subject:(Riemannian manifold)

McMaster University

1. Liang, Jiaping. DETECTION OF NARROW-BAND SONAR SIGNALS ON A RIEMANNIAN MANIFOLD.

Degree: MASc, 2015, McMaster University

►

We consider the problem of narrow-band signal detection in a passive sonar environment. The collected signals are passed to a fast Fourier Transform (FFT) delay-sum… (more)

Subjects/Keywords: RIEMANNIAN MANIFOLD; NARROW-BAND SONAR SIGNALS DETECTION

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Liang, J. (2015). DETECTION OF NARROW-BAND SONAR SIGNALS ON A RIEMANNIAN MANIFOLD. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/18100

Chicago Manual of Style (16^th Edition):

Liang, Jiaping. “DETECTION OF NARROW-BAND SONAR SIGNALS ON A RIEMANNIAN MANIFOLD.” 2015. Masters Thesis, McMaster University. Accessed March 07, 2021. http://hdl.handle.net/11375/18100.

MLA Handbook (7^th Edition):

Liang, Jiaping. “DETECTION OF NARROW-BAND SONAR SIGNALS ON A RIEMANNIAN MANIFOLD.” 2015. Web. 07 Mar 2021.

Vancouver:

Liang J. DETECTION OF NARROW-BAND SONAR SIGNALS ON A RIEMANNIAN MANIFOLD. [Internet] [Masters thesis]. McMaster University; 2015. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/11375/18100.

Council of Science Editors:

Liang J. DETECTION OF NARROW-BAND SONAR SIGNALS ON A RIEMANNIAN MANIFOLD. [Masters Thesis]. McMaster University; 2015. Available from: http://hdl.handle.net/11375/18100

University of Illinois – Chicago

2. Pajda-De La O, Jennifer. On the Law of Iterated Logarithms for Brownian Motion on Compact Manifolds.

Degree: 2016, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/20938

► Let M be a compact and smooth Riemannian manifold. Take a Brownian motion on the manifold. We take a family of measures defined by the… (more)

Subjects/Keywords: Law of Iterated Logarithm; Brownian Motion; Riemannian Manifold

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APA (6^th Edition):

Pajda-De La O, J. (2016). On the Law of Iterated Logarithms for Brownian Motion on Compact Manifolds. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/20938

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Pajda-De La O, Jennifer. “On the Law of Iterated Logarithms for Brownian Motion on Compact Manifolds.” 2016. Thesis, University of Illinois – Chicago. Accessed March 07, 2021. http://hdl.handle.net/10027/20938.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Pajda-De La O, Jennifer. “On the Law of Iterated Logarithms for Brownian Motion on Compact Manifolds.” 2016. Web. 07 Mar 2021.

Vancouver:

Pajda-De La O J. On the Law of Iterated Logarithms for Brownian Motion on Compact Manifolds. [Internet] [Thesis]. University of Illinois – Chicago; 2016. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10027/20938.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Pajda-De La O J. On the Law of Iterated Logarithms for Brownian Motion on Compact Manifolds. [Thesis]. University of Illinois – Chicago; 2016. Available from: http://hdl.handle.net/10027/20938

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Northeastern University

3. Zhang, Xikang. Classification of dynamics on Riemannian manifold.

Degree: PhD, Department of Electrical and Computer Engineering, 2018, Northeastern University

URL: http://hdl.handle.net/2047/D20290581

► Comparison and classification of temporal sequences is a key problem in action recognition, event detection and abnormal activity detection. The current methods either fail to… (more)

Subjects/Keywords: dynamics; efficient; embedding; motion segmentation; Riemannian manifold; switched system identification

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APA (6^th Edition):

Zhang, X. (2018). Classification of dynamics on Riemannian manifold. (Doctoral Dissertation). Northeastern University. Retrieved from http://hdl.handle.net/2047/D20290581

Chicago Manual of Style (16^th Edition):

Zhang, Xikang. “Classification of dynamics on Riemannian manifold.” 2018. Doctoral Dissertation, Northeastern University. Accessed March 07, 2021. http://hdl.handle.net/2047/D20290581.

MLA Handbook (7^th Edition):

Zhang, Xikang. “Classification of dynamics on Riemannian manifold.” 2018. Web. 07 Mar 2021.

Vancouver:

Zhang X. Classification of dynamics on Riemannian manifold. [Internet] [Doctoral dissertation]. Northeastern University; 2018. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/2047/D20290581.

Council of Science Editors:

Zhang X. Classification of dynamics on Riemannian manifold. [Doctoral Dissertation]. Northeastern University; 2018. Available from: http://hdl.handle.net/2047/D20290581

Université Catholique de Louvain

4. Chau, Van Vinh. Advances in spectral analysis for multivariate, nonstationary and replicated time series.

Degree: 2018, Université Catholique de Louvain

URL: http://hdl.handle.net/2078.1/203016

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Spectral analysis of time series refers to the analysis of a time series in terms of its Fourier or power spectrum to study cross-dependencies or… (more)

Subjects/Keywords: Fourier Spectrum; Wavelets; Nonparametric Regression; Riemannian manifold; Data Depth; Time Series

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APA (6^th Edition):

Chau, V. V. (2018). Advances in spectral analysis for multivariate, nonstationary and replicated time series. (Thesis). Université Catholique de Louvain. Retrieved from http://hdl.handle.net/2078.1/203016

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Chau, Van Vinh. “Advances in spectral analysis for multivariate, nonstationary and replicated time series.” 2018. Thesis, Université Catholique de Louvain. Accessed March 07, 2021. http://hdl.handle.net/2078.1/203016.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Chau, Van Vinh. “Advances in spectral analysis for multivariate, nonstationary and replicated time series.” 2018. Web. 07 Mar 2021.

Vancouver:

Chau VV. Advances in spectral analysis for multivariate, nonstationary and replicated time series. [Internet] [Thesis]. Université Catholique de Louvain; 2018. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/2078.1/203016.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chau VV. Advances in spectral analysis for multivariate, nonstationary and replicated time series. [Thesis]. Université Catholique de Louvain; 2018. Available from: http://hdl.handle.net/2078.1/203016

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Delft University of Technology

5. Versendaal, R. (author). The Riesz transform on a complete Riemannian manifold with Ricci curvature bounded from below.

Degree: 2016, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:878a94cc-5839-42f4-9ccf-ff48742526ef

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We study the Riesz transform and Hodge-Dirac operator on a complete Riemannian manifold with Ricci curvature bounded from below. We define the Hodge-Dirac operator ∏… (more)

Subjects/Keywords: Riesz transform; Riemannian manifold; Hodge-Dirac operator; Ricci curvature

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APA (6^th Edition):

Versendaal, R. (. (2016). The Riesz transform on a complete Riemannian manifold with Ricci curvature bounded from below. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:878a94cc-5839-42f4-9ccf-ff48742526ef

Chicago Manual of Style (16^th Edition):

Versendaal, R (author). “The Riesz transform on a complete Riemannian manifold with Ricci curvature bounded from below.” 2016. Masters Thesis, Delft University of Technology. Accessed March 07, 2021. http://resolver.tudelft.nl/uuid:878a94cc-5839-42f4-9ccf-ff48742526ef.

MLA Handbook (7^th Edition):

Versendaal, R (author). “The Riesz transform on a complete Riemannian manifold with Ricci curvature bounded from below.” 2016. Web. 07 Mar 2021.

Vancouver:

Versendaal R(. The Riesz transform on a complete Riemannian manifold with Ricci curvature bounded from below. [Internet] [Masters thesis]. Delft University of Technology; 2016. [cited 2021 Mar 07]. Available from: http://resolver.tudelft.nl/uuid:878a94cc-5839-42f4-9ccf-ff48742526ef.

Council of Science Editors:

Versendaal R(. The Riesz transform on a complete Riemannian manifold with Ricci curvature bounded from below. [Masters Thesis]. Delft University of Technology; 2016. Available from: http://resolver.tudelft.nl/uuid:878a94cc-5839-42f4-9ccf-ff48742526ef

Loughborough University

6. Omenyi, Louis Okechukwu. On the second variation of the spectral zeta function of the Laplacian on homogeneous Riemanniann manifolds.

Degree: PhD, 2014, Loughborough University

URL: http://hdl.handle.net/2134/16167

► The spectral zeta function, introduced by Minakshisundaram and Pleijel in [36] and denoted by ζg(s), encodes important spectral information for the Laplacian on Riemannian manifolds.… (more)

Subjects/Keywords: 516.3; Spectral zeta function; Riemannian manifold; Meromorphic continuation; Harmonic analysis

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APA (6^th Edition):

Omenyi, L. O. (2014). On the second variation of the spectral zeta function of the Laplacian on homogeneous Riemanniann manifolds. (Doctoral Dissertation). Loughborough University. Retrieved from http://hdl.handle.net/2134/16167

Chicago Manual of Style (16^th Edition):

Omenyi, Louis Okechukwu. “On the second variation of the spectral zeta function of the Laplacian on homogeneous Riemanniann manifolds.” 2014. Doctoral Dissertation, Loughborough University. Accessed March 07, 2021. http://hdl.handle.net/2134/16167.

MLA Handbook (7^th Edition):

Omenyi, Louis Okechukwu. “On the second variation of the spectral zeta function of the Laplacian on homogeneous Riemanniann manifolds.” 2014. Web. 07 Mar 2021.

Vancouver:

Omenyi LO. On the second variation of the spectral zeta function of the Laplacian on homogeneous Riemanniann manifolds. [Internet] [Doctoral dissertation]. Loughborough University; 2014. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/2134/16167.

