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Beauchamp, Robert Edward. "Mathematical modeling using Maple." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1996. http://handle.dtic.mil/100.2/ADA319951.
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Phillips, Donovan D. "Mathematical modeling using MATLAB." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1998. http://handle.dtic.mil/100.2/ADA358796.
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Thesis (M.S. in Applied Mathematics) Naval Postgraduate School, December 1998."December 1998." Thesis advisor(s): Maurice D. Weir. Includes bibliographical references (p. 121). Also available online.
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Green, Terrell J. "Mathematical modeling of fire /." The Ohio State University, 1987. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487331541710161.
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Pillutla, R. R. "Mathematical modeling of biosystems." Thesis(Ph.D.), CSIR-National Chemical Laboratory, Pune, 1991. http://dspace.ncl.res.in:8080/xmlui/handle/20.500.12252/3013.
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Wilmer, Archie. "Javelin analysis using mathematical modeling." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1994. http://handle.dtic.mil/100.2/ADA283466.
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Thesis (M.S. in Applied Mathematics) Naval Postgraduate School, June 1994.Thesis advisor(s): Bard K. Mansager, Maurice D. Weir. "June 1994." Includes bibliographical references. Also available online.
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Pratikakis, Nikolaos. "Mathematical modeling of rail gun." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2006. http://library.nps.navy.mil/uhtbin/hyperion/06Sep%5FPratikakis.pdf.
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Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, September 2006.Thesis Advisor(s): Kwon Young. "September 2006." Includes bibliographical references (p. 77-78). Also available in print.
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Weens, William. "Mathematical modeling of liver tumor." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2012. http://tel.archives-ouvertes.fr/tel-00779177.
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Comme démontre récemment pour la régénération du foie après un dommage cause par intoxication, l'organisation et les processus de croissance peuvent être systématiquement analyses par un protocole d'expériences, d'analyse d'images et de modélisation [43]. Les auteurs de [43] ont quantitativement caractérise l'architecture des lobules du foie, l'unité fonctionnelle fondamentale qui constitue le foie, et en ont conçu un modèle mathématique capable de prévoir un mécanisme jusqu'alors inconnu de division ordonnée des cellules. La prédiction du modèle fut ensuite validée expérimentalement. Dans ce travail, nous étendons ce modèle a l'échelle de plusieurs lobules sur la base de résultats expérimentaux sur la carcinogène dans le foie [15]. Nous explorons les scénarios possibles pouvant expliquer les différents phénotypes de tumeurs observés dans la souris. Notre modèle représente les hépatocytes, principal type de cellule dans le foie, comme des unités individuels avec un modèle a base d'agents centré sur les cellules et le système vasculaire est représenté comme un réseau d'objets extensibles. L'équation de Langevin qui modélise le mouvement des objets est calculée par une discrétisation explicite. Les interactions mécaniques entre cellules sont modélisées avec la force de Hertz ou de JKR. Le modèle est paramètre avec des valeurs mesurables a l'échelle de la cellule ou du tissue et ses résultats sont directement comparés avec les résultats expérimentaux. Dans une première étape fondamentale, nous étudions si les voies de transduction du signal de Wnt et Ras peuvent expliquer les observations de [15] où une prolifération instantanée dans les souris mutées est observée seulement si 70% des hépatocytes sont dépourvues d'APC. Dans une deuxième étape, nous présentons une analyse de sensibilité du modèle sur la rigidité de la vasculature et nous la mettons en relation avec un phénotype de tumeur (observe expérimentalement) où les cellules tumorales sont bien différentiées. Nous intégrons ensuite dans une troisième 'étape la destruction de la vasculature par les cellules tumorales et nous la mettons en relation avec un autre phénotype observe expérimentalement caractérise par l'absence de vaisseaux sanguins. Enfin, dans la dernière étape de notre étude nous montrons que des effets qui sont détectables dans les petits nodules tumoraux et qui reflètent les propriétés des cellules tumorales, ne sont plus présents dans la forme ou dans le phénotype des tumeurs d'une taille excédant la moitié de celle d'un lobule.
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Blomqvist, Oscar, Sebastian Bremberg, and Richard Zauer. "Mathematical modeling of flocking behavior." Thesis, KTH, Optimeringslära och systemteori, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-103812.
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In this thesis, the ocking behaviour of prey when threatened by a group of predators, is investigated using dynamical systems. By implementing the unicycle model, a simulation is created using Simulink and Matlab. A set of forces are set up to describe the state of the prey, that in turn determines their behaviour in dierent scenarios. An eective strategy is found so all members of the ock can survive the predator attack, taking into account the advantages of the predator's greater translational velocity and the prey's higher angular velocity. Multiple obstacles and an energy constraint are added to make the model more realistic. The objective of this thesis is to develop a strategy that maximizes the chance of survival of each ock member by not only staying together in a group but also making use of environmental advantages.
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Keller, Peter. "Mathematical modeling of molecular motors." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6304/.
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Amongst the many complex processes taking place in living cells, transport of cargoes across the cytosceleton is fundamental to cell viability and activity. To move cargoes between the different cell parts, cells employ Molecular Motors. The motors operate by transporting cargoes along the so-called cellular micro-tubules, namely rope-like structures that connect, for instance,
the cell-nucleus and outer membrane. We introduce a new Markov Chain, the killed Quasi-Random-Walk, for such transport molecules and derive properties like the maximal run length and time. Furthermore we introduce permuted balance, which is a more flexible extension of the ordinary reversibility and introduce the notion of Time Duality, which compares certain passage times pathwise. We give a number of sufficient conditions for Time Duality based on the geometry of the transition graph. Both notions are closely related to properties of the killed Quasi-Random-Walk.
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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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Emmons, Nelson L. "Mathematical modeling using Microsoft Excel." Monterey, California. Naval Postgraduate School, 1997. http://hdl.handle.net/10945/26053.
