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Algorithmic information, fractal geometry, and distributed dynamics

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TitleInfo
Title
Algorithmic information, fractal geometry, and distributed dynamics
Name (type = personal)
NamePart (type = family)
Lutz
NamePart (type = given)
Neil J.
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Neil J. Lutz
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author
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Wright
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Rebecca N
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Rebecca N Wright
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Advisory Committee
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chair
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Eric
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Eric Allender
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Advisory Committee
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internal member
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Saraf
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Shubhangi
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Shubhangi Saraf
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Advisory Committee
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internal member
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Braverman
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Mark
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Mark Braverman
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Advisory Committee
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outside member
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Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
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School of Graduate Studies
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school
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Text
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theses
OriginInfo
DateCreated (qualifier = exact)
2017
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2017-10
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2017
Place
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xx
Language
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eng
Abstract (type = abstract)
This dissertation applies two distinct algorithmic perspectives to questions in the field of fractal geometry and dynamics. In Part I, we establish connections between algorithmic information theory and classical fractal geometry. Working in Euclidean spaces, we characterize Hausdorff and packing dimensions in terms of relativized Kolmogorov complexity, and we develop conditional dimensions. These tools give rise to new dimensional bounding techniques, which we apply to problems in fractal geometry. Most significantly, we prove that a classical dimension bound for intersections of Borel sets holds for arbitrary sets, and we give a new lower bound on the Hausdorff dimension of generalized Furstenberg sets. In Part II, we use ideas from distributed computing and game theory to study dynamic and decentralized environments in which computational nodes interact strategically and with limited information. We exhibit a general non-convergence result for a broad class of dynamics in asynchronous settings. For uncoupled game dynamics, in which preferences are private inputs, we give new bounds on the recall necessary for self stabilization to an equilibrium.
Subject (authority = RUETD)
Topic
Computer Science
Subject (authority = ETD-LCSH)
Topic
Kolmogorov complexity
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TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
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ETD_8228
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electronic resource
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Extent
1 online resource (vi, 122 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Neil J. Lutz
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Title
School of Graduate Studies Electronic Theses and Dissertations
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rucore10001600001
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Identifier (type = doi)
doi:10.7282/T3639SV4
Genre (authority = ExL-Esploro)
ETD doctoral
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Rights

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The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Lutz
GivenName
Neil
MiddleName
J.
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2017-06-09 15:22:08
AssociatedEntity
Name
Neil Lutz
Role
Copyright holder
Affiliation
Rutgers University. School of Graduate Studies
AssociatedObject
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Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical

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2017-06-09T15:17:34
DateCreated (point = end); (encoding = w3cdtf); (qualifier = exact)
2017-06-09T15:17:34
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