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North Carolina State University
1.
DiCasoli, Carl Matthew.
Bayesian Regression Methods for Crossing Survival Curves.
Degree: PhD, Statistics, 2009, North Carolina State University
URL: http://www.lib.ncsu.edu/resolver/1840.16/4743 
► In survival data analysis, the proportional hazards (PH), accelerated failure time (AFT), and proportional odds (PO) models are commonly used semiparametric models for the comparison…
(more)
▼ In survival data analysis, the proportional hazards (PH), accelerated failure time
(AFT), and proportional odds (PO) models are commonly used semiparametric models for
the comparison of survivability in subjects. These models assume that the survival curves
do not cross. However, in some clinical applications, the survival curves pertaining to the two groups of subjects under the study may cross each other, especially for long-duration
studies. Hence, these three models stated above may no longer be suitable for making inference
Yang and Prentice (2005) proposed a model which separately models the short-term and long-term hazard ratios nesting both PH and PO. This feature allows for the survival functions to cross. First, we study the estimation procedure in the Yang-Prentice model with regards to the two-sample case. We propose two different approaches: (1) Bayesian bootstrap and (2) smoothing
methods. The first approach involves Bayesian bootstrap
with likelihoods corresponding to binomial and Poisson forms while the second approach
involves kernel smoothing
methods as well as smoothing spline
methods. A simulation is
conducted to compare various
methods under the two-sample case. Next, we extend the
Yang-Prentice model to a regression version involving predictors and examine three likelihood
approaches including Poisson form, pseudo-likelihood, and Bayesian smoothing. The
effects of model misspecification on asymptotic relative efficiency are also studied empirically. The results from simulation studies indicate that the PH, AFT, and PO models are not robust to model misspecifications when the survival functions are allowed to cross.
Finally, we calculate the marginal density via
variational methods to determine
the Bayes factor. Either a full Bayesian or Bayesian approach is implemented to perform
model selection. Both approaches accurately identify the correct model, even under slight
misspecification, and are computationally more efficient than MCMC techniques.
Advisors/Committee Members: Dr. Charles Apperson, Committee Member (advisor), Dr. Wenbin Lu, Committee Member (advisor), Dr. Brian Reich, Committee Member (advisor), Dr. Subhashis Ghosal, Committee Co-Chair (advisor), Dr. Sujit Ghosh, Committee Chair (advisor).
Subjects/Keywords: variational methods; Bayesian inference; survival analysis
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APA (6th Edition):
DiCasoli, C. M. (2009). Bayesian Regression Methods for Crossing Survival Curves. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/4743
Chicago Manual of Style (16th Edition):
DiCasoli, Carl Matthew. “Bayesian Regression Methods for Crossing Survival Curves.” 2009. Doctoral Dissertation, North Carolina State University. Accessed January 23, 2021.
http://www.lib.ncsu.edu/resolver/1840.16/4743.
MLA Handbook (7th Edition):
DiCasoli, Carl Matthew. “Bayesian Regression Methods for Crossing Survival Curves.” 2009. Web. 23 Jan 2021.
Vancouver:
DiCasoli CM. Bayesian Regression Methods for Crossing Survival Curves. [Internet] [Doctoral dissertation]. North Carolina State University; 2009. [cited 2021 Jan 23].
Available from: http://www.lib.ncsu.edu/resolver/1840.16/4743.
Council of Science Editors:
DiCasoli CM. Bayesian Regression Methods for Crossing Survival Curves. [Doctoral Dissertation]. North Carolina State University; 2009. Available from: http://www.lib.ncsu.edu/resolver/1840.16/4743
New Jersey Institute of Technology
2.
Zhong, Xing.
Energy methods for reaction-diffusion problems.
Degree: PhD, Mathematical Sciences, 2012, New Jersey Institute of Technology
URL: https://digitalcommons.njit.edu/dissertations/301
► Nonlinear reaction-diffusion equations arise in many areas of applied sciences such as combustion modeling, population dynamics, chemical kinetics, etc. A fundamental problem in the…
(more)
▼ Nonlinear reaction-diffusion equations arise in many areas of applied sciences such as combustion modeling, population dynamics, chemical kinetics, etc. A fundamental problem in the studies of these equations is to understand the long time behavior of solutions of the associated Cauchy problem. These kinds of questions were originally studied in the context of combustion modeling.
For suitable nonlinearity and a monotone increasing one-parameter family of initial data starting with zero data, small values of the parameter lead to extinction, whereas large values of the parameter may lead to spreading, i.e., the solution converging locally uniformly to a positive spatially independent stable steady state. A natural question is the existence of the threshold set of the parameters for which neither extinction nor spreading occurs. Even in one space dimension, this long standing question concerning threshold phenomena is far from trivial.
Recent results show that if the initial data are compactly supported, then there exists a sharp transition between extinction and spreading, i.e., the threshold set contains only one point. However, these results rely in an essential way on compactly supported initial data assumption and only give limited information about the solutions when spreading occurs.
In this dissertation, energy
methods based on the gradient flow structure of reaction-diffusion equations are developed. The long time behavior of solutions of the Cauchy problem for nonlinear reaction-diffusion equations in one space dimension with the nonlinearity of bistable, ignition or monostable type is analyzed. For symmetric decreasing initial data in L
2 (R) n L
8 (R), the convergence results for the considered equations are studied, and the existence of a one-to-one relation between the long time behavior of the solution and the limit value of its energy is proved.
In addition, by employing a weighted energy functional, a mathematical description of the equivalence between spreading and propagation of the solutions of the considered equations is given. More precisely, if spreading occurs, then the leading and the trailing edge of the solution propagate faster than some constant speed. Therefore, if the solution spreads, it also propagates. Furthermore, for a monotone family of symmetric decreasing initial data, there exists a sharp threshold between propagation and extinction.
Advisors/Committee Members: Cyrill B. Muratov, John Kenneth Bechtold, Amitabha Koshal Bose.
Subjects/Keywords: Variational methods; Reaction-diffusion equations; Combustion; Mathematics
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APA (6th Edition):
Zhong, X. (2012). Energy methods for reaction-diffusion problems. (Doctoral Dissertation). New Jersey Institute of Technology. Retrieved from https://digitalcommons.njit.edu/dissertations/301
Chicago Manual of Style (16th Edition):
Zhong, Xing. “Energy methods for reaction-diffusion problems.” 2012. Doctoral Dissertation, New Jersey Institute of Technology. Accessed January 23, 2021.
https://digitalcommons.njit.edu/dissertations/301.
MLA Handbook (7th Edition):
Zhong, Xing. “Energy methods for reaction-diffusion problems.” 2012. Web. 23 Jan 2021.
Vancouver:
Zhong X. Energy methods for reaction-diffusion problems. [Internet] [Doctoral dissertation]. New Jersey Institute of Technology; 2012. [cited 2021 Jan 23].
Available from: https://digitalcommons.njit.edu/dissertations/301.
Council of Science Editors:
Zhong X. Energy methods for reaction-diffusion problems. [Doctoral Dissertation]. New Jersey Institute of Technology; 2012. Available from: https://digitalcommons.njit.edu/dissertations/301
University of Minnesota
3.
Huang, Hsin-Yuan.
Variational methods and the orbits with collisions in the N-body problem.
Degree: PhD, Mathematics, 2011, University of Minnesota
URL: http://purl.umn.edu/107964
► The objective of this thesis is to study variational methods in the Newtonian N-body problem. Chapter 1 contains the introduction of Chapters 2 and 3.…
(more)
▼ The objective of this thesis is to study variational methods in the Newtonian N-body
problem.
Chapter 1 contains the introduction of Chapters 2 and 3. Chapter 2 is devoted to
the variational proof of the Schubart-like orbits in the collinear four-body problem. In
Chapter 3, we discuss the limiting configurations of the action-minimizing triple collision
orbits in the planar three body problem.
Subjects/Keywords: N-body Problem; Variational Methods; Mathematics
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APA (6th Edition):
Huang, H. (2011). Variational methods and the orbits with collisions in the N-body problem. (Doctoral Dissertation). University of Minnesota. Retrieved from http://purl.umn.edu/107964
Chicago Manual of Style (16th Edition):
Huang, Hsin-Yuan. “Variational methods and the orbits with collisions in the N-body problem.” 2011. Doctoral Dissertation, University of Minnesota. Accessed January 23, 2021.
http://purl.umn.edu/107964.
MLA Handbook (7th Edition):
Huang, Hsin-Yuan. “Variational methods and the orbits with collisions in the N-body problem.” 2011. Web. 23 Jan 2021.
Vancouver:
Huang H. Variational methods and the orbits with collisions in the N-body problem. [Internet] [Doctoral dissertation]. University of Minnesota; 2011. [cited 2021 Jan 23].
Available from: http://purl.umn.edu/107964.
Council of Science Editors:
Huang H. Variational methods and the orbits with collisions in the N-body problem. [Doctoral Dissertation]. University of Minnesota; 2011. Available from: http://purl.umn.edu/107964
4.
NC DOCKS at The University of North Carolina at Greensboro; Rapp, Aaron Frost.
Symmetric dual-wind discontinuous Galerkin methods for elliptic variational inequalities.
Degree: 2020, NC Docks
URL: http://libres.uncg.edu/ir/uncg/f/Rapp_uncg_0154D_13093.pdf
► The main goal of this dissertation is to formulate and analyze a dual wind discontinuous Galerkin method for approximating solutions to elliptic variational inequalities. A…
(more)
▼ The main goal of this dissertation is to formulate and analyze a dual wind discontinuous Galerkin method for approximating solutions to elliptic variational inequalities. A discontinuous Galerkin (DG) finite-element interior calculus is used as a common framework to describe various DG approximation methods for second-order elliptic problems. The dual-wind discontinuous Galerkin method is formulated for the obstacle problem with Dirichlet boundary conditions, ??_u _ f on with u = g on @, u _ on , and (_u ?? f)(u ?? ) = 0 on . A complete convergence analysis is developed and numerical experiments are recorded that verify these results. A secondary goal of this dissertation is to explore the effect of the penalty parameter on the error of the dual-wind discontinuous Galerkin method’s approximation to an elliptic partial differential equation. The dual-wind discontinuous Galerkin method is applied to the Poisson problem in two dimensions. The dual-wind discontinuous Galerkin approximation to the Poisson problem is constructed using various penalty parameters and the error is recorded for each approximation across various initial meshes and their refinements. [This abstract has been edited to remove characters that will not display in this system. Please see the PDF for the full abstract.]
Subjects/Keywords: Galerkin methods; Discontinuous functions; Variational inequalities (Mathematics)
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APA (6th Edition):
NC DOCKS at The University of North Carolina at Greensboro; Rapp, A. F. (2020). Symmetric dual-wind discontinuous Galerkin methods for elliptic variational inequalities. (Thesis). NC Docks. Retrieved from http://libres.uncg.edu/ir/uncg/f/Rapp_uncg_0154D_13093.pdf
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
NC DOCKS at The University of North Carolina at Greensboro; Rapp, Aaron Frost. “Symmetric dual-wind discontinuous Galerkin methods for elliptic variational inequalities.” 2020. Thesis, NC Docks. Accessed January 23, 2021.
http://libres.uncg.edu/ir/uncg/f/Rapp_uncg_0154D_13093.pdf.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
NC DOCKS at The University of North Carolina at Greensboro; Rapp, Aaron Frost. “Symmetric dual-wind discontinuous Galerkin methods for elliptic variational inequalities.” 2020. Web. 23 Jan 2021.
Vancouver:
NC DOCKS at The University of North Carolina at Greensboro; Rapp AF. Symmetric dual-wind discontinuous Galerkin methods for elliptic variational inequalities. [Internet] [Thesis]. NC Docks; 2020. [cited 2021 Jan 23].
Available from: http://libres.uncg.edu/ir/uncg/f/Rapp_uncg_0154D_13093.pdf.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
NC DOCKS at The University of North Carolina at Greensboro; Rapp AF. Symmetric dual-wind discontinuous Galerkin methods for elliptic variational inequalities. [Thesis]. NC Docks; 2020. Available from: http://libres.uncg.edu/ir/uncg/f/Rapp_uncg_0154D_13093.pdf
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Virginia Tech
5.
Sharma, Harsh Apurva.
Structure-preserving Numerical Methods for Engineering Applications.
