l’économie. La plupart des IAM actuels se concentrent principalement sur le secteur énergétique pour les mesures d’abattement, et ne tiennent compte des émissions provenant de l'utilisation des terres que comme un forçage exogène. Le CoCEB a donc été étendu en ajoutant une équation pour la biomasse ses échanges de carbone. Cela permet d’étudier les aspects économiques de la séquestration de carbone du au contrôle du déboisement dans les forêts, et aussi à l’application généralisée des technologies de capture et stockage du carbone (CCS). L’étude confirme que ces mesures réduisent l’impact du changement climatique sur la croissance économique, mais ces résultats restent très dépendants des grandes incertitudes sur le cout des CCS et du contrôle de la deforestation. Ce modèle est un cadre formel qui représente de façon simple les différents éléments du système couplé et leurs interactions, il rassemble les différentes estimations des coûts afférents aux mesures de mitigation et permet de les comparer de façon cohérenteThe goal of this study is to build a global reduced-complexity model of coupled climate-economy-biosphere interactions, which uses the minimum number of variables and equations needed to capture the fundamental mechanisms involved and can thus help clarify the role of the different mechanisms and parameters. The Coupled Climate-Economy-Biosphere (CoCEB) model takes an integrated assessment approach to simulating global change. While many integrated assessment models treat abatement costs merely as an unproductive loss of income, the study considered abatement activities also as an investment in overall energy efficiency of the economy and decrease of overall carbon intensity of the energy system. The study shows that these efforts help to abate climate change and lead to positive effects in economic growth. Due to the fact that integrated assessment models in the literature mainly focus on mitigation in the energy sector and consider emissions from land-use as exogenous, the global climate-economy-biosphere (CoCEB) model was extended by adding a biomass equation and the related exchanges of CO2 and used to investigate the relationship between the effects of using carbon capture and storage (CCS) and deforestation control, and the economy growth rate. These measures are found to reduce the impacts of climate change and positively affect the economy growth. These results remain nevertheless sensitive to the formulation of CCS costs while those for deforestation control were less sensitive. The model developed brings together and summarizes information from diverse estimates of climate change mitigation measures and their associated costs, and allows comparing them in a coherent way
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Ogutu, Benjamin Keroboto Za'Ngoti. "Energy balance mathematical model on climate change". Electronic Thesis or Diss., Paris 6, 2015. http://www.theses.fr/2015PA066224.
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Dans cet étude, un modèle de complexité réduite des interactions et rétroactions du système couplé climat-économie-biosphère est construit avec le minimum de variables et d'équations nécessaires. Le Coupled Climate-Economy-Biosphere (CoCEB) est un modèle d’évaluation intégrée (IAM pour Integrated assessment model) du changement globale. Alors que beaucoup IAM traitent les coûts de réduction des émissions (abattement) simplement comme une perte non productive de revenu, cet étude considère également les activités d’abattement comme un investissement dans l'efficacité énergétique globale de l'économie et dans la diminution de l’ « intensité carbone » du système énergétique. L’étude montre que ces efforts aident à l’abattement du changement climatique et ont un effet positif sur l’économie. La plupart des IAM actuels se concentrent principalement sur le secteur énergétique pour les mesures d’abattement, et ne tiennent compte des émissions provenant de l'utilisation des terres que comme un forçage exogène. Le CoCEB a donc été étendu en ajoutant une équation pour la biomasse ses échanges de carbone. Cela permet d’étudier les aspects économiques de la séquestration de carbone du au contrôle du déboisement dans les forêts, et aussi à l’application généralisée des technologies de capture et stockage du carbone (CCS). L’étude confirme que ces mesures réduisent l’impact du changement climatique sur la croissance économique, mais ces résultats restent très dépendants des grandes incertitudes sur le cout des CCS et du contrôle de la deforestation. Ce modèle est un cadre formel qui représente de façon simple les différents éléments du système couplé et leurs interactions, il rassemble les différentes estimations des coûts afférents aux mesures de mitigation et permet de les comparer de façon cohérenteThe goal of this study is to build a global reduced-complexity model of coupled climate-economy-biosphere interactions, which uses the minimum number of variables and equations needed to capture the fundamental mechanisms involved and can thus help clarify the role of the different mechanisms and parameters. The Coupled Climate-Economy-Biosphere (CoCEB) model takes an integrated assessment approach to simulating global change. While many integrated assessment models treat abatement costs merely as an unproductive loss of income, the study considered abatement activities also as an investment in overall energy efficiency of the economy and decrease of overall carbon intensity of the energy system. The study shows that these efforts help to abate climate change and lead to positive effects in economic growth. Due to the fact that integrated assessment models in the literature mainly focus on mitigation in the energy sector and consider emissions from land-use as exogenous, the global climate-economy-biosphere (CoCEB) model was extended by adding a biomass equation and the related exchanges of CO2 and used to investigate the relationship between the effects of using carbon capture and storage (CCS) and deforestation control, and the economy growth rate. These measures are found to reduce the impacts of climate change and positively affect the economy growth. These results remain nevertheless sensitive to the formulation of CCS costs while those for deforestation control were less sensitive. The model developed brings together and summarizes information from diverse estimates of climate change mitigation measures and their associated costs, and allows comparing them in a coherent way
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Alharthi, Muteb. "Bayesian model assessment for stochastic epidemic models". Thesis, University of Nottingham, 2016. http://eprints.nottingham.ac.uk/33182/.