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Approved for public release; distribution is unlimitedThe entry into higher mathematics begins with calculus. Rarely, however, does the calculus student recognize the full power and applications for the mathematical concepts and tools that are taught. Frank R. Giordano, Maurice D. Weir, and William P. Fox produced A First Course in Mathematical Modeling a unique text designed to address this shortcoming and teach the student how to identify, formulate, and interpret the real world in mathematical terms. Mathematical modeling is the application of mathematics to explain or predict real world behavior. Often real world data are collected and used to veriiy or validate (and sometimes formulate) a hypothetical model or scenario. Inevitably, in such situations, it is desirable and necessary to have computational support available to analyze the large amounts of data. Certainly this eliminates the tedious and inefficient hand calculations necessary to validate and apply the model (assuming the calculations can even be reasonably done by hand). The primary purpose of Mathematical Modeling Using Microsoft Excel is to provide instructions and examples for using the spreadsheet program Microsoft Excel to support a wide range of mathematical modeling applications. Microsoft Excel is a powerful spreadsheet program which allows the user to organize numerical data into an easy to follow on-screen grid of columns and rows. Our version of Excel is based on Microsoft Windows. In this text, it is not the intent to teach mathematical modeling, but rather to provide computer support for most of the modeling topics covered in A First Course in Mathematical Modeling. The examples given here are support that text as well
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Been, Amy L., and Amy L. Been. "Teacher Views of Mathematical Modeling." Thesis, The University of Arizona, 2016. http://hdl.handle.net/10150/621172.
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As mathematical modeling gains popularity in K-12 classrooms, it is important to define what this entails for both students and teachers. The following study reviews various definitions of mathematical modeling and how these definitions are relevant for middle grades (5-9) teachers. Following a professional development workshop on mathematical modeling, four middle school teachers expressed their views about teaching mathematics through modeling tasks. This study documents the teachers' perceptions of what it means to model with mathematics, which tasks are most appropriate for their students, and why this is important in each of their classrooms. Although the teachers varied in their views depending on the context and circumstances surrounding each modeling task, they agreed that mathematical modeling helps students build critical thinking skills and provides an opportunity to align mathematics concepts with engaging, realistic phenomena.
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Andrade, Restrepo Martín. "Mathematical modeling and evolutionary processes." Thesis, Sorbonne Paris Cité, 2019. http://www.theses.fr/2019USPCC021.
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La recherche présentée dans cette thèse concerne différents sujets dans le domaine de la biomathématique. J’aborde diverses questions en biologie (et liées aux systèmes complexes) avec des méthodes mathématiques et numériques. Ces questions sont les suivantes: (i) Les processus passifs sont-ils suffisants pour justifier la distribution asymétrique des protéines endommagées pendant et après la cytokinèse de la levure? (ii) Quels processus sont à l’origine des schémas complexes d’expansion de l’amyloïde bêta dans le cerveau des patients atteints de la maladie d’Alzheimer? (iii) Qu’y a-t-il derrière la dichotomie de ‘clusters’ vs. ‘cline-like’ dans les modèles d’évolution le long de gradients environnementaux? (iv) Comment cette dichotomie affecte-t-elle la dynamique spatiale des invasions? (v) Comment la multi-stabilité se manifeste-t-elle dans ces modèles? Ces questions sont abordées (à différentes échelles, certaines totalement et certaines partiellement) avec différentes méthodes théoriques. Les résultats devraient permettre de mieux comprendre les processus biologiques analysés et de motiver la poursuite des travaux expérimentaux et empiriques susceptibles de contribuer à résoudre les incertitudes persistantesThe research presented in this thesis concerns different topics in the field of Biomathematics. I address diverse questions arising in biology (and related to complex systems) with mathematical and numerical methods. These questions are: (i) Are passive-processes enough to justify the asymmetric distribution of damaged proteins during and after yeast cytokinesis? (ii) What processes are behind the complex patterns of expansion of Amyloid beta in the brains of patients with Alzheimer’s disease? (iii) What is behind the clustering and cline-like dichotomy in models of evolution along environmental gradients? (iv) How does this dichotomy affect the spatial dynamics of invasions and range expansions? (v) How does multi-stability manifest in these models? These questions are approached (at different scales, some fully and some partially) with different theoretical methods. Results are expected to shed light on the biological processes analyzed and to motivate further experimental and empirical work which can help solve lingering uncertainties
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Shoemaker, Katherine L. Shoemaker. "The Mathematical Modeling of Magnetostriction." Bowling Green State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1522694644858063.
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Perdomo, Joana L. "Mathematical Modeling of Blood Coagulation." Scholarship @ Claremont, 2016. https://scholarship.claremont.edu/hmc_theses/71.
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Blood coagulation is a series of biochemical reactions that take place to form a blood clot. Abnormalities in coagulation, such as under-clotting or over- clotting, can lead to significant blood loss, cardiac arrest, damage to vital organs, or even death. Thus, understanding quantitatively how blood coagulation works is important in informing clinical decisions about treating deficiencies and disorders. Quantifying blood coagulation is possible through mathematical modeling. This review presents different mathematical models that have been developed in the past 30 years to describe the biochemistry, biophysics, and clinical applications of blood coagulation research. This review includes the strengths and limitations of models, as well as suggestions for future work.
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Agi, Egemen. "Mathematical Modeling Of Gate Control Theory." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/3/12611468/index.pdf.
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The purpose of this thesis work is to model the gate control theory, which explains the modulation of pain signals, with a motivation of finding new possible targets for pain treatment and to find novel control algorithms that can be used in engineering practice. The difference of the current study from the previous modeling trials is that morphologies of neurons that constitute gate control system are also included in the model by which structure-function relationship can be observed. Model of an excitable neuron is constructed and the response of the model for different perturbations are investigated. The simulation results of the excitable cell model is obtained and when compared with the experimental findings obtained by using crayfish, it is found that they are in good agreement. Model encodes stimulation intensity information as firing frequency and also it can add sub-threshold inputs and fire action potentials as real neurons. Moreover, model is able to predict depolarization block. Absolute refractory period of the single cell model is found as 3.7 ms. The developed model, produces no action potentials when the sodium channels are blocked by tetrodotoxin. Also, frequency and amplitudes of generated action potentials increase when the reversal potential of Na is increased. In addition, propagation of signals along myelinated and unmyelinated fibers is simulated and input current intensity-frequency relationships for both type of fibers are constructed. Myelinated fiber starts to conduct when current input is about 400 pA whereas this minimum threshold value for unmyelinated fiber is around 1100 pA. Propagation velocity in the 1 cm long unmyelinated fiber is found as 0.43 m/s whereas velocity along myelinated fiber with the same length is found to be 64.35 m/s. Developed synapse model exhibits the summation and tetanization properties of real synapses while simulating the time dependency of neurotransmitter concentration in the synaptic cleft. Morphometric analysis of neurons that constitute gate control system are done in order to find electrophysiological properties according to dimensions of the neurons. All of the individual parts of the gate control system are connected and the whole system is simulated. For different connection configurations, results of the simulations predict the observed phenomena for the suppression of pain. If the myelinated fiber is dissected, the projection neuron generates action potentials that would convey to brain and elicit pain. However, if the unmyelinated fiber is dissected, projection neuron remains silent. In this study all of the simulations are preformed using Simulink.
