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1
Ambrose, Joseph Paul. "Dynamic field theory applied to fMRI signal analysis." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2035.
Повний текст джерелаАнотація:
In the field of cognitive neuroscience, there is a need for theory-based approaches to fMRI data analysis. The dynamic neural field model-based approach has been developing to meet this demand. This dissertation describes my contributions to this approach. The methods and tools were demonstrated through a case study experiment on response selection and inhibition. The experiment was analyzed via both the standard behavioral approach and the new model-based method, and the two methods were compared head to head. The methods were quantitatively comparable at the individual-level of the analysis. At the group level, the model-based method reveals distinct functional networks localized in the brain. This validates the dynamic neural field model-based approach in general as well as my recent contributions.
2
Whalen, Patrick. "Full Field Propagation Models And Methods For Extreme Nonlinear Optics." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/347238.
Повний текст джерелаАнотація:
This dissertation examines models, methods, and applications of electric field pulse propagation in nonlinear optics. Standard nonlinear optical propagation models such as the NLS equation are derived using a procedure invoking a slowly-varying wave approximation which amounts to discarding second order derivatives in the propagation direction. This work follows a more intuitive procedure emphasizing unidirectionality, the core trait of laser light propagation, by projecting a nonlinear wave system onto a unidirectional subspace. The projection method is discussed as a general theory and then applied to a series of different electric field configurations. Two important full-field propagation models are examined. The unidirectional pulse propagation equations (UPPE's) are generated from Maxwell's equations with the sole approximation being that of unidirectionality. The second model studied is the MKP equation which is a canonical full-field propagation equation particularly amenable to mathematical analysis due to its status as a conserved system. Applications unique to full-field propagation including electric field shock and harmonic walk-off induced collapse arrest are studied through numerical simulations. An emphasis is placed on the mid-infrared to long-infrared wavelength regime where significant differences between envelope models and electric field models manifest as a result of extremely weak dispersion. Presented are the first embedded Runge-Kutta exponential time-differencing (RKETD) methods of fourth order with third order embedding and fifth order with third order embedding for non-Rosenbrock type nonlinear systems. A procedure for constructing RKETD methods that accounts for both order conditions and stability is outlined. In the stability analysis, the fast time scale is represented by a full linear operator in contrast to particular scalar cases considered before. An effective time-stepping strategy based on reducing both ETD function evaluations and rejected steps is described. Comparisons of performance with adaptive-stepping integrating factor (IF) are carried out on a set of canonical partial differential equations including the standard z-propagated UPPE.
3
Kahle, A. "Cosmic microwave background anisotropies in the presence of a weak magnetic field." Master's thesis, University of Cape Town, 2003. http://hdl.handle.net/11427/4894.
Повний текст джерелаАнотація:
Bibliography: leaves 87-90.One of the questions cosmology still has not satisfactorily resolved is the origin of magnetic fields in the universe. These have been observed at all scales where man has c:evised means to observe them, from stellar scales, to intergalactic and intercluster scales. Indeed, there is no reason to believe that they are not present, at some level, at even larger scales. However, a satisfactory explanation for their origin is yet to be found. The two most popular theories for the creation of these magnetic fields, namely the Galactic dynamo, and primordial field amplification, both rely on the presence of a seed field, which they then amplify. However, the galactic dynamo requires a far weaker seed field compared to primordial field amplification. It would thus be helpful, in trying to understand magnetogenesis, if one could discover some means to detect such a seed field. One way to do so would be to search for a signature that such a magnetic field might leave on the CMB, and then look for the presence of this signature in CMB observations. This is the principal aim of this thesis.
4
Murugan, Jeffrey. "Geometrical and nonperturbative aspects of low dimensional field theories." Master's thesis, University of Cape Town, 2000. http://hdl.handle.net/11427/7681.
Повний текст джерелаАнотація:
Bibliography: leaves 84-88We present a collection of results on solitons in low-dimensional classical field theory. We begin by reviewing the geometrical setting of he nonlinear ơ-model and demonstrate the integrability of the theory in two-dimensions on a symmetric target manifold. After reviewing the construction of soliton solutions in the 0(3) ơ-model we consider a class of gauged nonlinear ơ-models on two-dimensional axially-symmetric target spaces. We show that, for a certain choice of self-interaction, these models are all self-dual and analyze the resulting Bogomol'nyi equations in the BPS limit using techniques from dynamical systems theory. Our analysis is then extended to topologically massive gauge fields. We conclude with a deviation into exploring links between four-dimensional self-dual Yang-Mills equations and various lower-dimensional field theories. In particular, we show that at the level of equations of motion, the Euclidean Yang-Mills equations in light-cone coordinates reduce to the two-dimensional nonlinear ơ-model.
5
Kuehn, T. "Approximation of anisotropic and advected mean curvature flows by phase field models." Thesis, University of Sussex, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318501.
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Webber, Matthew. "Stochastic neural field models of binocular rivalry waves." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:c444a73e-20e3-454d-85ae-bbc8831fdf1f.
Повний текст джерелаАнотація:
Binocular rivalry is an interesting phenomenon where perception oscillates between different images presented to the two eyes. This thesis is primarily concerned with modelling travelling waves of visual perception during transitions between these perceptual states. In order to model this effect in such a way that we retain as much analytical insight into the mechanisms as possible we employed neural field theory. That is, rather than modelling individual neurons in a neural network we treat the cortical surface as a continuous medium and establish integro-differential equations for the activity of a neural population. Our basic model which has been used by many previous authors both within and outside of neural field theory is to consider a one dimensional network of neurons for each eye. It is assumed that each network responds maximally to a particular feature of the underlying image, such as orientation. Recurrent connections within each network are taken to be excitatory and connections between the networks are taken to be inhibitory. In order for such a topology to exhibit the oscillations found in binocular rivalry there needs to be some form of slow adaptation which weakens the cross-connections under continued firing. By first considering a deterministic version of this model, we will show that, in fact, this slow adaptation also serves as a necessary "symmetry breaking" mechanism. Using this knowledge to make some mild assumptions we are then able to derive an expression for the shape of a travelling wave and its wave speed. We then go on to show that these predictions of our model are consistent not only with numerical simulations but also experimental evidence. It will turn out that it is not acceptable to completely ignore noise as it is a fundamental part of the underlying biology. Since methods for analyzing stochastic neural fields did not exist before our work, we first adapt methods originally intended for reaction-diffusion PDE systems to a stochastic version of a simple neural field equation. By regarding the motion of a stochastic travelling wave as being made up of two distinct components, firstly, the drift-diffusion of its overall position, secondly, fast fluctuations in its shape around some average front shape, we are able to derive a stochastic differential equation for the front position with respect to time. It is found that the front position undergoes a drift-diffusion process with constant coefficients. We then go on to show that our analysis agrees with numerical simulation. The original problem of stochastic binocular rivalry is then re-visited with this new toolkit and we are able to predict that the first passage time of a perceptual wave hitting a fixed barrier should be an inverse Gaussian distribution, a result which could potentially be experimentally tested. We also consider the implications of our stochastic work on different types of neural field equation to those used for modelling binocular rivalry. In particular, for neural fields which support pulled fronts propagating into an unstable state, the stochastic version of such an equation has wave fronts which undergo subdiffusive motion as opposed to the standard diffusion in the binocular rivalry case.