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Acrucial practical advantage of infectious diseases modelling as a public health tool lies in its application to evaluate various disease-control policies. However, such evaluation is of limited use, unless a sufficiently accurate epidemic model is applied. If the model provides an adequate fit, it is possible to interpret parameter estimates, compare disease epidemics and implement control procedures. Methods to assess and compare stochastic epidemic models in a Bayesian framework are not well-established, particularly in epidemic settings with missing data. In this thesis, we develop novel methods for both model adequacy and model choice for stochastic epidemic models. We work with continuous time epidemic models and assume that only case detection times of infected individuals are available, corresponding to removal times. Throughout, we illustrate our methods using both simulated outbreak data and real disease data. Data augmented Markov Chain Monte Carlo (MCMC) algorithms are employed to make inference for unobserved infection times and model parameters. Under a Bayesian framework, we first conduct a systematic investigation of three different but natural methods of model adequacy for SIR (Susceptible-Infective-Removed) epidemic models. We proceed to develop a new two-stage method for assessing the adequacy of epidemic models. In this two stage method, two predictive distributions are examined, namely the predictive distribution of the final size of the epidemic and the predictive distribution of the removal times. The idea is based onlooking explicitly at the discrepancy between the observed and predicted removal times using the posterior predictive model checking approach in which the notion of Bayesian residuals and the and the posterior predictive p−value are utilized. This approach differs, most importantly, from classical likelihood-based approaches by taking into account uncertainty in both model stochasticity and model parameters. The two-stage method explores how SIR models with different infection mechanisms, infectious periods and population structures can be assessed and distinguished given only a set of removal times. In the last part of this thesis, we consider Bayesian model choice methods for epidemic models. We derive explicit forms for Bayes factors in two different epidemic settings, given complete epidemic data. Additionally, in the setting where the available data are partially observed, we extend the existing power posterior method for estimating Bayes factors to models incorporating missing data and successfully apply our missing-data extension of the power posterior method to various epidemic settings. We further consider the performance of the deviance information criterion (DIC) method to select between epidemic models.
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Zhou, Xiaobin. "Mathematical and Physical Simulations of BOF Converters". Doctoral thesis, KTH, Tillämpad processmetallurgi, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-175462.
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The purpose of this study is to develop mathematical models to explore the mixing and its related phenomena in converter bath. Specifically, first, a mathematical model of a physical model converter, which was scaled down to 1/6th of a 30 t vessel, was developed in this study. A number of parameters were studied and their effects on the mixing time were recorded in a top blown converter. Second, a mathematical model for a combined top-bottom blown was built to investigate the optimization process. Then, a side tuyere was introduced in the combined top-bottom blown converter and its effects on the mixing and wall shear stress were studied. Moreover, based on the above results, the kinetic energy transfer phenomena in a real converter were investigated by applying the mathematical models. A simplified model, in which the calculation region was reduced to save calculation compared to simulations of the whole region of the converter, was used in the mathematical simulation. In addition, this method was also used in the simulation of real converters. This approach makes it possible to simulate the Laval nozzle flow jet and the cavity separately when using different turbulence models. In the top blown converter model, a comparison between the physical model and the mathematical model showed a good relative difference of 2.5% and 6.1% for the cavity depth and radius, respectively. In addition, the predicted mixing time showed a good relative difference of 2.8% in comparison to the experimental data. In an optimization of a combined top-bottom blown converter, a new bottom tuyere scheme with an asymmetrical configuration was found to be one of the best cases with respect to a decreased mixing time in the bath. An industrial investigation showed that the application effects of the new tuyere scheme yield a better stirring condition in the bath compared to the original case. Furthermore, the results indicated that the mixing time for a combined top-bottom-side blown converter was decreased profoundly compared to a conventional combined top-bottom blown converter. It was found that the side wall shear stress is increased by introducing side blowing, especially in the region near the side blowing plume. For a 100 t converter in real, the fundamental aspects of kinetic energy transfer from a top and bottom gas to the bath were explored. The analyses revealed that the energy transfer is less efficient when the top lance height is lowered or the flowrate is increased in the top blowing operations. However, an inverse trend was found. Namely, that the kinetic energy transfer is increased when the bottom flowrate is increased in the current bottom blowing operations. In addition, the slag on top of the bath is found to dissipate 6.6%, 9.4% and 11.2% for the slag masses 5, 9 and 15 t compared to the case without slag on top of the surface of the bath, respectively.QC 20151015
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Kleinstreuer, Nicole Churchill. "Mathematical modeling of renal autoregulation". Thesis, University of Canterbury. Bioengineering, 2009. http://hdl.handle.net/10092/2532.
