Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 43 for “"non-Euclidean"”.
-
Geographically weighted Regression with non-Euclidean distance metrics
Available with hard copy only.
-
Maximum principle, mean value operators and quasi boundedness in non-euclidean settings
… second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The …
-
Modelos para geometria hiperbólica.
… description of the discovery of a type of non-Euclidean geometry, namely the hyperbolic geometry. Featuring some of their properties and that the models represent.
-
Structure-preserving Numerical Methods for Engineering Applications
… extends those methods to systems that evolve on non-Euclidean manifolds. The dissertation is focused on numerical schemes derived from variational principles – schemes that are general enough to apply to a large class of engineering problems. A theoretical framework that encapsulates variational …
-
Statistical Analysis on Diffusion Tensor Estimation
… insight structure of the human body in vivo and non-invasively. It displays water molecule movement by a 3×3 diffusion tensor at each voxel. Tensor field processing, visualisation and tractography are all based on the diffusion tensors. The accuracy of estimating diffusion tensor is essential in …
-
Optimal anticipatory control as a theory of motor preparation
… of most LVMs, however, is that they assume a Euclidean latent space, while many kinematic variables, such as head rotations and the configuration of an arm, are naturally described by variables that live on non-Euclidean latent spaces (e.g., SO(3) and tori). To address this shortcoming, we …
-
Geometric Methods for Point Estimation
… the estimation of location parameters for non-Euclidean data that lies in a known manifold or metric space. Ideas from statistical decision theory motivate the construction of new estimators for location parameters. The second half of this work explores information geometric aspects of …
-
Applications and limits of convex optimization
… known algorithm uses convex optimization in non-Euclidean space. We expose a fundamental obstruction to such techniques by proving that, under realistic noise conditions, hyperbolic space admits no analogue of Nesterov’s accelerated gradient descent. Finally, we generalize Bresler’s structure …
-
Structured Diffusion Processes in Deep Generative Models
… by operating over a lower-dimensional, non-Euclidean space. Both approaches simultaneously improve sample quality and reduce inference runtime while preserving existing capabilities—and developing new ones—of diffusion generative models.
-
Mathematical Advancements in Geometric Algebra for 3D Registration Problems
… geometric problems in higher-dimensional and non-Euclidean spaces, and provides a general and efficient approach that not only solves existing problems but also opens up new possibilities for a wide range of practical applications. The thesis begins by applying 3D Euclidean CMs to the Absolute …
-
Generative Models Driven Graph Outlier Detection
… fall short of effectively modeling the complex non-Euclidean graph data. Recently, generative models have exhibited extraordinary performance on image and language data, but their capabilities in graph outlier detection remain largely underexplored. In this dissertation, I systematically …
-
A History of Complex Simple Lie Algebras
… around the same time, Wilhelm Killing’s work on non-Euclidean geometry encountered related topics. As mathematicians recognized this as a division of abstract algebra, the area became known as “continuous transformation groups," but we now refer to them as Lie groups.</p> <p>Patterns and …
-
Piecewise Bézier curve trajectory generation and control for quadrotors
… describes a control design approach in the non-Euclidean state space of quadrotors to achieve improved tracking performance for complex trajectories. A novel trajectory generation method is presented to achieve smooth and graceful paths for quadrotors. The trajectory generation is formulated …
-
Lobachevski Illuminated: Content, Methods, and Context of the Theory of Parallels
… and began to explore the world's first non-Euclidean geometry. This crucial development in the history of mathematics was not recognized as such in his own lifetime. When his work finally found a sympathetic audience in the late 19th century, it was reinterpreted in the light of various …
-
Lobachevski Illuminated: Content, Methods, and Context of the Theory of Parallels
… and began to explore the world's first non-Euclidean geometry. This crucial development in the history of mathematics was not recognized as such in his own lifetime. When his work finally found a sympathetic audience in the late 19th century, it was reinterpreted in the light of various …
-
3D Mapping of Islamic Geometric Motifs
… forms a motif by given grammar rules including, Euclidean transformations and Boolean operations. Next, APSG was used to construct the architectural structures that manipulates the motif by automating the grammar rules. The APSG forms a wall, a column, a self-similarity star and a dome, the main …
-
3D Mapping of Islamic Geometric Motifs
… forms a motif by given grammar rules including, Euclidean transformations and Boolean operations. Next, APSG was used to construct the architectural structures that manipulates the motif by automating the grammar rules. The APSG forms a wall, a column, a self-similarity star and a dome, the main …
-
A posteriori error estimates for the Poisson problem on closed, two-dimensional surfaces
The solution of partial differential equations on non-Euclidean Domains is an area of much research in recent years. The Poisson Problem is a partial differential equation that is useful on curved surfaces. On a curved surface, the Poisson Problem features the Laplace-Beltrami Operator, which is a …
-
Modeling the Geometry of Neural Network Representation Spaces
… using simple geometric quantities such as Euclidean distances. This thesis studies the geometric structure of this space and its influence on key properties of the learning process, including how much data is needed to acquire new skills, when predictions will fail, and the computational …
-
Cosmographic Origins for a New Classicism
… that of the Renaissance or of classical Greece. Non-Euclidean geometry and the math of higher dimensional space begin to break free of their abstract character as these symbolic disciplines now inform and reconcile the reality of cosmic space. It is therefore appropriate to understand the …
Page 1 of 3