Council of Science Editors:

Omenyi LO. On the second variation of the spectral zeta function of the Laplacian on homogeneous Riemanniann manifolds. [Doctoral Dissertation]. Loughborough University; 2014. Available from: http://hdl.handle.net/2134/16167

University of Waterloo

7. Li, Xiao-Bo. Protein Structure Elastic Network Models and the Rank 3 Positive Semidefinite Matrix Manifold.

Degree: 2019, University of Waterloo

URL: http://hdl.handle.net/10012/14331

► This thesis is a contribution to the study of protein dynamics using elastic network models (ENMs). An ENM is an abstraction of a protein structure… (more)

▼ This thesis is a contribution to the study of protein dynamics using elastic network models (ENMs). An ENM is an abstraction of a protein structure where inter-atomic interactions are assumed to be modelled by a Hookean potential energy which is a function if inter-atomic distances. This model has been studied by various authors, and despite being a very simple model, can nonetheless provide a realistic understanding of protein dynamics. For example, it was shown by Tirion, that the Hookean potential energy can reproduce the normal mode fluctuations of the more complicated semi-empirical potential. In addition, it was shown by Tekpinar and Zheng that an ENM can correctly model the order of local conformational changes before global conformational changes during ATP-driven conformational changes. The purpose of this thesis is to provide a second mathematical formulation for modelling ENMs. This thesis suggests removing the square-root in the Hookean potential which leads to a positive semidefinite (PSD) potential that is a function of quadrances rather than distances. There are many similarities between the two approaches, but also many differences. One main difference is PSD matrices are linearly related to quadrance, the square of distance, which opens the way to model the PSD potential using perceptrons whose weight matrix is a rank 3 PSD matrix. This interesting consequence is left as a topic of future research. The PSD potential is just as appropriate for modelling ENMs as observed by the following two agreements: The PSD potential produces normal mode fluctuations that agree with the Hookean potential introduced by Tirion. This agreement suggests both potentials provide the same information about a protein structure's flexibility. The generalization of the Hookean iENM potential (introduced by Tekpinar and Zheng) to the PSD iENM potential also interpolates the local conformational changes before the global conformational changes, in agreement with the original Hookean observations. Recall that the equations of motion in classical mechanics is formulated using an abstract Riemannian manifold. This abstraction gives modellers the flexibility to consider different Riemannian manifolds appropriate to the problem. After the introduction of the Hookean potential, the study of protein dynamics still uses the 3n dimensional Euclidean space as the Riemannian manifold, the same Riemannian manifold used by the semi-empirical potential. This is because both the semi-empirical potential and the Hookean potential assume the atomic coordinates of a protein structure are represented by a 3n by 1 vector. However, with the introduction of the PSD potential, the protein structure's atomic coordinates are represented as a point on the rank 3 n by n PSD matrix manifold. Consequently, a new Riemannian manifold for modelling protein dynamics has been proposed. In order to model protein dynamics on the rank 3 PSD matrix manifold, the equations of motion needs to be defined. This thesis presents the…

Subjects/Keywords: protein structure; positive semidefinite; Gram matrix; Euclidean distance matrix; elastic network model; matrix manifold optimization; Riemannian manifold

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APA (6^th Edition):

Li, X. (2019). Protein Structure Elastic Network Models and the Rank 3 Positive Semidefinite Matrix Manifold. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/14331

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Li, Xiao-Bo. “Protein Structure Elastic Network Models and the Rank 3 Positive Semidefinite Matrix Manifold.” 2019. Thesis, University of Waterloo. Accessed March 07, 2021. http://hdl.handle.net/10012/14331.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Li, Xiao-Bo. “Protein Structure Elastic Network Models and the Rank 3 Positive Semidefinite Matrix Manifold.” 2019. Web. 07 Mar 2021.

Vancouver:

Li X. Protein Structure Elastic Network Models and the Rank 3 Positive Semidefinite Matrix Manifold. [Internet] [Thesis]. University of Waterloo; 2019. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10012/14331.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Li X. Protein Structure Elastic Network Models and the Rank 3 Positive Semidefinite Matrix Manifold. [Thesis]. University of Waterloo; 2019. Available from: http://hdl.handle.net/10012/14331

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Universidade do Rio Grande do Sul

8. Pereira, Luiz Felipe Licks. Gráficos de curvatura média constante em H² X R com bordo em planos paralelos.

Degree: 2016, Universidade do Rio Grande do Sul

URL: http://hdl.handle.net/10183/149113

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Neste trabalho apresentamos condições suficientes para a existência de gráficos de curvatura média constante (CMC) com bordo em dois planos paralelos. Também são feitas estimativas… (more)

Subjects/Keywords: Gráficos de curvatura média constante; Mean curvature; Superficies; Surfaces; Geometria; Geometry; Riemannian manifold

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APA (6^th Edition):

Pereira, L. F. L. (2016). Gráficos de curvatura média constante em H² X R com bordo em planos paralelos. (Thesis). Universidade do Rio Grande do Sul. Retrieved from http://hdl.handle.net/10183/149113

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Pereira, Luiz Felipe Licks. “Gráficos de curvatura média constante em H² X R com bordo em planos paralelos.” 2016. Thesis, Universidade do Rio Grande do Sul. Accessed March 07, 2021. http://hdl.handle.net/10183/149113.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Pereira, Luiz Felipe Licks. “Gráficos de curvatura média constante em H² X R com bordo em planos paralelos.” 2016. Web. 07 Mar 2021.

Vancouver:

Pereira LFL. Gráficos de curvatura média constante em H² X R com bordo em planos paralelos. [Internet] [Thesis]. Universidade do Rio Grande do Sul; 2016. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10183/149113.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Pereira LFL. Gráficos de curvatura média constante em H² X R com bordo em planos paralelos. [Thesis]. Universidade do Rio Grande do Sul; 2016. Available from: http://hdl.handle.net/10183/149113

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Delft University of Technology

9. Corstanje, Marc (author). Likelihood-based Inference on Nonlinear spaces: Using Diffusion Processes on Riemannian Manifolds.

Degree: 2019, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:7a7fad85-d29d-414e-a254-7b864c4e5042

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When data in higher dimensions with a certain constraint on it, say a set of locations on a sphere, is encountered, some classical statistical analysis… (more)

Subjects/Keywords: Diffusion Process; Riemannian manifold; Diffusion Bridge; Stochastic Differential Equations; Stochastic Simulation; Geometric Statistics

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APA (6^th Edition):

Corstanje, M. (. (2019). Likelihood-based Inference on Nonlinear spaces: Using Diffusion Processes on Riemannian Manifolds. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:7a7fad85-d29d-414e-a254-7b864c4e5042

Chicago Manual of Style (16^th Edition):

Corstanje, Marc (author). “Likelihood-based Inference on Nonlinear spaces: Using Diffusion Processes on Riemannian Manifolds.” 2019. Masters Thesis, Delft University of Technology. Accessed March 07, 2021. http://resolver.tudelft.nl/uuid:7a7fad85-d29d-414e-a254-7b864c4e5042.

MLA Handbook (7^th Edition):

Corstanje, Marc (author). “Likelihood-based Inference on Nonlinear spaces: Using Diffusion Processes on Riemannian Manifolds.” 2019. Web. 07 Mar 2021.

Vancouver:

Corstanje M(. Likelihood-based Inference on Nonlinear spaces: Using Diffusion Processes on Riemannian Manifolds. [Internet] [Masters thesis]. Delft University of Technology; 2019. [cited 2021 Mar 07]. Available from: http://resolver.tudelft.nl/uuid:7a7fad85-d29d-414e-a254-7b864c4e5042.

Council of Science Editors:

Corstanje M(. Likelihood-based Inference on Nonlinear spaces: Using Diffusion Processes on Riemannian Manifolds. [Masters Thesis]. Delft University of Technology; 2019. Available from: http://resolver.tudelft.nl/uuid:7a7fad85-d29d-414e-a254-7b864c4e5042

Delft University of Technology

10. van Ginkel, Bart (author). Invariance principle and hydrodynamic limits on Riemannian manifolds.

Degree: 2017, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:e6258e4f-9b41-4eb2-9f41-adcbfb689694

► In this report we study Markov processes on compact and connected Riemannian manifolds. We define a random walk on such manifolds and give a direct… (more)

▼ In this report we study Markov processes on compact and connected Riemannian manifolds. We define a random walk on such manifolds and give a direct proof of the invariance principle. This principle says that under some conditions on the jumping distributions (i.e. the distributions of single steps), the random walk converges to Brownian motion when space is scaled by 1/N, time by N² and N tends to infinity (which has been shown with more general methods by Jorgensen and by Blum). To prove this, we show convergence of the generators on the set of smooth functions and we apply the Trotter-Kurtz theorem (as has been done by Blum, in a rather sketchy way and in a slightly different setting). We also show convergence of the corresponding Dirichlet forms. Then we show that the conditions on the jumping distributions are satisfied if they are compactly supported and have mean 0 and a covariance matrix which is invariant under orthogonal transformations. Next, we define random grids on a Riemannian manifold and we define random walks on them. We show that their Dirichlet forms converge to the Dirichlet form of Brownian motion, using the results above. We also prove a result that is a bit weaker than convergence of the generators in this case. Finally, these grids allow us to define the Symmetric Exclusion Process (SEP) on a manifold. Using the convergence results above, we follow the line of a proof of Seppäläinen to show that the hydrodynamic limit of the SEP satisfies the heat equation. Some details still need to be filled in, but we believe that this method will allow us to study interacting particle systems and their hydrodynamic limits on Riemannian manifolds. Before all of this we start with an introduction to Markov processes, their semigroups and generators. In particular we focus on time-reversible (or symmetric) processes and the Dirichlet form with its properties. We also give an introduction to Riemannian manifolds and related notions. Advisors/Committee Members: Redig, Frank (mentor), van Neerven, Jan (graduation committee), Ruszel, Wioletta (graduation committee), Delft University of Technology (degree granting institution).

Subjects/Keywords: Riemannian manifold; invariance principle; hydrodynamic limit; geodesic random walk; interacting particle system

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APA (6^th Edition):

van Ginkel, B. (. (2017). Invariance principle and hydrodynamic limits on Riemannian manifolds. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:e6258e4f-9b41-4eb2-9f41-adcbfb689694

Chicago Manual of Style (16^th Edition):

van Ginkel, Bart (author). “Invariance principle and hydrodynamic limits on Riemannian manifolds.” 2017. Masters Thesis, Delft University of Technology. Accessed March 07, 2021. http://resolver.tudelft.nl/uuid:e6258e4f-9b41-4eb2-9f41-adcbfb689694.

MLA Handbook (7^th Edition):

van Ginkel, Bart (author). “Invariance principle and hydrodynamic limits on Riemannian manifolds.” 2017. Web. 07 Mar 2021.

Vancouver:

van Ginkel B(. Invariance principle and hydrodynamic limits on Riemannian manifolds. [Internet] [Masters thesis]. Delft University of Technology; 2017. [cited 2021 Mar 07]. Available from: http://resolver.tudelft.nl/uuid:e6258e4f-9b41-4eb2-9f41-adcbfb689694.

