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 18 of 18 for “"hyperbolic space"”.
-
Isometric Immersions and Embeddings of Nonnegatively Curved Hypersurfaces in Hyperbolic Space
Embargo set by: Seth Robbins for item 71390 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs
-
Boundaries and hierarchically hyperbolic spaces
Although the hierarchically hyperbolic space boundary is a generalization of the Gromov boundary, we will show there are fundamental differences between the two. First, we provide negative answers to questions posed by Durham, Hagen, and Sisto on the existence of boundary maps for some …
-
Self-similarity of Random Aggregation Trees in Hyperbolic Spaces
… naturally once a network is embedded into a hyperbolic space of a negative curvature. This thesis develops this general idea in application to the self-similar structure of rooted trees. We use a self-similarity framework based on the Horton-Strahler orders of tree branches and Tokunaga …
-
β-Uniform Convexity and Divisible Domains
… the Hilbert geometry it induces is the hyperbolic space. In general, strictly convex divisible domains exhibit negative curvature properties, but only the ellipsoid is a CAT(-1) space. The notion of p-uniform convexity from the theory of Banach spaces has been proposed as a …
-
Twistor Space and Celestial Holography
… the complexification of 3 and 5 dimensional hyperbolic space. We discuss the minitwistor space of the bulk and its relation to the ambitwistor space of the boundary. The third part of my thesis is a paper on spectral flow and localisation in AdS$_3$ string theory. The fourth and final part of …
-
Rigidity and invariance properties of certain geometric frameworks
… (n + 1)-simplex in a n-dimensional Euclidean space Rn, which is embedded in a (n + 1)-dimensional Euclidean space Rn+l. We allow all its vertices to have continuous motion in the space, either in Rn+l or restricted in Rn. For a given k, based on certain rules, we separate all its k-faces into …
-
THE LOW-INTENSITY LIMIT OF BERNOULLI-VORONOI AND POISSON-VORONOI MEASURES
… model, which can be defined on any metric space. In this setting, the nuclei of the Voronoi tiles are obtained by a Poisson process, with intensity lambda, and the random set we study is the boundary of the Voronoi tiles. We study various properties of the low-intensity limit, as lambda …
-
Multimodal Representation Learning for Textual Reasoning over Knowledge Graphs
… KGs, respectively, and (iv) introduce a novel hyperbolic learning framework to enable the scalability of hyperbolic neural networks over large graphs using meta-learning. The proposed work is distinct from current research because it models the logical flow of textual queries in hyperbolic …
-
Applications and limits of convex optimization
… 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 learning …
-
Fully Hyperbolic Graph Convolutional Neural Networks for Age Prediction with Multi-Modal Brain Data
… disease. In this study, we utilize a Fully Hyperbolic Neural Network (FHNN) to embed functional brain connectivity graphs, derived from magnetoencephalography (MEG) data, into low dimensions on a Lorentz Hyperboloid model for hyperbolic space. Using these embeddings, we aim to detect changes …
-
Self-supervised Representation Learning in Computer Vision and Reinforcement Learning
… method employs a world model of the SSL latent space, and the prediction error of this model indicates novel states required to explore. It shows strong performance on exploration-hard benchmarks, especially on the notorious Montezuma's Revenge. Finally, we consider the metric learning problem, …
-
Applications of the fourier transform to convex geometry
… We solve the Busemann-Petty problem in hyperbolic and spherical spaces, and the lower dimensional Busemann-Petty problem in the hyperbolic space. In the Euclidean space we modify the assumptions of the original Busemann-Petty problem to guarantee the affirmative answer in all dimensions. …
-
Estimation and Inference for Network Data
… type, dimension, and curvature of the latent space model. The second problem we consider concerns network data collection. Collecting full network data is often prohibitively expensive and time-consuming. A common form of cheaper network data, known as Aggregated Relational Data (ARD), asks …
-
Aspects of higher degree forms with symmetries
… anticommutative polynomial; define alternating spaces and their direct sum; establish decomposition and cancellation results for alternating spaces; and construct a Witt-Grothendieck group of alternating spaces. In Chapter Two we discuss hyperbolic alternating space. We compute the centre, …
-
Geometric mapping theory of the Heisenberg group, sub-Riemannian manifolds, and hyperbolic spaces
… expansions and continued fractions. As a metric space, $\Heis^n$ serves as an infinitesimal model (metric tangent space) of some sub-Riemannian manifolds and allows one to study derivatives of mappings between such spaces. As a subgroup of the isometry group of complex hyperbolic space …
-
1. ΕΠΙΦΑΝΕΙΕΣ ΜΕ ΙΣΟΜΕΤΡΙΚΕΣ ΣΚΙΟΓΡΑΜΜΕΣ 2. ΕΠΙΦΑΝΕΙΕΣ ΜΕ ΙΣΟΜΕΤΡΙΚΕΣ ΓΕΩΔΑΙΣΙΑΚΕΣ
… STRICTLY CONVEX SURFACE EMBEDDED INTHE EUCLIDEAN SPACE E3 OR IN THE HYPERBOLIC SPACE H3. WE SUPPOSE THAT ALL SHADOW-LINES OF M ARE CONGRUENT. THEN M IS A EUCLIDEAN 2-SPHERE OR A HYPERBOLIC 2-SPHERE RESPECTIVELY. ROUGHLY SPEAKING, TO EACH POINT E OF THE SPHERE S2 CORRESPONDS A DIFFERENT SHADOW-LINE …
-
Detecting topological properties of boundaries of hyperbolic groups
… to admit a nice action by isometries on a space with a negative curvature property, such as Gromov hyperbolicity. Such groups are surprisingly common: there is a sense in which a random group admits such an action, as do some groups of classical interest, such as fundamental groups of …
-
Linear and non-linear collisionless many-particle systems
… system, in the torus and the whole space. The main result is based on quantitative a priori estimates for the Gevrey norm and the radius of Gevrey regularity of the solution, in terms of the force field and the volume of the momentum support of the distribution function. …