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Renal autoregulation is unique and critically important in maintaining homeostasis in the body via control
of renal blood flow and filtration. The myogenic reflex responds directly to pressure variation and is present throughout the vasculature in varying degrees, while the tubuloglomerular feedback (TGF) mechanism adjusts microvascular resistance and glomerular filtration rate (GFR) to maintain distal tubular NaCl delivery. No simple models are available which allow the independent contributions of the myogenic and TGF responses to be compared and which include control over multiple metabolic and physiological parameters. Independently developed mathematical models of myogenic autoregulation and TGF control of GFR have been combined to produce a comprehensive model for the rat kidney which is responsive to multiple small step changes in mean arterial pressure. The system encompasses every level of the renal vasculature and the tubular system of the nephrons while simultaneously incorporating the modulatory effects of changes in viscosity and shear stress-induced nitric oxide (NO) production. The vasculature of the rat kidney has
previously been divided via a Strahler ordering scheme using morphological data derived from micro-CT imaging. This data, combined with an extensive literature review of the relevant experimental data, led to the development of order-specific parameter sets for each of the eleven vascular levels. The model of the myogenic response depends primarily on circumferential wall tension, corresponding to a distally dominant
resistance distribution with the highest contributions localized to the afferent arterioles and interlobular arteries. The constrictive response is tempered by the vasodilatory influence of flow-induced NO. Experimental
comparison with data from groups that inhibited the TGF mechanism showed that the model was able to accurately reproduce the characteristics of renal myogenic autoregulation. This myogenic model was coupled with a system of equations that represented both spatial and temporal changes in concentration of the filtrate in the tubular system of the nephrons and the corresponding resistance changes of the afferent arteriole via the TGF mechanism. Computer simulation results of the system response to pressure perturbations were examined, as well as the interaction between mechanisms and the modulatory influences of metabolic and hemodynamic factors on the steady state and transient characteristics of whole-organ renal autoregulation.
The responses of the model were consistent with experimental observations and showed that the frequency of the myogenic reflex was approximately 0.4 Hz while that of TGF was 0.06 Hz, corresponding to a 2-3
sec response time for myogenic contraction and 16.7 sec for TGF. Within the autoregulatory range step increases in pressure induced damped oscillations in tubular flow, macula densa NaCl concentration, arteriolar
diameter, and renal blood flow. The model demonstrated that these oscillations were triggered by TGF and
confined to vessels less than 100 micrometer in diameter. The pressure response in larger vessels remained
important in characterizing total autoregulatory efficacy. Examination of the steady-state and transient
characteristics of the model results demonstrates the necessity of considering the whole organ response in
studies of renal autoregulation. A comprehensive model of autoregulation also allows for the examination of
pathological states, such as the altered NO production in hypertension or the excess tubular reabsorption
of water seen in diabetes. The model was able to reproduce experimental results when simulating diseased
states, enabling the analysis of impaired autoregulation as well as the identification of key factors affecting
the autoregulatory response.
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Howes, S. "A mathematical hydrological model for the ungauged catchment". Thesis, University of Bristol, 1985. http://hdl.handle.net/1983/1affdf54-f3d2-4dbe-83b0-836695ef0c8e.
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In geographical hydrology the~e has been more interest in scientific rather than in practical application of mathematical models of catchment hydrology. This thesis emphasizes the importance of examining the potential of developments in scientific research programmes for practical hydrological applications, and in particular provides discussion upon the following five issues: 1 The application of hydrological models to ungauged catchments where no historical streamflow record is available for calibration. 2 The potential of hydrological models for routine and operational application. This application limits the data and computer resources which are available for use. 3 The development and application of a thorough model evaluation strategy which examines the suitability of a model in the context of a specific application requirement. 4 The selection of a conceptually sound model structure. S The development and evaluation of a suitable methodology for the incorporation of the spatial variability of catchments into hydrological" models. To provide a basis for the discussion of these five issues, this thesis provides the details of the modification of a currently used hydrological model, RYMO. The modification of this model involves the replacement of the empirical curve number model for runoff derivation with a physically based parameter infiltration model. A number of comparisons of HYMO and the modified version, HYM02, indicates that conceptual, parameter estimation, prediction, and sensitivity improvements have indeed been secured by the development of the modified model.