Council of Science Editors:

van Ginkel B(. Invariance principle and hydrodynamic limits on Riemannian manifolds. [Masters Thesis]. Delft University of Technology; 2017. Available from: http://resolver.tudelft.nl/uuid:e6258e4f-9b41-4eb2-9f41-adcbfb689694

Université Catholique de Louvain

11. Gousenbourger, Pierre-Yves. Interpolation and fitting on Riemannian manifolds.

Degree: 2020, Université Catholique de Louvain

URL: http://hdl.handle.net/2078.1/240620

►

The access to constantly increasing computational capacities has revolutionized the way engineering is seen. We are now able to produce a large quantity of data,… (more)

▼

The access to constantly increasing computational capacities has revolutionized the way engineering is seen. We are now able to produce a large quantity of data, thanks to cheap sensors. However, processing such data remains costly both in computational time and in energy. One of the reasons is that the structure of the data is often omitted or unknown. The search space becomes so large that finding the solution to simple problems often turns out to be finding a needle in a haystack. A classical problem in data processing is called the “fitting problem”. It consists in fitting a d-dimensional curve to a set of data points associated to d parameters. The curve must pass sufficiently close to the data points while being regular enough. When the underlying structure of the data points (i.e., the manifold) is known, one can impose to the curve to preserve this structure (i.e., to remain on the manifold), such that the search space is drastically reduced. The goal of this thesis is to develop methods to (approximately) solve this fitting problem; the bet is to require “less” (less computational capabilities, power, storage, time) by leveraging “more” knowledge on the search space. The objective is the following: provide a toolbox that produces a differentiable fitting curve to data points on manifolds, based on very few and simple geometric tools, at low computational cost and storage capacity, all this while maintaining an acceptable quality of the solutions. The algorithms are applied to different illustrative problems. In 3D shape reconstruction, the data points are organs contours acquired via MRI, and the parameter is the acquisition depth; in wind fields estimation, the data points belong to the manifold of positive semi-definite matrices of given rank, and the parameters are the prevalent wind amplitudes and angles. We also show the performances of our algorithms in applications for parametric model order reduction.

(FSA - Sciences de l'ingénieur) – UCL, 2020

Advisors/Committee Members: UCL - SST/ICTM - Institute of Information and Communication Technologies, Electronics and Applied Mathematics, UCL - SST/ICTM/ELEN - Pôle en ingénierie électrique, UCL - SST/ICTM/INMA - Pôle en ingénierie mathématique, UCL - Ecole Polytechnique de Louvain, Absil, Pierre-Antoine, Jacques, Laurent, Remacle, Jean-François, Peyré, Gabriel, Wirth, Benedikt, Raskin, Jean-Pierre.

Subjects/Keywords: Riemannian manifolds; Rotations; Shapes; Differentiability; Manifold; Numerical analysis; Fitting; Interpolation; Surface; Bézier curves; Bézier

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gousenbourger, P. (2020). Interpolation and fitting on Riemannian manifolds. (Thesis). Université Catholique de Louvain. Retrieved from http://hdl.handle.net/2078.1/240620

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Gousenbourger, Pierre-Yves. “Interpolation and fitting on Riemannian manifolds.” 2020. Thesis, Université Catholique de Louvain. Accessed March 07, 2021. http://hdl.handle.net/2078.1/240620.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Gousenbourger, Pierre-Yves. “Interpolation and fitting on Riemannian manifolds.” 2020. Web. 07 Mar 2021.

Vancouver:

Gousenbourger P. Interpolation and fitting on Riemannian manifolds. [Internet] [Thesis]. Université Catholique de Louvain; 2020. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/2078.1/240620.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Gousenbourger P. Interpolation and fitting on Riemannian manifolds. [Thesis]. Université Catholique de Louvain; 2020. Available from: http://hdl.handle.net/2078.1/240620

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

12. Chapron, Aurélie. Mosaïques de Poisson-Voronoï sur une variété riemannienne : Poisson-Voronoi tessellation in a Riemannian manifold.

Degree: Docteur es, Mathématiques appliquées et applications des mathématiques, 2018, Université Paris X – Nanterre

URL: http://www.theses.fr/2018PA100098

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Une mosaïque de Poisson-Voronoï est une partition aléatoire de l'espace euclidien en polyèdres, appelés cellules, obtenue à partir d'un ensemble aléatoire discret de points appelés… (more)

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Une mosaïque de Poisson-Voronoï est une partition aléatoire de l'espace euclidien en polyèdres, appelés cellules, obtenue à partir d'un ensemble aléatoire discret de points appelés germes. A chaque germe correspond une cellule, qui est l'ensemble des points de l'espace qui sont plus proches de ce germes que des autres germes. Ces modèles sont souvent utilisées dans divers domaines tels que la biologie, les télécommunications, l'astronomie, etc. Les caractéristiques de ces mosaïques et des cellules associées ont été largement étudiées dans l'espace euclidien mais les travaux sur les mosaïques de Voronoï dans un cadre non-euclidien sont rares.Dans cette thèse, on étend la définition de mosaïque de Voronoï à une variétériemannienne de dimension finie et on s'intéresse aux caractéristiques des cellules associées. Plus précisément, on mesure dans un premier temps l'influence que peut avoir la géométrie locale de la variété, c'est-à-dire les courbures sur les caractéristiques moyennes d'une cellule, comme son volume ou son nombre de sommets, en calculant des développements asymptotiques des ces caractéristiques moyennes à grande intensité. Dans un deuxième temps, on s'interroge sur la possibilité de retrouver la géométrie locale de la variété à partir des caractéristiques combinatoires de la mosaïque sur la variété. En particulier, on établit desthéorèmes limites, quand l'intensité du processus des germes tend vers l'infini, pour le nombre de sommets de la mosaïque dans une fenêtre, ce qui permet de construire un estimateur de la courbure et d'en donner quelques propriétés.Les principaux résultats de cette thèse reposent sur la combinaison de méthodesprobabilistes et de techniques issues de la géométrie différentielle.

A Poisson-Voronoi tessellation is a random partition of the Euclidean space intopolytopes, called cells, obtained from a discrete set of points called germs. To each germ corresponds a cell which is the set of the points of the space which are closer to this germ than to the other germs. These models are often used in several domains such as biology, telecommunication, astronomy, etc. The caracteristics of these tessellations and cells have been widely studied in the Euclidean space but only a few works concerns non-Euclidean Voronoi tessellation. In this thesis, we extend the definition of Poisson-Voronoi tessellation to a Riemannian manifold with finite dimension and we study the caracteristics of the associated cells. More precisely, we first measure the influence of the local geometry of the manifold, namely the curvatures, on the caracteristics of the cells, e.g. the mean volume or the mean number of vertices. Second, we aim to recover the local geometry of the manifold from the combinatorial properties of the tessellation on the manifolds. In particular, we establish limit theorems for the number of vertices of the tessellation, when the intensity of the process of the germs tends to infinity. This leads to the construction of an estimator of the curvature of the manifold and makes it possible to…

Advisors/Committee Members: Enriquez, Nathanaël (thesis director), Calka, Pierre (thesis director).

Subjects/Keywords: Mosaïque de Voronoi; Géométrie aléatoire; Géométrie riemannienne; Théorème limite; Variété riemannienne; Formule de Blaschke- Petkantchin; Voronoi tessellation; Stochastic geometry; Riemannian geometry; Limit theorem; Riemannian manifold; Blaschke- Petkantschin formula

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Chapron, A. (2018). Mosaïques de Poisson-Voronoï sur une variété riemannienne : Poisson-Voronoi tessellation in a Riemannian manifold. (Doctoral Dissertation). Université Paris X – Nanterre. Retrieved from http://www.theses.fr/2018PA100098

Chicago Manual of Style (16^th Edition):

Chapron, Aurélie. “Mosaïques de Poisson-Voronoï sur une variété riemannienne : Poisson-Voronoi tessellation in a Riemannian manifold.” 2018. Doctoral Dissertation, Université Paris X – Nanterre. Accessed March 07, 2021. http://www.theses.fr/2018PA100098.

MLA Handbook (7^th Edition):

Chapron, Aurélie. “Mosaïques de Poisson-Voronoï sur une variété riemannienne : Poisson-Voronoi tessellation in a Riemannian manifold.” 2018. Web. 07 Mar 2021.

Vancouver:

Chapron A. Mosaïques de Poisson-Voronoï sur une variété riemannienne : Poisson-Voronoi tessellation in a Riemannian manifold. [Internet] [Doctoral dissertation]. Université Paris X – Nanterre; 2018. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2018PA100098.

Council of Science Editors:

Chapron A. Mosaïques de Poisson-Voronoï sur une variété riemannienne : Poisson-Voronoi tessellation in a Riemannian manifold. [Doctoral Dissertation]. Université Paris X – Nanterre; 2018. Available from: http://www.theses.fr/2018PA100098

University of Kentucky

13. Wells, Matthew J. ASPECTS OF THE GEOMETRY OF METRICAL CONNECTIONS.

Degree: 2009, University of Kentucky

URL: https://uknowledge.uky.edu/gradschool_diss/749

► Differential geometry is about space (a manifold) and a geometric structure on that space. In Riemann’s lecture (see [17]), he stated that “Thus arises the… (more)

Subjects/Keywords: Riemannian Geometry|metrical connections|Riemannian curvature|compact 2-manifold|Gauss-Bonnet Theorem; Mathematics

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APA (6^th Edition):

Wells, M. J. (2009). ASPECTS OF THE GEOMETRY OF METRICAL CONNECTIONS. (Doctoral Dissertation). University of Kentucky. Retrieved from https://uknowledge.uky.edu/gradschool_diss/749

Chicago Manual of Style (16^th Edition):

Wells, Matthew J. “ASPECTS OF THE GEOMETRY OF METRICAL CONNECTIONS.” 2009. Doctoral Dissertation, University of Kentucky. Accessed March 07, 2021. https://uknowledge.uky.edu/gradschool_diss/749.

MLA Handbook (7^th Edition):

Wells, Matthew J. “ASPECTS OF THE GEOMETRY OF METRICAL CONNECTIONS.” 2009. Web. 07 Mar 2021.

Vancouver:

Wells MJ. ASPECTS OF THE GEOMETRY OF METRICAL CONNECTIONS. [Internet] [Doctoral dissertation]. University of Kentucky; 2009. [cited 2021 Mar 07]. Available from: https://uknowledge.uky.edu/gradschool_diss/749.

Council of Science Editors:

Wells MJ. ASPECTS OF THE GEOMETRY OF METRICAL CONNECTIONS. [Doctoral Dissertation]. University of Kentucky; 2009. Available from: https://uknowledge.uky.edu/gradschool_diss/749

14. Rondinelle Marcolino Batista. Rigidez de solitons gradiente.

Degree: Master, 2010, Universidade Federal do Ceará

URL: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11142 ;

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Nosso objetivo nesse trabalho Ã apresentar um teorema que caracteriza os solitons gradiente rÃgidos para caso nÃo compacto. Como aplicaÃÃo provaremos que os solitons gradiente… (more)

Subjects/Keywords: GEOMETRIA DIFERENCIAL; variedades completas; curvatura escalar constante; complete manifold; constant scalar curvature; Variedades riemanianas; Riemannian manifolds

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APA (6^th Edition):

Batista, R. M. (2010). Rigidez de solitons gradiente. (Masters Thesis). Universidade Federal do Ceará. Retrieved from http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11142 ;

Chicago Manual of Style (16^th Edition):

Batista, Rondinelle Marcolino. “Rigidez de solitons gradiente.” 2010. Masters Thesis, Universidade Federal do Ceará. Accessed March 07, 2021. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11142 ;.

