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Dissertations / Theses on the topic 'Inverse Problems (Mathematics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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1

Agapiou, Sergios. "Aspects of Bayesian inverse problems." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/60138/.

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The goal of this thesis is to contribute to the formulation and understanding of the Bayesian approach to inverse problems in function space. To this end we examine two important aspects of this approach: the frequentist asymptotic properties of the posterior, and the extraction of information from the posterior via sampling. We work in a separable Hilbert space setting and consider Gaussian priors on the unknown in conjugate Gaussian models. In the first part of this work we consider linear inverse problems with Gaussian additive noise and study the contraction in the small noise limit of the

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2

Wokiyi, Dennis. "Non-linear inverse geothermal problems." Licentiate thesis, Linköpings universitet, Matematik och tillämpad matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-143031.

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The inverse geothermal problem consist of estimating the temperature distribution below the earth’s surface using temperature and heat-flux measurements on the earth’s surface. The problem is important since temperature governs a variety of the geological processes including formation of magmas, minerals, fosil fuels and also deformation of rocks. Mathematical this problem is formulated as a Cauchy problem for an non-linear elliptic equation and since the thermal properties of the rocks depend strongly on the temperature, the problem is non-linear. This problem is ill-posed in the sense that i

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3

Klimmek, Martin. "On inverse problems in mathematical finance." Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/55821/.

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We consider two inverse problems motivated by questions in mathematical finance. In the first two chapters (Part 1) we recover processes consistent with given perpetual American option prices. In the third and fourth chapters (Part 2) we construct model-independent bounds for prices of contracts based on the realized variance of an asset price process. The two parts are linked by the question of how to recover information about asset price dynamics from option prices: in part one we assume knowledge of perpetual American option prices while in the second part we will assume knowledge of Europe

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4

Attalla, Atia May Ramsis. "Inverse eigenvalue problems : theory and algorithms." Thesis, Imperial College London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299725.

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5

Cheang, Ka Hang. "Two problems on inverse eigenvalue problems and Hadamard finite part integrals." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2182891.

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6

Chada, Neil Kumar. "Ensemble based methods for geometric inverse problems." Thesis, University of Warwick, 2018. http://wrap.warwick.ac.uk/111386/.

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Since the development of the ensemble Kalman filter, it has seen a wide application to many scientific fields ranging from signal processing to weather forecasting and reservoir simulation. One field which has recently seen a keen interest towards filtering techniques is that of inverse problems. Ensemble-based methods are a popular choice of filtering techniques as they provide a computational advantage over traditional methods whilst retaining a good level of accuracy. This thesis is concerned with developing analysis and numerics of ensemble Kalman inversion (EKI) in the context of Bayesian

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7

Dunlop, Matthew M. "Analysis and computation for Bayesian inverse problems." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/86136/.

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Many inverse problems involve the estimation of a high dimensional quantity, such as a function, from noisy indirect measurements. These problems have received much study from both classical and statistical directions, with each approach having its own advantages and disadvantages. In this thesis we focus on the Bayesian approach, in which all uncertainty is modelled probabilistically. Recently the Bayesian approach to inversion has been developed in function space. Much of the existing work in the area has been focused on the case when the prior distribution produces samples which are continu

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8

Tian, Na. "Novel optimisation methods for numerical inverse problems." Thesis, University of Greenwich, 2011. http://gala.gre.ac.uk/9099/.

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Inverse problems involve the determination of one or more unknown quantities usually appearing in the mathematical formulation of a physical problem. These unknown quantities may be boundary heat flux, various source terms, thermal and material properties, boundary shape and size. Solving inverse problems requires additional information through in-situ data measurements of the field variables of the physical problems. These problems are also ill-posed because the solution itself is sensitive to random errors in the measured input data. Regularisation techniques are usually used in order to dea

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9

Zhong, Ming. "Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems." Thesis, University of Maryland, College Park, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10128674.