7
Michlin, Tracie L. "Using wavelet bases to separate scales in quantum field theory." Diss., University of Iowa, 2017. https://ir.uiowa.edu/etd/5572.
Повний текст джерелаАнотація:
This thesis investigates the use of Daubechies wavelets to separate scales in local quantum field theory. Field theories have an infinite number of degrees of freedom on all distance scales. Quantum field theories are believed to describe the physics of subatomic particles. These theories have no known mathematically convergent approximation methods. Daubechies wavelet bases can be used separate degrees of freedom on different distance scales. Volume and resolution truncations lead to mathematically well-defined truncated theories that can be treated using established methods. This work demonstrates that flow equation methods can be used to block diagonalize truncated field theoretic Hamiltonians by scale. This eliminates the fine scale degrees of freedom. This may lead to approximation methods and provide an understanding of how to formulate well-defined fine resolution limits.
8
Loubaton, Rodolphe. "Modélisation des effets d’une intervention dans un programme génique temporel." Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0322.
Повний текст джерелаАнотація:
Les cellules cancéreuses peuvent présenter des anomalies de l'expression de certains gènes qui altèrent le fonctionnement normal des programmes de fonctionnement cellulaire, provoquant une prolifération incontrôlée de ces cellules. Ces programmes cellulaires sont constitués de l'expression de milliers de gènes qui s'activent et interagissent de façon concertée. Ces interactions peuvent être représentées sous forme d'un réseau de régulation de gènes. L'objectif général de cette thèse, qui s'inscrit dans la continuité des travaux de Vallat et al (2021) consiste à modéliser un programme cellulaire à partir de données temporelles d'expression de gènes. Le modèle construit permettra d'identifier des gènes cibles dont la diminution d'expression pourrait diminuer la prolifération cellulaire dans un but thérapeutique. Dans le premier chapitre, nous faisons une revue des modèles de réseaux de gènes existant afin de justifier le choix de notre modèle qui est détaillé dans le deuxième chapitre. Ce modèle (appelé modèle LiRE) est un modèle statistique paramétrique gaussien qui permet de prendre en compte la dynamique d'expression de gènes à l'aide de paramètres décrivant, entre autres, les interactions entre les gènes. Les différentes propriétés théoriques de notre modèle nous ont permis de développer un algorithme itératif pour inférer les paramètres en combinant des étapes de régressions linéaires pénalisées lasso et régressions avec contraintes de positivité et contraintes sur la somme des coefficients. Nous menons également dans ce chapitre une étude numérique de ce modèle pour étudier sa performance sur des données simulées. Dans le troisième chapitre, nous décrivons des méthodes qui permettent de modéliser et prédire les résultats d'expériences d'interventions biologiques modifiant l'expression de certains gènes, afin de prédire les meilleurs gènes cibles dont il faudrait diminuer l'expression dans le programme cellulaire pour diminuer la prolifération des cellules cancéreuses. Nous donnons des résultats théoriques sur différents modèles y compris notre modèle LiRE. Dans le dernier chapitre, nous détaillons notre package R MultiRNAflow qui nous a permis de réaliser des analyses statistiques de données dynamiques et complexes d'expressions de gènes afin de caractériser les gènes retenus pour l'inférence de notre modèle LiRECancer cells can exhibit abnormalities in the expression of certain genes that alter the normal functioning of cellular programs, causing them to proliferate uncontrollably. These cellular programs are made up of the expression of thousands of genes that activate and interact in a concerted fashion. These interactions can be represented as a gene regulatory network. The general objective of this thesis, which follows on from the work of Vallat et al (2021), is to model a cellular program using temporal gene expression data. The model constructed will make it possible to identify target genes whose reduced expression could reduce cell proliferation for therapeutic purposes. In the first chapter, we review existing gene network models in order to justify the choice of our model, which is detailed in the second chapter. This model (called the LiRE model) is a Gaussian parametric statistical model that allows us to take into account gene expression dynamics using parameters describing, among other things, the interactions between genes. The various theoretical properties of our model have enabled us to develop an iterative algorithm for inferring parameters, combining steps of penalized linear regressions lasso and regressions with positivity constraints and constraints on the sum of coefficients. In this chapter, we also carry out a numerical study of this model to investigate its performance on simulated data. In the third chapter, we describe methods for modeling and predicting the results of biological intervention experiments modifying the expression of certain genes, in order to predict the best target genes whose expression should be decreased in the cellular program to reduce cancer cell proliferation. We give theoretical results on different models including our LiRE model. In the final chapter, we detail our R package MultiRNAflow, which enabled us to perform statistical analyses of dynamic and complex gene expression data in order to characterize the genes selected for inference in our model LiRE
9
Verma, Vishash. "Improved Slope Estimation in Organic Field-Effect Transistor Mobility Estimation." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1618703169092189.
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Cairns, Melissa Ann. "Weak Anchoring Effects on Magnetic Field Induced Transitions of a Cholesteric Liquid Crystal Filmwith Negative Magnetic Anisotropy." Kent State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=kent1563550315014445.
Повний текст джерела
11
Bagherian, Maryam. "Field Quantization for Radiative Decay of Plasmons in Finite and Infinite Geometries." Scholar Commons, 2019. https://scholarcommons.usf.edu/etd/7734.
Повний текст джерелаАнотація:
We investigate field quantization in high-curvature geometries. The models and calculations can help with understanding the elastic and inelastic scattering of photons and electrons in nanostructures and probe-like metallic domains. The results find important applications in high-resolution photonic and electronic modalities of scanning probe microscopy, nano-optics, plasmonics, and quantum sensing.
Quasistatic formulation, leading to nonretarded quantities, is employed and justified on the basis of the nanoscale, here subwavelength, dimensions of the considered domains of interest.
Within the quasistatic framework, we represent the nanostructure material domains with frequency-dependent dielectric functions. Quantities associated with the normal modes of the electronic systems, the nonretarded plasmon dispersion relations, eigenmodes, and fields are then calculated for several geometric entities of use in nanoscience and nanotechnology.
From the classical energy of the charge density oscillations in the modeled nanoparticle, we then derive the Hamiltonian of the system, which is used for quantization.
The quantized plasmon field is obtained and, employing an interaction Hamiltonian derived from the first-order perturbation theory within the hydrodynamic model of an electron gas, we obtain an analytical expression for the radiative decay rate of the plasmons.
The established treatment is applied to multiple geometries to investigate the quantized charge density oscillations on their bounding surfaces. Specifically, using one sheet of a two-sheeted hyperboloid of revolution, paraboloid of revolution, and cylindrical domains, all with one infinite dimension, and the finite spheroidal and toroidal domains are treated.
In addition to a comparison of the paraboloidal and hyperboloidal results, interesting similarities are observed for the paraboloidal domains with respect to the surface modes and radiation patterns of a prolate spheroid, a finite geometric domain highly suitable for modeling of nanoparticles such as quantum dots. The prolate and oblate spheroidal calculations are validated by comparison to the spherical case, which is obtained as a special case of a spheroid.