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Kat, Bora. "Mathematical Modeling For Energy Policy Analysis." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613762/index.pdf.
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As is now generally accepted, climate change and environmental degradation has largely been triggered by carbon emissions and energy modeling for policy analysis has therefore attained renewed urgency. It is important for governments to satisfy emission targets and timetables set down by international agreements without disregarding macroeconomic concerns and restrictions. In this study, we present a large-scale nonlinear optimization model that allows the analysis of macroeconomic and multi-sectoral energy policies in respect of technological and environmental options and scenarios. The model consists of a detailed representation of energy activities and disaggregates the rest of the economy into five main sectors. Economy-wide solutions are obtained by computing a utility maximizing aggregate consumption bundle on the part of a representative household. Intersectoral and foreign transaction balances are maintained using a modified accounting matrix. The model also computes the impact on macroeconomic variables of greenhouse gas (GHG) emission strategies and abatement schemes. As such the model is capable of producing solutions that can be used to benchmark regulatory instruments and policies. Several scenarios are presented for the case of Turkey in which the impact of a nuclear power programme and power generation coupled with carbon-capture-and-storage schemes are investigated as well as setting quotas on total and sectoral GHG emissions.
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Wolska, Magdalena, and Ivana Kruijff-Korbayová. "Modeling anaphora in informal mathematical dialogue." Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2006/1045/.
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We analyze anaphoric phenomena in
the context of building an input understanding
component for a conversational
system for tutoring mathematics.In this paper, we report the results of data analysis of two sets of corpora of dialogs on mathematical theorem proving. We exemplify anaphoric phenomena, identify factors relevant to anaphora resolution in our domain and extensions to the input interpretation component to support it.
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Fagereng, Christian. "Mathematical Modeling for Marine Crane Operations." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for marin teknikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-15511.
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As mathematical models for marine vessel dynamics are frequently used for several different purposes there is a need for finding ways of facilitating connection of sub models to extend these models to include various equipment of interest which affects the vessel dynamics. The bond graph modeling language is a natural platform for this since it can be used to describe several different disciplines or energy domains using the same basic system elements. Thus for example electrical systems affecting mechanical systems can easily be modeled and connected. However the basic bond graph modeling concept has to be extended for use in multi-dimensional problems since standard procedures soon become difficult or impossible for larger systems. Using rigid body dynamics such systems can easily be created and incorporated with vessel dynamic equations. Rigid body bond graph can also be used to develop models of various other equipment. But when connecting several such systems together rigidly, causality problems will arise. The solution is to use the mathematical equivalent to a stiff spring in between the rigid bodies, thus the connection will not be entirely rigid. In this thesis the development of such multi-dimensional bond graph has been research. A model for a simplified barge has been developed. It is clear that such models has great potential, but as with all other mathematical models of marine vessel dynamics accurate simulation results rely on accurate hydrodynamic coefficients which can be hard to derive. Using the same procedure for multi-dimensional bond graph as for vessel modeling it is possible derive a model representing a pendulum. Which with some modification such as actuators represent a crane beam. Using three dimensional bond graph joints based on the concept of stiff springs to connect several such models a crane model is developed. The model is tested and it is found that the stiff springs in the connections may induce high vibrational natural frequencies which can affect simulation time. For such problems damping in the joint may be adopted. The barge model and the crane model are interfaced using bond graph joints and it is shown that the movement of the crane indeed will induce forces on the barge as expected. This proves that 6DOF systems (six degrees of freedom) for several different mechanical component can be interfaced and facilitate the modeling of marine vessel dynamics and the connection of sub systems. Thus an efficient way of modeling such systems has been achieved. To demonstrate the simulation result of the models developed in the thesis animations have been generated and is included in the attached CD.
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Tang, Terry, and University of Lethbridge Faculty of Arts and Science. "Mathematical modeling of eukaryotic gene expression." Thesis, Lethbridge, Alta. : University of Lethbridge, Dept. of Chemistry and Biochemistry, 2010, 2010. http://hdl.handle.net/10133/2567.
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Using the Gillespie algorithm, the export of the mRNA molecules from their transcription
site to the nuclear pore complex is simulated. The effect of various structures in the nu-
cleus on the efficiency of export is discussed. The results show that having some of the
space filled by chromatin near the mRNA synthesis site shortens the transport time. Next, the complete eukaryotic gene expression including transcription, splicing, mRNA export, translation, and mRNA degradation is modeled using delay stochastic simulation. This allows for the study of stochastic effects during the process and on the protein production rate patterns. Various protein production patterns can be produced by adjusting the poly-A tail length of the mRNA and the promoter efficiency of the gene. After that, the opposing effects of the chromatin density on the seeking time of the transcription factors for the promoter and the exit time of the mRNA product are discussed.xi, 102 leaves ; 28 cm
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Karimov, Vladimir Rustemovich. "Mathematical modeling of ephemeral gully erosion." Diss., Kansas State University, 2017. http://hdl.handle.net/2097/38230.
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Doctor of PhilosophyDepartment of Biological & Agricultural Engineering
Aleksey Y. Sheshukov
As the world faces an increasing demand for food due to the growing global population and the pernicious effects of land degradation, there is a need to overcome this challenge by using sustainable management practices for agricultural productions. One of the problems, which sustainable agriculture seeks to address, is the loss of topsoil due to soil erosion. Changing weather patterns also contribute to the average annual rainfall across the globe with an excess precipitation, which creates runoff and causes soil erosion. One of the significant yet less studied types of soil erosion is ephemeral gully erosion. Formed by the concentrated overland flow during intensive rainfall events, ephemeral gullies are channels on agricultural fields that can be removed by tillage operations but appear at the same location every year. Even though simplified ephemeral gully models estimate soil losses, they do not account for complicated hydrological and soil erosion processes of channel formations. The purpose of this research work is to investigate sediment sources and develop tools that can predict ephemeral gully erosion more efficiently. To achieve this goal, an experimental study was conducted on an agricultural field in central Kansas by tracking channel development, monitoring soil moisture content, and recording the amount of rainfall. Runoff and sediment loads from contributing catchment and critical and actual shear stresses were estimated by the computer model, and conclusions were made on the effect of saturation dynamics on the erosion processes. Furthermore, a two-dimensional subsurface water flow and soil erosion model was developed with the variable soil erodibility parameters which account for the subsurface fluxes and the effects on the soil detachment process. The model was applied to study the impacts of variable soil erodibility parameters on the erosion process for different soils and various antecedent soil moisture conditions. Also developed to estimate the soil losses at the field scale was an integrated spatially-distributed ephemeral gully model with dynamic time-dependent channel development. The model showed good fit by matching the experimental data. The results from this work can be used to advance the research of soil erosion prediction from concentrated flow channels and ephemeral gullies formed on agricultural fields.
