Open Access. Powered by Scholars. Published by Universities.®
Discrete Mathematics and Combinatorics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 3 of 3
Full-Text Articles in Discrete Mathematics and Combinatorics
Vertex Weighted Spectral Clustering, Mohammad Masum
Vertex Weighted Spectral Clustering, Mohammad Masum
Electronic Theses and Dissertations
Spectral clustering is often used to partition a data set into a specified number of clusters. Both the unweighted and the vertex-weighted approaches use eigenvectors of the Laplacian matrix of a graph. Our focus is on using vertex-weighted methods to refine clustering of observations. An eigenvector corresponding with the second smallest eigenvalue of the Laplacian matrix of a graph is called a Fiedler vector. Coefficients of a Fiedler vector are used to partition vertices of a given graph into two clusters. A vertex of a graph is classified as unassociated if the Fiedler coefficient of the vertex is close to …
On T-Restricted Optimal Rubbling Of Graphs, Kyle Murphy
On T-Restricted Optimal Rubbling Of Graphs, Kyle Murphy
Electronic Theses and Dissertations
For a graph G = (V;E), a pebble distribution is defined as a mapping of the vertex set in to the integers, where each vertex begins with f(v) pebbles. A pebbling move takes two pebbles from some vertex adjacent to v and places one pebble on v. A rubbling move takes one pebble from each of two vertices that are adjacent to v and places one pebble on v. A vertex x is reachable under a pebbling distribution f if there exists some sequence of rubbling and pebbling moves that places a pebble on x. A pebbling distribution where every …
Differentiating Between A Protein And Its Decoy Using Nested Graph Models And Weighted Graph Theoretical Invariants, Hannah E. Green
Differentiating Between A Protein And Its Decoy Using Nested Graph Models And Weighted Graph Theoretical Invariants, Hannah E. Green
Electronic Theses and Dissertations
To determine the function of a protein, we must know its 3-dimensional structure, which can be difficult to ascertain. Currently, predictive models are used to determine the structure of a protein from its sequence, but these models do not always predict the correct structure. To this end we use a nested graph model along with weighted invariants to minimize the errors and improve the accuracy of a predictive model to determine if we have the correct structure for a protein.