MLA Handbook (7^th Edition):

Batista, Rondinelle Marcolino. “Rigidez de solitons gradiente.” 2010. Web. 07 Mar 2021.

Vancouver:

Batista RM. Rigidez de solitons gradiente. [Internet] [Masters thesis]. Universidade Federal do Ceará 2010. [cited 2021 Mar 07]. Available from: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11142 ;.

Council of Science Editors:

Batista RM. Rigidez de solitons gradiente. [Masters Thesis]. Universidade Federal do Ceará 2010. Available from: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11142 ;

15. Le Brigant, Alice. Probability on the spaces of curves and the associated metric spaces via information geometry; radar applications : Probabilités sur les espaces de chemins et dans les espaces métriques associés via la géométrie de l’information ; applications radar.

Degree: Docteur es, Mathématiques appliquées et calcul scientifique, 2017, Bordeaux

URL: http://www.theses.fr/2017BORD0640

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Nous nous intéressons à la comparaison de formes de courbes lisses prenant leurs valeurs dans une variété riemannienne M. Dans ce but, nous introduisons une… (more)

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Nous nous intéressons à la comparaison de formes de courbes lisses prenant leurs valeurs dans une variété riemannienne M. Dans ce but, nous introduisons une métrique riemannienne invariante par reparamétrisations sur la variété de dimension infinie des immersions lisses dans M. L’équation géodésique est donnée et les géodésiques entre deux courbes sont construites par tir géodésique. La structure quotient induite par l’action du groupe des reparamétrisations sur l’espace des courbes est étudiée. À l’aide d’une décomposition canonique d’un chemin dans un fibré principal, nous proposons un algorithme qui construit la géodésique horizontale entre deux courbes et qui fournit un matching optimal. Dans un deuxième temps, nous introduisons une discrétisation de notre modèle qui est elle-même une structure riemannienne sur la variété de dimension finie Mn+1 des "courbes discrètes" définies par n + 1 points, où M est de courbure sectionnelle constante. Nous montrons la convergence du modèle discret vers le modèle continu, et nous étudions la géométrie induite. Des résultats de simulations dans la sphère, le plan et le demi-plan hyperbolique sont donnés. Enfin, nous donnons le contexte mathématique nécessaire à l’application de l’étude de formes dans une variété au traitement statistique du signal radar, où des signaux radars localement stationnaires sont représentés par des courbes dans le polydisque de Poincaré via la géométrie de l’information.

We are concerned with the comparison of the shapes of open smooth curves that take their values in a Riemannian manifold M. To this end, we introduce a reparameterization invariant Riemannian metric on the infinite-dimensional manifold of these curves, modeled by smooth immersions in M. We derive the geodesic equation and solve the boundary value problem using geodesic shooting. The quotient structure induced by the action of the reparametrization group on the space of curves is studied. Using a canonical decomposition of a path in a principal bundle, we propose an algorithm that computes the horizontal geodesic between two curves and yields an optimal matching. In a second step, restricting to base manifolds of constant sectional curvature, we introduce a detailed discretization of the Riemannian structure on the space of smooth curves, which is itself a Riemannian metric on the finite-dimensional manifold Mn+1 of "discrete curves" given by n + 1 points. We show the convergence of the discrete model to the continuous model, and study the induced geometry. We show results of simulations in the sphere, the plane, and the hyperbolic halfplane. Finally, we give the necessary framework to apply shape analysis of manifold-valued curves to radar signal processing, where locally stationary radar signals are represented by curves in the Poincaré polydisk using information geometry.

Advisors/Committee Members: Arnaudon, Marc (thesis director), Barbaresco, Frédéric (thesis director).

Subjects/Keywords: Étude de formes; Géométrie de l’information; Matching entre courbes; Variété riemannienne; Shape analysis; Information geometry; Optimal matching between curves; Riemannian manifold

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APA (6^th Edition):

Le Brigant, A. (2017). Probability on the spaces of curves and the associated metric spaces via information geometry; radar applications : Probabilités sur les espaces de chemins et dans les espaces métriques associés via la géométrie de l’information ; applications radar. (Doctoral Dissertation). Bordeaux. Retrieved from http://www.theses.fr/2017BORD0640

Chicago Manual of Style (16^th Edition):

Le Brigant, Alice. “Probability on the spaces of curves and the associated metric spaces via information geometry; radar applications : Probabilités sur les espaces de chemins et dans les espaces métriques associés via la géométrie de l’information ; applications radar.” 2017. Doctoral Dissertation, Bordeaux. Accessed March 07, 2021. http://www.theses.fr/2017BORD0640.

MLA Handbook (7^th Edition):

Le Brigant, Alice. “Probability on the spaces of curves and the associated metric spaces via information geometry; radar applications : Probabilités sur les espaces de chemins et dans les espaces métriques associés via la géométrie de l’information ; applications radar.” 2017. Web. 07 Mar 2021.

Vancouver:

Le Brigant A. Probability on the spaces of curves and the associated metric spaces via information geometry; radar applications : Probabilités sur les espaces de chemins et dans les espaces métriques associés via la géométrie de l’information ; applications radar. [Internet] [Doctoral dissertation]. Bordeaux; 2017. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2017BORD0640.

Council of Science Editors:

Le Brigant A. Probability on the spaces of curves and the associated metric spaces via information geometry; radar applications : Probabilités sur les espaces de chemins et dans les espaces métriques associés via la géométrie de l’information ; applications radar. [Doctoral Dissertation]. Bordeaux; 2017. Available from: http://www.theses.fr/2017BORD0640

Brigham Young University

16. Ready, Bryce Benson. Filtering Techniques for Pose Estimation with Applications to Unmanned Air Vehicles.

Degree: PhD, 2012, Brigham Young University

URL: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4489&context=etd

► This work presents two novel methods of estimating the state of a dynamic system in a Kalman Filtering framework. The first is an application specific… (more)

Subjects/Keywords: Riemannian manifold; Kalman filter; unmanned air vehicles; homography; image registration; direct image registration; visual odometry; Electrical and Computer Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ready, B. B. (2012). Filtering Techniques for Pose Estimation with Applications to Unmanned Air Vehicles. (Doctoral Dissertation). Brigham Young University. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4489&context=etd

Chicago Manual of Style (16^th Edition):

Ready, Bryce Benson. “Filtering Techniques for Pose Estimation with Applications to Unmanned Air Vehicles.” 2012. Doctoral Dissertation, Brigham Young University. Accessed March 07, 2021. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4489&context=etd.

MLA Handbook (7^th Edition):

Ready, Bryce Benson. “Filtering Techniques for Pose Estimation with Applications to Unmanned Air Vehicles.” 2012. Web. 07 Mar 2021.

Vancouver:

Ready BB. Filtering Techniques for Pose Estimation with Applications to Unmanned Air Vehicles. [Internet] [Doctoral dissertation]. Brigham Young University; 2012. [cited 2021 Mar 07]. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4489&context=etd.

Council of Science Editors:

Ready BB. Filtering Techniques for Pose Estimation with Applications to Unmanned Air Vehicles. [Doctoral Dissertation]. Brigham Young University; 2012. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=4489&context=etd

University of Colorado

17. Tembarai Krishnamachari, Rajesh. A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback.

Degree: PhD, Electrical, Computer & Energy Engineering, 2011, University of Colorado

URL: https://scholar.colorado.edu/ecen_gradetds/38

► We study the performance of multiple-antenna systems under finite-rate feedback of some function of the current channel realization from a channel-aware receiver to the… (more)

▼ We study the performance of multiple-antenna systems under finite-rate feedback of some function of the current channel realization from a channel-aware receiver to the transmitter. Our analysis is based on a novel geometric paradigm whereby the feedback information is modeled as a source distributed over a Riemannian manifold. While the right singular vectors of the channel matrix and the subspace spanned by them are located on the traditional Stiefel and Grassmann surfaces, the optimal input covariance matrix is located on a new manifold of positive semi-definite matrices - specified by rank and trace constraints - called the Pn manifold. The geometry of these three manifolds is studied in detail; in particular, the precise series expansion for the volume of geodesic balls over the Grassmann and Stiefel manifolds is obtained. Using these geometric results, the distortion incurred in quantizing sources using either a sphere-packing or a random code over an arbitrary manifold is quantified. Perturbative expansions are used to evaluate the susceptibility of the ergodic information rate to the quality of feedback information, and thereby to obtain the tradeoff of the achievable rate with the number of feedback bits employed. For a given system strategy, the gap between the achievable rates in the infinite and finite-rate feedback cases is shown to be O(2^-\frac{2N_f{N}}) for Grassmann feedback and O(2^-\frac{N_f{N}}) for other cases, where N is the dimension of the manifold used for quantization and N_f is the number of bits used by the receiver per block for feedback. The geometric framework developed enables the results to hold for arbitrary distributions of the channel matrix and extends to all covariance computation strategies including, waterfilling in the short-term/long-term power constraint case, antenna selection and other rank-limited scenarios that could not be analyzed using previous probabilistic approaches. Advisors/Committee Members: Mahesh K. Varanasi, Youjian(Eugene) Liu, Shannon M. Hughes.

Subjects/Keywords: Finite-rate Feedback; Grassmann/Stiefel Manifold; Information Theory; MIMO; Riemannian Geometry; Wireless Communications; Electrical and Computer Engineering; Mathematics

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APA (6^th Edition):

Tembarai Krishnamachari, R. (2011). A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/ecen_gradetds/38

Chicago Manual of Style (16^th Edition):

Tembarai Krishnamachari, Rajesh. “A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback.” 2011. Doctoral Dissertation, University of Colorado. Accessed March 07, 2021. https://scholar.colorado.edu/ecen_gradetds/38.

MLA Handbook (7^th Edition):

Tembarai Krishnamachari, Rajesh. “A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback.” 2011. Web. 07 Mar 2021.

Vancouver:

Tembarai Krishnamachari R. A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback. [Internet] [Doctoral dissertation]. University of Colorado; 2011. [cited 2021 Mar 07]. Available from: https://scholar.colorado.edu/ecen_gradetds/38.

