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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 21 for “"Laplacian matrix"”.
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Network connectivity tracking for a team of unmanned aerial vehicles
… is the second-smallest eigenvalue of the Laplacian matrix and can be used as a metric for the robustness and efficiency of a network. This connectivity concept applies to teams of multiple unmanned aerial vehicles (UAVs) performing cooperative tasks, such as arriving at a consensus. As a …
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Spectrum of some regular graphs with widely spaced modifications
… we show that the eigenvalues of the adjacency matrix and Laplacian matrix have high multiplicities. As the trees grow, the graphs of those eigenvalues approach a piecewise-constant "Cantor function", which is different from the corresponding properties of the infinite tree. The second part …
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Learning Sparse Graph Laplacian with K Eigenvector Prior via Iterative GLASSO and Projection
… In this thesis, given an empirical covariance matrix computed from data as input, an eigen-structural assumption on the graph Laplacian matrix is considered: the first K eigenvectors of the graph Laplacian are pre-selected, e.g., based on domain-specific criteria, and the remaining eigenvectors …
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Stability thresholds for signed Laplacians on locally-connected networks
… defined on graphs, and we use signed graph Laplacians as our tool. In chapter 1, we give the formal definition of the Laplacian matrix for a graph, and point out several references on it. In chapter 2, we give the main result from one of the references, along with other preliminaries we need …
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Fractional Chromatic Numbers and Spectra of Graphs
… spectra of edge-independent random graphs, Laplacian spectra of hypergraphs, and loose Laplacian spectra of random hypergraphs.</p> <p>For a graph $G$, let $\chi_f(G)$ be the fractional chromatic number of $G$. Based on the study of independence numbers of triangle-free graphs with maximum …
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Interpretable Deep Image Denoiser by Unrolling Graph Laplacian Regularizer
… optimization problem regularized using a graph Laplacian prior. To guarantee a minimum level of performance, we initialize the network to a known (pseudo-)linear denoiser, which is mapped to a corresponding graph Laplacian matrix specifying the MAP problem, leveraging a previous linear algebraic …
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Properties and Recent Applications in Spectral Graph Theory
… of graphs, such as the walks and the adjacency matrix are explored. In addition, bipartite graphs are discussed along with properties that apply strictly to bipartite graphs. The main focus is on the characteristic polynomial and the eigenvalues that it produces, because most of the applications …
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Consensus Algorithms for Estimation and Discrete Averaging in Networked Control Systems
… in a decentralized way the spectrum of the Laplacian matrix that encodes the network topology. As emergent behavior, each agent's state oscillates only at frequencies corresponding to the eigenvalues of the Laplacian matrix thus mapping the spectrum estimation problem into a signal …
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Decentralised network prediction and reconstruction algorithms
… (mEEP) that can be directly computed from the Laplacian matrix of the graph and from the underlying network structure. Later, we consider a number of possible theoretical extensions of the proposed algorithm to issues arising from practical applications, e.g., time-delays, noise, external …
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Distributed adaptive control methods for uncertain multiagent systems with coupled dynamics
… using global information by user-assigned Laplacian matrix nullspaces.</p> <p>First, a literature review and motivation, followed by contribution, are given. Then, the problems are formulated for scalar and high-order multiagent systems, adaptive control designs along with the stability …
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Combinatorics of acyclic orientations of graphs : algebra, geometry and probability
… of the thesis, we will use eigenvectors of the Laplacian matrix of a graph, in particular, those corresponding to the largest eigenvalue, to label its vertex-set and to induce partial orientations of its edge-set. What information about the graph can be gathered from these partial orientations? …
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Applications of Geometric and Spectral Methods in Graph Theory
… the second-smallest eigenvalue of the normalized Laplacian matrix of <em>G</em>, then <em>G</em> contains at least [δλ<sub>1</sub>/ <em>C</em> log <em>n</em>] edge-disjoint rainbow spanning trees.</p> <p>We show how curvature lower bounds can be used in the context of understanding (personalized) …
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Dynamical systems on networks
… of such fixed points can be studied with a Laplacian matrix. We give a formula for the inertia of these matrices, characterizing the real parts of the spectrum, by relating them to another matrix depending on the network topology. We then study the Kuramoto model, and in particular, the …
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Coupling in SPDEs and spectral analysis of heavy-tailed random operators
… induced on the diagonal of a finite-volume 1-d Laplacian matrix) where the coefficients of the potential scale down with respect to the volume size. The results are: (1) a scaling limit at the spectral edge at a particular rate of downward scaling; and (2) a large deviation result in the …
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Components of the Emerton-Gee Moduli Stack of Galois Representations for GL2 and A Graph-Theoretic Approach to Computing Selmer Groups of Elliptic Curves over Q(i)
… interpretation of the φ-Selmer group through the Laplacian matrix of G_b. Using our algorithm, we explicitly construct several subfamilies of elliptic curves E_b over Q(i) with trivial Mordell–Weil rank. Furthermore, by combining our method with Tao’s Constellation Theorem for Gaussian primes, we …
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Medical Image Analysis Based on Graph Machine Learning and Variational Methods
… Our Spectral-Spatial GNN model, integrating the Laplacian matrix, demonstrated significant improvements in segmenting distinct tumor sub-regions of Necrosis, Edema, and Enhancing Tumor. Our research shows that GNNs, combining spectral and spatial aspects, provide a superior approach for accurate …
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Inferring Undirected and Causally Directed Graph Structures from Multivariate Time Series
… the graph smoothness defined by minimization the Laplacian quadratic form is used to infer the connectivity map (adjacency matrix of the graph). The cortical evoked potential (CEP) map, which is the measure of underlying physiological connectivity is used as the groundtruth. The maps obtained by …
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A general state-based temporal pattern recognition
… from basketball videos is introduced, where the Laplacian Matrix-based algorithm is extended to take into account the effects from zoom and single defender‘s translation in zone-defence graph matching and a set of character-angle based features was proposed to describe the zone-defence graph. The …
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Consistent community detection in uni-layer and multi-layer networks
… modularity score and (3) based on spectral and matrix factorization methods. In Chapter 2 we consider two random graph models for community detection in multi-layer networks, the multi-layer stochastic block model (MLSBM) and a model with a restricted parameter space, the restricted multi-layer …
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Real-time analytics for complex structure data
… features as gauge to classify unlabeled nodes. A Laplacian based quality criterion is proposed to guide the node classification, where the Laplacian matrix is generated based on node labels and network topology structures. Node classification is achieved by finding the class label that results in …
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