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<p> We present a detailed analysis of the application of a multi-scale Hierarchical Reconstruction method for solving a family of ill-posed linear inverse problems. When the observations on the unknown quantity of interest and the observation operators are known, these inverse problems are concerned with the recovery of the unknown from its observations. Although the observation operators we consider are linear, they are inevitably ill-posed in various ways. We recall in this context the classical Tikhonov regularization method with a stabilizing function which targets the specific ill-posedne

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10

Kempton, Mark Condie. "The Minimum Rank, Inverse Inertia, and Inverse Eigenvalue Problems for Graphs." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2182.

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For a graph G we define S(G) to be the set of all real symmetric n by n matrices whose off-diagonal zero/nonzero pattern is described by G. We show how to compute the minimum rank of all matrices in S(G) for a class of graphs called outerplanar graphs. In addition, we obtain results on the possible eigenvalues and possible inertias of matrices in S(G) for certain classes of graph G. We also obtain results concerning the relationship between two graph parameters, the zero forcing number and the path cover number, related to the minimum rank problem.

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11

Vollmer, Sebastian J. "Efficient MCMC and posterior consistency for Bayesian inverse problems." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/58785/.

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Many mathematical models used in science and technology often contain parameters that are not known a priori. In order to match a model to a physical phenomenon, the parameters have to be adapted on the basis of the available data. One of the most important statistical concepts applied to inverse problems is the Bayesian approach which models the a priori and a posteriori uncertainty through probability distributions, called the prior and posterior, respectively. However, computational methods such as Markov Chain Monte Carlo (MCMC) have to be used because these probability measures are only g

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12

Lian, Duan. "Bayesian methods for inverse problems." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:b4000e98-7d56-4274-8210-a22b04be436c.

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This thesis describes two novel Bayesian methods: the Iterative Ensemble Square Filter (IEnSRF) and the Warp Ensemble Square Root Filter (WEnSRF) for solving the barcode detection problem, the deconvolution problem in well testing and the history matching problem of facies patterns. For the barcode detection problem, at the expanse of overestimating the posterior uncertainty, the IEnSRF efficiently achieves successful detections with very challenging real barcode images which the other considered methods and commercial software fail to detect. It also performs reliable detection on low-resolut

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13

Palansuriya, Charaka Jeewana. "Domain decomposition based algorithms for some inverse problems." Thesis, University of Greenwich, 2000. http://gala.gre.ac.uk/8226/.

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The work presented in this thesis develop algorithms to solve inverse problems where source terms are unknown. The algorithms are developed 011frameworks provided by domain decomposition methods and the numerical schemes use finite volume and finite difference discretisations. Three algorithms are developed in the context of a metal cutting problem. The algorithms require measurement data within the physical body in order to retrieve the temperature field and the unknown source terms. It is shown that the algorithms can retrieve both the temperature field and the unknown source accurately. App

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14

Krainer, Thomas. "On the inverse of parabolic boundary value problems for large times." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2631/.

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We construct algebras of Volterra pseudodifferential operators that contain, in particular, the inverses of the most natural classical systems of parabolic boundary value problems of general form. Parabolicity is determined by the invertibility of the principal symbols, and as a result is equivalent to the invertibility of the operators within the calculus. Existence, uniqueness, regularity, and asymptotics of solutions as t → ∞ are consquences of the mapping properties of the operators in exponentially weighted Sobolev spaces and subspaces with asymptotics. An important aspect of this work is

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15

Jalalzai, Khalid. "Regularization of inverse problems in image processing." Phd thesis, Ecole Polytechnique X, 2012. http://pastel.archives-ouvertes.fr/pastel-00787790.

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Les problèmes inverses consistent à retrouver une donnée qui a été transformée ou perturbée. Ils nécessitent une régularisation puisque mal posés. En traitement d'images, la variation totale en tant qu'outil de régularisation a l'avantage de préserver les discontinuités tout en créant des zones lisses, résultats établis dans cette thèse dans un cadre continu et pour des énergies générales. En outre, nous proposons et étudions une variante de la variation totale. Nous établissons une formulation duale qui nous permet de démontrer que cette variante coïncide avec la variation totale sur des ense

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16

Blanchard, Gilles, and Peter Mathé. "Discrepancy principle for statistical inverse problems with application to conjugate gradient iteration." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5711/.