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Viberg, Victor. "Quantifying metabolic fluxes using mathematical modeling." Thesis, Linköpings universitet, Institutionen för medicinsk teknik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-149588.
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Background Cancer is one of the leading causes of death in Sweden. In order to develop better treatments against cancer we need to better understand it. One area of special interest is cancer metabolism and the metabolic fluxes. As these fluxes cannot be directly measured, modeling is required to determine them. Due to the complexity of cell metabolism, some limitations in the metabolism model are required. As the TCA-cycle (TriCarboxylic Acid cycle) is one of the most important parts of cell metabolism, it was chosen as a starting point. The primary goal of this project has been to evaluate the previously constructed TCA-cycle model. The first step of the evaluation was to determine the CI (Confidence Interval) of the model parameters, to determine the parameters’ identifiability. The second step was to validate the model to see if the model could predict data for which the model had not been trained for. The last step of the evaluation was to determine the uncertainty of the model simulation. Method The TCA-cycle model was created using Isotopicaly labeled data and EMUs (ElementaryMetabolic Units) in OpenFlux, an open source toolbox. The CIs of the TCA-cycle model parameters were determined using both OpenFlux’s inbuilt functionality for it as well as using amethod called PL (Profile Likelihood). The model validation was done using a leave one out method. In conjunction with using the leave on out method, a method called PPL (Prediction Profile Likelihood) was used to determine the CIs of the TCA-cycle model simulation. Results and Discussion Using PL to determine CIs had mixed success. The failures of PL are most likely caused by poor choice of settings. However, in the cases in which PL succeeded it gave comparable results to those of OpenFLux. However, the settings in OpenFlux are important, and the wrong settings can severely underestimate the confidence intervals. The confidence intervals from OpenFlux suggests that approximately 30% of the model parameters are identifiable. Results from the validation says that the model is able to predict certain parts of the data for which it has not been trained. The results from the PPL yields a small confidence interval of the simulation. These two results regarding the model simulation suggests that even though the identifiability of the parameters could be better, that the model structure as a whole is sound. Conclusion The majority of the model parameters in the TCA-cycle model are not identifiable, which is something future studies needs to address. However, the model is able to to predict data for which it has not been trained and the model has low simulation uncertainty.
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Nikin-Beers, Ryan Patrick. "Mathematical Modeling of Dengue Viral Infection." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/48594.
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In recent years, dengue viral infection has become one of the most widely-spread mosquito-borne diseases in the world, with an estimated 50-100 million cases annually, resulting in 500,000 hospitalizations. Due to the nature of the immune response to each of the four serotypes of dengue virus, secondary infections of dengue put patients at higher risk for more severe infection as opposed to primary infections. The current hypothesis for this phenomenon is antibody-dependent enhancement, where strain-specific antibodies from the primary infection enhance infection by a heterologous serotype. To determine the mechanisms responsible for the increase in disease severity, we develop mathematical models of within-host virus-cell interaction, epidemiological models of virus transmission, and a combination of the within-host and between-host models. The main results of this thesis focus on the within-host model. We model the effects of antibody responses against primary and secondary virus strains. We find that secondary infections lead to a reduction of virus removal. This is slightly different than the current antibody-dependent enhancement hypothesis, which suggests that the rate of virus infectivity is higher during secondary infections due to antibody failure to neutralize the virus. We use the results from the within-host model in an epidemiological multi-scale model. We start by constructing a two-strain SIR model and vary the parameters to account for the effect of antibody-dependent enhancement.Master of Science
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Narala, Sowmya Reddy. "MATHEMATICAL MODELING OF DC CARDIAC ABLATION." Cleveland State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=csu1337099981.
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Kim, Cheongtag. "Modeling individual differences in mathematical psychology /." The Ohio State University, 1998. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487950153602217.
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Wu, Gianna. "Mathematical Modeling of Type 1 Diabetes." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/hmc_theses/231.
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Type 1 Diabetes (T1D) is an autoimmune disease where the pancreas produces little to no insulin, which is a hormone that regulates blood glucose levels. This happens because the immune system attacks (and kills) the beta cells of the pancreas, which are responsible for insulin production. Higher levels of glucose in the blood could have very negative, long term effects such as organ damage and blindness.
To date, T1D does not have a defined cause nor cure, and research for this disease is slow and difficult due to the invasive nature of T1D experimentation. Mathematical modeling provides an alternative approach for treatment development and can greatly advance T1D research. This thesis describes both a single-compartment and multi-compartment model for Type 1 Diabetes.
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Coletti, Roberta. "Mathematical modeling of prostate cancer immunotherapy." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/265805.
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Immunotherapy, by enhancing the endogenous anti-tumor immune responses, is showing promising results for the treatment of numerous cancers refractory to conventional therapies. However, its effectiveness for advanced castration-resistant prostate cancer remains unsatisfactory and new therapeutic strategies need to be developed. To this end, mathematical modeling provides a quantitative framework for testing in silico the efficacy of new treatments and combination therapies, as well as understanding unknown biological mechanisms. In this dissertation we present two mathematical models of prostate cancer immunotherapy defined as systems of ordinary differential equations.
The first work, introduced in Chapter 2, provides a mathematical model of prostate cancer immunotherapy which has been calibrated using data from pre-clinical experiments in mice. This model describes the evolution of prostate cancer, key components of the immune system, and seven treatments. Numerous combination therapies were evaluated considering both the degree of tumor inhibition and the predicted synergistic effects, integrated into a decision tree. Our simulations predicted cancer vaccine combined with immune checkpoint blockade as the most effective dual-drug combination immunotherapy for subjects treated with androgen-deprivation therapy that developed resistance. Overall, this model serves as a computational framework to support drug development, by generating hypotheses that can be tested experimentally in pre-clinical models.
The Chapter 3 is devoted to the description of a human prostate cancer mathematical model. The potential effect of immunotherapies on castration-resistant form has been analyzed. In particular, the model includes the dendritic vaccine sipuleucel-T, the only currently available immunotherapy option for advanced prostate cancer, and the ipilimumab, a drug targeting the cytotoxic T-lymphocyte antigen 4 , exposed on the CTLs membrane, currently under Phase II clinical trial. From a mathematical analysis of a simplified model, it seems likely that, under continuous administration of ipilimumab, the system lies in a bistable situation where both the no-tumor equilibrium and the high-tumor equilibrium are attractive. The schedule of periodic treatments could then determine the outcome, and mathematical models could help in deciding an optimal schedule.