Degree: PhD, Aerospace Engineering, 2020, Virginia Tech
URL: http://hdl.handle.net/10919/99912
► Accurate numerical simulation of dynamical systems over long time horizons is essential in applications ranging from particle physics to geophysical fluid flow to space hazard…
(more)
▼ Accurate numerical simulation of dynamical systems over long time horizons is essential in applications ranging from particle physics to geophysical fluid flow to space hazard analysis. In many of these applications, the governing physical equations derive from a
variational principle and their solutions exhibit physically meaningful invariants such as momentum, energy, or vorticity. Unfortunately, most traditional numerical
methods do not account for the underlying geometric structure of the physical system, leading to simulation results that may suggest nonphysical behavior. In this dissertation, tools from geometric mechanics and computational
methods are used to develop numerical integrators that respect the qualitative features of the physical system. The research presented here focuses on numerical schemes derived from
variational principles– schemes that are general enough to apply to a large class of engineering problems. Energy-preserving algorithms are developed for mechanical systems by exploiting the underlying geometric properties. Numerical performance comparisons demonstrate that these algorithms provide almost exact energy preservation and lead to more accurate prediction. The advantages of these
methods in the numerical simulation are illustrated by various representative examples from engineering applications, which include limit cycle oscillations of an aeroelastic system, dynamics of a neutrally buoyant underwater vehicle, and optimization for spherical shape correlation and matching.
Advisors/Committee Members: Patil, Mayuresh J. (committeechair), Woolsey, Craig A. (committeechair), Ross, Shane D. (committee member), Lee, Taeyoung (committee member), Sultan, Cornel (committee member).
Subjects/Keywords: Structure-preserving methods; Geometric numerical integration; Variational integrators; Lie group methods
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APA (6th Edition):
Sharma, H. A. (2020). Structure-preserving Numerical Methods for Engineering Applications. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/99912
Chicago Manual of Style (16th Edition):
Sharma, Harsh Apurva. “Structure-preserving Numerical Methods for Engineering Applications.” 2020. Doctoral Dissertation, Virginia Tech. Accessed January 23, 2021.
http://hdl.handle.net/10919/99912.
MLA Handbook (7th Edition):
Sharma, Harsh Apurva. “Structure-preserving Numerical Methods for Engineering Applications.” 2020. Web. 23 Jan 2021.
Vancouver:
Sharma HA. Structure-preserving Numerical Methods for Engineering Applications. [Internet] [Doctoral dissertation]. Virginia Tech; 2020. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10919/99912.
Council of Science Editors:
Sharma HA. Structure-preserving Numerical Methods for Engineering Applications. [Doctoral Dissertation]. Virginia Tech; 2020. Available from: http://hdl.handle.net/10919/99912
UCLA
6.
Zhu, Wei.
Nonlocal Variational Methods in Image and Data Processing.
Degree: Mathematics, 2017, UCLA
URL: http://www.escholarship.org/uc/item/1b16b6q7
► In this dissertation, two nonlocal variational models for image and data processing are presented: nonlocal total variation (NLTV) for unsupervised hyperspectral image classification, and low…
(more)
▼ In this dissertation, two nonlocal variational models for image and data processing are presented: nonlocal total variation (NLTV) for unsupervised hyperspectral image classification, and low dimensional manifold model (LDMM) for general image and data processing problems. Both models utilize the nonlocal patch-based structures in natural images and data, and modern optimization techniques are used to solve the corresponding variational problems. The proposed algorithms achieve state-of-the-art results on various image and data processing problems, in particular unsupervised hyperspectral image classification and image or data interpolation.First, a graph-based nonlocal total variation method is proposed for unsupervised classification of hyperspectral images (HSI). The variational problem is solved by the primal-dual hybrid gradient (PDHG) algorithm. By squaring the labeling function and using a stable simplex clustering routine, an unsupervised clustering method with random initialization can be implemented. The effectiveness of the proposed algorithm is illustrated on both synthetic and real-world HSI, and numerical results show that the proposed algorithm outperforms other standard unsupervised clustering methods such as spherical K-means, nonnegative matrix factorization (NMF), and the graph-based Merriman-Bence-Osher (MBO) scheme.Next, we present a novel low dimensional manifold model for general image processing problems. LDMM is based on the fact that the patch manifolds of many natural images have low dimensional structures. Based on this observation, the dimension of the patch manifold is used as a regularization to recover the image. The key step in LDMM is to solve a Laplace-Beltrami equation over a point cloud, and it is tackled by the point integral method (PIM). The point integral method enforces the sample point constraints correctly and yields better results than the standard graph Laplacian. LDMM can be used for various image processing problems, and it achieves state-of-the-art results for image inpainting from random subsampling.Lastly, we present an alternative way to solve the Laplace-Beltrami equation in LDMM. Although the point integral method correctly enforces the sample point constraints and achieves excellent results for image inpainting, the resulting linear system is on the patch domain, and hundreds of linear systems need to be solved each iteration. This causes LDMM to be computationally infeasible for large images and high dimensional data. An alternative way is to discretize the Laplace-Beltrami operator with the weighted graph Laplacian (WGL). After such discretization, we only need to solve one symmetric sparse linear system per iteration of manifold update for image inpainting. Moreover, semi-local patches that in- corporate coordinate information of the patches are used in the weight update, which leads to a faster convergence of LDMM. Numerical experiments on normal image, hyperspectral image, and high dimensional scientific data interpolation demonstrate the effectiveness of…
Subjects/Keywords: Applied mathematics; hyperspectral images; image processing; manifold learning; nonlocal variational methods
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APA ·
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APA (6th Edition):
Zhu, W. (2017). Nonlocal Variational Methods in Image and Data Processing. (Thesis). UCLA. Retrieved from http://www.escholarship.org/uc/item/1b16b6q7
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Zhu, Wei. “Nonlocal Variational Methods in Image and Data Processing.” 2017. Thesis, UCLA. Accessed January 23, 2021.
http://www.escholarship.org/uc/item/1b16b6q7.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Zhu, Wei. “Nonlocal Variational Methods in Image and Data Processing.” 2017. Web. 23 Jan 2021.
Vancouver:
Zhu W. Nonlocal Variational Methods in Image and Data Processing. [Internet] [Thesis]. UCLA; 2017. [cited 2021 Jan 23].
Available from: http://www.escholarship.org/uc/item/1b16b6q7.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Zhu W. Nonlocal Variational Methods in Image and Data Processing. [Thesis]. UCLA; 2017. Available from: http://www.escholarship.org/uc/item/1b16b6q7
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Utah
7.
Tyndall, Daniel Paul.
Sensitivity of surface meteorological analyses to observation networks.
Degree: PhD, Atmospheric Sciences, 2011, University of Utah
URL: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/314/rec/2163
► A computationally efficient variational analysis system for two-dimensional meteorological fields is developed and described. This analysis approach is most efficient when the number of analysis…
(more)
▼ A computationally efficient variational analysis system for two-dimensional meteorological fields is developed and described. This analysis approach is most efficient when the number of analysis grid points is much larger than the number of available observations, such as for large domain mesoscale analyses. The analysis system is developed using MATLAB software and can take advantage of multiple processors or processor cores. A version of the analysis system has been exported as a platform independent application (i.e., can be run on Windows, Linux, or Macintosh OS X desktop computers without a MATLAB license) with input/output operations handled by commonly available internet software combined with data archives at the University of Utah. The impact of observation networks on the meteorological analyses is assessed by utilizing a percentile ranking of individual observation sensitivity and impact, which is computed by using the adjoint of the variational surface assimilation system. This methodology is demonstrated using a case study of the analysis from 1400 UTC 27 October 2010 over the entire contiguous United States domain. The sensitivity of this approach to the dependence of the background error covariance on observation density is examined. Observation sensitivity and impact provide insight on the influence of observations from heterogeneous observing networks as well as serve as objective metrics for quality control procedures that may help to identify stations with significant siting, reporting, or representativeness issues.
Subjects/Keywords: Data assimilation; Mesonet; Mesoscale analysis; Meteorology; Surface analysis; Variational assimilation methods
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APA (6th Edition):
Tyndall, D. P. (2011). Sensitivity of surface meteorological analyses to observation networks. (Doctoral Dissertation). University of Utah. Retrieved from http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/314/rec/2163
Chicago Manual of Style (16th Edition):
Tyndall, Daniel Paul. “Sensitivity of surface meteorological analyses to observation networks.” 2011. Doctoral Dissertation, University of Utah. Accessed January 23, 2021.
http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/314/rec/2163.
MLA Handbook (7th Edition):
Tyndall, Daniel Paul. “Sensitivity of surface meteorological analyses to observation networks.” 2011. Web. 23 Jan 2021.
Vancouver:
Tyndall DP. Sensitivity of surface meteorological analyses to observation networks. [Internet] [Doctoral dissertation]. University of Utah; 2011. [cited 2021 Jan 23].
Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/314/rec/2163.
Council of Science Editors:
Tyndall DP. Sensitivity of surface meteorological analyses to observation networks. [Doctoral Dissertation]. University of Utah; 2011. Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/314/rec/2163
8.
Pimenta, Marcos Tadeu de Oliveira.
Estudo de alguns problemas elÃpticos para o operador biharmônico.
Degree: PhD, Matemática, 2011, University of São Paulo
URL: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-07062011-084414/
;
► Nesse trabalho estudamos questões de existência, multiplicidade e concentração de soluções de uma classe de problemas elÃpticos biharmônicos. Nos três primeiros capÃtulos são utilizados métodos…
(more)
▼ Nesse trabalho estudamos questões de existência, multiplicidade e concentração de soluções de uma classe de problemas elÃpticos biharmônicos. Nos três primeiros capÃtulos são utilizados métodos variacionais para estudar a existência, multiplicidade e comportamento assintótico das soluções fracas não-triviais de equações de Schrödinger estacionárias biharmônicas com diferentes hipóteses sobre o potencial e sobre a não-linearidade. No último capÃtulo, o método de decomposição em cones duais é empregado para obter a existência de três soluções (positiva, negativa e nodal) para uma equação biharmônica
In this work we study some problems on existence, multiplicity and concentration of solutions of biharmonic elliptic equtions. In the first three chapters, variational methods are used to study the existence, multiplicity and the asymptotic behavior of weak nontrivial solutions of stationary Schrödinger biharmonic equations under certain assumptions on the potential function and the nonlinearity. In the last chapter we use variational methods again and also the dual decomposition method to get existence of positive, negative and sign-changing solutions for a biharmonic equation
Advisors/Committee Members: Soares, Sérgio Henrique Monari.
Subjects/Keywords: Biharmonic equations; Equações biharmônicas. Métodos variacionais; Variational methods
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APA (6th Edition):
Pimenta, M. T. d. O. (2011). Estudo de alguns problemas elÃpticos para o operador biharmônico. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/55/55135/tde-07062011-084414/ ;
Chicago Manual of Style (16th Edition):
Pimenta, Marcos Tadeu de Oliveira. “Estudo de alguns problemas elÃpticos para o operador biharmônico.” 2011. Doctoral Dissertation, University of São Paulo. Accessed January 23, 2021.
http://www.teses.usp.br/teses/disponiveis/55/55135/tde-07062011-084414/ ;.
MLA Handbook (7th Edition):
Pimenta, Marcos Tadeu de Oliveira. “Estudo de alguns problemas elÃpticos para o operador biharmônico.” 2011. Web. 23 Jan 2021.
Vancouver:
Pimenta MTdO. Estudo de alguns problemas elÃpticos para o operador biharmônico. [Internet] [Doctoral dissertation]. University of São Paulo; 2011. [cited 2021 Jan 23].
Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-07062011-084414/ ;.
Council of Science Editors:
Pimenta MTdO. Estudo de alguns problemas elÃpticos para o operador biharmônico. [Doctoral Dissertation]. University of São Paulo; 2011. Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-07062011-084414/ ;
University of Michigan
9.
Teichert, Gregory.
Mathematical Framework and Numerical Methods for the Modeling of Mechanochemistry in Multi-Phase Materials.
Degree: PhD, Mechanical Engineering, 2017, University of Michigan
URL: http://hdl.handle.net/2027.42/138690
► This dissertation presents a suite of mathematical formulations and numerical methods for modeling the interactions between solid mechanics and chemistry in multi-phase materials. In all…
(more)
▼ This dissertation presents a suite of mathematical formulations and numerical
methods for modeling the interactions between solid mechanics and chemistry in multi-phase materials. In all cases, the treatments rely on the free energy of the system, which potentially includes the strain energy, the chemical free energy, and the interfacial energy.
Variational methods are applied to the free energy functionals to derive equilibrium conditions for mechanics and to identify constraints on kinetic laws for chemistry. The applications of this class of
variational methods include evolving material configurations associated with phase changes, both diffusive (e.g. oxidation) and non-diffusive (e.g. martensitic transformations). Motivated by the need to represent multi-well, oscillatory, free energy densities, a study is presented comparing spline and polynomial forms for these functions. An alternative approach to phase-field dynamics for finding a minimum energy state is demonstrated, with Mg alloy precipitates as an example. It involves learning the free energy surface as a function of key geometric features with machine learning techniques, which are then used to predict a minimum energy state. This collection of mathematical formulations and numerical
methods is aimed at explorations of the physics underlying observed phenomena in multi-phase materials, with potential use in materials' design.
