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Algebraic and combinatorial aspects of group factorizations
Title
Algebraic and combinatorial aspects of group factorizations.
Creator
Bozovic, Vladimir., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
The aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the so-called free mappings, a powerful tool for factorization of a wide class of abelian and non-abelian groups. By applying a certain group action on the blocks of a factorization, a number...
Show moreThe aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the so-called free mappings, a powerful tool for factorization of a wide class of abelian and non-abelian groups. By applying a certain group action on the blocks of a factorization, a number of combinatorial and computational problems were noted and studied. In particular, we analyze the case of the group Aut(Zn) acting on blocks of factorization of Zn. We present new theoretical facts that reveal the numerical structure of the stabilizer of a set in Zn, under the action of Aut(Zn). New algorithms for finding the stabilizer of a set and checking whether two sets belong to the same orbit are proposed.
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Date Issued
2008
PURL
http://purl.flvc.org/FAU/107805
Subject Headings
Physical measurements, Mapping (Mathematics), Combinatorial enumeration problems, Algebra, Abstract
Format
Document (PDF)
Self-organizing dynamics of coupled map systems
Title
Self-organizing dynamics of coupled map systems.
Creator
Liebovitch, Larry S., Zochowski, Michal
Date Issued
1999-03
PURL
http://purl.flvc.org/fau/165481
Subject Headings
Dynamics--Mathematical models, Chaotic behavior in systems, Self-organizing maps, Self-organizing systems-Mathematical models
Format
Document (PDF)
discrete logarithm problem in non-abelian groups
Title
The discrete logarithm problem in non-abelian groups.
Creator
Iliâc, Ivana., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
This dissertation contains results of the candidate's research on the generalized discrete logarithm problem (GDLP) and its applications to cryptology, in non-abelian groups. The projective special linear groups PSL(2; p), where p is a prime, represented by matrices over the eld of order p, are investigated as potential candidates for implementation of the GDLP. Our results show that the GDLP with respect to specic pairs of PSL(2; p) generators is weak. In such cases the groups PSL(2; p) are...
Show moreThis dissertation contains results of the candidate's research on the generalized discrete logarithm problem (GDLP) and its applications to cryptology, in non-abelian groups. The projective special linear groups PSL(2; p), where p is a prime, represented by matrices over the eld of order p, are investigated as potential candidates for implementation of the GDLP. Our results show that the GDLP with respect to specic pairs of PSL(2; p) generators is weak. In such cases the groups PSL(2; p) are not good candidates for cryptographic applications which rely on the hardness of the GDLP. Results are presented on generalizing existing cryptographic primitives and protocols based on the hardness of the GDLP in non-abelian groups. A special instance of a cryptographic primitive dened over the groups SL(2; 2n), the Tillich-Zemor hash function, has been cryptanalyzed. In particular, an algorithm for constructing collisions of short length for any input parameter is presented. A series of mathematical results are developed to support the algorithm and to prove existence of short collisions.
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Date Issued
2010
PURL
http://purl.flvc.org/FAU/3356783
Subject Headings
Data encryption (Computer science), Computer security, Cryptography, Combinatorial group theory, Data processing, Mapping (Mathematics)
Format
Document (PDF)
Data Fusion of LiDAR and Aerial Imagery to Map the Campus of Florida Atlantic University
Title
Data Fusion of LiDAR and Aerial Imagery to Map the Campus of Florida Atlantic University.
Creator
Gamboa, Nicole, Zhang, Caiyun, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Geosciences
Abstract/Description
Reliable geographic intelligence is essential for urban areas; land-cover classification creates the data for urban spatial decision making. This research tested a methodology to create a land-cover map for the main campus of Florida Atlantic University in Boca Raton, Florida. The accuracy of nine separate land-cover classification results were tested; the one with the highest accuracy was chosen for the final map. Object-based image segmentation was applied to fused and LiDAR point cloud ...
Show moreReliable geographic intelligence is essential for urban areas; land-cover classification creates the data for urban spatial decision making. This research tested a methodology to create a land-cover map for the main campus of Florida Atlantic University in Boca Raton, Florida. The accuracy of nine separate land-cover classification results were tested; the one with the highest accuracy was chosen for the final map. Object-based image segmentation was applied to fused and LiDAR point cloud (elevation and intensity) data and aerial imagery. These were classified by Random Forest, k-Nearest Neighbor and Support Vector Machines classifiers. Shadow features were reclassified hierarchically in order to create a complete map. The Random Forest classifier used with the fused data set gave the highest overall accuracy at 82.3%, and a Kappa value at 0.77. When combined with the results from the shadow reclassification, the overall accuracy increased to 86.3% and the Kappa value improved to 0.82.
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Date Issued
2016
PURL
http://purl.flvc.org/fau/fd/FA00004595, http://purl.flvc.org/fau/fd/FA00004595
Subject Headings
Spatial analysis (Statistics), Geographic information systems., Cartography--Remote sensing., Thematic maps., Geospatial data--Mathematical models., Criminal justice, Administration of., African Americans, Violence against.
Format
Document (PDF)