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Coletti, Roberta. "Mathematical modeling of prostate cancer immunotherapy." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/265805.
Full textAbstract:
Immunotherapy, by enhancing the endogenous anti-tumor immune responses, is showing promising results for the treatment of numerous cancers refractory to conventional therapies. However, its effectiveness for advanced castration-resistant prostate cancer remains unsatisfactory and new therapeutic strategies need to be developed. To this end, mathematical modeling provides a quantitative framework for testing in silico the efficacy of new treatments and combination therapies, as well as understanding unknown biological mechanisms. In this dissertation we present two mathematical models of prostate cancer immunotherapy defined as systems of ordinary differential equations.
The first work, introduced in Chapter 2, provides a mathematical model of prostate cancer immunotherapy which has been calibrated using data from pre-clinical experiments in mice. This model describes the evolution of prostate cancer, key components of the immune system, and seven treatments. Numerous combination therapies were evaluated considering both the degree of tumor inhibition and the predicted synergistic effects, integrated into a decision tree. Our simulations predicted cancer vaccine combined with immune checkpoint blockade as the most effective dual-drug combination immunotherapy for subjects treated with androgen-deprivation therapy that developed resistance. Overall, this model serves as a computational framework to support drug development, by generating hypotheses that can be tested experimentally in pre-clinical models.
The Chapter 3 is devoted to the description of a human prostate cancer mathematical model. The potential effect of immunotherapies on castration-resistant form has been analyzed. In particular, the model includes the dendritic vaccine sipuleucel-T, the only currently available immunotherapy option for advanced prostate cancer, and the ipilimumab, a drug targeting the cytotoxic T-lymphocyte antigen 4 , exposed on the CTLs membrane, currently under Phase II clinical trial. From a mathematical analysis of a simplified model, it seems likely that, under continuous administration of ipilimumab, the system lies in a bistable situation where both the no-tumor equilibrium and the high-tumor equilibrium are attractive. The schedule of periodic treatments could then determine the outcome, and mathematical models could help in deciding an optimal schedule.
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Mascheroni, Pietro. "Mathematical modeling of avascular tumor growth." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3425310.
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Cancer is an extremely complex disease, both in terms of its causes and consequences to the body. Cancer cells acquire the ability to proliferate without control, invade the surrounding tissues and eventually form metastases. It is becoming increasingly clear that a description of tumors that is uniquely based on molecular biology is not enough to understand thoroughly this illness. Quantitative sciences, such as physics, mathematics and engineering, can provide a valuable contribution to this field, suggesting new ways to examine the growth of the tumor and to investigate its interaction with the neighboring environment. In this dissertation, we deal with mathematical models for avascular tumor growth. We evaluate the effects of physiological parameters on tumor development, with a particular focus on the mechanical response of the tissue. We start from tumor spheroids, an effective three-dimensional cell culture, to investigate the first stages of tumor growth. These cell aggregates reproduce the nutrient and proliferation gradients found in the early stages of cancer and can be grown with a strict control of their environmental conditions. The equations of the model are derived in the framework of porous media theory, and constitutive relations for the mass transfer terms and the mechanical stress are formulated on the basis of experimental observations. The growth curves of the model are compared to the experimental data, with good agreement for the different experimental settings. A new mathematical law regulating the inhibitory effect of mechanical compression on cancer cell proliferation is also presented. Then, we perform a parametric analysis to identify the key parameters that drive the system response. We conclude this part by introducing governing equations for transport and uptake of a chemotherapeutic agent, designed to target cell proliferation. In particular, we investigate the combined effect of compressive stresses and drug action. Interestingly, we find that variation in tumor spheroid volume, due to the presence of a drug targeting cell proliferation, depends considerably on the compressive stress level of the cell aggregate. In the second part of the dissertation, we study a constitutive law describing the mechanical response of biological tissues. We introduce this relation in a biphasic model for tumor growth based on the mechanics of fluid-saturated porous media. The internal reorganization of the tissue in response to mechanical and chemical stimuli is described by enforcing the multiplicative decomposition of the deformation gradient tensor associated with the solid phase motion. In this way, we are able to distinguish the contributions of growth, rearrangement of cellular bonds, and elastic distortion, occurring during tumor evolution. Results are presented for a benchmark case and for three biological configurations. We analyze the dependence of tumor development on the mechanical environment, with particular focus on cell reorganization and its role in stress relaxation. Finally, we conclude with a summary of the results and with a discussion of possible future extensions.Il cancro è una malattia estremamente complessa, sia per quanto riguarda le sue cause che per i suoi effetti sul corpo. Le cellule del cancro acquisiscono la capacità di proliferare senza controllo, invadere i tessuti vicini e infine sviluppare metastasi. Negli ultimi anni sta diventando sempre più chiaro che una descrizione dei tumori basata unicamente sulla biologia molecolare non può essere sufficiente per comprendere interamente la malattia. A questo riguardo, scienze quantitative come la Fisica, la Matematica e l'Ingegneria, possono fornire un valido contributo, suggerendo nuovi modi per esaminare la crescita di un tumore e studiare la sua interazione con l'ambiente circostante. In questa tesi ci occupiamo di modelli matematici per la crescita avascolare dei tumori. Valutiamo gli effetti dei parametri fisiologici sullo sviluppo del tumore, con un'attenzione particolare alla risposta meccanica del tessuto. Partiamo dagli sferoidi tumorali, una cultura cellulare tridimensionale, per studiare le prime fasi della crescita tumorale. Questi aggregati cellulari sono in grado di riprodurre i gradienti di nutriente e proliferazione che si ritrovano nei tumori avascolari. Inoltre, possono essere fatti crescere con un controllo molto severo delle condizioni ambientali. Le equazioni del modello sono derivate nell'ambito della teoria dei mezzi porosi dove, per chiudere il problema, definiamo opportune relazioni costitutive al fine di descrivere gli scambi di massa tra i diversi componenti del sistema e la risposta meccanica di quest'ultimo. Tali leggi sono formulate sulla base di osservazioni sperimentali. Le curve di crescita del modello sono quindi confrontate con dati sperimentali, con un buon accordo per le diverse condizioni. Presentiamo, inoltre, una nuova espressione matematica per descrivere gli effetti di inibizione della crescita da parte della compressione meccanica sulle cellule cancerose. In seguito, eseguiamo uno studio parametrico per identificare i parametri chiave che guidano la risposta del sistema. Concludiamo infine questa parte introducendo le equazioni di governo per il trasporto e il consumo di un agente chemioterapico, studiato per essere efficace sulle cellule proliferanti. In particolare, consideriamo l'effetto combinato di stress meccanici compressivi e di tale farmaco sullo sviluppo del tumore. A questo proposito, i nostri risultati indicano che una variazione di volume degli sferoidi tumorali, a causa dell'azione del farmaco, dipende sensibilmente dal livello di tensione a cui è sottoposto l'aggregato cellulare. Nella seconda parte di questa trattazione, studiamo una legge costitutiva per descrivere la risposta meccanica di tessuti biologici. Introduciamo questa relazione in un modello bifasico per la crescita tumorale basato sulla meccanica di mezzi porosi saturi. La riorganizzazione interna del tessuto in risposta a stimoli meccanici e chimici è descritta attraverso la decomposizione moltiplicativa del gradiente di deformazione associato con il moto della fase solida del sistema. In questo modo, risulta possibile distinguere i contributi di crescita, riarrangiamento dei legami cellulari e distorsione elastica che prendono luogo durante l'evoluzione del tumore. In seguito, presentiamo risultati per un caso di test e per tre configurazioni di interesse biologico. In particolare, analizziamo la dipendenza dello sviluppo del tumore dal suo ambiente meccanico, con un'attenzione particolare sulla riorganizzazione dei legami tra le cellule e il suo ruolo sul rilassamento degli stress meccanici. Infine, concludiamo la discussione con un breve riassunto dei risultati ottenuti e un resoconto dei possibili sviluppi.