In addition to calculating the potential and field distributions, and dispersion relations, we study the angular intensity and the relation between the emission angle with the rate of radiative decay.
The various morphologies are compared for their plasmon dispersion properties, field distributions, and radiative decay rates, which are shown to be consistent.
For the specific case of a nanoring, modeled in the toroidal geometry, significant complexity arises due to an inherent coupling among the various modes. Within reasonable approximations to decouple the modes, we study the radiative decay channel for a vacuum bounded single solid nanoring by quantizing the fields associated with charge density oscillations on the nanoring surface. Further suggestions are made for future studies. The obtained results are relevant to other material domains that model a nanostructure such as a probe tip, quantum dot, or nanoantenna.
12
Carstens, Jacobus Everhardus. "Fast generation of digitally reconstructed radiographs for use in 2D-3D image registration." Thesis, Link to the online version, 2008. http://hdl.handle.net/10019/1797.
Повний текст джерела
13
Green, Harry. "Mathematical modelling of cardiac rhythms in health and disease." Thesis, University of Exeter, 2017. http://hdl.handle.net/10871/31564.
Повний текст джерелаАнотація:
Cardiac disease is the most common cause of death among the adult population worldwide and atrial fibrillation (AF) is the most common cardiac arrhythmia. The state of the art in AF treatment involves creating lesions of heart tissue through radiofrequency ablation. In this thesis, mathematical modelling techniques are developed to design decision support tools that could help a cardiologist determine the best location to ablate in clinic. Firstly, parameter optimisation methods are explored to adapt a model designed for the ventricles to the atria, and a novel technique is introduced to characterise pathways through parameter space from a healthy state to a diseased state using a multi-objective genetic algorithm. Next, I reproduce clinical signals recorded during AF ablation through the use of a phenomenological model of the cardiac action potential on a cylinder and show how this model can enable us to recover information lost in clinic to improve clinical decision. This is followed by introducing a more simplistic approach to the same problem, by characterising the electrical activity on the recording by a sine wave. Finally, the effectiveness of these two approaches is compared in the clinical setting by testing both as decision support tools. The emphasis of the approaches throughout the thesis is on developing techniques with clinical applicability. We demonstrate that lost information in clinic can affect the decision made by an experienced clinician, and that the mathematical modelling approaches developed in the thesis can significantly reduce the impact that this information loss can have on clinical decision making.
14
Van, Wyk Barry-Michael Morne. "Verifying stereo vision using structure from motion." Thesis, Stellenbosch : Stellenbosch University, 2008. http://hdl.handle.net/10019.1/3017.
Повний текст джерелаАнотація:
Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--Stellenbosch University, 2008.The medical radiation treatment facility at iThemba Labs requires a precise and robust patient positioning system. The current system makes use of an accurately calibrated multi-camera stereophotogrammetry (SPG) setup that is vulnerable to physical disruptions that invalidate system calibration. The task in this thesis is to design a vision system that can be used to verify the correct operation of the SPG system. We propose an unscented Kalman filter (UKF) based structure from motion (SFM) system for this purpose. Our SFM system does not rely on calibration information used by the SPG system and provides accurate reconstruction for verification purposes. The system is critically evaluated against a set of synthetic and real motion sequences.
15
Yarimpabuc, Durmus. "Numerical Simulation Of Thermal Convection Under The Influence Of A Magnetic Field By Using Solenoidal Bases." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613393/index.pdf.
Повний текст джерелаАнотація:
The effect of an imposed magnetic field on the thermal convection between rigid plates heated from below under the influence of gravity is numerically simulated in a computational domain with periodic horizontal extent. The numerical technique is based on solenoidal basis functions satisfying the boundary conditions for both velocity and induced magnetic field. The
expansion bases for the thermal field are also constructed to satisfy the boundary conditions. The governing partial differential equations are reduced to a system of ordinary differential equations governing the time evolution of the expansion coefficients under Galerkin projection onto the subspace spanned by the dual bases. In the process, the pressure term in the momentum equation is eliminated. The system validated in the linear regime is then used for some numerical experiments in the nonlinear regime.
16
Cato, Denys, and mikewood@deakin edu au. "An examination of the 'all hazards' approach to disaster management as applied to field disaster management and pre-hospital care in Australia." Deakin University. School of Health Sciences, 2002. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20051017.140738.
Повний текст джерелаАнотація:
Disasters, emergencies, incidents, and major incidents - they all come back to the same thing regardless of what they are called. The common denominator is that there is loss of life, injury to people and animals and damage and destruction of property.
The management of such events relies on four phases:
1. Prevention
2. Preparation
3. Response
4. Recovery
Each of these phases is managed in a different way and often by different teams. Here, concentration has been given to phases 2 and 3, with particular emphasis on phase 3, Response.
The words used to describe such events are often related to legislation. The terminology is detailed later. However, whatever the description, whenever prevention is not possible, or fails, then the need is to respond. Response is always better when the responders are prepared. Training is a major part of response preparation and this book is designed to assist those in the health industry who need to be ready when something happens. One of the training packages for responders is the Major Incident Medical Management and Support (MIMMS) Course and this work was designed to supplement the manual prepared by Hodgetts and Macway-Jones(87) in the UK.
Included is what the health services responder, who may be sent to an event in which the main concern is trauma, should know. Concentration is on the initial response and does not deal in any detail with hospital reaction, the public health aspects, or the mental health support that provides psychological help to victims and responders, and which are also essential parts of disaster management.
People, in times of disaster, have always been quick to offer assistance. It is now well recognised however, that the 'enthusiastic amateur', whilst being a well meaning volunteer, isn't always what is needed. All too often such people have made things worse and have sometimes ended up as victims themselves. There is a place now for volunteers and there probably always will be. The big difference is that these people must be well informed, well trained and well practiced if they are to be effective.
Fortunately such people and organisations do exist. Without the work of the St John Ambulance, the State Emergency Service, the Rural Fire Service the Red Cross and the Volunteer Rescue Association, to mention only a few, our response to disasters would be far less effective.
There is a strong history of individuals being available to help the community in times of crisis. Mostly these people were volunteers but there has also always been the need for a core of professional support. In the recent past,
professional support mechanisms have been developed from lessons learned, particularly to situations that need a rapid and well organised response.
As lessons are learned from an analysis of events, philosophy and methods have changed. Our present system is not perfect and perhaps never will be. The need for an 'all-hazards approach' makes detailed planning very difficult and so there will probably always be criticisms about the way an event was handled. Hindsight is a wonderful thing, provided we learn from it. That means that this text is certainly not the 'last word' and revisions as we learn from experience will be inevitable.
Because the author works primarily in New South Wales, many of the explanations and examples are specific to that state. In Australia disaster response is a State, rather than a Commonwealth, responsibility and consequently, and inevitably, there are differences in management between the states and territories within Australia. With the influence of Emergency Management Australia, these differences are being reduced. This means that across state and territory boundaries, assistance is common and interstate teams can be deployed and assimilated into the response rapidly, safely, effectively and with minimum explanation. This text sets out to increase the understanding of what is required, what is in place and how the processes of response are managed.