Council of Science Editors:

Tembarai Krishnamachari R. A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback. [Doctoral Dissertation]. University of Colorado; 2011. Available from: https://scholar.colorado.edu/ecen_gradetds/38

University of Maryland

18. Galaz Garcia, Fernando. NONNEGATIVELY CURVED FIXED-POINT HOMOGENEOUS MANIFOLDS IN LOW DIMENSIONS.

Degree: Mathematics, 2009, University of Maryland

URL: http://hdl.handle.net/1903/9132

We classify fixed-point homogeneous Riemannian manifolds in dimensions 3 and 4 and determine which nonnegatively curved simply-connected 4-manifolds admit a smooth fixed-point homogeneous circle action with a given orbit space structure. Advisors/Committee Members: Grove, Karsten (advisor).

Subjects/Keywords: Mathematics; action; curvature; isometric; manifold; nonnegative; Riemannian

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APA (6^th Edition):

Galaz Garcia, F. (2009). NONNEGATIVELY CURVED FIXED-POINT HOMOGENEOUS MANIFOLDS IN LOW DIMENSIONS. (Thesis). University of Maryland. Retrieved from http://hdl.handle.net/1903/9132

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Galaz Garcia, Fernando. “NONNEGATIVELY CURVED FIXED-POINT HOMOGENEOUS MANIFOLDS IN LOW DIMENSIONS.” 2009. Thesis, University of Maryland. Accessed March 07, 2021. http://hdl.handle.net/1903/9132.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Galaz Garcia, Fernando. “NONNEGATIVELY CURVED FIXED-POINT HOMOGENEOUS MANIFOLDS IN LOW DIMENSIONS.” 2009. Web. 07 Mar 2021.

Vancouver:

Galaz Garcia F. NONNEGATIVELY CURVED FIXED-POINT HOMOGENEOUS MANIFOLDS IN LOW DIMENSIONS. [Internet] [Thesis]. University of Maryland; 2009. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/1903/9132.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Galaz Garcia F. NONNEGATIVELY CURVED FIXED-POINT HOMOGENEOUS MANIFOLDS IN LOW DIMENSIONS. [Thesis]. University of Maryland; 2009. Available from: http://hdl.handle.net/1903/9132

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of KwaZulu-Natal

19. Mavambou, Ange Maloko. On the geometry of locally conformal almost cosymplectic manifolds and 2-order Lagrange space.

Degree: 2017, University of KwaZulu-Natal

URL: https://researchspace.ukzn.ac.za/handle/10413/16915

Abstract available in pdf. Advisors/Committee Members: Massamba, Fortuné. (advisor).

Subjects/Keywords: Semi-Riemannian manifold.; Cosymplectic manifold.; Bundle-like foliation.; Newton transformation.; Lagrange space.

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APA (6^th Edition):

Mavambou, A. M. (2017). On the geometry of locally conformal almost cosymplectic manifolds and 2-order Lagrange space. (Thesis). University of KwaZulu-Natal. Retrieved from https://researchspace.ukzn.ac.za/handle/10413/16915

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Mavambou, Ange Maloko. “On the geometry of locally conformal almost cosymplectic manifolds and 2-order Lagrange space.” 2017. Thesis, University of KwaZulu-Natal. Accessed March 07, 2021. https://researchspace.ukzn.ac.za/handle/10413/16915.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Mavambou, Ange Maloko. “On the geometry of locally conformal almost cosymplectic manifolds and 2-order Lagrange space.” 2017. Web. 07 Mar 2021.

Vancouver:

Mavambou AM. On the geometry of locally conformal almost cosymplectic manifolds and 2-order Lagrange space. [Internet] [Thesis]. University of KwaZulu-Natal; 2017. [cited 2021 Mar 07]. Available from: https://researchspace.ukzn.ac.za/handle/10413/16915.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Mavambou AM. On the geometry of locally conformal almost cosymplectic manifolds and 2-order Lagrange space. [Thesis]. University of KwaZulu-Natal; 2017. Available from: https://researchspace.ukzn.ac.za/handle/10413/16915

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

20. Venet, Nil. Sur l'existence de champs browniens fractionnaires indexés par des variétés : On the existence of fractional brownian fields indexed by manifolds.

Degree: Docteur es, Mathématiques appliquées, 2016, Université Toulouse III – Paul Sabatier

URL: http://www.theses.fr/2016TOU30377

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Cette thèse porte sur l'existence de champs browniens fractionnaires indexés par des variétés riemanniennes. Ces objets héritent des propriétés qui font le succès du mouvement… (more)

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Cette thèse porte sur l'existence de champs browniens fractionnaires indexés par des variétés riemanniennes. Ces objets héritent des propriétés qui font le succès du mouvement brownien fractionnaire classique (H-autosimilarité des trajectoires ajustable, accroissements stationnaires), mais autorisent à considérer des applications où les données sont portées par un espace qui peut par exemple être courbé ou troué. L'existence de ces champs n'est assurée que lorsque la quantité 2H est inférieure à l'indice fractionnaire de la variété, qui n'est connu que dans un petit nombre d'exemples. Dans un premier temps nous donnons une condition nécessaire pour l'existence de champ brownien fractionnaire. Dans le cas du champ brownien (correspondant à H=1/2) indexé par des variétés qui ont des géodésiques fermées minimales, cette condition s'avère très contraignante : nous donnons des résultats de non-existence dans ce cadre, et montrons notamment qu'il n'existe pas de champ brownien indexé par une variété compacte non simplement connexe. La condition nécessaire donne également une preuve courte d'un fait attendu qui est la non-dégénérescence du champ brownien indexé par les espaces hyperboliques réels. Dans un second temps nous montrons que l'indice fractionnaire du cylindre est nul, ce qui constitue un exemple totalement dégénéré. Nous en déduisons que l'indice fractionnaire d'un espace métrique n'est pas continu par rapport à la convergence de Gromov-Hausdorff. Nous généralisons ce résultat sur le cylindre à un produit cartésien qui possède une géodésique fermée minimale, et donnons une majoration de l'indice fractionnaire de surfaces asymptotiquement proches du cylindre au voisinage d'une géodésique fermée minimale.

The aim of the thesis is the study of the existence of fractional Brownian fields indexed by Riemannian manifolds. Those fields inherit key properties of the classical fractional Brownian motion (sample paths with self-similarity of adjustable parameter H, stationary increments), while allowing to consider applications with data indexed by a space which can be for example curved or with a hole. The existence of those fields is only insured when the quantity 2H is inferior or equal to the fractional index of the manifold, which is known only in a few cases. In a first part we give a necessary condition for the fractional Brownian field to exist. In the case of the Brownian field (corresponding to H=1/2) indexed by a manifold with minimal closed geodesics this condition happens to be very restrictive. We give several nonexistence results in this situation. In particular we show that there exists no Brownian field indexed by a nonsimply connected compact manifold. Our necessary condition also gives a short proof of an expected result: we prove the nondegeneracy of fractional Brownian fields indexed by the real hyperbolic spaces. In a second part we show that the fractional index of the cylinder is null, which gives a totally degenerate case. We deduce from this result that the fractional index of a metric space is…

Advisors/Committee Members: Cohen, Serge (thesis director).

Subjects/Keywords: Champ aléatoire; Mouvement brownien; Fractionnaire; Exposant de Hurst; Auto-similarité; Variété riemannienne; Random field; Brownian motion; Fractional; Hurst exponent; Autosimilarity; Riemannian manifold

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APA (6^th Edition):

Venet, N. (2016). Sur l'existence de champs browniens fractionnaires indexés par des variétés : On the existence of fractional brownian fields indexed by manifolds. (Doctoral Dissertation). Université Toulouse III – Paul Sabatier. Retrieved from http://www.theses.fr/2016TOU30377

Chicago Manual of Style (16^th Edition):

Venet, Nil. “Sur l'existence de champs browniens fractionnaires indexés par des variétés : On the existence of fractional brownian fields indexed by manifolds.” 2016. Doctoral Dissertation, Université Toulouse III – Paul Sabatier. Accessed March 07, 2021. http://www.theses.fr/2016TOU30377.

MLA Handbook (7^th Edition):

Venet, Nil. “Sur l'existence de champs browniens fractionnaires indexés par des variétés : On the existence of fractional brownian fields indexed by manifolds.” 2016. Web. 07 Mar 2021.

Vancouver:

Venet N. Sur l'existence de champs browniens fractionnaires indexés par des variétés : On the existence of fractional brownian fields indexed by manifolds. [Internet] [Doctoral dissertation]. Université Toulouse III – Paul Sabatier; 2016. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2016TOU30377.

Council of Science Editors:

Venet N. Sur l'existence de champs browniens fractionnaires indexés par des variétés : On the existence of fractional brownian fields indexed by manifolds. [Doctoral Dissertation]. Université Toulouse III – Paul Sabatier; 2016. Available from: http://www.theses.fr/2016TOU30377

21. Logan, Andrew. The Steiner Problem on Closed Surfaces of Constant Curvature.

Degree: MS, 2015, Brigham Young University

URL: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=5419&context=etd

► The n-point Steiner problem in the Euclidean plane is to find a least length path network connecting n points. In this thesis we will… (more)

Subjects/Keywords: Steiner problem; Riemannian manifold; closed surfaces of constant curvature; Mathematics

…2.5 Riemannian Manifolds Let n be a positive integer. An n-dimensional manifold is a… …Riemannian metric. A manifold endowed with a Riemannian metric is called Riemannian. 2.5.1… …2.5.3. (i) For any point of a Riemannian manifold, and for any direction (… …distance between the points. 7 (iv) For any point of a Riemannian manifold there… …included in U . (v) On a complete (as a metric space) Riemannian manifold any…

1 more image…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Logan, A. (2015). The Steiner Problem on Closed Surfaces of Constant Curvature. (Masters Thesis). Brigham Young University. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=5419&context=etd

Chicago Manual of Style (16^th Edition):

Logan, Andrew. “The Steiner Problem on Closed Surfaces of Constant Curvature.” 2015. Masters Thesis, Brigham Young University. Accessed March 07, 2021. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=5419&context=etd.

MLA Handbook (7^th Edition):

Logan, Andrew. “The Steiner Problem on Closed Surfaces of Constant Curvature.” 2015. Web. 07 Mar 2021.

Vancouver:

Logan A. The Steiner Problem on Closed Surfaces of Constant Curvature. [Internet] [Masters thesis]. Brigham Young University; 2015. [cited 2021 Mar 07]. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=5419&context=etd.

Council of Science Editors:

Logan A. The Steiner Problem on Closed Surfaces of Constant Curvature. [Masters Thesis]. Brigham Young University; 2015. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=5419&context=etd

22. Coutant, Antoine. Déformation et construction de surfaces minimales : Deformation and construction of minimal surfaces.