Advisors/Committee Members: Garikipati, Krishnakumar R (committee member), Marquis, Emmanuelle (committee member), Gavini, Vikram (committee member), Van der Ven, Anton (committee member).
Subjects/Keywords: finite element method; computational materials science; variational methods; Mechanical Engineering; Engineering
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APA (6th Edition):
Teichert, G. (2017). Mathematical Framework and Numerical Methods for the Modeling of Mechanochemistry in Multi-Phase Materials. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/138690
Chicago Manual of Style (16th Edition):
Teichert, Gregory. “Mathematical Framework and Numerical Methods for the Modeling of Mechanochemistry in Multi-Phase Materials.” 2017. Doctoral Dissertation, University of Michigan. Accessed January 23, 2021.
http://hdl.handle.net/2027.42/138690.
MLA Handbook (7th Edition):
Teichert, Gregory. “Mathematical Framework and Numerical Methods for the Modeling of Mechanochemistry in Multi-Phase Materials.” 2017. Web. 23 Jan 2021.
Vancouver:
Teichert G. Mathematical Framework and Numerical Methods for the Modeling of Mechanochemistry in Multi-Phase Materials. [Internet] [Doctoral dissertation]. University of Michigan; 2017. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/2027.42/138690.
Council of Science Editors:
Teichert G. Mathematical Framework and Numerical Methods for the Modeling of Mechanochemistry in Multi-Phase Materials. [Doctoral Dissertation]. University of Michigan; 2017. Available from: http://hdl.handle.net/2027.42/138690
Colorado State University
10.
Duncan, David Ian.
Exploring the limits of variational passive microwave retrievals.
Degree: PhD, Atmospheric Science, 2017, Colorado State University
URL: http://hdl.handle.net/10217/183906
► Passive microwave observations from satellite platforms constitute one of the most important data records of the global observing system. Operational since the late 1970s, passive…
(more)
▼ Passive microwave observations from satellite platforms constitute one of the most important data records of the global observing system. Operational since the late 1970s, passive microwave data underpin climate records of precipitation, sea ice extent, water vapor, and more, and contribute significantly to numerical weather prediction via data assimilation. Detailed understanding of the observation errors in these data is key to maximizing their utility for research and operational applications alike. However, the treatment of observation errors in this data record has been lacking and somewhat divergent when considering the retrieval and data assimilation communities. In this study, some limits of passive microwave imager data are considered in light of more holistic treatment of observation errors. A
variational retrieval, named the CSU 1DVAR, was developed for microwave imagers and applied to the GMI and AMSR2 sensors for ocean scenes. Via an innovative method to determine forward model error, this retrieval accounts for error covariances across all channels used in the iteration. This improves validation in more complex scenes such as high wind speed and persistently cloudy regimes. In addition, it validates on par with a benchmark dataset without any tuning to in-situ observations. The algorithm yields full posterior error diagnostics and its physical forward model is applicable to other sensors, pending intercalibration. This retrieval is used to explore the viability of retrieving parameters at the limits of the available information content from a typical microwave imager. Retrieval of warm rain, marginal sea ice, and falling snow are explored with the
variational retrieval. Warm rain retrieval shows some promise, with greater sensitivity than operational GPM algorithms due to leveraging CloudSat data and accounting for drop size distribution variability. Marginal sea ice is also detected with greater sensitivity than a standard operational retrieval. These studies ultimately show that while a
variational algorithm maximizes the effective signal to noise ratio of these observations, hard limitations exist due to the finite information content afforded by a typical microwave imager.
Advisors/Committee Members: Kummerow, Christian D. (advisor), Boukabara, Sid-Ahmed (committee member), O'Dell, Christopher W. (committee member), Reising, Steven C. (committee member), Rutledge, Steven A. (committee member), Schumacher, Russ S. (committee member).
Subjects/Keywords: remote sensing; variational methods; satellite meteorology; passive microwave
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APA (6th Edition):
Duncan, D. I. (2017). Exploring the limits of variational passive microwave retrievals. (Doctoral Dissertation). Colorado State University. Retrieved from http://hdl.handle.net/10217/183906
Chicago Manual of Style (16th Edition):
Duncan, David Ian. “Exploring the limits of variational passive microwave retrievals.” 2017. Doctoral Dissertation, Colorado State University. Accessed January 23, 2021.
http://hdl.handle.net/10217/183906.
MLA Handbook (7th Edition):
Duncan, David Ian. “Exploring the limits of variational passive microwave retrievals.” 2017. Web. 23 Jan 2021.
Vancouver:
Duncan DI. Exploring the limits of variational passive microwave retrievals. [Internet] [Doctoral dissertation]. Colorado State University; 2017. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10217/183906.
Council of Science Editors:
Duncan DI. Exploring the limits of variational passive microwave retrievals. [Doctoral Dissertation]. Colorado State University; 2017. Available from: http://hdl.handle.net/10217/183906
Université Catholique de Louvain
11.
Di Cosmo, Jonathan.
Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit.
Degree: 2011, Université Catholique de Louvain
URL: http://hdl.handle.net/2078.1/93557
► The nonlinear Schrödinger equation appears in different fields of physics, for example in the theory of Bose-Einstein condensates or in wave propagation models. From a…
(more)
▼ The nonlinear Schrödinger equation appears in different fields of physics, for example in the theory of Bose-Einstein condensates or in wave propagation models. From a mathematical point of view, the study of this equation is interesting and delicate, notably because it can have a very rich set of solutions with various behaviours.
In this thesis, we have been interested in standing waves, which satisfy an elliptic partial differential equation. When this equation is seen as a singularly perturbed problem, its solutions concentrate, in the sense that they converge uniformly to zero outside some concentration set, while they remain positive on this set.
We have obtained three kind of new results. Firstly, under symmetry assumptions, we have found solutions concentrating on a sphere. Secondly, we have obtained the same type of solutions for the Schrödinger-Poisson system. The method consists in applying the mountain pass theorem to a penalized problem. Thirdly, we have proved the existence of solutions of the nonlinear Schrödinger equation concentrating at a local maximum of the potential. These solutions are found by a more general minimax principle. Our results are characterized by very weak assumptions on the potential.
L'équation de Schrödinger non-linéaire apparaît dans différents domaines de la physique, par exemple dans la théorie des condensats de Bose-Einstein ou dans des modèles de propagation d'ondes. D'un point de vue mathématique, l'étude de cette équation est intéressante et délicate, notamment parce qu'elle peut posséder un ensemble très riche de solutions avec des comportements variés.
Dans cette thèse , nous nous sommes intéressés aux ondes stationnaires, qui satisfont une équation aux dérivées partielles elliptique. Lorsque cette équation est vue comme un problème de perturbations singulières, ses solutions se concentrent, dans le sens où elles tendent uniformément vers zéro en dehors d'un certain ensemble de concentration, tout en restant positives sur cet ensemble.
Nous avons obtenu trois types de résultats nouveaux. Premièrement, sous des hypothèses de symétrie, nous avons trouvé des solutions qui se concentrent sur une sphère. Deuxièmement, nous avons obtenu le même type de solutions pour le système de Schrödinger-Poisson. La méthode consiste à appliquer le théorème du col à un problème pénalisé. Troisièmement, nous avons démontré l'existence de solutions de l'équation de Schrödinger non-linéaire qui se concentrent en un maximum local du potentiel. Ces solutions sont obtenues par un principe de minimax plus général. Nos résultats se caractérisent par des hypothèses très faibles sur le potentiel.
(MATH 3)  – UCL, 2011
Advisors/Committee Members: UCL - SST/IRMP/IRMP - Institut de recherche en mathématique et physique, Bonheure, Denis, Van Schaftingen, Jean, Félix, Yves, Gossez, Jean-Pierre, Jeanjean, Louis, Lami Dozo, Enrique, Ponce, Augusto, Willem, Michel.
Subjects/Keywords: Partial differential equations; Nonlinear Schrödinger equation; Variational methods
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APA (6th Edition):
Di Cosmo, J. (2011). Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit. (Thesis). Université Catholique de Louvain. Retrieved from http://hdl.handle.net/2078.1/93557
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Di Cosmo, Jonathan. “Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit.” 2011. Thesis, Université Catholique de Louvain. Accessed January 23, 2021.
http://hdl.handle.net/2078.1/93557.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Di Cosmo, Jonathan. “Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit.” 2011. Web. 23 Jan 2021.
Vancouver:
Di Cosmo J. Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit. [Internet] [Thesis]. Université Catholique de Louvain; 2011. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/2078.1/93557.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Di Cosmo J. Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit. [Thesis]. Université Catholique de Louvain; 2011. Available from: http://hdl.handle.net/2078.1/93557
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Illinois – Urbana-Champaign
12.
Huang, Xichen.
Fast algorithms for Bayesian variable selection.
Degree: PhD, Statistics, 2017, University of Illinois – Urbana-Champaign
URL: http://hdl.handle.net/2142/98201
► Variable selection of regression and classification models is an important but challenging problem. There are generally two approaches, one based on penalized likelihood, and the…
(more)
▼ Variable selection of regression and classification models is an important but challenging problem. There are generally two approaches, one based on penalized likelihood, and the other based on Bayesian framework. We focus on the Bayesian framework in which a hierarchical prior is imposed on all unknown parameters including the unknown variable set. The Bayesian approach has many advantages, for example, we can access unknown obtain the posterior distribution of the sub-models. And more accurate prediction may be obtained by model averaging.
However, as the posterior distribution of the model parameters is usually not in closed form, posterior inference that relies on Markov Chain Monte Carlo (MCMC) has high computational cost especially in high-dimensional settings, which makes Bayesian approaches undesirable. In order to deal with datasets with large number of features, we aim to develop fast algorithms for Bayesian variable selection, which approximate the true posterior distribution, but yet still return the right inference (at least asymptotically).
In this thesis, we start with a
variational algorithm for linear regression. Our algorithm is based on the work by Carbonetto and Stephens (2012), and with essential modifications including updating scheme and truncation of posterior inclusion probabilities. We have shown that our algorithm achieves both frequentist and Bayesian variable selection consistency.
Then we extend our
variational algorithm to logistic regression by incorporating the Polya-Gamma data-augmentation trick (Polson et al., 2013), which links our algorithm for linear regression with logistic regression. However, as the
variational algorithm needs to update the
variational distribution of all the latent Polya-Gamma random variables of the same size of the observations at every iteration, this algorithm is slow when there are huge amount of observations, or even be infeasible when the data is too large to be loaded into computer memory. We propose an online algorithm for the logistic regression, under the framework of online convex optimization. Our algorithm is fast, and achieves similar accuracy (log-loss) as the state-of-art algorithm (Follow-the-Regularized-Proximal algorithm).
Advisors/Committee Members: Liang, Feng (advisor), Liang, Feng (Committee Chair), Fellouris, Georgios (committee member), Qu, Annie (committee member), Shao, Xiaofeng (committee member).
Subjects/Keywords: Bayesian variable selection; Variational Bayesian methods; Online learning
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APA (6th Edition):
Huang, X. (2017). Fast algorithms for Bayesian variable selection. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98201
Chicago Manual of Style (16th Edition):
Huang, Xichen. “Fast algorithms for Bayesian variable selection.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed January 23, 2021.
http://hdl.handle.net/2142/98201.
MLA Handbook (7th Edition):
Huang, Xichen. “Fast algorithms for Bayesian variable selection.” 2017. Web. 23 Jan 2021.
Vancouver:
Huang X. Fast algorithms for Bayesian variable selection. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/2142/98201.
Council of Science Editors:
Huang X. Fast algorithms for Bayesian variable selection. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98201
UCLA
13.
Dragomiretskiy, Konstantin.
Variational Methods in Signal Decomposition and Image Processing.
