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.
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Showing 1 to 20 of 34 for “"spectral graph"”.
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Properties and Recent Applications in Spectral Graph Theory
… applications of mathematics, specifically spectral graph theory, within the sciences and many other fields. This paper is an exploration of recent applications of spectral graph theory, including the fields of chemistry, biology, and graph coloring. Topics such as the isomers of alkanes, …
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Spectral graph theory analysis of software-defined networks to improve performance and security
… is based on the eigendecomposition of a weighted graph that accounts for the network topology and traffic load. A software-defined network closed-loop control scheme is developed; the scheme is modeled after a closed-loop control system that includes an observer and a controller. A particle filter …
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Spectra of Hypergraphs
<p>We present a spectral theory of uniform hypergraphs that closely parallels Spectral Graph Theory. A number of developments building upon classical work has led to a rich understanding of 'symmetric hyperdeterminants' of hypermatrices, a.k.a. multidimensional arrays. Symmetric hyperdeterminants …
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Graphs, Principal Minors, and Eigenvalue Problems
… point processes, extremal problems in spectral graph theory, force-directed layouts, and eigenvalue algorithms. For determinantal point processes (DPPs), we consider the classes of symmetric and signed DPPs, respectively, and in both cases connect the problem of learning the parameters …
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Discrepancy Inequalities in Graphs and Their Applications
<p>Spectral graph theory, which is the use of eigenvalues of matrices associated with graphs, is a modern technique that has expanded our understanding of graphs and their structure. A particularly useful tool in spectral graph theory is the Expander Mixing Lemma, also known as the discrepancy …
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Applications of Geometric and Spectral Methods in Graph Theory
<p>Networks, or graphs, are useful for studying many things in today’s world. Graphs can be used to represent connections on social media, transportation networks, or even the internet. Because of this, it’s helpful to study graphs and learn what we can say about the structure of a given graph or …
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On the minimum rank of certain graphs with path cover number 2
… problem is an interesting and ongoing problem in spectral graph theory which seeks to answer the question "Given a simple graph G what is the minimum rank of a matrix whose off-diagonal zero/nonzero pattern is described by G?" In recent years, the minimum rank of trees, unicyclic graphs, and cases …
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Localization and sensing applications in the Pushpin Computer Network
… non-linear optimization techniques, namely spectral graph drawing and mesh relaxation. In both cases, localization is accomplished by generating distance constraints based on ultrasound time-of-flight measurements to distinct, global sensor stimuli. These distance constraints alone are …
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Spectral Properties of Quaternionic Unit Gain Cycles
… ring that extends the complex numbers. A gain graph is a simple graph together with a gain function that assigns a value from an arbitrary group to each edge of the graph. We can define certain concepts on these graphs such as adjacency and Laplacian matrices, gains of paths, and more. If we …
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Nonlinear Dimensionality Reduction for the Thermodynamics of Small Clusters of Particles
… such clusters is studied using techniques from spectral graph theory (SGT) and machine learning (ML). SGT is used to define the structure of the clusters and ML is used on ensembles of cluster configurations to detect state variables that can be used to model the thermodynamic properties of the …
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New geometric techniques for linear programming and graph partitioning
… theory of linear programming, polytope theory, spectral graph theory, and graph partitioning. The thesis consists of two main parts. In the first part, which is joint work with Daniel Spielman, we present the first randomized polynomial-time simplex algorithm for linear programming, answering a …
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On Some Geometry of Graphs
… this thesis we study the intrinsic geometry of graphs via the constants that appear in discretized partial differential equations associated to those graphs. By studying the behavior of a discretized version of Bochner's inequality for smooth manifolds at the cone point for a cone over the set …
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Graph spectra and modal dynamics of oscillatory networks
… how the interconnection topology relates to the spectral properties of the system. Such oscillatory networks are ubiquitous, extending from miniature electronic circuits to large-scale power networks. We tap into the rich mathematical literature on graph spectra, and develop theoretical …
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Graphs, matrices, and populations : linear algebraic techniques in theoretical computer science and population genetics
… several algorithmic results for problems in spectral graph theory and computational biology. The first part concerns the problem of spectral sparsification. It is known that every dense graph can be approximated in a strong sense by a sparse subgraph, known as a spectral sparsifier of the …
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Active flows and networks
… systems, the spectrum of the underlying graph Laplacian plays a key role in controlling the flow. Spectral graph theory has traditionally prioritized analyzing Laplacians of unweighted networks with specified adjacency properties. For the second part of the thesis, we introduce a …
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TOWARDS DATA DRIVEN NETWORK EPIDEMIC MODELING.
… theoretical result combining measure theory and spectral graph theory to produce estimates of the spectral radius of a network based on local measurements; which is known to be the epidemic threshold of many epidemic models over networks. Second is a data-driven approach, in which we validate …
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Multilevel spectral clustering : graph partitions and image segmentation
While the spectral graph partitioning method gives high quality segmentation, segmenting large graphs by the spectral method is computationally expensive. Numerous multilevel graph partitioning algorithms are proposed to reduce the segmentation time for the spectral partition of large graphs. …
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Spectral analysis of neutral evolution
… In this work, we build on recent results from spectral graph theory and utilize numerical methods to enhance our understanding of how populations distribute themselves over neutral networks. We demonstrate that, in the presence of certain topological features, the population will undergo an …
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Iterative methods, combinatorial optimization, and linear programming beyond the universal barrier
… techniques from diverse disciplines including spectral graph theory, numerical analysis, data structures, and convex optimization we provide the first theoretical improvements in decades for multiple classic problems ranging from linear programming to linear system solving to maximum flow. Key …
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Algorithms and Systems for Scalable Multi-Agent Geometric Estimation
… this end, this thesis presents distributed pose graph optimization algorithms with the goals of achieving certifiable global optimality and convergence under asynchronous communication. Leveraging the developed algorithms, this thesis then develops a complete system for distributed simultaneous …
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