By way of introduction and background, examples are given of those situations that have occurred, or could happen.
Man Made Disasters has been divided into two distinct sections. Those which are related to structures or transport and those related directly to people. The first section, Chapter 3, includes:
Transport accidents involving land, rail, sea or air vehicles.
Collapse of buildings for reasons other than earthquakes or storms.
Industrial accidents, including the release of hazardous substances and nuclear events.
A second section dealing with the consequences of the direct actions of people is separated as Chapter 4, entitled 'People Disasters'. Included are:
Crowd incidents involving sports and entertainment venues.
Terrorism
From Chapter 4 on, the emphasis is on the Response phase and deals with organisation and response techniques in detail.
Finally there is a section on terminology and abbreviations. An appendix details a typical disaster pack content.
War, the greatest of all man made disasters is not considered in this text.
17
Torres, Marcella. "DETERMINATION OF OPTIMAL PARAMETER ESTIMATES FOR MEDICAL INTERVENTIONS IN HUMAN METABOLISM AND INFLAMMATION." VCU Scholars Compass, 2019. https://scholarscompass.vcu.edu/etd/5890.
Повний текст джерелаАнотація:
In this work we have developed three ordinary differential equation models of biological systems: body mass change in response to exercise, immune system response to a general inflammatory stimulus, and the immune system response in atherosclerosis. The purpose of developing such computational tools is to test hypotheses about the underlying biological processes that drive system outcomes as well as possible real medical interventions. Therefore, we focus our analysis on understanding key interactions between model parameters and outcomes to deepen our understanding of these complex processes as a means to developing effective treatments in obesity, sarcopenia, and inflammatory diseases.
We develop a model of the dynamics of muscle hypertrophy in response to resistance exercise and have shown that the parameters controlling response vary between male and female group means in an elderly population. We further explore this individual variability by fitting to data from a clinical obesity study. We then apply logistic regression and classification tree methods to the analysis of between- and within-group differences in underlying physiology that lead to different long-term body composition outcomes following a diet or exercise program. Finally, we explore dieting strategies using optimal control methods.
Next, we extend an existing model of inflammation to include different macrophage phenotypes. Complications with this phenotype switch can result in the accumulation of too many of either type and lead to chronic wounds or disease. With this model we are able to reproduce the expected timing of sequential influx of immune cells and mediators in a general inflammatory setting. We then calibrate this base model for the sequential response of immune cells with peritoneal cavity data from mice. Next, we develop a model for plaque formation in atherosclerosis by adapting the current inflammation model to capture the progression of macrophages to inflammatory foam cells in response to cholesterol consumption. The purpose of this work is ultimately to explore points of intervention that can lead to homeostasis.
18
Olmez, Fatih. "SLEEP-WAKE TRANSITION DYNAMICS AND POWER-LAW FITTING WITH AN UPPER BOUND." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1397648163.
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Van, der Bijl Leendert. "Verification of patient position for proton therapy using portal X-Rays and digitally reconstructed radiographs." Thesis, Link to the online version, 2006. http://hdl.handle.net/10019/1250.
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Judkovich, Michael. "An Active Contour Approach for 3D Thigh Muscle Segmentation." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1618866341802777.
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21
Cattoën, Céline. "Applied mathematics of space-time & space+time : problems in general relativity and cosmology : a thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics /." ResearchArchive@Victoria e-thesis, 2009. http://hdl.handle.net/10063/972.
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Evans, Oliver Graham Evans. "Modeling the Light Field in Macroalgae Aquaculture." University of Akron / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron1542810712432336.
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Ozcan, Ayca Bahar. "Performance Analysis Of Elliptic Curve Multiplication Algorithms For Elliptic Curve Cryptography." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12607698/index.pdf.
Повний текст джерелаАнотація:
Elliptic curve cryptography (ECC) has been introduced as a public-key cryptosystem, which offers smaller key sizes than the other known public-key systems at equivalent security level. The key size advantage of ECC provides faster computations, less memory consumption, less processing power and efficient bandwidth usage. These properties make ECC attractive especially for the next generation public-key cryptosystems. The implementation of ECC involves so many arithmetic operationsone of them is the elliptic curve point multiplication operation, which has a great influence on the performance of ECC protocols. In this thesis work, we have studied on elliptic curve point multiplication methods which are proposed by many researchers. The software implementations of these methods are developed in C programming language on Pentium 4 at 3 GHz. We have used NIST-recommended elliptic curves over prime and binary fields, by using efficient finite field arithmetic. We have then applied our elliptic curve point multiplication implementations to Elliptic Curve Digital Signature Algorithm (ECDSA), and compared different methods. The timing results are presented and comparisons with recent studies have been done.
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Guzman, Roca Juan Alberto. "Quantification of track-weighted functional connectivity longitudinally during Constraint Induced Movement Therapy for poststroke hemiparesis: An application of Graph Theory." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1492621365041026.
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Garapati, Kumar Vijay. "Structural Analysis of Poloidal and Toroidal Plasmons and Fields of Multilayer Nanorings." Scholar Commons, 2017. http://scholarcommons.usf.edu/etd/6843.
Повний текст джерелаАнотація:
Multilayered metallo-dielectric nanoparticles are increasingly considered in various applications to control the spatial and temporal behavior of electromagnetic fields. In particular, the surface mode excitation by photons or electrons in metal nanorings finds significant applications because of the implied field distribution and electromagnetic energy confinement. However, most solid nanorings that are multilayered and/or embedded in a medium have non-simply connected geometry resulting in surface modes which are not linearly independent. That is, unlike particle plasmon eigenmodes in other geometries, the amplitudes of the eigenmodes of tori exhibit a distinct forward and backward coupling. We investigate the surface modes of such toroidal nano-structures and obtain the canonical plasmon dispersion relations and resonance modes for arbitrarily layered nanorings. When seeking the nonretarded surface modes for a stratified solid torus, we obtain a three-term difference equation which plays an important role in obtaining the needed dispersion relations. The obtained dispersion relations are investigated in depth in terms of the involved matrix continued fractions and their convergence properties including their determinant forms for computing the plasmon eigenmodes. The numerical solutions of the dispersion relations in case of a solid ring are presented for comparison and the resonance frequencies for the first few dominant modes of a ring composed of plasmon supporting materials such as gold, silver, and aluminum are provided and compared to those for a silicon ring. The mode complementarity and hybridization in multilayered toroidal structures is discussed and different ring configurations are simulated in the quasistatic limit by selecting number of layers modeled by their local dielectric functions. A generalized Green’s function with derivation intricacies addressed for multilayer tori is obtained from which one may calculate and study the scattering behavior of any of the modes that may exist in the many layer system. In particular, the electric potential distribution corresponding to individual poloidal and toroidal modes in response to an arbitrarily polarized external field and the field of electrons is obtained. The results are applied to obtain the local density of states and decay rate of a dipole near the center of the torus. Finally, two new types of toroidal particles in the form of janus nanorings are introduced.