Degree: Docteur es, Mathématiques, 2012, Université Paris-Est

URL: http://www.theses.fr/2012PEST1069

►

L'objet de cette thèse consiste en la construction de nouveaux exemples de surfaces (ou hypersurfaces) minimales dans les espaces euclidiens R³, R^n x R avec… (more)

▼

L'objet de cette thèse consiste en la construction de nouveaux exemples de surfaces (ou hypersurfaces) minimales dans les espaces euclidiens R³, R^n x R avec n≻2 ou dans l'espace homogène S² x R. Nous prouvons l'existence de surfaces minimales dans R³ arbitrairement proches d'un polygone convexe. Nous prouvons également l'existence d'hypersurfaces minimales de type Riemann dans R^n x R, n≻2. Celles-ci peuvent être interprétées comme étant une famille d'hyperplans horizontaux (des bouts) reliés les uns aux autres par des morceaux de caténoïdes déformés (des cous). Nous donnons un résultat général pour ce type d'objet quand il est périodique ou bien quand il a un nombre fini de bouts horizontaux. Cela se fait sous certaines hypothèses de contraintes sur les forces intervenant dans la construction. Nous finissons en donnant plusieurs exemples, notamment l'existence d'une hypersurface de type Wei verticale qui n'existe pas en dimension 3. Nous donnons aussi la preuve de l'existence d'une surface minimale de type Riemann dans S² x R telle que deux bouts sphériques sont reliés entre eux alternativement par 1 cou et 2 cous. Là aussi, nous mettons en évidence le rôle joué par les forces lors de la construction. De même que dans le chapitre précédent, la méthode repose sur un processus de recollement. Nous donnons une description très précise de la caténoïde et la surface de Riemann dans S² x R. Enfin, nous établissons l'existence dans R^n x R d'hypersurfaces de type Scherk lorsque n≻2

This thesis is devoted to the construction of numerous examples of minimal surfaces (or hypersurfaces) in the 3-Euclidean space, R^n x R with n≻2 or in the homogeneous space S² x R . We prove the existence of minimal surfaces in R³ as close as we want of a convex polygon. We prove the existence of minimal hypersurfaces in R^n x R, n≻2, whose have Riemann's type. These ones could be considered as a family of horizontal hyperplanes (the ends) which are linked to each other by pieces of deformed catenoids (the necks). We provide a general result in the case simply-periodic together with the case of a finite number of hyperplanar ends. Our construction lies on some conditions associates with the forces that characterize the different configurations. We end with giving some examples ; in particular, we exhibit the existence of vertical Wei example that does not exists in the 3-dimensional case. We also prove the existence of the analogous of the Wei example in S² x R. The surface is such that two spherical ends are linked by 1 neck and 2 necks alternatively. Here again, we highlight the role that the forces play in the construction. Moreover, like in the previous chapter, the method lies on a gluing process. We give an accurate description of the catenoid and the Riemann's minimal example in S² x R. Finally, we demonstrate the existence of Scherk type hypersurfaces in R^n x R when n≻2

Advisors/Committee Members: Pacard, Frank (thesis director).

Subjects/Keywords: Surface minimale; Espace homogène; Géométrie riemanienne; Surface de Scherk; Méthode de recollement; Surface de Riemann; Minimal manifold; Homogeneous space; Riemannian geometry; Scherk's surface; Riemann's surface; Gluing method

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APA (6^th Edition):

Coutant, A. (2012). Déformation et construction de surfaces minimales : Deformation and construction of minimal surfaces. (Doctoral Dissertation). Université Paris-Est. Retrieved from http://www.theses.fr/2012PEST1069

Chicago Manual of Style (16^th Edition):

Coutant, Antoine. “Déformation et construction de surfaces minimales : Deformation and construction of minimal surfaces.” 2012. Doctoral Dissertation, Université Paris-Est. Accessed March 07, 2021. http://www.theses.fr/2012PEST1069.

MLA Handbook (7^th Edition):

Coutant, Antoine. “Déformation et construction de surfaces minimales : Deformation and construction of minimal surfaces.” 2012. Web. 07 Mar 2021.

Vancouver:

Coutant A. Déformation et construction de surfaces minimales : Deformation and construction of minimal surfaces. [Internet] [Doctoral dissertation]. Université Paris-Est; 2012. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2012PEST1069.

Council of Science Editors:

Coutant A. Déformation et construction de surfaces minimales : Deformation and construction of minimal surfaces. [Doctoral Dissertation]. Université Paris-Est; 2012. Available from: http://www.theses.fr/2012PEST1069

Duke University

23. Streets, Jeffrey D. Ricci Yang-Mills Flow .

Degree: 2007, Duke University

URL: http://hdl.handle.net/10161/192

► Let (Mn, g) be a Riemannian manifold. Say K ! E ! M is a principal K-bundle with connection A. We define a natural evolution… (more)

Subjects/Keywords: riemannian manifold; Global differential geometry; Ricci flow; Yang-Mills theory

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APA (6^th Edition):

Streets, J. D. (2007). Ricci Yang-Mills Flow . (Thesis). Duke University. Retrieved from http://hdl.handle.net/10161/192

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Streets, Jeffrey D. “Ricci Yang-Mills Flow .” 2007. Thesis, Duke University. Accessed March 07, 2021. http://hdl.handle.net/10161/192.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Streets, Jeffrey D. “Ricci Yang-Mills Flow .” 2007. Web. 07 Mar 2021.

Vancouver:

Streets JD. Ricci Yang-Mills Flow . [Internet] [Thesis]. Duke University; 2007. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10161/192.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Streets JD. Ricci Yang-Mills Flow . [Thesis]. Duke University; 2007. Available from: http://hdl.handle.net/10161/192

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

24. Álvarez Vizoso, Javier. Covariance integral invariants of embedded Riemannian manifolds for manifold learning.

Degree: PhD, Mathematics, 2018, Colorado State University

URL: http://hdl.handle.net/10217/191299

► This thesis develops an effective theoretical foundation for the integral invariant approach to study submanifold geometry via the statistics of the underlying point-set, i.e., Manifold… (more)

▼ This thesis develops an effective theoretical foundation for the integral invariant approach to study submanifold geometry via the statistics of the underlying point-set, i.e., Manifold Learning from covariance analysis. We perform Principal Component Analysis over a domain determined by the intersection of an embedded Riemannian manifold with spheres or cylinders of varying scale in ambient space, in order to generalize to arbitrary dimension the relationship between curvature and the eigenvalue decomposition of covariance matrices. In the case of regular curves in general dimension, the covariance eigenvectors converge to the Frenet-Serret frame and the corresponding eigenvalues have ratios that asymptotically determine the generalized curvatures completely, up to a constant that we determine by proving a recursion relation for a certain sequence of Hankel determinants. For hypersurfaces, the eigenvalue decomposition has series expansion given in terms of the dimension and the principal curvatures, where the eigenvectors converge to the Darboux frame of principal and normal directions. In the most general case of embedded Riemannian manifolds, the eigenvalues and limit eigenvectors of the covariance matrices are found to have asymptotic behavior given in terms of the curvature information encoded by the third fundamental form of the manifold, a classical tensor that we generalize to arbitrary dimension, and which is related to the Weingarten map and Ricci operator. These results provide descriptors at scale for the principal curvatures and, in turn, for the second fundamental form and the Riemann curvature tensor of a submanifold, which can serve to perform multi-scale Geometry Processing and Manifold Learning, making use of the advantages of the integral invariant viewpoint when only a discrete sample of points is available. Advisors/Committee Members: Peterson, Christopher (advisor), Kirby, Michael (advisor), Bates, Dan (committee member), Cavalieri, Renzo (committee member), Eykholt, Richard (committee member).

Subjects/Keywords: curvature; PCA; covariance analysis; Riemannian manifold; integral invariants

…set of data points in some configuration space, typically a Riemannian manifold, often… …parametrize the hypersurface as a graph manifold. 3 Embedded Riemannian manifolds [16]… …manifold isometrically embedded in an pn ` kq-dimensional Riemannian manifold pN , gq, and let… …g « 1 ` 21 tr h, i.e., The natural volume form of a Riemannian manifold is given by « ˙2… …of an pn ` kq-dimensional Riemannian manifold pN , gq, with the induced metric g|M . For…

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APA (6^th Edition):

Álvarez Vizoso, J. (2018). Covariance integral invariants of embedded Riemannian manifolds for manifold learning. (Doctoral Dissertation). Colorado State University. Retrieved from http://hdl.handle.net/10217/191299

Chicago Manual of Style (16^th Edition):

Álvarez Vizoso, Javier. “Covariance integral invariants of embedded Riemannian manifolds for manifold learning.” 2018. Doctoral Dissertation, Colorado State University. Accessed March 07, 2021. http://hdl.handle.net/10217/191299.

MLA Handbook (7^th Edition):

Álvarez Vizoso, Javier. “Covariance integral invariants of embedded Riemannian manifolds for manifold learning.” 2018. Web. 07 Mar 2021.

Vancouver:

Álvarez Vizoso J. Covariance integral invariants of embedded Riemannian manifolds for manifold learning. [Internet] [Doctoral dissertation]. Colorado State University; 2018. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/10217/191299.

Council of Science Editors:

Álvarez Vizoso J. Covariance integral invariants of embedded Riemannian manifolds for manifold learning. [Doctoral Dissertation]. Colorado State University; 2018. Available from: http://hdl.handle.net/10217/191299

University of Maryland

25. Afsari, Bijan. MEANS AND AVERAGING ON RIEMANNIAN MANIFOLDS.

Degree: Mathematics, 2009, University of Maryland

URL: http://hdl.handle.net/1903/9978

► Processing of manifold-valued data has received considerable attention in recent years. Standard data processing methods are not adequate for such data. Among many related data… (more)

▼ Processing of manifold-valued data has received considerable attention in recent years. Standard data processing methods are not adequate for such data. Among many related data processing tasks finding means or averages of manifold-valued data is a basic and important one. Although means on Riemannian manifolds have a long history, there are still many unanswered theoretical questions about them, some of which we try to answer. We focus on two classes of means: the Riemannian L^p mean and the recursive-iterative means. The Riemannian L^p mean is defined as the solution(s) of a minimization problem, while the recursive-iterative means are defined based on the notion of Mean-Invariance (MI) in a recursive and iterative process. We give a new existence and uniqueness result for the Riemannian L^p mean. The significant consequence is that it shows the local and global definitions of the Riemannian L^p mean coincide under an uncompromised condition which guarantees the uniqueness of the local mean. We also study smoothness, isometry compatibility, convexity and noise sensitivity properties of the L^p mean. In particular, we argue that positive sectional curvature of a manifold can cause high sensitivity to noise for the L² mean which might lead to a non-averaging behavior of that mean. We show that the L² mean on a manifold of positive curvature can have an averaging property in a weak sense. We introduce the notion of MI, and study a large class of recursive-iterative means. MI means are related to an interesting class of dynamical systems that can find Riemannian convex combinations. A special class of the MI means called pairwise mean, which through an iterative scheme called Perimeter Shrinkage is related to cyclic pursuit on manifolds, is also studied. Finally, we derive results specific to the special orthogonal group and the Grassmannian manifold, as these manifolds appear naturally in many applications. We distinguish the 2-norm Finsler balls of appropriate radius in these manifolds as domains for existence and uniqueness of the studied means. We also introduce some efficient numerical methods to perform the related calculations in the specified manifolds. Advisors/Committee Members: Krishnaprasad, P.S. (advisor), Grove, Karsten (advisor).