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The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which takes into account both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration this modification is shown to yield order optimal a priori error bounds under general smoothness assump

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17

Reeve, Thomas Henry. "The method of fundamental solutions for some direct and inverse problems." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4278/.

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We propose and investigate applications of the method of fundamental solutions (MFS) to several parabolic time-dependent direct and inverse heat conduction problems (IHCP). In particular, the two-dimensional heat conduction problem, the backward heat conduction problem (BHCP), the two-dimensional Cauchy problem, radially symmetric and axisymmetric BHCPs, the radially symmetric IHCP, inverse one and two-phase linear Stefan problems, the inverse Cauchy-Stefan problem, and the inverse two-phase one-dimensional nonlinear Stefan problem. The MFS is a collocation method therefore it does not require

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18

Kolbjørnsen, Odd. "Nonlinear Topics in the Bayesian Approach to Inverse Problems with Applications to Seismic Inversion." Doctoral thesis, Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, 2002. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-489.

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<p>Paper I considers piecewise affine inverse problems. This is a large group of nonlinear inverse problems. Problems that obey certain variational structures are of this type. In inverse problems it is frequently such that some features are well determined by the observations while others are poorly resolved. In the Bayesian approach this imply that the likelihood forces the posterior distribution to be concentrated near hyper surfaces in the parameter space. In nonlinear problems this causes most generic sampling algorithms to be slow. The structure that is enforced in piecewise affine inver

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19

Gassama, Edrissa. "PIEZOELECTRIC INVERSE PROBLEMS WITH RESONANCE DATA: A SEQUENTIAL MONTE CARLO ANALYSIS." Case Western Reserve University School of Graduate Studies / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=case1396623563.

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20

Chue, Bryan C. "Efficient Hessian computation in inverse problems with application to uncertainty quantification." Thesis, Boston University, 2013. https://hdl.handle.net/2144/21138.

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Thesis (M.Sc.Eng.) PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.<br>This thesis considers the efficient Hessian computation in inverse problems with specific application to the elastography inverse problem. Inverse problems use measurements of observable parameters to infer information about m

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21

Brett, Charles E. A. "Optimal control and inverse problems involving point and line functionals and inequality constraints." Thesis, University of Warwick, 2014. http://wrap.warwick.ac.uk/66437/.

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In this thesis we consider some problems related to the optimal control of partial differential equations (PDEs) and variational inequalities (VIs) with various constraints. Such problems are important because in real world applications we are typically more interested in optimising and controlling processes than just simulating them. We focus on developing efficient solution methods for these problems. The first part of this thesis considers optimal control of PDEs and VIs but with the usual L2 fidelity term replaced by ones which encourages the state to take certain values at points or along

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22

Devathi, Duttaabhinivesh. "Uncertainty Quantification for Underdetermined Inverse Problems via Krylov Subspace Iterative Solvers." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case155446130705089.

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23

Xiao, Jingni. "Theoretical advances on scattering theory, fractional operators and their inverse problems." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/513.

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Inverse problems arise in numerous fields of science and engineering where one tries to find out the desired information of an unknown object or the cause of an observed effect. They are of fundamental importance in many areas including radar and sonar applications, nondestructive testing, image processing, medical imaging, remote sensing, geophysics and astronomy among others. This study is concerned with three issues in scattering theory, fractional operators, as well as some of their inverse problems. The first topic is scattering problems for electromagnetic waves governed by Maxwell equat

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24

Ambartsoumian, Gaik. "Spherical radon transforms and mathematical problems of thermoacoustic tomography." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1807.

