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 27 for “"Spectral Graph Theory"”.
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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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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
… we resolve several longstanding questions in the 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 …
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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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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.
… to make contributions on both fronts and span theory and applications. Our contributions to the estimation of the epidemic networks are twofold. First, we propose a theoretical result combining measure theory and spectral graph theory to produce estimates of the spectral radius of a network …
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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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Infection processes on networks with structural uncertainty
… focus on the impact of network topology via the spectral radius of the adjacency matrix of the network. It is rare, however, that one has complete information about every potential disease-transmitting interaction; this uncertainty in the network structure is often ignored in deterministic …
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Dynamics of spectral algorithms for distributed routing
… new techniques in metric embeddings and spectral graph theory. The distributed computability of "oblivious routes", a core combinatorial property of every graph and a key ingredient in route engineering, opens interesting questions in the natural and experimental sciences as well. …
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From graphs to matrices, and back : new techniques for graph algorithms
… the above question in the context of algorithmic graph theory. To pursue this direction, we develop a toolkit that combines a diverse set of modern algorithmic techniques, including sparsification, low-stretch spanning trees, the multiplicative-weights-update method, dynamic graph algorithms, fast …
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Prediction and Control of Thermal History in Laser Powder Bed Fusion
… thermal modeling method based on the concept of spectral graph theory, which is more than 10 times faster than existing finite element-based methods for the same level of accuracy. The central hypothesis is that physics-guided prediction, optimization, and control of thermal history mitigates …
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