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Gaone, Joseph Michael II. "A Mathematical Model of a Microbial Fuel Cell". University of Akron / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=akron1376400246.
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Ngwenza, Dumisani. "Quantifying Model Risk in Option Pricing and Value-at-Risk Models". Master's thesis, Faculty of Commerce, 2019. http://hdl.handle.net/11427/31059.
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Financial practitioners use models in order to price, hedge and measure risk. These models are reliant on assumptions and are prone to ”model risk”. Increased innovation in complex financial products has lead to increased risk exposure and has spurred research into understanding model risk and its underlying factors. This dissertation quantifies model risk inherent in Value-at-Risk (VaR) on a variety of portfolios comprised of European options written on the ALSI futures index across various maturities. The European options under consideration will be modelled using the Black-Scholes, Heston and Variance-Gamma models.
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Sarfo, Amponsah Eric. "Mathematical Modeling of Epidemics: Parametric Heterogeneity and Pathogen Coexistence". Diss., North Dakota State University, 2020. https://hdl.handle.net/10365/31862.
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No two species can indefinitely occupy the same ecological niche according to the competitive exclusion principle. When competing strains of the same pathogen invade a homogeneous population, the strain with the largest basic reproductive ratio R0 will force the other strains to extinction. However, over 51 pathogens are documented to have multiple strains [3] coexisting, contrary to the results from homogeneous models. In reality, the world is heterogeneous with the population varying in susceptibility. As such, the study of epidemiology, and hence the problem of pathogen coexistence should entail heterogeneity. Heterogeneous models tend to capture dynamics such as resistance to infection, giving more accurate results of the epidemics. This study will focus on the behavior of multi-pathogen heterogeneous models and will try to answer the question: what are the conditions on the model parameters that lead to pathogen coexistence? The goal is to understand the mechanisms in heterogeneous populations that mediate pathogen coexistence. Using the moment closure method, Fleming et. al. [22] used a two pathogen heterogeneous model (1.9) to show that pathogen coexistence was possible between strains of the baculovirus under certain conditions. In the first part of our study, we consider the same model using the hidden keystone variable (HKV) method. We show that under some conditions, the moment closure method and the HKV method give the same results. We also show that pathogen coexistence is possible for a much wider range of parameters, and give a complete analysis of the model (1.9), and give an explanation for the observed coexistence.
The host population (gypsy moth) considered in the model (1.9) has a year life span, and hence, demography was introduced to the model using a discrete time model (1.12). In the second part of our study, we will consider a multi-pathogen compartmental heterogeneous model (3.1) with continuous time demography. We show using a Lyapunov function that pathogen coexistence is possible between multiple strains of the same pathogen. We provide analytical and numerical evidence that multiple strains of the same pathogen can coexist in a heterogeneous population.
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Yin, Weiwei. "A Mathematical Model of the Sleep-Wake Cycle". Thesis, Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/14508.
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The daily sleep-wake cycle usually consists of three distinct states: wakefulness, non-rapid-eye-movement (NREM) and rapid-eye-movement (REM). The process of switching between different states is complex, but a common assumption is that it is regulated primarily by two processes (the circadian and the homeostatic process) via reciprocal interactions of several downstream neuron groups. These interactions not only result in often rapid transitions from one state to another, but also allow for a certain degree of bi-stability that locks the organism in a given state for some while before it switches back. In order to better understand how the behavioral states are regulated by different neuron groups, I describe how to use the S-system method for the development of a mathematical model consisting of two phases. The first phase covers the switch between wakefulness and sleep, which is controlled by the interactions between wake- and sleep-promoting neurons, whereas the second phase addresses the generation of NREM-REM alternation, which is believed to be regulated by REM-OFF and REM-ON neurons. In this set-up I interpret the circadian rhythm as external input and homeostatic regulation as a feedback controller. Both open-loop and closed-loop forms of the two-phase model are investigated and implemented. Discharging activities of the corresponding neuron groups and the switches of behavioral states are shown in the simulation results, from which we can easily identify the basic roles of wake- and sleep-promoting neurons, REM-OFF and REM-ON neurons. The special regulatory function of the neuropeptide orexin is also tested by simulation.
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Manukyan, Edgar. "Mathematical model of size sorting in aeolian ripples /". [Sedeh Boker] : Ben-Gurion University of the Negev, 2006. http://aranne5.lib.ad.bgu.ac.il/others/ManuKyanEdgar.pdf.
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Pounder, Joseph R. "A mathematical model of high intensity paper drying". Diss., Georgia Institute of Technology, 1986. http://hdl.handle.net/1853/5689.
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