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25

Prezioso, Jamie. "An Inverse Problem of Cerebral Hemodynamics in the Bayesian Framework." Case Western Reserve University School of Graduate Studies / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=case1492108014359289.

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26

Nakkireddy, Sumanth Reddy R. "BAYESIAN METHODS FOR BRIDGING THE CONTINUOUS ANDELECTRODE DATA, AND LAYER STRIPPING IN ELECTRICALIMPEDANCE TOMOGRAPHY." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1618579073807699.

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27

Visco, Comandini Filippo. "Some inverse scattering problems on star-shaped graphs: application to fault detection on electrical transmission line networks." Phd thesis, Université de Versailles-Saint Quentin en Yvelines, 2011. http://tel.archives-ouvertes.fr/tel-00748216.

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In this thesis, having in mind applications to the fault-detection/diagnosis of electrical networks, we consider some inverse scattering problems for the Zakharov-Shabat equations and time-independent Schrödinger operators over star-shaped graphs. The first chapter is devoted to describe reflectometry methods applied to electrical networks as an inverse scattering problems on the star-shaped network. Reflectometry methods are presented and modeled by the telegrapher's equations. Reflectometry experiments can be written as inverse scattering problems for Schrödinger operator in the lossless cas

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28

Kusiak, Steven J. "The scattering support and the inverse scattering problem at fixed frequency /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/6779.

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29

Alberti, Giovanni S. "On local constraints and regularity of PDE in electromagnetics : applications to hybrid imaging inverse problems." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:1b30b3b7-29b1-410d-ae30-bd0a87c9720b.

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The first contribution of this thesis is a new regularity theorem for time harmonic Maxwell's equations with less than Lipschitz complex anisotropic coefficients. By using the L<sup>p</sup> theory for elliptic equations, it is possible to prove H<sup>1</sup> and Hölder regularity results, provided that the coefficients are W<sup>1,p</sup> for some p = 3. This improves previous regularity results, where the assumption W<sup>1,∞</sup> for the coefficients was believed to be optimal. The method can be easily extended to the case of bi-anisotropic materials, for which a separate approach turns out

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30

El, Arwadi Toufic. "NOUVELLE APPROCHE DE LA MÉTHODE DE D-BAR POUR LA RÉSOLUTION DU PROBLÈME DE CONDUCTIVITÉ INVERSE." Phd thesis, Université de Poitiers, 2010. http://tel.archives-ouvertes.fr/tel-00538091.

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Le problème de conductivité inverse est la traduction mathématiques de l'impédance par tomographie électrique , qui est un problème mal posé , introduit en 1980. Le but est de reconstruire la conductivité d'un matériel ou organe en utilisant les mesures faites au bord (dite la donnée de Cauchy). A.Nachman et Brown-Uhlmann ont montré l'existence et l'unicité de ce problème en utilisant la méthode de Beals et Coifman. Les méthodes de Nachman, Brown-Uhlmann (modifiée ensuite par Knudsen-Tamasan) sont décomposées en deux étapes : calcul des transformées scattering par la donnée de Cauchy ensuite l

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31

Sarikaya, Sedat. "Combination Of Conventional Regularization Methods And Genetic Algorithms For Solving The Inverse Problem Of Electrocardiography." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/2/12611669/index.pdf.

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Distribution of electrical potentials over the surface of the heart, i.e., the epicardial potentials, is a valuable tool to understand whether there is a defect in the heart. However, it is not easy to detect these potentials non-invasively. Instead, body surface potentials, which occur as a result of the electrical activity of the heart, are measured to diagnose heart defects. However the source electrical signals loose some critical details because of the attenuation and smoothing they encounter due to body tissues such as lungs, fat, etc. Direct measurement of these epicardial potentials re

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32

Nelson, Curtis G. "Diagonal Entry Restrictions in Minimum Rank Matrices, and the Inverse Inertia and Eigenvalue Problems for Graphs." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3246.