Degree: Mathematics, 2015, UCLA
URL: http://www.escholarship.org/uc/item/4zx6s9zs
► The work presented in this dissertation is motivated by classical problems in signal and image processing from the perspective of variational and PDE-based methods. Analytically…
(more)
▼ The work presented in this dissertation is motivated by classical problems in signal and image processing from the perspective of variational and PDE-based methods. Analytically encoding qualitative features of signals into variational energies in conjunction with modern methods in sparse optimization allows for well-founded and robust models, the optimization of which yields meaningful and cohesive signal decomposition.Part I of this dissertation is based on joint work Variational Mode Decomposition [DZ14] with Dominique Zosso, in which the goal is to recursively decompose a signal into different modes of separate spectral bands, which are unknown beforehand. In the late nineties,Huang [HSL98] introduced the Hilbert-Huang transform, also known as Empirical Mode Decomposition, in order to decompose a signal into so-called intrinsic mode functions (IMF) along with a trend, and obtain instantaneous frequency data. The HHT/EMD algorithm is widely used today, although there is no exact mathematical model corresponding to this algorithm, and, consequently, the exact properties and limits are widely unknown. Wepropose an entirely non-recursive variational mode decomposition model, where the modes are extracted concurrently. The model looks for a number of modes and their respective center frequencies, such that the modes reproduce the input signal, while being smooth after demodulation into baseband. In Fourier domain, this corresponds to a narrow-band prior. Our model provides a solution to the decomposition problem that is theoretically well-founded, tractable, and motivated. The variational model is efficiently optimized usingan alternating direction method of multipliers approach. Preliminary results show excellent performance with respect to existing mode decomposition models.Part II of this dissertation is the n-dimensional extension of the Variational Mode Decomposition. Decomposing multidimensional signals, such as images, into spatially compact, potentially overlapping modes of essentially wavelike nature makes these components accessible for further downstream analysis such as space-frequency analysis, demodulation, estimation of local orientation, edge and corner detection, texture analysis, denoising, inpainting,and curvature estimation. The model decomposes the input signal into modes with narrow Fourier bandwidth; to cope with sharp region boundaries, incompatible with narrow bandwidth, we introduce binary support functions that act as masks on the narrow-band mode for image re-composition. L1 and TV-terms promote sparsity and spatial compactness. Constraining the support functions to partitions of the signal domain, we effectively get an image segmentation model based on spectral homogeneity. By coupling several submodes together with a single support function we are able to decompose an image into several crystal grains. Our efficient algorithm is based on variable splitting and alternate direction optimization; we employ Merriman-Bence-Osher-like [MBO92] threshold dynamics to handle eciently the motion by…
Subjects/Keywords: Applied mathematics; Image Processing; Image Segmentation; Mode Decomposition; Signal Decomposition; Signal Processing; Variational Methods
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APA (6th Edition):
Dragomiretskiy, K. (2015). Variational Methods in Signal Decomposition and Image Processing. (Thesis). UCLA. Retrieved from http://www.escholarship.org/uc/item/4zx6s9zs
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Dragomiretskiy, Konstantin. “Variational Methods in Signal Decomposition and Image Processing.” 2015. Thesis, UCLA. Accessed January 23, 2021.
http://www.escholarship.org/uc/item/4zx6s9zs.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Dragomiretskiy, Konstantin. “Variational Methods in Signal Decomposition and Image Processing.” 2015. Web. 23 Jan 2021.
Vancouver:
Dragomiretskiy K. Variational Methods in Signal Decomposition and Image Processing. [Internet] [Thesis]. UCLA; 2015. [cited 2021 Jan 23].
Available from: http://www.escholarship.org/uc/item/4zx6s9zs.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Dragomiretskiy K. Variational Methods in Signal Decomposition and Image Processing. [Thesis]. UCLA; 2015. Available from: http://www.escholarship.org/uc/item/4zx6s9zs
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
14.
Tran, Minh-Phuong.
Analyse d'images 3D par méthodes variationnelles et ondelettes : application à l'imagerie médicale : 3D image analysis with variational methods and wavelets : applications to medical image processing.
Degree: Docteur es, Mathématiques, 2012, Université d'Orléans
URL: http://www.theses.fr/2012ORLE2030
► L’imagerie médicale joue un rôle de plus en plus important avec le développement de nombreuses techniques d’acquisition. Il faut principalement pouvoir restaurer (débruiter) les images…
(more)
▼ L’imagerie médicale joue un rôle de plus en plus important avec le développement de nombreuses techniques d’acquisition. Il faut principalement pouvoir restaurer (débruiter) les images et en faire une segmentation. Ainsi toute l’information qualitative et quantitative sera disponible pour affiner les diagnostics. Dans cette thèse nous proposons une contribution à cette analyse dans un contexte 3D. Nous étudions deux grands types de méthodes : les méthodes variationnelles et les méthodes par ondelettes. Nous commençons par présenter les modèles variationnels du second ordre, qui s’avèrent plus performants que la classique méthode du premier ordre de Rudin-Osher-Fatemi. Nous l’utilisons pour débruiter et segmenter après avoir donné un bref état de l’art des procédés d’acquisition des images en médecine. Nous introduisons ensuite la transformée en ondelettes et présentons des algorithmes basés sur cette méthode. Les résultats numériques montrent que ces méthodes sont performantes et compétitives. Le coeur de notre travail est de développer des rerésentations 3D qui sont bien adaptées à des données médicales complexes comme des images IRM sous échantillonnées, peu contrastées (cervelets de souris) ou des images IRM d’angiographie (cerveaux de souris). Chaque technique a ses avantages et ses inconvénients. Aussi nous proposons un modèle variationnel mixte second ordre / seuillage par ondelettes. Ce modèle se comporte particulièrement bien : le bruit est correctement éliminé et les contours et textures préservés. Pour finir, nous adaptons plusieurs méthodes de fermeture de contours (hystérésis et distance de chanfrein) dans un contexte 3D. Le mémoire se termine par une synthèses des résultats et une présentation de futures directions de recherche.
Medical procedures have become a critical application area that makes substantial use of image processing. Medical image processing tasks mainly deal with image restoration, image segmentation that bring out medical image details, measure quantitatively medical conditions etc. The diagnosis of a health problem is now highly dependent on the quality and the credibility of the image analysis. The practical contributions of this thesis can be considered in many directions for medical domain. This manuscript addresses a 3D image analysis with variational methods and wavelet transform in the context of medical image processing. We first survey the second-order variational minimization model, which was proved that better than the classical Rudin-Osher-Fatemi model. This method is considered in problems associated to image denoising, image segmentation, that makes a short state of the art on medical imaging processing techniques. Then we introduce the concept of wavelet transform and present some algorithms that also used in this domain. Experimental results show that these tools are very useful and competitive. The core of this research is the development of new 3D representations, which are well adapted to representing complicated medical data, and filament structures in 3D…
Advisors/Committee Members: Bergounioux, Maïtine (thesis director), Péteri, Renaud (thesis director).
Subjects/Keywords: Analyse d'images 3D; Imagerie médicale; Méthodes variationnelles; 3D image analysis; Medical image; Variational methods
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APA ·
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APA (6th Edition):
Tran, M. (2012). Analyse d'images 3D par méthodes variationnelles et ondelettes : application à l'imagerie médicale : 3D image analysis with variational methods and wavelets : applications to medical image processing. (Doctoral Dissertation). Université d'Orléans. Retrieved from http://www.theses.fr/2012ORLE2030
Chicago Manual of Style (16th Edition):
Tran, Minh-Phuong. “Analyse d'images 3D par méthodes variationnelles et ondelettes : application à l'imagerie médicale : 3D image analysis with variational methods and wavelets : applications to medical image processing.” 2012. Doctoral Dissertation, Université d'Orléans. Accessed January 23, 2021.
http://www.theses.fr/2012ORLE2030.
MLA Handbook (7th Edition):
Tran, Minh-Phuong. “Analyse d'images 3D par méthodes variationnelles et ondelettes : application à l'imagerie médicale : 3D image analysis with variational methods and wavelets : applications to medical image processing.” 2012. Web. 23 Jan 2021.
Vancouver:
Tran M. Analyse d'images 3D par méthodes variationnelles et ondelettes : application à l'imagerie médicale : 3D image analysis with variational methods and wavelets : applications to medical image processing. [Internet] [Doctoral dissertation]. Université d'Orléans; 2012. [cited 2021 Jan 23].
Available from: http://www.theses.fr/2012ORLE2030.
Council of Science Editors:
Tran M. Analyse d'images 3D par méthodes variationnelles et ondelettes : application à l'imagerie médicale : 3D image analysis with variational methods and wavelets : applications to medical image processing. [Doctoral Dissertation]. Université d'Orléans; 2012. Available from: http://www.theses.fr/2012ORLE2030
University of Cambridge
15.
Andres Terre, Helena.
Interpreting deep learning for cell differentiation : supervised and unsupervised models viewed through the lens of information and perturbation theory.
Degree: PhD, 2019, University of Cambridge
URL: https://doi.org/10.17863/CAM.54136
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.810089
► "Predicting the future isn't magic, it's artificial intelligence" Dave Waters. In the last decades there has been an unprecedented growth in the field of machine…
(more)
▼ "Predicting the future isn't magic, it's artificial intelligence" Dave Waters. In the last decades there has been an unprecedented growth in the field of machine learning, and particularly within deep learning models. The combination of big data and computational power has nurtured the evolution of a variety of new methods to predict and interpret future scenarios. These data centric models can achieve exceptional performances on specific tasks, with their prediction boundaries continuously expanding towards new and more complex challenges. However, the model complexity often translates into a lack of interpretability from a scientific c perspective, it is not trivial to identify the factors involved in final outcomes. Explainability may not always be a requirement for some machine learning tasks, specially when it comes in detriment of performance power. But for some applications, such as biological discoveries or medical diagnostics, understanding the output and determining factors that influence decisions is essential. In this thesis we develop both a supervised and unsupervised approach to map from genotype to phenotype. We emphasise the importance of interpretability and feature extraction from the models, by identifying relevant genes for cell differentiation. We then continue to explore the rules and mechanisms behind the models from a theoretical perspective. Using information theory to explain the learning process and applying perturbation theory to transform the results into a generalisable representation. We start by building a supervised approach to mapping cell profiles from genotype to phenotype, using single cell RNA-Seq data. We leverage non-linearities among gene expressions to identify cellular levels of differentiation. The ambiguity and even absence of labels in most biological studies instigated the development of novel unsupervised techniques, leading to a new general and biologically interpretable framework based on Variational Autoencoders. The application and validation of the methods has proven to be successful, but questions regarding the learning process and generative nature of the results remained unanswered. I use information theory to define a new approach to interpret training and the converged solutions of our models. The variational and generative nature of Autoencoders provides a platform to develop general models. Their results should extrapolate and allow generalisation beyond the boundaries of the observed data. To this extent, we introduce for the first time a new interpretation of the embedded generative functions through Perturbation Theory. The embedding multiplicity is addressed by transforming the distributions into a new set of generalisable functions, while characterising their energy spectrum under a particular energy landscape. We outline the combination of theoretical and machine learning based methods, for moving towards interpretable and generalisable models. Developing a theoretical framework to map from genotype to phenotype, we provide both supervised and…
Subjects/Keywords: Artificial Intelligence; Unsupervised Learning; Variational Autoencoders; Single Cell RNA-Seq; Information Theory; Generative methods
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APA ·
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APA (6th Edition):
Andres Terre, H. (2019). Interpreting deep learning for cell differentiation : supervised and unsupervised models viewed through the lens of information and perturbation theory. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.54136 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.810089
Chicago Manual of Style (16th Edition):
Andres Terre, Helena. “Interpreting deep learning for cell differentiation : supervised and unsupervised models viewed through the lens of information and perturbation theory.” 2019. Doctoral Dissertation, University of Cambridge. Accessed January 23, 2021.
https://doi.org/10.17863/CAM.54136 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.810089.
MLA Handbook (7th Edition):
Andres Terre, Helena. “Interpreting deep learning for cell differentiation : supervised and unsupervised models viewed through the lens of information and perturbation theory.” 2019. Web. 23 Jan 2021.
Vancouver:
Andres Terre H. Interpreting deep learning for cell differentiation : supervised and unsupervised models viewed through the lens of information and perturbation theory. [Internet] [Doctoral dissertation]. University of Cambridge; 2019. [cited 2021 Jan 23].
Available from: https://doi.org/10.17863/CAM.54136 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.810089.
Council of Science Editors:
Andres Terre H. Interpreting deep learning for cell differentiation : supervised and unsupervised models viewed through the lens of information and perturbation theory. [Doctoral Dissertation]. University of Cambridge; 2019. Available from: https://doi.org/10.17863/CAM.54136 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.810089
National University of Ireland – Galway
16.
Duggan, Noirin.
Topology preserving and robust variational image segmentation models with applications in medical imaging
.
Degree: 2015, National University of Ireland – Galway
URL: http://hdl.handle.net/10379/5309
► Computer vision refers to the process of enabling computers to mimic the human visual system. The central concern of this thesis is a sub-task of…
(more)
▼ Computer vision refers to the process of enabling computers to mimic the human visual system. The central concern of this thesis is a sub-task of computer vision known as image segmentation, which refers to the decomposition of an image into its most relevant regions.