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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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Livescu, Silviu. "Mathematical and numerical modeling of coating flows." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file 3.48 Mb., 279 p, 2006. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3221057.
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Clipii, Tudor. "On mathematical modeling of shaped charge penetration." Thesis, Linköping University, Department of Management and Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11996.
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Shaped charges are a well established type of projectile, subjected to a lot of research ever since emerging as a viable technology in the 1940s. The penetration achieved by shaped charges decreases with increased standoff distance. This is often attributed to the shaped charge jet losing its coherence. The Swedish Defence Research Agency however, noted no such loss of coherence in its experiments. An alternative explanation to the decrease of penetration was instead proposed. The object of this thesis was to investigate this proposed theory. To this end, the hydrocode Autodyn was used, modelling the impact of a high-velocity projectile into a generic target and analysing the resulting behaviour of the target. Several setups were used and several parameters were considered when evaluating the results. The conclusion of this thesis is that the alternative explanation offered is not supported by the observed behaviour of the target in the computer model.
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Apostu, Raluca. "Understanding cyclical thrombocytopenia : a mathematical modeling approach." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=101834.
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Cyclical thrombocytopenia (CT) is a rare hematological disease characterized by periodic oscillations in the platelet count. Although first reported in 1936, the pathogenesis and an effective therapy remain to be identified. Since besides fluctuations in platelet levels the patients hematological profile have been consistently normal, a destabilization of a peripheral control mechanism might play an important role in the genesis of this disorder. In this thesis, we investigate through computer simulations the mechanisms underlying the platelet oscillations observed in CT. First, we collected the data published in the last 40 years and quantified the significance of the platelet fluctuations using Lomb-Scargle periodograms. Our analysis reveals that the incidence of the statistically significant periodic data is equally distributed in men and women. The mathematical model proposed in this thesis captures the essential features of hematopoiesis and successfully duplicates the characteristics of CT. With the same parameter changes, the model is able to fit the platelet counts and to qualitatively reproduce the TPO oscillations (when data is available). Our results indicate that a variation in the megakaryocyte maturity, a slower relative growth rate of megakaryocytes, as well as an increased random destruction of platelets are the critical elements generating the platelet oscillations in CT.La thrombocytopénie cyclique (TC) est une rare maladie hématologique caracteriséepar des oscillations périodiques dans les plaquettes sanguines. Bien qu'elle fût évoquéepour la première fois en 1936, la maladie et une thérapie efficace restent à trouver.Puisque malgré les fluctuations au niveau des plaquettes, les profiles hématologiquesdes patients restent toujour normaux, une destabilisation du méchanisme de contrôlepériphérique peut jouer un rôle important dans la formation de ce maladie. Dans cettethèse, nous recherchons à travers des simulations informatiques les mechanismes sousjacentaux oscillations des plaquettes observées dans TC. En premier lieu, nous avonscollecté les données publiées ces 40 dernière années et quantifié l'importance des fluctuationsdes plaquettes en utilisant les périodograms Lomb-Scargle. Notre analysestatistique révèle que les données périodiques sont équitablement distribuée chez leshommes et les femmes. Le modèle mathématique proposé dans cette thèse prenden compte les caractéristiques essentielles de la production des cellules sanguineset reproduit avec succès les charactéristiques de TC. Avec les même changementde parametèrs, le modèle reproduit bien le comportement des plaquettes sanguineset donne qualitativement les même oscillations que TPO (quand les données sontdisponibles). Nos résultats indiquent que les éléments critiques générant les oscillationsdes plaquettes dans TC sont une variation dans la maturité du mégakaryocytes,un taux de croissance relativement lent des mégakaryo cytes , ainsi que une augmentationaléatoire de destruction des plaquettes.
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Isangulov, Rustam. "Mathematical modeling applied to oil field processes." Thesis, Imperial College London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.511882.
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Menzies, Nicolas Alan. "Mathematical Modeling to Evaluate Disease Control Policy." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11356.
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In this dissertation I assessed three distinct policy questions: the implications of introducing a new tuberculosis diagnostic in southern Africa, the potential value of research related to HIV treatment policy in South Africa, and the causal effect of state cigarette taxes imposed between 1996 and 2013 on health outcomes in the United States.
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LAWOT, NIWAS. "MATHEMATICAL MODELING OF SMALLPOX WITHOPTIMAL INTERVENTION POLICY." Master's thesis, University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3397.
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In this work, two differential equation models for smallpox are numerically solved to find the optimal intervention policy. In each model we look for the range of values of the parameters that give rise to the worst case scenarios. Since the scale of an epidemic is determined by the number of people infected, and eventually dead, as a result of infection, we attempt to quantify the scale of the epidemic and recommend the optimum intervention policy. In the first case study, we mimic a densely populated city with comparatively big tourist population, and heavily used mass transportation system. A mathematical model for the transmission of smallpox is formulated, and numerically solved. In the second case study, we incorporate five different stages of infection: (1) susceptible (2) infected but asymptomatic, non infectious, and vaccine-sensitive; (3) infected but asymptomatic, noninfectious, and vaccine-in-sensitive; (4) infected but asymptomatic, and infectious; and (5) symptomatic and isolated. Exponential probability distribution is used for modeling this case. We compare outcomes of mass vaccination and trace vaccination on the final size of the epidemic.M.S.