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Let F be a field, let G be an undirected graph on n vertices, and let SF(G) be the set of all F-valued symmetric n x n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let MRF(G) be defined as the set of matrices in SF(G) whose rank achieves the minimum of the ranks of matrices in SF(G). We develop techniques involving Z-hat, a process termed nil forcing, and induced subgraphs, that can determine when diagonal entries corresponding to specific vertices of G must be zero or nonzero for all matrices in MRF(G). We call these vertices nil

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33

Giraud, François. "Analyse des modèles particulaires de Feynman-Kac et application à la résolution de problèmes inverses en électromagnétisme." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00834920.

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Dans une première partie théorique, nous nous penchons sur une analyse rigoureuse des performances de l'algorithme Sequential Monte Carlo (SMC) conduisant à des résultats de type bornes L^p et inégalités de concentration. Nous abordons notamment le cas particulier des SMC associés à des schémas de température, et analysons sur ce sujet un processus à schéma adaptatif.Dans une seconde partie appliquée, nous illustrons son utilisation par la résolution de problèmes inverses concrets en électromagnétisme. Le plus important d'entre eux consiste à estimer les propriétés radioélectriques de matériau

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錢匡裕 and Hong-yu Chin. "Defect sensitivity and resolvability limits in positron-lifetime spectroscopy." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31225822.

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Israeli, Yeshayahu D. "Whitney Element Based Priors for Hierarchical Bayesian Models." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1621866603265673.

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Chin, Hong-yu. "Defect sensitivity and resolvability limits in positron-lifetime spectroscopy /." Hong Kong : University of Hong Kong, 2001. http://sunzi.lib.hku.hk/hkuto/record.jsp?B24728913.

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Stachura, Eric Christopher. "On Generalized Solutions to Some Problems in Electromagnetism and Geometric Optics." Diss., Temple University Libraries, 2016. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/403050.

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Mathematics<br>Ph.D.<br>The Maxwell equations of electromagnetism form the foundation of classical electromagnetism, and are of interest to mathematicians, physicists, and engineers alike. The first part of this thesis concerns boundary value problems for the anisotropic Maxwell equations in Lipschitz domains. In this case, the material parameters that arise in the Maxwell system are matrix valued functions. Using methods from functional analysis, global in time solutions to initial boundary value problems with general nonzero boundary data and nonzero current density are obtained, only assumi

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38

Pasha, Mirjeta. "Krylov subspace type methods for the computation of non-negative or sparse solutions of ill-posed problems." Kent State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1586459362313778.

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Van, Nevel Alan J. "Wavelet based noise removal for ultrasonic non-destructive evaluation /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9737876.

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Bai, Xianglan. "Non-Krylov Non-iterative Subspace Methods For Linear Discrete Ill-posed Problems." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1627042947894919.

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Rigaud, Gaël. "Study of generalized Radon transforms and applications in Compton scattering tomography." Phd thesis, Université de Cergy Pontoise, 2013. http://tel.archives-ouvertes.fr/tel-00945739.

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Since the advent of the first ionizing radiation imaging devices initiated by Godfrey Newbold Hounsfield and Allan MacLeod Cormack, Nobel Prizes in 1979, the requirement for new non-invasive imaging techniques has grown. These techniques rely upon the properties of penetration in the matter of X and gamma radiation for detecting a hidden structure without destroying the illuminated environment. They are used in many fields ranging from medical imaging to non-destructive testing through. However, the techniques used so far suffer severe degradation in the quality of measurement and reconstructe

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Lu, Wei. "Hough transforms for shape identification and applications im medical image processing /." free to MU campus, to others for purchase, 2003. http://wwwlib.umi.com/cr/mo/fullcit?p3115568.

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Pirbudak, Ozan. "Reconstruction of Radar Images by Using Spherical Mean and Regular Radon Transforms." Scholar Commons, 2019. https://scholarcommons.usf.edu/etd/7889.