Subjects/Keywords: Applied Mathematics; Statistics; Engineering, General; computations on manifolds; nonlinear signal processing; Riemannian Center of Mass; Riemannian Manifolds; statisitcal analysis of shapes; Statisitcs of Manifold-valued data

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Afsari, B. (2009). MEANS AND AVERAGING ON RIEMANNIAN MANIFOLDS. (Thesis). University of Maryland. Retrieved from http://hdl.handle.net/1903/9978

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Afsari, Bijan. “MEANS AND AVERAGING ON RIEMANNIAN MANIFOLDS.” 2009. Thesis, University of Maryland. Accessed March 07, 2021. http://hdl.handle.net/1903/9978.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Afsari, Bijan. “MEANS AND AVERAGING ON RIEMANNIAN MANIFOLDS.” 2009. Web. 07 Mar 2021.

Vancouver:

Afsari B. MEANS AND AVERAGING ON RIEMANNIAN MANIFOLDS. [Internet] [Thesis]. University of Maryland; 2009. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/1903/9978.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Afsari B. MEANS AND AVERAGING ON RIEMANNIAN MANIFOLDS. [Thesis]. University of Maryland; 2009. Available from: http://hdl.handle.net/1903/9978

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

26. Shouman, Abdolhakim. Comparaison de valeurs propres de Laplaciens et inégalités de Sobolev sur des variétés riemanniennes à densité : Eigenvalue comparison for Laplacians and Sobolev inequalities on weighed Riemannian manifolds.

Degree: Docteur es, Mathématiques, 2017, Université François-Rabelais de Tours

URL: http://www.theses.fr/2017TOUR4034

►

Le but de cette thèse est triple : INÉGALITÉS DE SOBOLEV AVEC DES CONSTANTES EXPLICITES SUR DES VARIÉTÉS RIEMANNIENNES À DENSITÉ ET À BORD CONVEXE… (more)

Subjects/Keywords: Inégalités de Sobolev; Inégalité d’Onofri; Laplacien de Witten; Drift laplacien; Problème de Dirichlet; Problème de Neumann; Valeurs propres; Variété riemannienne à densité; Courbure de Bakry-Émery; Première variation; "p-Laplace"; Sobolev inequalities; Onofri’s inequality; Weighted Laplacian; Drifting Laplacian; Dirichlet problem; Neumann problem; Eigenvalues; Weighted Riemannian manifold; Manifold with density; Bakry-Emery-Ricci curvatures; First variation; "p-Laplacian"

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Shouman, A. (2017). Comparaison de valeurs propres de Laplaciens et inégalités de Sobolev sur des variétés riemanniennes à densité : Eigenvalue comparison for Laplacians and Sobolev inequalities on weighed Riemannian manifolds. (Doctoral Dissertation). Université François-Rabelais de Tours. Retrieved from http://www.theses.fr/2017TOUR4034

Chicago Manual of Style (16^th Edition):

Shouman, Abdolhakim. “Comparaison de valeurs propres de Laplaciens et inégalités de Sobolev sur des variétés riemanniennes à densité : Eigenvalue comparison for Laplacians and Sobolev inequalities on weighed Riemannian manifolds.” 2017. Doctoral Dissertation, Université François-Rabelais de Tours. Accessed March 07, 2021. http://www.theses.fr/2017TOUR4034.

MLA Handbook (7^th Edition):

Shouman, Abdolhakim. “Comparaison de valeurs propres de Laplaciens et inégalités de Sobolev sur des variétés riemanniennes à densité : Eigenvalue comparison for Laplacians and Sobolev inequalities on weighed Riemannian manifolds.” 2017. Web. 07 Mar 2021.

Vancouver:

Shouman A. Comparaison de valeurs propres de Laplaciens et inégalités de Sobolev sur des variétés riemanniennes à densité : Eigenvalue comparison for Laplacians and Sobolev inequalities on weighed Riemannian manifolds. [Internet] [Doctoral dissertation]. Université François-Rabelais de Tours; 2017. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2017TOUR4034.

Council of Science Editors:

Shouman A. Comparaison de valeurs propres de Laplaciens et inégalités de Sobolev sur des variétés riemanniennes à densité : Eigenvalue comparison for Laplacians and Sobolev inequalities on weighed Riemannian manifolds. [Doctoral Dissertation]. Université François-Rabelais de Tours; 2017. Available from: http://www.theses.fr/2017TOUR4034

Kyoto University / 京都大学

27. Le, Thanh Tam. Geometry-Aware Learning Algorithms for Histogram Data Using Adaptive Metric Embeddings and Kernel Functions : 距離の適応埋込みとカーネル関数を用いたヒストグラムデータからの幾何認識学習アルゴリズム.

Degree: 博士(情報学), 2016, Kyoto University / 京都大学

URL: http://hdl.handle.net/2433/204594 ; http://dx.doi.org/10.14989/doctor.k19417

新制・課程博士

甲第19417号

情博第596号

Subjects/Keywords: Metric learning; Kernel method; Histogram; Aitchison geometry; the probability simplex; Bag of features; Riemannian manifold

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APA (6^th Edition):

Le, T. T. (2016). Geometry-Aware Learning Algorithms for Histogram Data Using Adaptive Metric Embeddings and Kernel Functions : 距離の適応埋込みとカーネル関数を用いたヒストグラムデータからの幾何認識学習アルゴリズム. (Thesis). Kyoto University / 京都大学. Retrieved from http://hdl.handle.net/2433/204594 ; http://dx.doi.org/10.14989/doctor.k19417

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Le, Thanh Tam. “Geometry-Aware Learning Algorithms for Histogram Data Using Adaptive Metric Embeddings and Kernel Functions : 距離の適応埋込みとカーネル関数を用いたヒストグラムデータからの幾何認識学習アルゴリズム.” 2016. Thesis, Kyoto University / 京都大学. Accessed March 07, 2021. http://hdl.handle.net/2433/204594 ; http://dx.doi.org/10.14989/doctor.k19417.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Le, Thanh Tam. “Geometry-Aware Learning Algorithms for Histogram Data Using Adaptive Metric Embeddings and Kernel Functions : 距離の適応埋込みとカーネル関数を用いたヒストグラムデータからの幾何認識学習アルゴリズム.” 2016. Web. 07 Mar 2021.

Vancouver:

Le TT. Geometry-Aware Learning Algorithms for Histogram Data Using Adaptive Metric Embeddings and Kernel Functions : 距離の適応埋込みとカーネル関数を用いたヒストグラムデータからの幾何認識学習アルゴリズム. [Internet] [Thesis]. Kyoto University / 京都大学; 2016. [cited 2021 Mar 07]. Available from: http://hdl.handle.net/2433/204594 ; http://dx.doi.org/10.14989/doctor.k19417.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Le TT. Geometry-Aware Learning Algorithms for Histogram Data Using Adaptive Metric Embeddings and Kernel Functions : 距離の適応埋込みとカーネル関数を用いたヒストグラムデータからの幾何認識学習アルゴリズム. [Thesis]. Kyoto University / 京都大学; 2016. Available from: http://hdl.handle.net/2433/204594 ; http://dx.doi.org/10.14989/doctor.k19417

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

28. Cerocchi, Filippo. Dynamical and Spectral applications of Gromov-Hausdorff Theory : Applications dynamiques et spectrales de la théorie de Gromov-Hausdorff.

Degree: Docteur es, Mathématiques, 2013, Grenoble; Università degli studi La Sapienza (Rome)

URL: http://www.theses.fr/2013GRENM077

►

Cette thèse est divisée en deux parties. La première est consacrée à la méthode du barycentre, introduite en 1995 par G. Besson, G. Courtois et… (more)

▼

Cette thèse est divisée en deux parties. La première est consacrée à la méthode du barycentre, introduite en 1995 par G. Besson, G. Courtois et S. Gallot pour résoudre la conjecture de l'Entropie Minimale. Dans le Chapitre 1 nous décrivons ses développements les plus récents, notamment l'extension de cette méthode au cadre des variétés dont la courbure sectionnelle est de signe quelconque (voir les énoncés 1.2.1 et 1.4.1). Dans le Chapitre 2 et 3 nous présentons des résultats dans lesquels la méthode du barycentre joue un rôle important. Le problème “deux variétés dont les flots géodésiques sont conjugués sont-elles isométriques ?” (problème de la rigidité par conjugaison des flots) est le thème du Chapitre 2. Après avoir montré que deux telles variétés ont la même géométrie à grande échelle, on montre comment on peut utiliser ce résultat et la méthode du barycentre pour donner une nouvelle preuve de la rigidité (par conjugaison des flots) des variétés plates. Dans le Chapitre 3 nous utilisons la méthode du barycentre (en courbure de signe quelconque) et des inégalités de Sobolev itérées pour démontrer un théorème de comparaison entre les spectres de deux variétés riemanniennes (Y , g) et (X , g') de volumes proches, sachant qu'il existe une approximation de Gromov-Hausdorff de degré non nul entre ces deux variétés. Il s'agit d'un résultat d'approximation avec majoration de l'erreur d'approximation (et pas seulement d'un résultat de convergence). Remarquons qu'il n'est fait aucune autre hypothèse géométrique (et en particulier aucune hypothèse de courbure) sur la variété (Y , g), ce qui autorise un grand nombre de contre-exemples prouvant que le résultat est optimal. Dans la deuxième partie de la thèse (chapitre 4), on démontre un Lemme de Margulis sans hypothèse sur la courbure, qui s'applique aux variétés dont les groupes fondamentaux sont des produits libres (et qui ne possèdent pas d'élément de torsion d'ordre 2). Nous donnons également une borne inférieure de la systole des variétés dont le diamètre et l'entropie volumique sont majorés et dont le groupe fondamental est isomorphe à un produit libre sans torsion. Comme conséquences de ce dernier résultat nous obtenons des résultats de précompacité et de finitude topologique ou différentiable pour les variétés riemanniennes et une minoration de leur volume, tout ceci sans faire d'hypothèse de courbure.