Department of Mathematics
Sciences
Mathematics
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Xin, Fen. "Mathematical Modeling of Ultra-Superheated Steam Gasification." Ohio University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1364825034.
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Gupta, Shailesh. "Mathematical Modeling of Thin Strip Casting Processes." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1391679731.
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Groshong, Kimberly A. "Defining mathematical modeling for K-12 education." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1534374871189434.
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Myers, Lance Jonathan. "Mathematical modeling of foetal arterial blood flow." Doctoral thesis, University of Cape Town, 2001. http://hdl.handle.net/11427/5143.
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Bibliography: leaves 187-211.The aim of this thesis was to develop an accurate and comprehensive computer model of the foetal circulatory system and to use this model to investigate influences of various haemodynamic viriables on common Doppler blood flow velocity waveform indices. The foetal model consists of an number of vascular compartments, cascaded together using electrical transmission line analogies.
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Haddon, Antoine. "Mathematical Modeling and Optimization for Biogas Production." Thesis, Montpellier, 2019. http://www.theses.fr/2019MONTS047.
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La digestion anaérobique est un processus biologique au cours duquel des micro-organismes décomposent de la matière organique pour produire du biogaz (dioxyde de carbone et methane) qui peut être utilisé comme source d'énergie renouvelable. Cette thèse porte sur l'élaboration de stratégies de contrôle et la conception de bioréacteurs qui maximisent la production de biogaz.La première partie se concentre sur le problème de contrôle optimal de la maximisation de la production de biogaz dans un chemostat avec un modèle à une réaction, en contrôlant le taux de dilution. Pour le problème à horizon fini, nous étudions des commandes type feedback, similaires à ceux utilisés en pratique et consistant à conduire le réacteur vers un niveau de substrat donné et à le maintenir à ce niveau. Notre approche repose sur une estimation de la fonction de valeur inconnue en considérant différentes fonctions de coût pour lesquelles la solution optimale admet un feedback optimal explicite et autonome. En particulier, cette technique fournit une estimation de la sous-optimalité des régulateurs étudiés pour une large classe de fonctions de croissance dépendant du substrat et de la biomasse. À l'aide de simulations numériques, on montre que le choix du meilleur feedback dépend de l'horizon de temps et de la condition initiale.Ensuite, nous examinons le problème sur un horizon infini, pour les coûts moyen et actualisé. On montre que lorsque le taux d'actualisation tends vers à 0, la fonction de valeur du problème actualisé converge vers la fonction de valeur pour le coût moyen. On identifie un ensemble de solutions optimales pour le problème de limite et avec coût moyen comme étant les contrôles qui conduisent le système vers un état qui maximise le débit de biogaz sur un ensemble invariant.Nous revenons ensuite au problème sur à horizon fini fixe et avec le Principe du Maximum de Pontryagin, on montre que le contrôle optimal à une structure bang arc singulier. On construit une famille de contrôles extremal qui dépendent de la valeur constante du Hamiltonien. En utilisant l'équation de Hamilton-Jacobi-Bellman, on identifie le contrôle optimal comme étant celui associé à la valeur du Hamiltonien qui satisfait une équation de point fixe. On propose ensuite un algorithme pour calculer la commande optimale en résolvant cette équation de point fixe. On illustre enfin cette méthode avec les deux principales types de fonctions de croissance de Monod et Haldane.Dans la deuxième partie, on modélise et on étudie l'impact de l'hétérogénéité du milieu réactionnel sur la production de biogaz. Pour cela, on introduit un modèle de bioréacteur pilote qui décrit les caractéristiques spatiales. Ce modèle tire parti de la géométrie du réacteur pour réduire la dimension spatiale de la section contenant un lit fixe et, dans les autres sections, on considère les équations 3D de Navier-Stokes en régime permanent pour la dynamique des fluides. Pour représenter l'activité biologique, on utilise un modèle à deux réactions et pour les substrats, des équations advection-diffusion-réaction. On considère seulement les biomasses qui sont attachées au lit fixe et on modélise leur croissance avec une fonction densité dépendante. On montre que ce modèle peut reproduire le gradient spatial de données expérimentales et permet de mieux comprendre la dynamique interne du réacteur. En particulier, les simulations numériques indiquent qu'en mélangeant moins, le réacteur est plus efficace, élimine plus de matières organiques et produit plus de biogazAnaerobic digestion is a biological process in which organic compounds are degraded by different microbial populations into biogas (carbon dioxyde and methane), which can be used as a renewable energy source. This thesis works towards developing control strategies and bioreactor designs that maximize biogas production.The first part focuses on the optimal control problem of maximizing biogas production in a chemostat in several directions. We consider the single reaction model and the dilution rate is the controlled variable.For the finite horizon problem, we study feedback controllers similar to those used in practice and consisting in driving the reactor towards a given substrate level and maintaining it there. Our approach relies on establishing bounds of the unknown value function by considering different rewards for which the optimal solution has an explicit optimal feedback that is time-independent. In particular, this technique provides explicit bounds on the sub-optimality of the studied controllers for a broad class of substrate and biomass dependent growth rate functions. With numerical simulations, we show that the choice of the best feedback depends on the time horizon and initial condition.Next, we consider the problem over an infinite horizon, for averaged and discounted rewards. We show that, when the discount rate goes to 0, the value function of the discounted problem converges and that the limit is equal to the value function for the averaged reward. We identify a set of optimal solutions for the limit and averaged problems as the controls that drive the system towards a state that maximizes the biogas flow rate on an special invariant set.We then return to the problem over a fixed finite horizon and with the Pontryagin Maximum Principle, we show that the optimal control has a bang singular arc structure. We construct a one parameter family of extremal controls that depend on the constant value of the Hamiltonian. Using the Hamilton-Jacobi-Bellman equation, we identify the optimal control as the extremal associated with the value of the Hamiltonian which satisfies a fixed point equation. We then propose a numerical algorithm to compute the optimal control by solving this fixed point equation. We illustrate this method with the two major types of growth functions of Monod and Haldane.In the second part, we investigate the impact of mixing the reacting medium on biogas production. For this we introduce a model of a pilot scale upflow fixed bed bioreactor that offers a representation of spatial features. This model takes advantage of reactor geometry to reduce the spatial dimension of the section containing the fixed bed and in other sections, we consider the 3D steady-state Navier-Stokes equations for the fluid dynamics. To represent the biological activity, we use a 2 step model and for the substrates, advection-diffusion-reaction equations. We only consider the biomasses that are attached in the fixed bed section and we model their growth with a density dependent function. We show that this model can reproduce the spatial gradient of experimental data and helps to better understand the internal dynamics of the reactor. In particular, numerical simulations indicate that with less mixing, the reactor is more efficient, removing more organic matter and producing more biogas
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Baker, Nathan Andrew. "Mathematical and computational modeling of biomolecular systems /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2001. http://wwwlib.umi.com/cr/ucsd/fullcit?p3007138.