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The goal of this study is the recovery of functions and finite parametric distributions from their spherical means over spheres and designing a general formula or algorithm for the reconstruction of a function f via its spherical mean transform. The theoretical study is and supported with a numerical implementation based on radar data. In this study, we approach the reconstruction problem in two different way. The first one is to show how the reconstruction problem could be converted to a Prony-type system of equations. After solving this Prony-type system of equations, one can extract the par

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Vogt, Andreas. "Analytische und numerische Untersuchung von direkten und inversen Randwertproblemen in Gebieten mit Ecken mittels Integralgleichungsmethoden." [S.l.] : [s.n.], 2001. http://webdoc.sub.gwdg.de/diss/2002/vogt/vogt.pdf.

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Seppecher, Laurent. "Modélisation de l'imagerie biomédicale hybride par perturbations mécaniques." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2014. http://tel.archives-ouvertes.fr/tel-01021279.

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Dans cette thèse, nous introduisons et développons une approche mathématiques originale des techniques d'imagerie biomédicales dites "hybrides". L'idée et d'appliquer une méthode d'imagerie mal posée, tout en perturbant le milieu à imager par des déplacements mécaniques. Ces déplacements provenant d'une équation de type onde élastique perturbent les mesures effectuées. En utilisant ces mesures perturbées, et profitant du caractère local des perturbations mécaniques, il est possible d'augmenter considérablement la résolution de la méthode de base. Le problème direct est donc un couplage d'une E

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Flanagan, Michael Brady. "Optimal shape design for a layered periodic structure." Texas A&M University, 2002. http://hdl.handle.net/1969/382.

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Pham, Ngoc Thanh Mai. "Problèmes inverses et analyse en ondelettes adaptées." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2009. http://tel.archives-ouvertes.fr/tel-00439112.

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Nous abordons l'étude de deux problèmes inverses, le problème des moments de Hausdorff et celui de la déconvolution sur la sphère ainsi qu'un problème de régression en design aléatoire. Le problème des moments de Hausdorff consiste à estimer une densité de probabilité à partir d'une séquence de moments bruités. Nous établissons une borne supérieure pour notre estimateur ainsi qu'une borne inférieure pour la vitesse de convergence, démontrant ainsi que notre estimateur converge à la vitesse optimale pour les classes de régularité de type Sobolev. Quant au problème de déconvolution sur la sphère

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Alonzo, Flavien. "Méthodes numériques pour le Glioblastome Multiforme et pour la résolution de problèmes inverses autour des systèmes de réaction-diffusion." Electronic Thesis or Diss., Ecole centrale de Nantes, 2022. http://www.theses.fr/2022ECDN0059.

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Le Glioblastome Multiforme est la tumeur cérébrale gliale la plus fréquente et la plus mortelle chez l’Homme. Les mathématiques ont l’opportunité de pouvoir innover la prise en charge des patients dans la démarche actuelle de médecine personnalisée. Cette thèse propose deux contributions majeures autour de cette thématique. Une premièrecontribution porte sur la modélisation et la simulation la plus réaliste possible de la propagation des cellules tumorales du Glioblastome Multiforme chez un patient après son diagnostic. Ce travail modélise le phénomène d’angiogenèse induite par la tumeur. Un s

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Ringer, Hayden J. "A Method for Reconstructing Historical Destructive Earthquakes Using Bayesian Inference." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8645.

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Seismic hazard analysis is concerned with estimating risk to human populations due to earthquakes and the other natural disasters that they cause. In many parts of the world, earthquake-generated tsunamis are especially dangerous. Assessing the risk for seismic disasters relies on historical data that indicate which fault zones are capable of supporting significant earthquakes. Due to the nature of geologic time scales, the era of seismological data collection with modern instruments has captured only a part of the Earth's seismic hot zones. However, non-instrumental records, such as anecdotal

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Cowen, Benjamin E. "Bregman Operator Splitting with Variable Stepsize for TotalGeneralized Variation Based Multi-Channel MRIReconstruction." Case Western Reserve University School of Graduate Studies / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=case1433176806.

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