This Ph.D. Thesis is divided into two parts. In the first part we present the barycenter method, a technique which has been introduced by G. Besson, G. Courtois and S. Gallot in 1995, in order to solve the Minimal Entropy conjecture. In Chapter 1 we are interested in the more recent developments of this method, more precisely in the recent extension of the method to the case of manifolds having sectional curvature of variable sign. In Chapters 2 and 3 we shall present some new results whose proofs make use of the barycenter method. The Conjugacy Rigidity problem is the theme of Chapter 2. First we show a general result which provide a comparison between the large…

Advisors/Committee Members: Gallot, Sylvestre (thesis director), Sambusetti, Andrea (thesis director).

Subjects/Keywords: Distance de Hausdorff-Gromov; Théorème de comparaison; Flot Géodesique; Méthode du barycentre; Spectre d'une variété Riemannienne; Lemme de Margulis; Hausdorff-Gromov distance; Lenght spectrum; Geodesic Flow; Barycenter method; Spectrum of a Riemannian manifold; Margulis Lemma; 510

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APA (6^th Edition):

Cerocchi, F. (2013). Dynamical and Spectral applications of Gromov-Hausdorff Theory : Applications dynamiques et spectrales de la théorie de Gromov-Hausdorff. (Doctoral Dissertation). Grenoble; Università degli studi La Sapienza (Rome). Retrieved from http://www.theses.fr/2013GRENM077

Chicago Manual of Style (16^th Edition):

Cerocchi, Filippo. “Dynamical and Spectral applications of Gromov-Hausdorff Theory : Applications dynamiques et spectrales de la théorie de Gromov-Hausdorff.” 2013. Doctoral Dissertation, Grenoble; Università degli studi La Sapienza (Rome). Accessed March 07, 2021. http://www.theses.fr/2013GRENM077.

MLA Handbook (7^th Edition):

Cerocchi, Filippo. “Dynamical and Spectral applications of Gromov-Hausdorff Theory : Applications dynamiques et spectrales de la théorie de Gromov-Hausdorff.” 2013. Web. 07 Mar 2021.

Vancouver:

Cerocchi F. Dynamical and Spectral applications of Gromov-Hausdorff Theory : Applications dynamiques et spectrales de la théorie de Gromov-Hausdorff. [Internet] [Doctoral dissertation]. Grenoble; Università degli studi La Sapienza (Rome); 2013. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2013GRENM077.

Council of Science Editors:

Cerocchi F. Dynamical and Spectral applications of Gromov-Hausdorff Theory : Applications dynamiques et spectrales de la théorie de Gromov-Hausdorff. [Doctoral Dissertation]. Grenoble; Università degli studi La Sapienza (Rome); 2013. Available from: http://www.theses.fr/2013GRENM077

Université de Bordeaux I

29. Assaad, Joyce. Transformées de Riesz associées aux opérateurs de Schrödinger avec des potentiels négatifs : Control of the dynamics of chronic myeloid leukemia by Imatinib.

Degree: Docteur es, Mathématiques pures - Analyse, 2010, Université de Bordeaux I

URL: http://www.theses.fr/2010BOR14106

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Dans cette thèse nous étudions la bornitude des transformées de Riesz associées aux opérateurs de Schrödinger avec des potentiels qui admettent des parties négatives.Cette étude… (more)

Subjects/Keywords: Transformées de Riesz; Opérateur de Schrödinger; Opérateur d’intégrale singulière; Estimations Gaussiennes; Estimations hors-diagonales; Variétés Riemanniennes; Classe de Muckenhoupt; Classe de Hölder inverse; Riesz transform; Schrödinger operator; Singular integral operator; Gaussian estimates; Oﬀ-diagonal estimates; Riemannian manifold; Muckenhoupt class; Reverse Hölder class

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Assaad, J. (2010). Transformées de Riesz associées aux opérateurs de Schrödinger avec des potentiels négatifs : Control of the dynamics of chronic myeloid leukemia by Imatinib. (Doctoral Dissertation). Université de Bordeaux I. Retrieved from http://www.theses.fr/2010BOR14106

Chicago Manual of Style (16^th Edition):

Assaad, Joyce. “Transformées de Riesz associées aux opérateurs de Schrödinger avec des potentiels négatifs : Control of the dynamics of chronic myeloid leukemia by Imatinib.” 2010. Doctoral Dissertation, Université de Bordeaux I. Accessed March 07, 2021. http://www.theses.fr/2010BOR14106.

MLA Handbook (7^th Edition):

Assaad, Joyce. “Transformées de Riesz associées aux opérateurs de Schrödinger avec des potentiels négatifs : Control of the dynamics of chronic myeloid leukemia by Imatinib.” 2010. Web. 07 Mar 2021.

Vancouver:

Assaad J. Transformées de Riesz associées aux opérateurs de Schrödinger avec des potentiels négatifs : Control of the dynamics of chronic myeloid leukemia by Imatinib. [Internet] [Doctoral dissertation]. Université de Bordeaux I; 2010. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2010BOR14106.

Council of Science Editors:

Assaad J. Transformées de Riesz associées aux opérateurs de Schrödinger avec des potentiels négatifs : Control of the dynamics of chronic myeloid leukemia by Imatinib. [Doctoral Dissertation]. Université de Bordeaux I; 2010. Available from: http://www.theses.fr/2010BOR14106

30. Tholozan, Nicolas. Uniformisation des variétés pseudo-riemanniennes localement homogènes : Uniformization of pseudo-riemannian locally homogeneous manifolds.

Degree: Docteur es, Mathématiques, 2014, Nice

URL: http://www.theses.fr/2014NICE4079

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Ce travail étudie les variétés pseudo-riemanniennes compactes localement homogènes à travers le prisme des (G,X)-structures, introduites par Thurston dans son programme de géométrisation. Nous commençons… (more)

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Ce travail étudie les variétés pseudo-riemanniennes compactes localement homogènes à travers le prisme des (G,X)-structures, introduites par Thurston dans son programme de géométrisation. Nous commençons par présenter la problématique générale et discutons notamment du rapport entre la complétude géodésique de ces variétés et une autre notion de complétude propre aux (G,X)-structures. Nous donnons également dans le chapitre 1 une nouvelle preuve d’un théorème de Bromberg et Medina qui classifie les métriques lorentziennes invariantes à gauche sur SL(2,R) dont le flot géodésique est complet. Conjecturalement, toute (G,X)-structure pseudo-riemannienne sur une variété compacte est complète. Nous prouvons ici que cela est vrai pour certaines géométries, sous l’hypothèse que la (G,X)-structure est a priori kleinienne. On en déduit que, pour ces géométries, la complétude est une condition fermée. Lorsque X est un groupe de Lie de rang 1 muni de sa métrique de Killing, ce résultat complète un théorème de Guéritaud–Guichard–Kassel–Wienhard selon lequel la complétude est une condition ouverte. Nous nous tournons ensuite vers l’étude des représentations d’un groupe de surface à valeurs dans les isométries d’une variété riemannienne M complète simplement connexe de courbure sectionnelle inférieure à -1. Étant donnée une telle représentation ρ, nous montrons que l’ensemble des représentations fuchsiennes j telles qu’il existe une application (j,ρ)-équivariante et contractante de H2 dans M est un ouvert non vide et contractile de l’espace de Teichmüller (sauf lorsque ρ est elle-même fuchsienne). Ce résultat nous permet de décrire l’espace des métriques lorentziennes de courbure constante -1 sur un fibré en cercle au-dessus d’une surface compacte. Nous montrons que cet espace possède un nombre fini de composantes connexes classifiées par un invariant que nous appelons longueur de la fibre. Nous prouvons également que le volume total de ces métriques ne dépend que de la topologie du fibré et de la longueur de la fibre.

In this work, we study closed locally homogeneous pseudo-Riemannian manifolds through the notion of (G,X)-structure, introduced by Thurston in his geometrization program. We start by presenting the general problem. In particular, we discuss the link between geodesical completeness of those manifolds and another notion of completeness specific to (G,X)-structures. In chapter 1, we also give a new proof of a theorem by Bromberg and Medina which classifies left invariant Lorentz metrics on SL(2,R) that are geodesically complete. Conjecturally, every pseudo-riemannian (G,X)-structure on a closed manifold is complete. Here we prove that it holds for certain geometries, provided that the (G,X )-structure is a priori Kleinian . This implies that, for such geometries, completeness is a closed condition. When X is a Lie group of rank 1 handled with its Killing metric, this result complements a theorem of Guéritaud–Guichard–Kassel–Wienhard, acording to which completeness is an open condition. We then turn to the study of…

Advisors/Committee Members: Dumitrescu, Sorin (thesis director).

Subjects/Keywords: Variété pseudo-riemannienne; (G,X) -structure; Espace homogène; Flot géodésique; Complétude; Représentation; Groupe de surface; Anti-de Sitter; Pseudo-Riemannian manifold; (G,X) -structure; Homogeneous space; Geodesic flow; Completeness; Representation; Surface group; Anti-de Sitter

Record Details Similar Records Cite « Share

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Tholozan, N. (2014). Uniformisation des variétés pseudo-riemanniennes localement homogènes : Uniformization of pseudo-riemannian locally homogeneous manifolds. (Doctoral Dissertation). Nice. Retrieved from http://www.theses.fr/2014NICE4079

Chicago Manual of Style (16^th Edition):

Tholozan, Nicolas. “Uniformisation des variétés pseudo-riemanniennes localement homogènes : Uniformization of pseudo-riemannian locally homogeneous manifolds.” 2014. Doctoral Dissertation, Nice. Accessed March 07, 2021. http://www.theses.fr/2014NICE4079.

MLA Handbook (7^th Edition):

Tholozan, Nicolas. “Uniformisation des variétés pseudo-riemanniennes localement homogènes : Uniformization of pseudo-riemannian locally homogeneous manifolds.” 2014. Web. 07 Mar 2021.

Vancouver:

Tholozan N. Uniformisation des variétés pseudo-riemanniennes localement homogènes : Uniformization of pseudo-riemannian locally homogeneous manifolds. [Internet] [Doctoral dissertation]. Nice; 2014. [cited 2021 Mar 07]. Available from: http://www.theses.fr/2014NICE4079.

Council of Science Editors:

Tholozan N. Uniformisation des variétés pseudo-riemanniennes localement homogènes : Uniformization of pseudo-riemannian locally homogeneous manifolds. [Doctoral Dissertation]. Nice; 2014. Available from: http://www.theses.fr/2014NICE4079

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