26
Margetis, Alexander. "Beltrami Flows." Kent State University Honors College / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ksuhonors1525299172164402.
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27
Karaman, Mesut. "A Genetic Algorithm For The Multi-level Maximal Covering Ambulance Location Problem." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12610099/index.pdf.
Повний текст джерелаАнотація:
The emergency medical services (EMS) provide the preliminary assistance and transportation for patients in need of urgent medical care in order to decrease the mortality rate and reduce the non-reversible effects of injuries. Since the objective is directly related to the human life, the value of the proposed solutions in order to improve the performance of EMS is highly welcomed. Mainly, there are three problems that EMS managers face with: location, allocation and redeployment of the EMS facilities/vehicles. Most of the studies in EMS literature focus on accurately modeling the probabilistic nature of the availability of an ambulance when it is called for. However, trivial changes in model parameters or estimates could dramatically change the optimal allocations generated by the probabilistic models and hence make the model invalid. In this study, we formulate the ambulance location problem as a deterministic multi-level maximal coverage model by which the total demand is tried to be covered as many as possible at multiple levels. Both a mathematical programming model and genetic algorithm-based heuristic approaches are proposed for the problem. The results indicate that the genetic algorithm-based solutions give reliable (near-optimal) and robust results in reasonable computational times for the problem. Moreover, the tradeoffs between the two performance measures, &lsquoresponsiveness&rsquo
and &lsquo
preparedness&rsquo
, are searched for
and our approaches with multi-level coverage are compared against the multiple coverage approaches in terms of these performance measures.
28
Perdomo, Joana L. "Mathematical Modeling of Blood Coagulation." Scholarship @ Claremont, 2016. https://scholarship.claremont.edu/hmc_theses/71.
Повний текст джерелаАнотація:
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.
29
Karimli, Nigar. "Parameter Estimation and Optimal Design Techniques to Analyze a Mathematical Model in Wound Healing." TopSCHOLAR®, 2019. https://digitalcommons.wku.edu/theses/3114.
Повний текст джерелаАнотація:
For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that considers identifiability of parameters, has been included in this work. Furthermore, to estimate parameters more efficiently and accurately, the standard error (SE- )optimal design method is employed, which calculates optimal observation times for clinical data to be collected. Finally, by combining different parameter subset selection methods and an optimal design problem, different cases for both finding optimal time points and intervals have been investigated.
30
Ke, Xinyou. "Fundamental Studies on Transport Phenomena in Redox Flow Batteries with Flow Field Structures and Slurry or Semi-Solid Electrodes: Modeling and Experimental Approaches." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case1543883710323558.
Повний текст джерела
31
ATTA-FOSU, THOMAS. "Fourier Based Method for Simultaneous Segmentation and Nonlinear Registration." Case Western Reserve University School of Graduate Studies / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=case1492439037011351.
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32
Gentry, Amanda E. "Penalized mixed-effects ordinal response models for high-dimensional genomic data in twins and families." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5575.
Повний текст джерелаАнотація:
The Brisbane Longitudinal Twin Study (BLTS) was being conducted in Australia and was funded by the US National Institute on Drug Abuse (NIDA). Adolescent twins were sampled as a part of this study and surveyed about their substance use as part of the Pathways to Cannabis Use, Abuse and Dependence project. The methods developed in this dissertation were designed for the purpose of analyzing a subset of the Pathways data that includes demographics, cannabis use metrics, personality measures, and imputed genotypes (SNPs) for 493 complete twin pairs (986 subjects.) The primary goal was to determine what combination of SNPs and additional covariates may predict cannabis use, measured on an ordinal scale as: “never tried,” “used moderately,” or “used frequently”. To conduct this analysis, we extended the ordinal Generalized Monotone Incremental Forward Stagewise (GMIFS) method for mixed models. This extension includes allowance for a unpenalized set of covariates to be coerced into the model as well as flexibility for user-specified correlation patterns between twins in a family. The proposed methods are applicable to high-dimensional (genomic or otherwise) data with ordinal response and specific, known covariance structure within clusters.
33
Saraf, Poonam S. "RGD based peptide amphiphiles as drug carriers for cancer targeting." Scholarly Commons, 2014. https://scholarlycommons.pacific.edu/uop_etds/137.
Повний текст джерелаАнотація:
Specific interactions of ligands with receptors is one of the approaches for active targeting of anticancer drugs to cancer cells. Over expression of integrin receptors is a physiological manifestation in several cancers and is associated with cancer progression and metastasis, which makes it an attractive target for cancer chemotherapy. The peptide sequence for this integrin recognition is the Arg-Gly-Asp (RGD). Self-assembly offers a unique way of presenting ligands to target receptors for recognition and binding. This study focuses on development of integrin specific peptide amphiphile self-assemblies as carriers for targeted delivery of paclitaxel to α v β 3 integrin overexpressing cancers. Amphiphiles composed of conjugates of different analogs of RGD (linear, cyclic or glycosylated) and aliphatic fatty acid with or without 8-amino-3,6-dioxaoctanoic acid (ADA) as linker were synthesized and characterized. The amphiphiles exhibited Critical Micellar Concentration in the range of 7-30 μM. Transmission electron microscopy images revealed the formation of spherical micelles in the size range of 10-40 nm. Forster Resonance Energy Transfer studies revealed entrapment of hydrophobic dyes within a tight micellar core and provided information regarding the cargo exchange within micelles. The RGD micelles exhibited competitive binding with 55% displacement of a bound fluorescent probe by the cyclic RGD micelles. The internalization of fluorescein isothiocynate (FITC) loaded RGD micelles was significantly higher in A2058 melanoma cells compared to free FITC within 20 minutes of incubation at 37°C. The same micelles showed significantly lower internalization at 4°C and on pretreatment with 0.45M sucrose confirming endocytotic uptake of the RGD micellar carriers. The IC50 of paclitaxel in A2058 melanoma cells was lower when treated within RGD micelles as compared to treatment of free drug. On the other hand, IC50 values increased by 2 to 9 fold for micellar treatment in comparison to free drug in Detroit 551 cells. In A2058 melanoma xenograft mice model, the Paclitaxel-RGD micelles exhibited a significant inhibition of tumor growth in comparison to control treatment for both alternate day and twice weekly treatments. The studies showed the feasibility of using the non covalent peptide based self-assemblies as vehicles for targeted delivery in cancer.
34
Ting, Samuel T. "An Efficient Framework for Compressed Sensing Reconstruction of Highly Accelerated Dynamic Cardiac MRI." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1452164320.
Повний текст джерела
35
Yao, Yuan. "Performance and mechanism on a high durable silica alumina based cementitious material composed of coal refuse and coal combustion byproducts." Scholarly Commons, 2012. https://scholarlycommons.pacific.edu/uop_etds/155.