Image segmentation by its nature is a poorly defined task, considering that what constitutes the `best' decomposition of an image changes according to the task at hand. In this context, the specific focus of this thesis is to investigate the general topic of segmentation robustness; toward this goal, three aspects of this topic have been explored, with a new algorithm proposed in each case.The first algorithm addresses the problem of boundary detection in low-contrast images. The proposed technique consists in solving the well-known Mumford-Shah functional using a highly efficient convex segmentation scheme, the output of which is a simplified binary representation of the original image. Using this binary representation, an edge detector is generated, the output of which is input into a geodesic active contour scheme to produce the final curve representing the boundary of the structure. Results indicate that the proposed scheme yields enhanced performance compared to existing
methods. The second algorithm addresses the issue of robustness with respect to topology preservation. In this context, a segmentation model is proposed that consists of a non-local topology preserving constraint and a data fidelity constraint that increases robustness in the presence of noise. Results indicate that the proposed method performs better than existing
methods at imposing a topology prior in the presence of noise. The third algorithm consists of a novel approach for lung nodule candidate detection in Computed Tomography which is based on the application of global segmentation
methods combined with mean curvature minimisation and simple rule-based filtering. Nodules with vascular connection tend to be characterised by irregular geometrical features that make them difficult to detect using local image metrics. Experimental results indicate that the proposed method can accurately detect nodules exhibiting a diverse range geometrical features. Taken together, the proposed techniques improve robustness in three important areas; namely, robustness with respect to image features, robustness with respect to topology preservation and finally, robustness with respect to diverse geometrical features of the target object.
Advisors/Committee Members: Glavin, Martin (advisor), Jones, Edward (advisor).
Subjects/Keywords: Image segmentation;
Convex optimization;
Variational methods;
Edge detection;
Echocardiography images;
Topology preserving;
Electronic engineering
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APA (6th Edition):
Duggan, N. (2015). Topology preserving and robust variational image segmentation models with applications in medical imaging
. (Thesis). National University of Ireland – Galway. Retrieved from http://hdl.handle.net/10379/5309
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Duggan, Noirin. “Topology preserving and robust variational image segmentation models with applications in medical imaging
.” 2015. Thesis, National University of Ireland – Galway. Accessed January 23, 2021.
http://hdl.handle.net/10379/5309.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Duggan, Noirin. “Topology preserving and robust variational image segmentation models with applications in medical imaging
.” 2015. Web. 23 Jan 2021.
Vancouver:
Duggan N. Topology preserving and robust variational image segmentation models with applications in medical imaging
. [Internet] [Thesis]. National University of Ireland – Galway; 2015. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10379/5309.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Duggan N. Topology preserving and robust variational image segmentation models with applications in medical imaging
. [Thesis]. National University of Ireland – Galway; 2015. Available from: http://hdl.handle.net/10379/5309
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Toronto
17.
Chung, Isaac Kwan Yin.
Functional Tensor-Train Decomposition models for Regression and Classification.
Degree: 2020, University of Toronto
URL: http://hdl.handle.net/1807/103699
► Low-rank tensor decomposition is a popular tool in functional approximation, and is becoming popular in solving supervised learning problems. Recent research has used functional tensor-train…
(more)
▼ Low-rank tensor decomposition is a popular tool in functional approximation, and is becoming popular in solving supervised learning problems. Recent research has used functional tensor-train (FTT) decomposition for multivariate regression problems, but has left classification unexplored. The contributions of this thesis are two-fold. Firstly, we extend FTT to binary and multi-class classification applications. Secondly, we propose a Bayesian FTT decomposition scheme using stochastic variational inference (SVI). This enables the FTT approach to provide statistical prediction error bars. Results on real and synthetic datasets show that, in some cases, performance gains over baseline methods can be achieved. FTT decomposition is a promising avenue of research on supervised learning problems, and should be explored further in other machine learning applications.
M.A.S.
Advisors/Committee Members: Nair, Prasanth B, Aerospace Science and Engineering.
Subjects/Keywords: Functional Tensor Train; Machine Learning; Stochastic methods; Supervised Learning; Tensor Decomposition; Variational Bayesian; 0364
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APA (6th Edition):
Chung, I. K. Y. (2020). Functional Tensor-Train Decomposition models for Regression and Classification. (Masters Thesis). University of Toronto. Retrieved from http://hdl.handle.net/1807/103699
Chicago Manual of Style (16th Edition):
Chung, Isaac Kwan Yin. “Functional Tensor-Train Decomposition models for Regression and Classification.” 2020. Masters Thesis, University of Toronto. Accessed January 23, 2021.
http://hdl.handle.net/1807/103699.
MLA Handbook (7th Edition):
Chung, Isaac Kwan Yin. “Functional Tensor-Train Decomposition models for Regression and Classification.” 2020. Web. 23 Jan 2021.
Vancouver:
Chung IKY. Functional Tensor-Train Decomposition models for Regression and Classification. [Internet] [Masters thesis]. University of Toronto; 2020. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/1807/103699.
Council of Science Editors:
Chung IKY. Functional Tensor-Train Decomposition models for Regression and Classification. [Masters Thesis]. University of Toronto; 2020. Available from: http://hdl.handle.net/1807/103699
University of Texas – Austin
18.
-5216-2437.
Variational methods with dependence structure.
Degree: PhD, Statistics, 2020, University of Texas – Austin
URL: http://dx.doi.org/10.26153/tsw/10973
► It is a common practice among humans to deduce, to explain and to make predictions based on concepts that are not directly observable. In Bayesian…
(more)
▼ It is a common practice among humans to deduce, to explain and to make predictions based on concepts that are not directly observable. In Bayesian statistics, the underlying propositions of the unobserved latent variables are summarized in the posterior distribution. With the increasing complexity of real-world data and statistical models, fast and accurate inference for the posterior becomes essential.
Variational methods, by casting the posterior inference problem in the optimization framework, are widely used for their flexibility and computational efficiency. In this thesis, we develop new
variational methods, studying their theoretical properties and applications.
In the first part of the thesis, we utilize dependence structures towards addressing fundamental problems in
variational inference (VI): posterior uncertainty estimation, convergence properties, and discrete optimization. Though it is flexible,
variational inference often underestimates the posterior uncertainty. This is a consequence of the over-simplified
variational family. Mean-field
variational inference (MFVI), for example, uses a product of independent distributions as a coarse approximation to the posterior. As a remedy, we propose a hierarchical
variational distribution with flexible parameterization that can model the dependence structure between latent variables. With a newly derived objective, we show that the proposed
variational method can achieve accurate and efficient uncertainty estimation.
We further theoretically study the structured
variational inference in the setting of the Stochastic Blockmodel (SBM). The
variational distribution is constructed with a pairwise structure among the nodes of a graph. We prove that, in a broad density regime and for general random initializations, the estimated class labels by structured VI converge to the ground truth with high probability. Empirically, we demonstrate structured VI is more robust compared with MFVI when the graph is sparse and the signal to noise ratio is low.
When the latent variables are discrete, gradient descent based VI often suffers from bias and high variance in the gradient estimation. With correlated random samples, we propose a novel unbiased, low-variance gradient estimator. We demonstrate that under certain constraints, such correlated sampling gives an optimal control variates for the variance reduction. The efficient gradient estimation can be applied to solve a wide range of problems such as the variable selection, reinforcement learning, natural language processing, among others.
For the second part of the thesis, we apply
variational methods to the study of generalization problems in the meta-learning. When trained over multiple-tasks, we identify that a variety of the meta-learning algorithms implicitly require the tasks to have a mutually-exclusive dependence structure. This prevents the task-level overfitting problem and ensures the fast adaptation of the algorithm in the face of a new task. However, such dependence structure may not exist for general…
Advisors/Committee Members: Zhou, Mingyuan (Assistant professor) (advisor), Sarkar, Purnamrita (committee member), Huang, Qixing (committee member), Mueller, Peter (committee member).
Subjects/Keywords: Variational methods; Dependence structure; Bayesian statistics; Uncertainty; Asymptotic; Discrete optimization; Meta-learning
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to Zotero / EndNote / Reference
Manager
APA (6th Edition):
-5216-2437. (2020). Variational methods with dependence structure. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/10973
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Chicago Manual of Style (16th Edition):
-5216-2437. “Variational methods with dependence structure.” 2020. Doctoral Dissertation, University of Texas – Austin. Accessed January 23, 2021.
http://dx.doi.org/10.26153/tsw/10973.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
MLA Handbook (7th Edition):
-5216-2437. “Variational methods with dependence structure.” 2020. Web. 23 Jan 2021.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Vancouver:
-5216-2437. Variational methods with dependence structure. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2020. [cited 2021 Jan 23].
Available from: http://dx.doi.org/10.26153/tsw/10973.
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Council of Science Editors:
-5216-2437. Variational methods with dependence structure. [Doctoral Dissertation]. University of Texas – Austin; 2020. Available from: http://dx.doi.org/10.26153/tsw/10973
Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete
Boston University
19.
Babaniyi, Olalekan.
Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities.
Degree: PhD, Mechanical Engineering, 2016, Boston University
URL: http://hdl.handle.net/2144/14640
► We consider the design of finite element methods for inverse problems with full-field data governed by elliptic forward operators. Such problems arise in applications in…
(more)
▼ We consider the design of finite element methods for inverse problems with
full-field data governed by elliptic forward operators. Such problems arise in
applications in inverse heat conduction, in mechanical property
characterization, and in medical imaging. For this class of problems, novel
finite element methods have been proposed (Barbone et al., 2010) that
give good performance, provided the solutions are in the H1(Ω) function
space. The material property distributions being estimated can be discontinuous,
however, and therefore it is desirable to have formulations that can
accommodate discontinuities in both data and solution. Toward this end, we
present a mixed variational formulation for this class of problems that handles
discontinuities well. We motivate the mixed formulation by examining the
possibility of discretizing using a discontinuous discretization in an irreducible finite
element method, and discuss the limitations of that approach. We then derive a
new mixed formulation based on a least-square error in the constitutive
equation. We prove that the continuous variational formulations are well-posed
for applications in both inverse heat conduction and plane stress elasticity. We
derive a priori error bounds for discretization error, valid in the limit
of mesh refinement. We demonstrate convergence of the method with mesh
refinement in cases with both continuous and discontinuous solutions. Finally we
apply the formulation to measured data to estimate the elastic shear modulus
distributions in both tissue mimicking phantoms and in breast masses from data
collected in vivo.
Subjects/Keywords: Mechanical engineering; Biomechanical imaging; Direct methods; Elastography; Inverse elasticity; Inverse heat conduction; Stabilized variational formulations
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APA ·
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Export
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Manager
APA (6th Edition):
Babaniyi, O. (2016). Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities. (Doctoral Dissertation). Boston University. Retrieved from http://hdl.handle.net/2144/14640
Chicago Manual of Style (16th Edition):
Babaniyi, Olalekan. “Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities.” 2016. Doctoral Dissertation, Boston University. Accessed January 23, 2021.
http://hdl.handle.net/2144/14640.
MLA Handbook (7th Edition):
Babaniyi, Olalekan. “Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities.” 2016. Web. 23 Jan 2021.
Vancouver:
Babaniyi O. Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities. [Internet] [Doctoral dissertation]. Boston University; 2016. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/2144/14640.
Council of Science Editors:
Babaniyi O. Stabilized variational formulation for direct solution of inverse problems in heat conduction and elasticity with discontinuities. [Doctoral Dissertation]. Boston University; 2016. Available from: http://hdl.handle.net/2144/14640
University of Arizona
20.
Pavanello, Michele.
Five Years in Theoretical and Computational Chemistry: From H3+ to DNA
.
Degree: 2010, University of Arizona
URL: http://hdl.handle.net/10150/194295
► The research described in this dissertation concerns two fields of theoretical chemistry: Part I concerns applications of Density Functional Theory, and part II high accuracy…
(more)
▼ The research described in this dissertation concerns two fields of theoretical chemistry: Part I concerns applications of Density Functional Theory, and part II high accuracy calculations within the Born-Oppenheimer approximation using explicitly correlated Gaussian functions.In the first part, after a brief introduction to Density Functional Theory and Hartree Fock
methods, the candidate's research in Density Functional Theory is described in two chapters. One treats the charge transport in B-DNA, specifically (GC)
N oligomers solvated by water. The second chapter treats the charge transfer between the Lithium atom and Fullerene-C
60 in the endohedral complex
[email protected]60. In both applications Density Functional Theory was the central quantum mechanical technique that allowed the approaching of such large molecular systems.In the second part of this dissertation, the candidate's development of a FORTRAN code using explicitly correlated Gaussian functions within the Born-Oppenheimer approximation is presented.Every item of the author's research during his graduate studies has been published in co-authorship with the author's scientific advisor and other collaborators in peer-reviewed journals. A total of 8 scientific articles and one letter have been published by the author while at The University of Arizona.
Advisors/Committee Members: Adamowicz, Ludwik (advisor), Adamowicz, Ludwik (committeemember), Hruby, Victor (committeemember), Salzman, Ron W. (committeemember), Visscher, Koen (committeemember).