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Saripalli, Manjeera. "Mathematical Modeling and Simulation of Colorectal Cancer." OpenSIUC, 2011. https://opensiuc.lib.siu.edu/theses/698.
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Understanding the cancer pathology and develop effective treatment strategies play significant roles in improving cancer survival rates. In this thesis, evaluations of mathematical modeling and simulation were studied and presented. Colorectal system was investigated from gene and cell levels. The Hardware Descriptive Language (HDL) package and codes were developed to simulate the cancer models. Representative codes and figures were illustrated. Results suggest that the HDL is an effective method to conduct the modeling and simulation of cancers. It is essential to develop advanced technology such as HDL modeling and simulation to improve our understandings to fight cancer and save lives.
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Fumanelli, Laura. "Mathematical modeling of amoeba-bacteria population dynamics." Doctoral thesis, Università degli studi di Trento, 2009. https://hdl.handle.net/11572/368763.
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We present a mathematical model describing the dynamics occurring between two interacting populations, one of amoebae and one of virulent bacteria; it is meant to describe laboratory experiments with these two species in a mathematical framework and help understanding the role of the different mechanisms involved. In particular we aim to focus on how bacterial virulence may affect the dynamics of the system.
The model is a modified reaction-diffusion-chemotaxis predator-prey one with a mechanism of redistribution of ingested biomass between amoeboid cells. The spatially homogeneous case is analyzed in detail; conditions for pattern formation are established; numerical simulations for the complete model are performed.
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Fumanelli, Laura. "Mathematical modeling of amoeba-bacteria population dynamics." Doctoral thesis, University of Trento, 2009. http://eprints-phd.biblio.unitn.it/157/1/Fumanelli_PhDthesis.pdf.
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We present a mathematical model describing the dynamics occurring between two interacting populations, one of amoebae and one of virulent bacteria; it is meant to describe laboratory experiments with these two species in a mathematical framework and help understanding the role of the different mechanisms involved. In particular we aim to focus on how bacterial virulence may affect the dynamics of the system.
The model is a modified reaction-diffusion-chemotaxis predator-prey one with a mechanism of redistribution of ingested biomass between amoeboid cells. The spatially homogeneous case is analyzed in detail; conditions for pattern formation are established; numerical simulations for the complete model are performed.
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El, Moustaid Fadoua. "MATHEMATICAL MODELING OF CYANOBACTERIAL DYNAMICS IN A CHEMOSTAT." Master's thesis, Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/335727.
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MathematicsM.S.
We present a mathematical model that describes how cyanobacterial communities use natural light as a source of energy and water as a source of electrons to perform photosynthesis and therefore, grow and co-survive together with other bacterial species. We apply our model to a phototrophic population of bacteria, namely, cyanobacteria. Our model involves the use of light as a source of energy and inorganic carbon as a source of nutrients. First, we study a single species model involving only cyanobacteria, then we include heterotrophs in the two species model. The model consists of ordinary differential equations describing bacteria and chemicals evolution in time. Stability analysis results show that adding heterotrophs to a population of cyanobacteria increases the level of inorganic carbon in the medium, which in turns allows cyanobacteria to perform more photosynthesis. This increase of cyanobacterial biomass agrees with experimental data obtained by collaborators at the Center for Biofilm Engineering at Montana State University.
Temple University--Theses
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Wu, Yilin. "Mathematical Models of Biofilm in Various Environments." Diss., Temple University Libraries, 2019. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/582206.
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MathematicsPh.D.
Microbial biofilms are defined as clusters of microbial cells living in self-produced extracellular polymeric substances (EPS), which always attached to various kinds of surfaces. In this thesis, we studied several mathematical models of biofilm in the human body and marble environment. Some related background of biofilm growth and some basic existing numerical models were introduced in the first chapter. In the first project, we introduced how biofilm affects the local oxygen concentration near the neutrophil cells in the human body with three one-dimensional reaction-diffusion models from different geometries. In nature, microbial biofilm development can be observed on almost all kinds of stone monuments and can also be associated with the problem of monument conservation. In the second part of my research, we built the deliquescence models for biofilm growth environment in the first model and added biomass into consideration in the second one. Also, we analyzed the stability of the equilibria. In the third part, we applied the weather data collected from the weather station on the roof of the Jefferson Memorial to the deliquescence model with biofilm. Furthermore, compared the simulation result for biofilm growth in cold and warm weathers. In the last part of this thesis, we analyzed the biofilm activity with support vector regression. The machine learning model we obtained can be used to find the growth trends of biofilm for any pair of temperature and relative humidity data.
Temple University--Theses
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Sargent, Aitbala. "Modeling Ice Streams." Fogler Library, University of Maine, 2009. http://www.library.umaine.edu/theses/pdf/SargentA2009.pdf.
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Su, Yong. "Mathematical modeling with applications in high-performance coding." Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1127139848.
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Thesis (Ph. D.)--Ohio State University, 2005.Title from first page of PDF file. Document formatted into pages; contains xiv, 130 p.; also includes graphics (some col.). Includes bibliographical references (p. 125-130). Available online via OhioLINK's ETD Center
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Dahl, Lars Oswald. "Numerical analysis and stochastic modeling in mathematical finance." Doctoral thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2002. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-1678.
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The main goal of this thesis has been to study and develop faster and more accurate methods for pricing and hedging exotic options. This has involved work on models describing prices and hedges as well as the stochastics driving them. We have also put effort into algorithmic interpretation and implementation of the models to enable efficiency measurement with regards to computing time. In some of the articles we have aspired to find criteria to decide whether the pricing methods we have developed can be expected to perform well, enabling practicians to find a good numerical method for their given pricing/hedging problem easier. However, the most optimistic reader must be warned: We have not found one single method that works best for all types of option pricing problems, and we do not think that sucj a method exists. Pricing and hedging of exotic options involve thorough knowledge of the problem at hand, and the mastering of a tool box of numerical methods from which a suitible one can be picket. We beleive, however, that the thesis contributes som to the enlargement of the tool box.