Повний текст джерелаАнотація:
Coal refuse and combustion byproducts as industrial solid waste stockpiles have become great threats to the environment. Recycling is one practical solution to utilize this huge amount of solid waste through activation as substitute for ordinary Portland cement. The central goal of this dissertation is to investigate and develop a new silica-alumina based cementitious material largely using coal refuse as a constituent that will be ideal for durable construction, mine backfill, mine sealing and waste disposal stabilization applications. This new material is an environment-friendly alternative to ordinary Portland cement. The main constituents of the new material are coal refuse and other coal wastes including coal sludge and coal combustion products (CCPs). Compared with conventional cement production, successful development of this new technology could potentially save energy and reduce greenhouse gas emissions, recycle vast amount of coal wastes, and significantly reduce production cost. A systematic research has been conducted to seek for an optimal solution for enhancing pozzolanic reactivity of the relatively inert solid waste-coal refuse in order to improve the utilization efficiency and economy benefit for construction and building materials. The results show that thermal activation temperature ranging from 20°C to 950°C significantly increases the workability and pozzolanic property of the coal refuse. The optimal activation condition is between 700°C to 800°C within a period of 30 to 60 minutes. Microanalysis illustrates that the improved pozzolanic reactivity contributes to the generated amorphous materials from parts of inert aluminosilicate minerals by destroying the crystallize structure during the thermal activation. In the coal refuse, kaolinite begins to transfer into metakaol in at 550°C, the chlorite minerals disappear at 750°C, and muscovite 2M 1 gradually dehydroxylates to muscovite HT. Furthermore, this research examines the environmental acceptance and economic feasibility of this technology and found that this silica alumina-based cementitious material not only meets EPA requirements but also shows several advantages in industrial application.
36
Hurdal, Monica Kimberly. "Mathematical and computer modelling of the human brain with reference to cortical magnification and dipole source localisation in the visual cortx." Thesis, Queensland University of Technology, 1998.
Знайти повний текст джерела
37
Friedlander, Holley Ann. "Twisted weyl group multiple Dirichlet series over the rational function field." 2013. https://scholarworks.umass.edu/dissertations/AAI3603084.
Повний текст джерелаАнотація:
In this thesis, we examine the relationship between Weyl group multiple Dirichlet series over the rational function field and their p-parts, which we define using the Chinta–Gunnells method [10]. We show that these series may be written as the finite sum of their p-parts (after a certain variable change), with “multiplicities” that are character sums. Because the p-parts and global series are closely related, this result follows from a series of local results concerning the p-parts. In particular, we give an explicit recurrence relation on the coefficients of the p-parts, which allows us to extend the results of Chinta, Friedberg, and Gunnells [9]. Additionally, we show that the p-parts of Chinta and Gunnells [10] agree with those constructed using the crystal graph technique of Brubaker, Bump, and Friedberg [4,5] (in the cases when both constructions apply).
38
Mthethwa, Thulani Richard. "New classes of exact solutions for charged perfect fluids." Thesis, 2012. http://hdl.handle.net/10413/10533.
Повний текст джерелаАнотація:
We investigate techniques to generate new classes of exact solutions to the Einstein-
Maxwell field equations which represent the gravitational field of charged perfect fluid
spherically symmetric distributions of matter. Historically, a large number of solutions
have been proposed but only a small number have been demonstrated to satisfy
elementary conditions for physical acceptability. Firstly we examine the case of the
constant density and constant electric field charged fluid sphere and show empirically
that such configurations of matter are unlikely to exist as basic physical requirements
are violated. We then make an ansatz relating the fluid's electric field intensity to
one of the gravitational potentials thereby simplifying the system of partial differential
equations. This prescription yields an algorithmic process to generate new classes of
exact solutions. We present a number of new solutions and comment on their viability
as stellar models. Graphical plots generated by symbolic software of the main dynamical
and geometrical quantities verify that one of our models is suitable to represent
a physically relevant distribution of charged matter in the form of a spherical shell.
In particular, positive definiteness of energy density and pressure are guaranteed, a
pressure free hypersurface denoting the boundary of the star exists, the sound speed
is shown to be sub-luminal and the energy conditions are satisfied everywhere in the
interior of the star.Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2012.
39
(9179663), Chase O. Mathison. "Microlocal Analysis and Applications to Medical Imaging." Thesis, 2020.
Знайти повний текст джерелаАнотація:
This thesis is a collection of the three projects I have worked on at Purdue. The first is a paper on thermoacoustic tomography involving circular integrating detectors that was published in Inverse Problems and Imaging. Results from this paper include demonstrating that the measurement operators involved are Fourier integral operators, as well as proving microlocal uniqueness in certain cases, and also stability. The second paper, submitted to the Journal of Inverse and Ill-Posed Problems, is much more of an application of sampling theory in to the specific case of thermoacoustic tomography. Results from this paper include demonstrating resolution limits imposed by sampling rates, and showing that aliasing artifacts appear in predictable locations in an image when the measurement operator is under sampled in either the time variable or space variables. We also show an application of a basic anti aliasing scheme based on averaging of data. The last project moves slightly away from microlocal analysis and considers the uniqueness in medical imaging of the restricted Radon transform in even dimensions. This is the classical interior problem, and we show a characterization of the range of the Radon transform, and from this are able to obtain a characterization of the kernel of the restricted Radon transform. We include figures throughout to illustrate results.
40
Kweyama, Mandlenkosi Christopher. "Analysis of shear-free spherically symmetric charged relativistic fluids." Thesis, 2011. http://hdl.handle.net/10413/5939.
Повний текст джерелаАнотація:
We study the evolution of shear-free spherically symmetric charged fluids
in general relativity. This requires the analysis of the coupled Einstein-Maxwell
system of equations. Within this framework, the master field equation to be
integrated is
yxx = f(x)y2 + g(x)y3
We undertake a comprehensive study of this equation using a variety of ap-
proaches. Initially, we find a first integral using elementary techniques (subject
to integrability conditions on the arbitrary functions f(x) and g(x)). As a re-
sult, we are able to generate a class of new solutions containing, as special
cases, the models of Maharaj et al (1996), Stephani (1983) and Srivastava
(1987). The integrability conditions on f(x) and g(x) are investigated in detail
for the purposes of reduction to quadratures in terms of elliptic integrals. We
also obtain a Noether first integral by performing a Noether symmetry analy-
sis of the master field equation. This provides a partial group theoretic basis
for the first integral found earlier. In addition, a comprehensive Lie symmetry
analysis is performed on the field equation. Here we show that the first integral
approach (and hence the Noether approach) is limited { more general results
are possible when the full Lie theory is used. We transform the field equation
to an autonomous equation and investigate the conditions for it to be reduced
to quadrature. For each case we recover particular results that were found pre-
viously for neutral fluids. Finally we show (for the first time) that the pivotal
equation, governing the existence of a Lie symmetry, is actually a fifth order
purely differential equation, the solution of which generates solutions to the
master field equation.Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2011.
41
Moodley, Jothi. "Applications of embedding theory in higher dimensional general relativity." Thesis, 2012. http://hdl.handle.net/10413/10594.