Subjects/Keywords: DNA;
Explicitly correlated methods;
H3+;
Variational
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Export
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Manager
APA (6th Edition):
Pavanello, M. (2010). Five Years in Theoretical and Computational Chemistry: From H3+ to DNA
. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/194295
Chicago Manual of Style (16th Edition):
Pavanello, Michele. “Five Years in Theoretical and Computational Chemistry: From H3+ to DNA
.” 2010. Doctoral Dissertation, University of Arizona. Accessed January 23, 2021.
http://hdl.handle.net/10150/194295.
MLA Handbook (7th Edition):
Pavanello, Michele. “Five Years in Theoretical and Computational Chemistry: From H3+ to DNA
.” 2010. Web. 23 Jan 2021.
Vancouver:
Pavanello M. Five Years in Theoretical and Computational Chemistry: From H3+ to DNA
. [Internet] [Doctoral dissertation]. University of Arizona; 2010. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10150/194295.
Council of Science Editors:
Pavanello M. Five Years in Theoretical and Computational Chemistry: From H3+ to DNA
. [Doctoral Dissertation]. University of Arizona; 2010. Available from: http://hdl.handle.net/10150/194295
University of Maryland
21.
Galante, Joseph Robert.
Cometary Escape in the Restricted Circular Planar Three Body Problem.
Degree: Mathematics, 2011, University of Maryland
URL: http://hdl.handle.net/1903/11641
► The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. This principle…
(more)
▼ The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. This principle is utilized along with Aubry-Mather theory to construct regions of instability for a certain three body problem, given by a Hamiltonian system of two degrees of freedom. In principle, these
methods can be applied to construct instability regions for a variety of Hamiltonian systems with 2 degrees of freedom.
The Hamiltonian model considered in this thesis describes the dynamics of a Sun-Jupiter-Comet system and under some simplifying assumptions, the existence of instabilities for the orbit of the comet is shown. In particular it is shown that a comet which starts close to an orbit in the shape of an ellipse of eccentricity e=0.66 can increase in eccentricity to beyond e=1. Furthermore, there exist ejection orbits for the comet. Such orbits are initially well within the range of our solar system. This might give an indication of why most objects rotating around the Sun in our solar system have relatively low eccentricity.
Several new theoretical tools are introduced in this thesis as well. The most notable is a checkable sufficient condition to verify that an exact area preserving map is an exact area preserving twist map in a certain coordinate system. This coordinate system is constructed by ``spreading the cumulative twist'' which arises from the long term dynamics of system. Many of the results of the thesis are `computer assisted' and utilize recent advances in rigorous numerical integration. It is through the application of these advances in computing that it has become possible to state deep results for realistic solar systems. This has been the dream of many since humans first observed the stars so long ago.
Advisors/Committee Members: Kaloshin, Vadim Yu (advisor).
Subjects/Keywords: Mathematics; Celestial Mechanics; Dynamical Systems; Hamiltonian Dynamics; Instabilities; Rigorous Numerics; Variational Methods
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APA (6th Edition):
Galante, J. R. (2011). Cometary Escape in the Restricted Circular Planar Three Body Problem. (Thesis). University of Maryland. Retrieved from http://hdl.handle.net/1903/11641
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Galante, Joseph Robert. “Cometary Escape in the Restricted Circular Planar Three Body Problem.” 2011. Thesis, University of Maryland. Accessed January 23, 2021.
http://hdl.handle.net/1903/11641.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Galante, Joseph Robert. “Cometary Escape in the Restricted Circular Planar Three Body Problem.” 2011. Web. 23 Jan 2021.
Vancouver:
Galante JR. Cometary Escape in the Restricted Circular Planar Three Body Problem. [Internet] [Thesis]. University of Maryland; 2011. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/1903/11641.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Galante JR. Cometary Escape in the Restricted Circular Planar Three Body Problem. [Thesis]. University of Maryland; 2011. Available from: http://hdl.handle.net/1903/11641
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Helsinki
22.
Jälkö, Joonas.
Privacy-aware variational inference.
Degree: Department of Mathematics and Statistics; Helsingfors universitet, Matematisk-naturvetenskapliga fakulteten, Institutionen för matematik och statistik, 2017, University of Helsinki
URL: http://hdl.handle.net/10138/228858
► This thesis focuses on privacy-preserving statistical inference. We use a probabilistic point of view of privacy called differential privacy. Differential privacy ensures that replacing one…
(more)
▼ This thesis focuses on privacy-preserving statistical inference. We use a probabilistic point of view of privacy called differential privacy. Differential privacy ensures that replacing one individual from the dataset with another individual does not affect the results drastically. There are different versions of the differential privacy. This thesis considers the ε-differential privacy also known as the pure differential privacy, and also a relaxation known as the (ε, δ)-differential privacy.
We state several important definitions and theorems of DP. The proofs for most of the theorems are given in this thesis. Our goal is to build a general framework for privacy preserving posterior inference. To achieve this we use an approximative approach for posterior inference called variational Bayesian (VB) methods. We build the basic concepts of variational inference with certain detail and show examples on how to apply variational inference.
After giving the prerequisites on both DP and VB we state our main result, the differentially private variational inference (DPVI) method. We use a recently proposed doubly stochastic variational inference (DSVI) combined with Gaussian mechanism to build a privacy-preserving method for posterior inference. We give the algorithm definition and explain its parameters.
The DPVI method is compared against the state-of-the-art method for DP posterior inference called the differentially private stochastic gradient Langevin dynamics (DP-SGLD). We compare the performance on two different models, the logistic regression model and the Gaussian mixture model. The DPVI method outperforms DP-SGLD in both tasks.
Subjects/Keywords: Differential privacy; Variational Bayesian methods; Machine learning; Bayesian inference; Tillämpad matematik; Applied Mathematics; Soveltava matematiikka
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APA (6th Edition):
Jälkö, J. (2017). Privacy-aware variational inference. (Masters Thesis). University of Helsinki. Retrieved from http://hdl.handle.net/10138/228858
Chicago Manual of Style (16th Edition):
Jälkö, Joonas. “Privacy-aware variational inference.” 2017. Masters Thesis, University of Helsinki. Accessed January 23, 2021.
http://hdl.handle.net/10138/228858.
MLA Handbook (7th Edition):
Jälkö, Joonas. “Privacy-aware variational inference.” 2017. Web. 23 Jan 2021.
Vancouver:
Jälkö J. Privacy-aware variational inference. [Internet] [Masters thesis]. University of Helsinki; 2017. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/10138/228858.
Council of Science Editors:
Jälkö J. Privacy-aware variational inference. [Masters Thesis]. University of Helsinki; 2017. Available from: http://hdl.handle.net/10138/228858
University of Cambridge
23.
Andres Terre, Helena.
Interpreting Deep Learning for cell differentiation. Supervised and Unsupervised models viewed through the lens of information and perturbation theory.
Degree: PhD, 2019, University of Cambridge
URL: https://www.repository.cam.ac.uk/handle/1810/307041
► "Predicting the future isn't magic, it's artificial intelligence" Dave Waters. In the last decades there has been an unprecedented growth in the field of machine…
(more)
▼ "Predicting the future isn't magic, it's artificial intelligence" Dave Waters. In the last decades there has been an unprecedented growth in the field of machine learning, and particularly within deep learning models. The combination of big data and computational power has nurtured the evolution of a variety of new methods to predict and interpret future scenarios. These data centric models can achieve exceptional performances on specific tasks, with their prediction boundaries continuously expanding towards new and more complex challenges. However, the model complexity often translates into a lack of interpretability from a scientific c perspective, it is not trivial to identify the factors involved in final outcomes. Explainability may not always be a requirement for some machine learning tasks, specially when it comes in detriment of performance power. But for some applications, such as biological discoveries or medical diagnostics, understanding the output and determining factors that influence decisions is essential. In this thesis we develop both a supervised and unsupervised approach to map from genotype to phenotype. We emphasise the importance of interpretability and feature extraction from the models, by identifying relevant genes for cell differentiation. We then continue to explore the rules and mechanisms behind the models from a theoretical perspective. Using information theory to explain the learning process and applying perturbation theory to transform the results into a generalisable representation. We start by building a supervised approach to mapping cell profiles from genotype to phenotype, using single cell RNA-Seq data. We leverage non-linearities among gene expressions to identify cellular levels of differentiation. The ambiguity and even absence of labels in most biological studies instigated the development of novel unsupervised techniques, leading to a new general and biologically interpretable framework based on Variational Autoencoders. The application and validation of the methods has proven to be successful, but questions regarding the learning process and generative nature of the results remained unanswered. I use information theory to define a new approach to interpret training and the converged solutions of our models. The variational and generative nature of Autoencoders provides a platform to develop general models. Their results should extrapolate and allow generalisation beyond the boundaries of the observed data. To this extent, we introduce for the first time a new interpretation of the embedded generative functions through Perturbation Theory. The embedding multiplicity is addressed by transforming the distributions into a new set of generalisable functions, while characterising their energy spectrum under a particular energy landscape. We outline the combination of theoretical and machine learning based methods, for moving towards interpretable and generalisable models. Developing a theoretical framework to map from genotype to phenotype, we provide both supervised and…
Subjects/Keywords: Artificial Intelligence; Unsupervised Learning; Variational Autoencoders; Single Cell RNA-Seq; Information Theory; Generative methods
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APA ·
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Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Andres Terre, H. (2019). Interpreting Deep Learning for cell differentiation. Supervised and Unsupervised models viewed through the lens of information and perturbation theory. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/307041
Chicago Manual of Style (16th Edition):
Andres Terre, Helena. “Interpreting Deep Learning for cell differentiation. Supervised and Unsupervised models viewed through the lens of information and perturbation theory.” 2019. Doctoral Dissertation, University of Cambridge. Accessed January 23, 2021.
https://www.repository.cam.ac.uk/handle/1810/307041.
MLA Handbook (7th Edition):
Andres Terre, Helena. “Interpreting Deep Learning for cell differentiation. Supervised and Unsupervised models viewed through the lens of information and perturbation theory.” 2019. Web. 23 Jan 2021.
Vancouver:
Andres Terre H. Interpreting Deep Learning for cell differentiation. Supervised and Unsupervised models viewed through the lens of information and perturbation theory. [Internet] [Doctoral dissertation]. University of Cambridge; 2019. [cited 2021 Jan 23].
Available from: https://www.repository.cam.ac.uk/handle/1810/307041.
Council of Science Editors:
Andres Terre H. Interpreting Deep Learning for cell differentiation. Supervised and Unsupervised models viewed through the lens of information and perturbation theory. [Doctoral Dissertation]. University of Cambridge; 2019. Available from: https://www.repository.cam.ac.uk/handle/1810/307041
Georgia Tech
24.
Gallego Bonet, Guillermo.
Variational image processing algorithms for the stereoscopic space-time reconstruction of water waves.
Degree: PhD, Electrical and Computer Engineering, 2011, Georgia Tech
URL: http://hdl.handle.net/1853/39480
► A novel video observational method for the space-time stereoscopic reconstruction of dynamic surfaces representable as graphs, such as ocean waves, is developed. Variational optimization algorithms…
(more)
▼ A novel video observational method for the
space-time stereoscopic reconstruction of
dynamic surfaces representable as graphs, such
as ocean waves, is developed.
Variational
optimization algorithms combining image
processing, computer vision and partial
differential equations are designed to address
the problem of the recovery of the shape of an
object's surface from sequences of synchronized
multi-view images. Several theoretical and numerical paths are discussed to solve the
problem. The
variational stereo method
developed in this thesis has several advantages
over existing 3-D reconstruction algorithms.
Our method follows a top-down approach or
object-centered philosophy in which an explicit
model of the target object in the scene is
devised and then related to image
measurements. The key advantages of our
method are the coherence (smoothness) of the
reconstructed surface caused by a coherent
object-centered design, the robustness to noise
due to a generative model of the observed
images, the ability to handle surfaces with
smooth textures where other
methods typically
fail to provide a solution, and the higher
resolution achieved due to a suitable graph
representation of the object's surface. The
method provides competitive results with
respect to existing
variational reconstruction
algorithms. However, our method is based upon
a simplified but complete physical model of the
scene that allows the reconstruction process to
include physical properties of the object's
surface that are otherwise difficult to take into
account with existing reconstruction
algorithms. Some initial steps are taken toward
incorporating the physics of ocean waves in the
stereo reconstruction process. The developed
method is applied to empirical data of ocean
waves collected at an off-shore oceanographic
platform located off the coast of Crimea,
Ukraine. An empirically-based physical model
founded upon current ocean engineering
standards is used to validate the results. Our
findings suggest that this remote sensing
observational method has a broad impact on
off-shore engineering to enrich the
understanding of sea states, enabling improved
design of off-shore structures. The exploration
of ways to incorporate dynamical properties,
such as the wave equation, in the
reconstruction process is discussed for future
research.
