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- Title
- Computing topological dynamics from time series.
- Creator
- Wess, Mark., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
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The topological entropy of a continuous map quantifies the amount of chaos observed in the map. In this dissertation we present computational methods which enable us to compute topological entropy for given time series data generated from a continuous map with a transitive attractor. A triangulation is constructed in order to approximate the attractor and to construct a multivalued map that approximates the dynamics of the linear interpolant on the triangulation. The methods utilize...
Show moreThe topological entropy of a continuous map quantifies the amount of chaos observed in the map. In this dissertation we present computational methods which enable us to compute topological entropy for given time series data generated from a continuous map with a transitive attractor. A triangulation is constructed in order to approximate the attractor and to construct a multivalued map that approximates the dynamics of the linear interpolant on the triangulation. The methods utilize simplicial homology and in particular the Lefschetz Fixed Point Theorem to establish the existence of periodic orbits for the linear interpolant. A semiconjugacy is formed with a subshift of nite type for which the entropy can be calculated and provides a lower bound for the entropy of the linear interpolant. The dissertation concludes with a discussion of possible applications of this analysis to experimental time series.
Show less - Date Issued
- 2008
- PURL
- http://purl.flvc.org/FAU/186294
- Subject Headings
- Algebraic topology, Graph theory, Fixed point theory, Singularities (Mathematics)
- Format
- Document (PDF)
- Title
- Graph labeling and non-separating trees.
- Creator
- Gottipati, Chenchu B., Locke, Stephen C., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
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This dissertation studies two independent problems, one is about graph labeling and the other problem is related to connectivity condition in a simple graph. Graph labeling is a rapidly developing area of research in graph theory, having connections with a variety of application-oriented areas such as VLSI optimization, data structures and data representation. Furthermore, the connectivity conditions in a simple graphs may help us to study the new aspects of ad hoc networks, social networks...
Show moreThis dissertation studies two independent problems, one is about graph labeling and the other problem is related to connectivity condition in a simple graph. Graph labeling is a rapidly developing area of research in graph theory, having connections with a variety of application-oriented areas such as VLSI optimization, data structures and data representation. Furthermore, the connectivity conditions in a simple graphs may help us to study the new aspects of ad hoc networks, social networks and web graphs. In chapter 2, we study path systems, reduced path systems and how to construct a super edge-graceful tree with any number of edges using path systems. First, we give an algorithm to reduce a labeled path system to a smaller labeled path system of a different type. First, we investigate the cases (m, k) = (3; 5) and (m, k) = (4; 7), where m is the number of paths and 2k is the length of each path, and then we give a generalization for any k, m = 3 and m = 4. We also describe a procedure to construct a super-edge-graceful tree with any number of edges.
Show less - Date Issued
- 2014
- PURL
- http://purl.flvc.org/fau/fd/FA00004289, http://purl.flvc.org/fau/fd/FA00004289
- Subject Headings
- Computational complexity, Computer graphics, Graph theory, Integrated circuits -- Very large scale integration, Mathematical optimization
- Format
- Document (PDF)
- Title
- LONESUM MATRICES AND ACYCLIC ORIENTATIONS: ENUMERATION AND ASYMPTOTICS.
- Creator
- Khera, Jessica, Lundberg, Erik, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
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An acyclic orientation of a graph is an assignment of a direction to each edge in a way that does not form any directed cycles. Acyclic orientations of a complete bipartite graph are in bijection with a class of matrices called lonesum matrices, which can be uniquely reconstructed from their row and column sums. We utilize this connection and other properties of lonesum matrices to determine an analytic form of the generating function for the length of the longest path in an acyclic...
Show moreAn acyclic orientation of a graph is an assignment of a direction to each edge in a way that does not form any directed cycles. Acyclic orientations of a complete bipartite graph are in bijection with a class of matrices called lonesum matrices, which can be uniquely reconstructed from their row and column sums. We utilize this connection and other properties of lonesum matrices to determine an analytic form of the generating function for the length of the longest path in an acyclic orientation on a complete bipartite graph, and then study the distribution of the length of the longest path when the acyclic orientation is random. We use methods of analytic combinatorics, including analytic combinatorics in several variables (ACSV), to determine asymptotics for lonesum matrices and other related classes.
Show less - Date Issued
- 2021
- PURL
- http://purl.flvc.org/fau/fd/FA00013716
- Subject Headings
- Matrices, Combinatorial analysis, Graph theory
- Format
- Document (PDF)
- Title
- THE MINIMUM K-CENTER PROBLEM FOR GRID GRAPH.
- Creator
- HSUEH, CHI-FU, Florida Atlantic University, Hadlock, Frank O., Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
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A study was made of the problem of locating M facilities on a connected grid graph, so that M is the minimum and so that every demand node on the graph is within given distance K of one of these M facilities. We call this problem briefly the G(N,K,M) problem, with N denoting the total number of demand nodes. An algorithm for solving this problem by using backtrack technique is presented in this thesis. A heuristic algorithm is also present; although the resulting M is not always minimum, it...
Show moreA study was made of the problem of locating M facilities on a connected grid graph, so that M is the minimum and so that every demand node on the graph is within given distance K of one of these M facilities. We call this problem briefly the G(N,K,M) problem, with N denoting the total number of demand nodes. An algorithm for solving this problem by using backtrack technique is presented in this thesis. A heuristic algorithm is also present; although the resulting M is not always minimum, it tends to be near minimum. The advantage over the backtrack algorithm is that the heuristic algorithm operates very quickly. Algorithms represented in this thesis are programmed in the Pascal language for the Univac 1100 computer at Florida Atlantic University, Boca Raton, Florida.
Show less - Date Issued
- 1981
- PURL
- http://purl.flvc.org/fcla/dt/14077
- Subject Headings
- Graph theory, Algorithms
- Format
- Document (PDF)