Повний текст джерелаАнотація:
The study of embeddings is applicable and signicant to higher dimensional theories of
our universe, high-energy physics and classical general relativity. In this thesis we investigate
local and global isometric embeddings of four-dimensional spherically symmetric
spacetimes into five-dimensional Einstein manifolds. Theorems have been established
that guarantee the existence of such embeddings. However, most known explicit results
concern embedded spaces with relatively simple Ricci curvature. We consider the four-dimensional
gravitational field of a global monopole, a simple non-vacuum space with
a more complicated Ricci tensor, which is of theoretical interest in its own right, and
occurs as a limit in Einstein-Gauss-Bonnet Kaluza-Klein black holes, and we obtain
an exact solution for its embedding into Minkowski space. Our local embedding space
can be used to construct global embedding spaces, including a globally
at space and
several types of cosmic strings. We present an analysis of the result and comment on
its signicance in the context of induced matter theory and the Einstein-Gauss-Bonnet
gravity scenario where it can be viewed as a local embedding into a Kaluza-Klein black
hole. Difficulties in solving the five-dimensional equations for given four-dimensional
spaces motivate us to investigate which embedded spaces admit bulks of a specific type.
We show that the general Schwarzschild-de Sitter spacetime and the Einstein Universe
are the only spherically symmetric spacetimes that can be embedded into an Einstein
space with a particular metric form, and we discuss their five-dimensional solutions.
Furthermore, we determine that the only spherically symmetric spacetime in retarded
time coordinates that can be embedded into a particular Einstein bulk is the general
Vaidya-de Sitter solution with constant mass. These analyses help to provide insight to
the general embedding problem. We also consider the conformal Killing geometry of a
five-dimensional Einstein space that embeds a static spherically symmetric spacetime,
and we show how the Killing geometry of the embedded space is inherited by its bulk.
The study of embedding properties such as these enables a deeper mathematical understanding
of higher dimensional cosmological models and is also of physical interest
as conformal symmetries encode conservation laws.Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2012.
42
Anicic, Rastko. "Effects of the Dielectric Environment on the Electrical Properties of Graphene." Thesis, 2013. http://hdl.handle.net/10012/7804.
Повний текст джерелаАнотація:
This thesis provides the study of graphene’s electrostatic interaction with the substrate surrounding it. Mathematical models based on current experimental configurations of graphene field-effect transistors (FET) are developed and analyzed. The conductivity and mobility of charge carriers in graphene are examined in the presence of impurities trapped in the substrate near graphene. The
impurities encompass a wide range of possible structures and parameters, including different types of impurities, their distance from graphene, and the spatial correlation between them. Furthermore, we extend our models to analyze the influence of impurities on the fluctuations of the electrostatic
potential and the charge carrier density in the plane of graphene. The results of our mathematical
models are compared with current experimental results in the literature.
43
Msomi, Alfred Mvunyelwa. "Applications of Lie symmetries to gravitating fluids." Thesis, 2011. http://hdl.handle.net/10413/8765.
Повний текст джерелаАнотація:
This thesis is concerned with the application of Lie's group theoretic method
to the Einstein field equations in order to find new exact solutions. We analyse
the nonlinear partial differential equation which arises in the study of non-
static, non-conformally flat fluid plates of embedding class one. In order to find
the group invariant solutions to the partial differential equation in a systematic and comprehensive manner we apply the method of optimal subgroups.
We demonstrate that the model admits linear barotropic equations of state in
several special cases. Secondly, we study a shear-free spherically symmetric
cosmological model with heat flow. We review and extend a method of generating solutions developed by Deng. We use the method of Lie analysis as a
systematic approach to generate new solutions to the master equation. Also,
general classes of solution are found in which there is an explicit relationship
between the gravitational potentials which is not present in earlier models.
Using our systematic approach, we can recover known solutions. Thirdly, we
study generalised shear-free spherically symmetric models with heat flow in
higher dimensions. The method of Lie generates new solutions to the master equation. We obtain an implicit solution or we can reduce the governing equation to a Riccati equation.Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2011.
44
"Ritz values and Arnoldi convergence for non-Hermitian matrices." Thesis, 2012. http://hdl.handle.net/1911/70215.
Повний текст джерелаАнотація:
This thesis develops ways of localizing the Ritz values of non-Hermitian matrices. The restarted Arnoldi method with exact shifts, useful for determining a few desired eigenvalues of a matrix, employs Ritz values to refine eigenvalue estimates. In the Hermitian case, using selected Ritz values produces convergence due to interlacing. No generalization of interlacing exists for non-Hermitian matrices, and as a consequence no satisfactory general convergence theory exists. To study Ritz values, I propose the inverse field of values problem for k Ritz values, which asks if a set of k complex numbers can be Ritz values of a matrix. This problem is always solvable for k = 1 for any complex number in the field of values; I provide an improved algorithm for finding a Ritz vector in this case. I show that majorization can be used to characterize, as well as localize, Ritz values. To illustrate the difficulties of characterizing Ritz values, this work provides a complete analysis of the Ritz values of two 3 × 3 matrices: a Jordan block and a normal matrix. By constructing conditions for localizing the Ritz values of a matrix with one simple, normal, sought-after eigenvalue, this work develops sufficient conditions that guarantee convergence of the restarted Arnoldi method with exact shifts. For general matrices, the conditions provide insight into the subspace dimensions that ensure that shifts do not cluster near the wanted eigenvalue. As Ritz values form the basis for many iterative methods for determining eigenvalues and solving linear systems, an understanding of Ritz value behavior for non-Hermitian matrices has the potential to inform a broad range of analysis.
45
"Magnetic Resonance Parameter Assessment from a Second Order Time-Dependent Linear Model." Doctoral diss., 2019. http://hdl.handle.net/2286/R.I.54899.
Повний текст джерелаАнотація:
abstract: This dissertation develops a second order accurate approximation to the magnetic resonance (MR) signal model used in the PARSE (Parameter Assessment by Retrieval from Single Encoding) method to recover information about the reciprocal of the spin-spin relaxation time function (R2*) and frequency offset function (w) in addition to the typical steady-state transverse magnetization (M) from single-shot magnetic resonance imaging (MRI) scans. Sparse regularization on an approximation to the edge map is used to solve the associated inverse problem. Several studies are carried out for both one- and two-dimensional test problems, including comparisons to the first order approximation method, as well as the first order approximation method with joint sparsity across multiple time windows enforced. The second order accurate model provides increased accuracy while reducing the amount of data required to reconstruct an image when compared to piecewise constant in time models. A key component of the proposed technique is the use of fast transforms for the forward evaluation. It is determined that the second order model is capable of providing accurate single-shot MRI reconstructions, but requires an adequate coverage of k-space to do so. Alternative data sampling schemes are investigated in an attempt to improve reconstruction with single-shot data, as current trajectories do not provide ideal k-space coverage for the proposed method.Dissertation/Thesis
Doctoral Dissertation Mathematics 2019
46
Cliche, Mathieu. "Information propagation and entanglement generation between two Unruh-DeWitt detectors." Thesis, 2010. http://hdl.handle.net/10012/5309.
Повний текст джерелаАнотація:
The setup in which two quantum systems, Alice and Bob, communicate using
bosonic field quanta can be viewed as a prototype for wireless quantum communication.