Advisors/Committee Members: Yezzi, Anthony (Committee Chair), Fedele, Francesco (Committee Co-Chair), Dellaert, Frank (Committee Member), Egerstedt, Magnus (Committee Member), Tannenbaum, Allen (Committee Member), Vela, Patricio (Committee Member).
Subjects/Keywords: Multigrid methods; Marine technology; Remote sensing; Image processing; Stereo vision; Ocean waves; Variational methods; Imaging systems; Water waves
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APA (6th Edition):
Gallego Bonet, G. (2011). Variational image processing algorithms for the stereoscopic space-time reconstruction of water waves. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/39480
Chicago Manual of Style (16th Edition):
Gallego Bonet, Guillermo. “Variational image processing algorithms for the stereoscopic space-time reconstruction of water waves.” 2011. Doctoral Dissertation, Georgia Tech. Accessed January 23, 2021.
http://hdl.handle.net/1853/39480.
MLA Handbook (7th Edition):
Gallego Bonet, Guillermo. “Variational image processing algorithms for the stereoscopic space-time reconstruction of water waves.” 2011. Web. 23 Jan 2021.
Vancouver:
Gallego Bonet G. Variational image processing algorithms for the stereoscopic space-time reconstruction of water waves. [Internet] [Doctoral dissertation]. Georgia Tech; 2011. [cited 2021 Jan 23].
Available from: http://hdl.handle.net/1853/39480.
Council of Science Editors:
Gallego Bonet G. Variational image processing algorithms for the stereoscopic space-time reconstruction of water waves. [Doctoral Dissertation]. Georgia Tech; 2011. Available from: http://hdl.handle.net/1853/39480
University of California – Berkeley
25.
Peters, Daniel Martinez.
Nonlinear Stability Criteria for Elastic Rod Structures.
Degree: Mechanical Engineering, 2011, University of California – Berkeley
URL: http://www.escholarship.org/uc/item/6km3q6b7
► Branched elastic rod structures are abundant in engineering and nature, in applications ranging from MEMS devices to human spine models. While buckling is well-understood for…
(more)
▼ Branched elastic rod structures are abundant in engineering and nature, in applications ranging from MEMS devices to human spine models. While buckling is well-understood for problems of this type, stability is often difficult to assess, especially when the model is derived from a nonlinear rod theory. The purpose of this research is to establish criteria for determining nonlinear stability, based upon the minimization of an energy functional. By utilizing variational principles, and Legendre'sclassical work in particular, a new necessary condition for stability featuring the existence of bounded solutions to a set of Riccati differential equations is established. For a single rod, building on classical results, this condition is also shown to be sufficient for stability.The stability criteria are demonstrated on a number of examples using a simple, planar rod theory. These examples range from a classical strut under axial load to a branched tree-like structure composed of several rods. In the branched model, the stability analysis consists of finding bounded solutions to a set of Riccati equations, which are coupled at branching points. The number of Riccati equations corresponds to the number of rods in the structure. The resulting condition is only necessary for stability of a branched structure, as a sufficient condition could not be established. However, this is the first instance of a stability criterion for branched structures that is based on the second variation of the total energy. The advantage is that this method provides a systematic means of identifying unstable, and therefore physically unrealizable, configurations of a branched structure. Finally, an extension of the stability criteria to other rod theories is discussed.
Subjects/Keywords: Mechanical engineering; Mechanics; Applied mathematics; Buckling; Elastica; Elastic stability; Rod theory; Tree-like structures; Variational methods
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APA (6th Edition):
Peters, D. M. (2011). Nonlinear Stability Criteria for Elastic Rod Structures. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/6km3q6b7
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Peters, Daniel Martinez. “Nonlinear Stability Criteria for Elastic Rod Structures.” 2011. Thesis, University of California – Berkeley. Accessed January 23, 2021.
http://www.escholarship.org/uc/item/6km3q6b7.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Peters, Daniel Martinez. “Nonlinear Stability Criteria for Elastic Rod Structures.” 2011. Web. 23 Jan 2021.
Vancouver:
Peters DM. Nonlinear Stability Criteria for Elastic Rod Structures. [Internet] [Thesis]. University of California – Berkeley; 2011. [cited 2021 Jan 23].
Available from: http://www.escholarship.org/uc/item/6km3q6b7.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Peters DM. Nonlinear Stability Criteria for Elastic Rod Structures. [Thesis]. University of California – Berkeley; 2011. Available from: http://www.escholarship.org/uc/item/6km3q6b7
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of California – Irvine
26.
Liu, Qiang.
Reasoning and Decisions in Probabilistic Graphical Models - A Unified Framework.
Degree: Computer Science, 2014, University of California – Irvine
URL: http://www.escholarship.org/uc/item/92p8w3xb
► Probabilistic graphical models such as Markov random fields, Bayesian networks and decision networks (a.k.a. influence diagrams) provide powerful frameworks for representing and exploiting dependence structures…
(more)
▼ Probabilistic graphical models such as Markov random fields, Bayesian networks and decision networks (a.k.a. influence diagrams) provide powerful frameworks for representing and exploiting dependence structures in complex systems. However, making predictions or decisions using graphical models involve challenging computational problems of optimization and/or estimation in high dimensional spaces. These include combinatorial optimization tasks such as maximum a posteriori (MAP), which finds the most likely configuration, or marginalization tasks that calculate the normalization constants or marginal probabilities. Even more challenging tasks require a hybrid of both: marginal MAP tasks find the optimal MAP prediction while marginalizing over missing information or latent variables, while decision-making problems search for optimal policies over decisions in single- or multi-agent systems, in order to maximize expected utility in uncertain environments.All these problems are generally NP-hard, creating a need for efficient approximations. The last two decades have witnessed significant progress on traditional optimization and marginalization problems, especially via the development of variational message passing algorithms. However, there has been less progress on the more challenging marginal MAP and decision-making problems.This thesis presents a unified variational representation for all these problems. Based on our framework, we derive a class of efficient algorithms that combines the advantages of several existing algorithms, resulting in improved performance on traditional marginalization and optimization tasks. More importantly, our framework allows us to easily extend most or all existing variational algorithms to hybrid inference and decision-making tasks, and significantly improves our ability to solve these difficult problems. In particular, we propose a spectrum of efficient belief propagation style algorithms with "message passing" forms, which are simple, fast and amenable to parallel or distributed computation. We also propose a set of convergent algorithms based on proximal point methods, which have the nice form of transforming the hybrid inference problem into a sequence of standard marginalization problems. We show that our algorithms significantly outperform existing approaches in terms of both empirical performance and theoretical properties.
Subjects/Keywords: Computer science; Artificial intelligence; Approximate inference; Belief propagation; Graphical models; Influence diagrams; Probabilistic inference; Variational methods
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APA (6th Edition):
Liu, Q. (2014). Reasoning and Decisions in Probabilistic Graphical Models - A Unified Framework. (Thesis). University of California – Irvine. Retrieved from http://www.escholarship.org/uc/item/92p8w3xb
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Liu, Qiang. “Reasoning and Decisions in Probabilistic Graphical Models - A Unified Framework.” 2014. Thesis, University of California – Irvine. Accessed January 23, 2021.
http://www.escholarship.org/uc/item/92p8w3xb.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Liu, Qiang. “Reasoning and Decisions in Probabilistic Graphical Models - A Unified Framework.” 2014. Web. 23 Jan 2021.
Vancouver:
Liu Q. Reasoning and Decisions in Probabilistic Graphical Models - A Unified Framework. [Internet] [Thesis]. University of California – Irvine; 2014. [cited 2021 Jan 23].
Available from: http://www.escholarship.org/uc/item/92p8w3xb.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Liu Q. Reasoning and Decisions in Probabilistic Graphical Models - A Unified Framework. [Thesis]. University of California – Irvine; 2014. Available from: http://www.escholarship.org/uc/item/92p8w3xb
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
27.
Pimenta, Marcos Tadeu de Oliveira.
Existência e concentração de soluções para sistemas elÃpticos com condição de Neumann.
Degree: Mestrado, Matemática, 2008, University of São Paulo
URL: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-06052008-095250/
;
► Estudamos uma classe de sistemas elÃpticos - \'elipson POT 2\́'DELTAú + u = g(v) em \'ÔMEGA-́ \'elipson POT 2\́'DELTAv́ + v f(u) em ÔMEGA ṔARTIAL\'u…
(more)
▼ Estudamos uma classe de sistemas elÃpticos - \'elipson POT 2\́'DELTAú + u = g(v) em \'ÔMEGA-́ \'elipson POT 2\́'DELTAv́ + v f(u) em ÔMEGA ṔARTIAL\'u SOBRE \'PARTIAL n = \'PARTIAL v SOBRE PARTIAL n = O sobre \"PARTIAL\'Ã́”MEGA ́onde Ã́”MEGA ESTA CONTIDO EM R POT. N ́é um domÃnio limitado, com bordo regular e N &́#62; ou =3́. As não linearidades f e g são funções com crescimento superlinear e subcrÃtico no infinito. Estudamos resultados sobre a existência de uma sequência de soluções que se concentram, quando o parâmetro \'epsilon ́tende a zero, em um ponto da fronteira que maximiza a sua curvatura. Para isso utilizamos um resultado abstrato sobre existência de pontos crÃticos para funcionais fortemente indefinidos
We study an singularly perturbed Hamiltonean elliptic system - \'elipson POT 2\́'DELTAú + u = g(v) in \'ÔMEGA-́ \'elipson POT 2\́'DELTAv́ + v f(u) in ÔMEGA ṔARTIAL\'u ON \'PARTIAL n = \'PARTIAL v ON PARTIAL n=́ O sobre \"PARTIAL\'Ã́”MEGA ́when \'ÔMEGA THIS CONTAINED R POT. N ́is a smooth bounded domain, N &́#62; or =3́ and f and g are nonlinearities having superlinear and subcritical growth at infinity. We study an abstract result about existence of critical points of strongly as épsilonǵoes to zero, at a point of the boundary which maximizes the mean curvature of the boundary
Advisors/Committee Members: Soares, Sérgio Henrique Monari.
Subjects/Keywords: Concentração de soluções; Concentration of solutions; Hamiltonean systems; Linking theorems; Métodos variacionais; Sistemas Hamiltonianos; Teoremas de link; Variational methods
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APA (6th Edition):
Pimenta, M. T. d. O. (2008). Existência e concentração de soluções para sistemas elÃpticos com condição de Neumann. (Masters Thesis). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/55/55135/tde-06052008-095250/ ;
Chicago Manual of Style (16th Edition):
Pimenta, Marcos Tadeu de Oliveira. “Existência e concentração de soluções para sistemas elÃpticos com condição de Neumann.” 2008. Masters Thesis, University of São Paulo. Accessed January 23, 2021.
http://www.teses.usp.br/teses/disponiveis/55/55135/tde-06052008-095250/ ;.
MLA Handbook (7th Edition):
Pimenta, Marcos Tadeu de Oliveira. “Existência e concentração de soluções para sistemas elÃpticos com condição de Neumann.” 2008. Web. 23 Jan 2021.
Vancouver:
Pimenta MTdO. Existência e concentração de soluções para sistemas elÃpticos com condição de Neumann. [Internet] [Masters thesis]. University of São Paulo; 2008. [cited 2021 Jan 23].
Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-06052008-095250/ ;.
Council of Science Editors:
Pimenta MTdO. Existência e concentração de soluções para sistemas elÃpticos com condição de Neumann. [Masters Thesis]. University of São Paulo; 2008. Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-06052008-095250/ ;
28.
Leuyacc, Yony Raúl Santaria.
Equações parciais elÃpticas com crescimento exponencial.
Degree: Mestrado, Matemática, 2014, University of São Paulo
URL: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-17032014-103611/
;
► Neste trabalho estudamos existência, multiplicidade e não existência de soluções não triviais para o seguinte problema elÃptico: { - \'DELTA=́ f(x, u), em \'OMEGA ́…
(more)
▼ Neste trabalho estudamos existência, multiplicidade e não existência de soluções não triviais para o seguinte problema elÃptico: { - \'DELTA=́ f(x, u), em \'OMEGA ́ u = 0, sobre \'\\PARTIAL\́'OMEGA\', onde \'OMEGA ́é um conjunto limitado de \'R POT. 2ćom fronteira suave e a função f possui crescimento exponencial. Para a existência de soluções são aplicados métodos variacionais combinados com as desigualdades de Trudinger-Moser. O resultado de não-existência é restrito ao caso de soluções radiais positivas e \'OMEGA=́ \'B IND.1\'(0). A prova usa técnicas de equações diferenciais ordinárias
In this work we study the existence, multiplicity and non-existence of non-trivial solutions to the following elliptic problem: { - \'DELTAú = f(x; u); in \'OMEGA\', ; u = 0; on \'\\PARTIAL\́'OMEGA ́where \"OMEGA ́is a bounded and smooth domain in \'R POT. 2ánd f possesses exponential growth. The existence results are proved by using variational methods and the Trudinger- Moser inequalities. The non-existence result is restricted to the case of positive radial solutions and \'OMEGA ́= \'B IND. 1\'(0). The proof uses techniques of the theory of ordinary differential equations.
