We present a distance metric based upon the notion of minimum-cost injective mappings between sets. Our function satisfies metric properties as long as the cost of the minimum mappings is derived from a semimetric, for which the triangle inequality is not necessarily satisfied. We show that the Jaccard distance (alternatively biotope, Tanimoto, or… (More)
For k = 0, 1, 2, 3, 4, 5, let P k be the class of k-edge-connected 5-regular planar graphs. In this paper, graph operations are introduced that generate all graphs in each P k .
Protein folding is frequently guided by local residue interactions that form clusters in the protein core. The interactions between residue clusters serve as potential nucleation sites in the folding process. Evidence postulates that the residue interactions are governed by the hydrophobic propensities that the residues possess. An array of hydrophobicity… (More)
—Positive definite kernels are an important tool in machine learning that enable efficient solutions to otherwise difficult or intractable problems by implicitly linearizing the problem geometry. In this paper we develop a set-theoretic interpretation of the Earth Mover's Distance (EMD) that naturally yields metric and kernel forms of EMD as generalizations… (More)
Let ; kkg be the class of k-connected cubic graphs of girth at least g. For several choices of k and g, w e determine a set O kkg of graph operations, for which, if G and H are graphs in ; kkg , G 6 = H, and G contains H topologically, then some operation in O kkg can be applied to G to result in a smaller graph G 0 in ; kkg such that, on one hand, G 0 is… (More)
me the opportunity to pursue my interest in the field of graph theory. I would like to thank all the people at LSU for their kindness and openness. Most of all, I wish to express my sincere appreciation to my advisor, Professor Guoli Ding for his strong support, useful advice, openness and endless patience without which this work would not have been… (More)
—We present a distributed algorithm for the navigation of an Unmanned Ground Vehicle (UGV) towards a set of identified target nodes in coordinate-free and localization-free wireless sensor and actuator networks. The navigation algorithm proceeds in two phases: first, a node level is determined based on a hop distance from the target nodes, which is… (More)