In this thesis we focus on the most basic case, where Alice and Bob
are modeled as Unruh-DeWitt detectors, i.e., as two-level quantum
systems that interact locally through a scalar quantum field. Our aim is to study how information propagation and entanglement generation between the two detectors are impacted by both relativity and by the unavoidable noise that is due to the quantum fluctuations of the field.
We start by studying information propagation between the two detectors. Concretely, we construct and study the information-theoretic quantum channel, ξ, i.e., the completely positive trace preserving map between the input density matrix ϱ, in which Alice prepares her detector for the emission, and the output density matrix ϱ '=ξ(ϱ) of Bob's detector at a later time. We confirm that the classical as well as the quantum channel capacity are strictly zero to all orders in perturbation theory for spacelike separations.
We then study entanglement generation between the two detectors. Specifically, we discuss how two Unruh-DeWitt detectors can extract entanglement from the vacuum. We show that the detectors can naturally and instantaneously become entangled through a Casimir-Polder effect. We then analyze the impact of various additions to this setup, such as the presence of a weak gravitational field, the presence of boundary conditions in the field, the presence of a weak classical potential, etc.
47
"Exploration, Mapping and Scalar Field Estimation using a Swarm of Resource-Constrained Robots." Doctoral diss., 2018. http://hdl.handle.net/2286/R.I.51727.
Повний текст джерелаАнотація:
abstract: Robotic swarms can potentially perform complicated tasks such as exploration and mapping at large space and time scales in a parallel and robust fashion. This thesis presents strategies for mapping environmental features of interest – specifically obstacles, collision-free paths, generating a metric map and estimating scalar density fields– in an unknown domain using data obtained by a swarm of resource-constrained robots. First, an approach was developed for mapping a single obstacle using a swarm of point-mass robots with both directed and random motion. The swarm population dynamics are modeled by a set of advection-diffusion-reaction partial differential equations (PDEs) in which a spatially-dependent indicator function marks the presence or absence of the obstacle in the domain. The indicator function is estimated by solving an optimization problem with PDEs as constraints. Second, a methodology for constructing a topological map of an unknown environment was proposed, which indicates collision-free paths for navigation, from data collected by a swarm of finite-sized robots. As an initial step, the number of topological features in the domain was quantified by applying tools from algebraic topology, to a probability function over the explored region that indicates the presence of obstacles. A topological map of the domain is then generated using a graph-based wave propagation algorithm. This approach is further extended, enabling the technique to construct a metric map of an unknown domain with obstacles using uncertain position data collected by a swarm of resource-constrained robots, filtered using intensity measurements of an external signal. Next, a distributed method was developed to construct the occupancy grid map of an unknown environment using a swarm of inexpensive robots or mobile sensors with limited communication. In addition to this, an exploration strategy which combines information theoretic ideas with Levy walks was also proposed. Finally, the problem of reconstructing a two-dimensional scalar field using observations from a subset of a sensor network in which each node communicates its local measurements to its neighboring nodes was addressed. This problem reduces to estimating the initial condition of a large interconnected system with first-order linear dynamics, which can be solved as an optimization problem.Dissertation/Thesis
Doctoral Dissertation Mechanical Engineering 2018
48
Krupanandan, Daniel D. "Solution generating algorithms in general relativity." Thesis, 2011. http://hdl.handle.net/10413/9766.
Повний текст джерелаАнотація:
We conduct a comprehensive investigative review of solution generating algorithms
for the Einstein field equations governing the gravitational behaviour of an isolated
neutral static spherical distribution of perfect fluid matter. Traditionally, the master
field equation generated from the condition of pressure isotropy has been interpreted
as a second order ordinary differential equation. However, since the pioneering work
of Wyman (1949) it was observed that more success can be enjoyed by regarding
the equation as a first order linear differential equation. There was a resurgence
of the ideas of Wyman in 2000 and various researchers have been able to generate
complete solutions to the field equations up to certain integrations. These have
been accomplished by working in Schwarzschild (curvature) coordinates, isotropic
coordinates, area coordinates and a coordinate system written in terms of the redshift
parameter. We have utilised Durgapal–Banerjee (1983) coordinates and produced a
new algorithm. The algorithm is used to generate new classes of perfect fluid solutions
as well as to regain familiar particular solutions reported in the literature. We find
that our solution is well behaved according to elementary physical requirements.
The pressure vanishes for a certain radius and this establishes the boundary of the
distribution. Additionally the pressure and energy density are both positive inside
the radius. The energy conditions are shown to be satisfied and it is particularly
pleasing to have the causality criterion satisfied to ensure that the speed of light is
not exceeded by the speed of sound. We also report some new solutions using the
algorithms proposed by Lake (2006).Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2011.
49
"Techniques for Realtime Viewing and Manipulation of Volumetric Data." Thesis, 2011. http://hdl.handle.net/1911/70348.
Повний текст джерелаАнотація:
Visualizing and manipulating volumetric data is a major component in many areas including anatomical registration in biomedical fields, seismic data analysis in the oil industry, machine part design in computer-aided geometric design, character animation in the movie industry, and fluid simulation. These industries have to meet the demands of the times and be able to make meaningful assertions about the data they generate. The shear size of this data presents many challenges to facilitating realtime interaction. In the recent decade, graphics hardware has become increasingly powerful and more sophisticated which has introduced a new realm of possibilities for processing volumetric data. This thesis focuses on a suite of techniques for viewing and editing volumetric data that efficiently use the processing power of central processing units (CPUs) as well as the large processing power of the graphics hardware (GPUs). This work begins with an algorithm to improve the efficiency of a texture-based volume rendering. We continue with a framework for performing realtime constructive solid geometry (CSG) with complex shapes and smoothing operations on watertight meshes based on a variation of Depth Peeling. We then move to an intuitive technique for deforming volumetric data using a collection of control points. Finally, we apply this technique to image registration of 3-dimensional computed tomography (CT) images used for lung cancel treatment, planning.
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Ngubelanga, Sifiso Allan. "Exact solutions for relativistic models." Thesis, 2011. http://hdl.handle.net/10413/9846.
Повний текст джерелаАнотація:
In this thesis we study spherically symmetric spacetimes related to the Einstein field equations. We consider only neutral matter and apply the Einstein field equations with isotropic pressures. Our object is to model relativistic stellar systems. We express the Einstein field equations and the condition of pressure isotropy in terms of Schwarzschild coordinates and isotropic coordinates. For Schwarzschild coordinates we consider the
transformations due to Buchdahl (1959), Durgapal and Bannerji (1983), Fodor (2000) and Tewari and Pant (2010). The condition of pressure isotropy is integrated and new exact solutions of the field equations are obtained utilizing the transformations of Buchdahl (1959) and Tewari and Pant (2010). These exact solutions are given in terms of elementary functions. For isotropic coordinates we can express the condition of pressure isotropy as a Riccati equation or a linear equation. An algorithm is developed that produces a new solution if a particular solution is known. The transformations reduce to a nonlinear Bernoulli equation in most instances. There are fundamentally three new classes of solutions to the condition of pressure isotropy.Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2011.