Advisors/Committee Members: Soares, Sérgio Henrique Monari.
Subjects/Keywords: Crescimento exponencial; Desigualdades de Trudinger-Moser; Equações parciais elÃpticas; Equations elliptic partial; Exponential growth; Métodos variacionais; Moser Trudinger inequalities; Variational methods
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APA (6th Edition):
Leuyacc, Y. R. S. (2014). Equações parciais elÃpticas com crescimento exponencial. (Masters Thesis). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/55/55135/tde-17032014-103611/ ;
Chicago Manual of Style (16th Edition):
Leuyacc, Yony Raúl Santaria. “Equações parciais elÃpticas com crescimento exponencial.” 2014. Masters Thesis, University of São Paulo. Accessed January 23, 2021.
http://www.teses.usp.br/teses/disponiveis/55/55135/tde-17032014-103611/ ;.
MLA Handbook (7th Edition):
Leuyacc, Yony Raúl Santaria. “Equações parciais elÃpticas com crescimento exponencial.” 2014. Web. 23 Jan 2021.
Vancouver:
Leuyacc YRS. Equações parciais elÃpticas com crescimento exponencial. [Internet] [Masters thesis]. University of São Paulo; 2014. [cited 2021 Jan 23].
Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-17032014-103611/ ;.
Council of Science Editors:
Leuyacc YRS. Equações parciais elÃpticas com crescimento exponencial. [Masters Thesis]. University of São Paulo; 2014. Available from: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-17032014-103611/ ;
29.
Haussaire, Jean-Matthieu.
Méthodes variationnelles d'ensemble itératives pour l'assimilation de données non-linéaire : Application au transport et la chimie atmosphérique : Iterative ensemble variational methods for nonlinear data assimilation : Application to transport and atmospheric chemistry.
Degree: Docteur es, Sciences et Techniques de l'Environnement, 2017, Université Paris-Est
URL: http://www.theses.fr/2017PESC1097
► Les méthodes d'assimilation de données sont en constante évolution pour s'adapter aux problèmes à résoudre dans les multiples domaines d’application. En sciences de l'atmosphère, chaque…
(more)
▼ Les méthodes d'assimilation de données sont en constante évolution pour s'adapter aux problèmes à résoudre dans les multiples domaines d’application. En sciences de l'atmosphère, chaque nouvel algorithme a d'abord été implémenté sur des modèles de prévision numérique du temps avant d'être porté sur des modèles de chimie atmosphérique. Ce fut le cas des méthodes variationnelles 4D et des filtres de Kalman d'ensemble par exemple. La nouvelle génération d'algorithmes variationnels d'ensemble quadridimensionnels (EnVar 4D) ne fait pas exception. Elle a été développée pour tirer partie des deux approches variationnelle et ensembliste et commence à être appliquée au sein des centres opérationnels de prévision numérique du temps, mais n'a à ce jour pas été testée sur des modèles opérationnels de chimie atmosphérique.En effet, la complexité de ces modèles rend difficile la validation de nouvelles méthodes d’assimilation. Il est ainsi nécessaire d'avoir à disposition des modèles d’ordre réduit, qui doivent être en mesure de synthétiser les phénomènes physiques à l'{oe}uvre dans les modèles opérationnels tout en limitant certaines des difficultés liées à ces derniers. Un tel modèle, nommé L95-GRS, a donc été développé. Il associe la météorologie simpliste du modèle de Lorenz-95 à un module de chimie de l'ozone troposphérique avec 7 espèces chimiques. Bien que de faible dimension, il reproduit des phénomènes physiques et chimiques observables en situation réelle. Une méthode d'assimilation de donnée, le lisseur de Kalman d'ensemble itératif (IEnKS), a été appliquée sur ce modèle. Il s'agit d'une méthode EnVar 4D itérative qui résout le problème non-linéaire variationnel complet. Cette application a permis de valider les méthodes EnVar 4D dans un contexte de chimie atmosphérique non-linéaire, mais aussi de soulever les premières limites de telles méthodes.Fort de cette expérience, les résultats ont été étendus au cas d’un modèle réaliste de prévision de pollution atmosphérique. Les méthodes EnVar 4D, via l'IEnKS, ont montré leur potentiel pour tenir compte de la non-linéarité du modèle de chimie dans un contexte maîtrisé, avec des observations synthétiques. Cependant, le passage à des observations réelles d'ozone troposphérique mitige ces résultats et montre la difficulté que représente l'assimilation de données en chimie atmosphérique. En effet, une très forte erreur est associée à ces modèles, provenant de sources d'incertitudes variées. Deux démarches doivent alors être entreprises pour pallier ce problème.Tout d’abord, la méthode d’assimilation doit être en mesure de tenir compte efficacement de l’erreur modèle. Cependant, la majorité des méthodes sont développées en supposant au contraire un modèle parfait. Pour se passer de cette hypothèse, une nouvelle méthode a donc été développée. Nommée IEnKF-Q, elle étend l'IEnKS au cas avec erreur modèle. Elle a été validée sur un modèle jouet, démontrant sa supériorité par rapport à des méthodes d'assimilation adaptées naïvement pour tenir compte de l’erreur modèle.Toutefois, une…
Advisors/Committee Members: Bocquet, Marc (thesis director).
Subjects/Keywords: Assimilation de donnée; Méthode variationnelle d'ensemble; 4D Var; EnKF; Chimie atmosphérique; Data assimilation; Ensemble variational methods; 4D Var; EnKF; Atmospheric chemistry
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APA ·
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APA (6th Edition):
Haussaire, J. (2017). Méthodes variationnelles d'ensemble itératives pour l'assimilation de données non-linéaire : Application au transport et la chimie atmosphérique : Iterative ensemble variational methods for nonlinear data assimilation : Application to transport and atmospheric chemistry. (Doctoral Dissertation). Université Paris-Est. Retrieved from http://www.theses.fr/2017PESC1097
Chicago Manual of Style (16th Edition):
Haussaire, Jean-Matthieu. “Méthodes variationnelles d'ensemble itératives pour l'assimilation de données non-linéaire : Application au transport et la chimie atmosphérique : Iterative ensemble variational methods for nonlinear data assimilation : Application to transport and atmospheric chemistry.” 2017. Doctoral Dissertation, Université Paris-Est. Accessed January 23, 2021.
http://www.theses.fr/2017PESC1097.
MLA Handbook (7th Edition):
Haussaire, Jean-Matthieu. “Méthodes variationnelles d'ensemble itératives pour l'assimilation de données non-linéaire : Application au transport et la chimie atmosphérique : Iterative ensemble variational methods for nonlinear data assimilation : Application to transport and atmospheric chemistry.” 2017. Web. 23 Jan 2021.
Vancouver:
Haussaire J. Méthodes variationnelles d'ensemble itératives pour l'assimilation de données non-linéaire : Application au transport et la chimie atmosphérique : Iterative ensemble variational methods for nonlinear data assimilation : Application to transport and atmospheric chemistry. [Internet] [Doctoral dissertation]. Université Paris-Est; 2017. [cited 2021 Jan 23].
Available from: http://www.theses.fr/2017PESC1097.
Council of Science Editors:
Haussaire J. Méthodes variationnelles d'ensemble itératives pour l'assimilation de données non-linéaire : Application au transport et la chimie atmosphérique : Iterative ensemble variational methods for nonlinear data assimilation : Application to transport and atmospheric chemistry. [Doctoral Dissertation]. Université Paris-Est; 2017. Available from: http://www.theses.fr/2017PESC1097
Pontifical Catholic University of Rio de Janeiro
30.
HELVIO DE FARIAS COSTA PEIXOTO.
[en] A FAST MULTIPOLE METHOD FOR HIGH ORDER BOUNDARY
ELEMENTS.
Degree: 2018, Pontifical Catholic University of Rio de Janeiro
URL: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=34740
► [pt] Desde a década de 1990, o Método Fast Multipole (FMM) tem sido usado em conjunto com o Métodos dos Elementos de Contorno (BEM) para…
(more)
▼ [pt] Desde a década de 1990, o Método Fast Multipole
(FMM) tem sido usado em conjunto com o Métodos dos Elementos de
Contorno (BEM) para a simulação de problemas de grande escala. Este
método utiliza expansões em série de Taylor para aglomerar pontos
da discretização do contorno, de forma a reduzir o tempo
computacional necessário para completar a simulação. Ele se tornou
uma ferramenta bastante importante para os BEMs, pois eles
apresentam matrizes cheias e assimétricas, o que impossibilita a
utilização de técnicas de otimização de solução de sistemas de
equação. A aplicação do FMM ao BEM é bastante complexa e requer
muita manipulação matemática. Este trabalho apresenta uma
formulação do FMM que é independente da solução fundamental
utilizada pelo BEM, o Método Fast Multipole Generalizado (GFMM),
que se aplica a elementos de contorno curvos e de qualquer ordem.
Esta caracterÃstica é importante, já que os desenvolvimentos de
fast multipole encontrados na literatura se restringem apenas a
elementos constantes. Todos os aspectos são abordados neste
trabalho, partindo da sua base matemática, passando por validação
numérica, até a solução de problemas de potencial com muitos
milhões de graus de liberdade. A aplicação do GFMM a problemas de
potencial e elasticidade é discutida e validada, assim como os
desenvolvimentos necessários para a utilização do GFMM com o Método
HÃbrido Simplificado de Elementos de Contorno (SHBEM). Vários
resultados numéricos comprovam a eficiência e precisão do método
apresentado. A literatura propõe que o FMM pode reduzir o tempo de
execução do algoritmo do BEM de O(N2) para O(N), em que N é o
número de graus de liberdade do problema. É demonstrado que esta
redução é de fato possÃvel no contexto do GFMM, sem a necessidade
da utilização de qualquer técnica de otimização
computacional.
[en] The Fast Multipole Method (FMM) has been used
since the 1990s with the Boundary Elements Method (BEM) for the
simulation of large-scale problems. This method relies on Taylor
series expansions of the underlying fundamental solutions to
cluster the nodes on the discretised boundary of a domain, aiming
to reduce the computational time required to carry out the
simulation. It has become an important tool for the BEMs, as they
present matrices that are full and nonsymmetric, so that the
improvement of storage allocation and execution time is not a
simple task. The application of the FMM to the BEM ends up with a
very intricate code, and usually changing from one problem s
fundamental solution to another is not a simple matter. This work
presents a kernel-independent formulation of the FMM, here called
the General Fast Multipole Method (GFMM), which is also able to
deal with high order, curved boundary elements in a straightforward
manner. This is an important feature, as the fast multipole
implementations reported in the literature only apply to constant
elements. All necessary aspects of this method are presented,
starting with the mathematical basics of both FMM and BEM, carrying
out some numerical…
Advisors/Committee Members: NEY AUGUSTO DUMONT.
Subjects/Keywords: [pt] ELEMENTOS DE CONTORNO; [en] BOUNDARY ELEMENTS; [pt] METODOS VARIACIONAIS; [en] VARIATIONAL METHODS; [pt] METODO FAST MULTIPOLE; [en] FAST MULTIPOLE METHOD
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APA (6th Edition):
PEIXOTO, H. D. F. C. (2018). [en] A FAST MULTIPOLE METHOD FOR HIGH ORDER BOUNDARY
ELEMENTS. (Thesis). Pontifical Catholic University of Rio de Janeiro. Retrieved from http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=34740
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
PEIXOTO, HELVIO DE FARIAS COSTA. “[en] A FAST MULTIPOLE METHOD FOR HIGH ORDER BOUNDARY
ELEMENTS.” 2018. Thesis, Pontifical Catholic University of Rio de Janeiro. Accessed January 23, 2021.
http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=34740.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
PEIXOTO, HELVIO DE FARIAS COSTA. “[en] A FAST MULTIPOLE METHOD FOR HIGH ORDER BOUNDARY
ELEMENTS.” 2018. Web. 23 Jan 2021.
Vancouver:
PEIXOTO HDFC. [en] A FAST MULTIPOLE METHOD FOR HIGH ORDER BOUNDARY
ELEMENTS. [Internet] [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2018. [cited 2021 Jan 23].
Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=34740.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
PEIXOTO HDFC. [en] A FAST MULTIPOLE METHOD FOR HIGH ORDER BOUNDARY
ELEMENTS. [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2018. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=34740
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
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