{"id":{"repo_id":"unr","oai_identifier":"oai:scholarwolf.unr.edu:11714/2053"},"canonical_url":"https://search.dev.ndltd.org/etd/unr/oai:scholarwolf.unr.edu:11714/2053","repository":{"repo_id":"unr","name":"University of Nevada - Reno","base_url":"https://scholarwolf.unr.edu/server/oai/request"},"display":{"title":"Self-similarity of Random Aggregation Trees in Hyperbolic Spaces","abstract":"Structure and function of complex networks is an intriguing area of research with numerous practical applications. It has been shown recently that several paradigmatic properties of complex networks, including power-law degree distribution and strong clustering, emerge 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 indices that describe aggregation of different orders. The main object of study is the nearest-neighbor aggregation in a hyperbolic metric. Extensive numerical experiments are used to formulate several hypotheses about Horton and Tokunaga self-similarity of the respective aggregation trees. The main results refer to an analytical Ring Model that describes order-based aggregation of particles in a 2-D hyperbolic space of a negative curvature -ζ^2 , ζ>0. We prove that the aggregation trees are Horton self-similar with the Horton exponent R related to the space curvature. Furthermore, we establish self-similar branching structure of the order aggregation that satisfies the Tokunaga constraint with parameters a = R - R^1/2 and c = R^1/2.","abstract_html":"Structure and function of complex networks is an intriguing area of research with numerous practical applications. It has been shown recently that several paradigmatic properties of complex networks, including power-law degree distribution and strong clustering, emerge 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 indices that describe aggregation of different orders. The main object of study is the nearest-neighbor aggregation in a hyperbolic metric. Extensive numerical experiments are used to formulate several hypotheses about Horton and Tokunaga self-similarity of the respective aggregation trees. The main results refer to an analytical Ring Model that describes order-based aggregation of particles in a 2-D hyperbolic space of a negative curvature -ζ^2 , ζ>0. We prove that the aggregation trees are Horton self-similar with the Horton exponent R related to the space curvature. Furthermore, we establish self-similar branching structure of the order aggregation that satisfies the Tokunaga constraint with parameters a = R - R^1/2 and c = R^1/2.","abstract_has_math":false,"creators":["Aberasturi, Dillon"],"institution":null,"degree_name":null,"degree_level":"Master's Degree","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Zaliapin, Ilya"],"committee_chairs":[],"committee_members":["Zaliapin, Ilya","Panorska, Anna","Schmidt, Deena","Nicolescu, Monica"],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-27T21:46:52Z","subjects":["Disk Model","Horton self-similar","hyperbolic space","Ring Model","self-similar","Tokunaga"],"languages":[],"rights":["In Copyright(All Rights Reserved)"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11714/2053","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Zaliapin, Ilya"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Zaliapin, Ilya","Panorska, Anna","Schmidt, Deena","Nicolescu, Monica"]},{"key":"dc:creator","label":"Author","values":["Aberasturi, Dillon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-09-12T16:11:09Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-09-12T16:11:09Z"]},{"key":"dc:date.issued","label":"Date","values":["2017"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's Degree"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Disk Model","Horton self-similar","hyperbolic space","Ring Model","self-similar","Tokunaga"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright(All Rights Reserved)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11714/2053"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Structure and function of complex networks is an intriguing area of research with numerous practical applications. It has been shown recently that several paradigmatic properties of complex networks, including power-law degree distribution and strong clustering, emerge 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 indices that describe aggregation of different orders. The main object of study is the nearest-neighbor aggregation in a hyperbolic metric. Extensive numerical experiments are used to formulate several hypotheses about Horton and Tokunaga self-similarity of the respective aggregation trees. The main results refer to an analytical Ring Model that describes order-based aggregation of particles in a 2-D hyperbolic space of a negative curvature -ζ^2 , ζ>0. We prove that the aggregation trees are Horton self-similar with the Horton exponent R related to the space curvature. Furthermore, we establish self-similar branching structure of the order aggregation that satisfies the Tokunaga constraint with parameters a = R - R^1/2 and c = R^1/2."]},{"key":"dc:format","label":"Dc Format","values":["PDF"]},{"key":"dc:title","label":"Title","values":["Self-similarity of Random Aggregation Trees in Hyperbolic Spaces"]}]}],"canonical_facts":{"dc:contributor.advisor":["Zaliapin, Ilya"],"dc:contributor.committeemember":["Zaliapin, Ilya","Panorska, Anna","Schmidt, Deena","Nicolescu, Monica"],"dc:creator":["Aberasturi, Dillon"],"dc:date.accessioned":["2017-09-12T16:11:09Z"],"dc:date.available":["2017-09-12T16:11:09Z"],"dc:date.issued":["2017"],"dc:description.abstract":["Structure and function of complex networks is an intriguing area of research with numerous practical applications. It has been shown recently that several paradigmatic properties of complex networks, including power-law degree distribution and strong clustering, emerge 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 indices that describe aggregation of different orders. The main object of study is the nearest-neighbor aggregation in a hyperbolic metric. Extensive numerical experiments are used to formulate several hypotheses about Horton and Tokunaga self-similarity of the respective aggregation trees. The main results refer to an analytical Ring Model that describes order-based aggregation of particles in a 2-D hyperbolic space of a negative curvature -ζ^2 , ζ>0. We prove that the aggregation trees are Horton self-similar with the Horton exponent R related to the space curvature. Furthermore, we establish self-similar branching structure of the order aggregation that satisfies the Tokunaga constraint with parameters a = R - R^1/2 and c = R^1/2."],"dc:format":["PDF"],"dc:identifier.uri":["http://hdl.handle.net/11714/2053"],"dc:rights":["In Copyright(All Rights Reserved)"],"dc:subject":["Disk Model","Horton self-similar","hyperbolic space","Ring Model","self-similar","Tokunaga"],"dc:title":["Self-similarity of Random Aggregation Trees in Hyperbolic Spaces"],"dc:type":["Thesis"],"thesis:degree_level":["Master's Degree"]},"updated_at":"2026-07-27T21:46:52Z"}