Optimal path shape for range-only underwater target localization using a Wave Glider

Underwater localization using acoustic signals is one of the main components in a navigation system for an autonomous underwater vehicle (AUV) as a more accurate alternative to dead-reckoning techniques. Although different methods based on the idea of multiple beacons have been studied, other approaches use only one beacon, which reduces the system’s costs and deployment complexity. The inverse approach for single-beacon navigation is to use this method for target localization by an underwater or surface vehicle. In this paper, a method of range-only target localization using a Wave Glider is presented, for which simulations and sea tests have been conducted to determine optimal parameters to minimize acoustic energy use and search time, and to maximize location accuracy and precision. Finally, a field mission is presented, where a Benthic Rover (an autonomous seafloor vehicle) is localized and tracked using minimal human intervention. This mission shows, as an example, the power of using autonomous vehicles in collaboration for oceanographic research.Peer ReviewedPostprint (author's final draft

Fair Sets of Some Class of Graphs

Given a non empty set $S$ of vertices of a graph, the partiality of a vertex with respect to $S$ is the difference between maximum and minimum of the distances of the vertex to the vertices of $S$. The vertices with minimum partiality constitute the fair center of the set. Any vertex set which is the fair center of some set of vertices is called a fair set. In this paper we prove that the induced subgraph of any fair set is connected in the case of trees and characterise block graphs as the class of chordal graphs for which the induced subgraph of all fair sets are connected. The fair sets of $K_{n}$, $K_{m,n}$, $K_{n}-e$, wheel graphs, odd cycles and symmetric even graphs are identified. The fair sets of the Cartesian product graphs are also discussed.Comment: 14 pages, 4 figure

Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices

Let \orig{A} be any matrix and let $A$ be a slight random perturbation of \orig{A}. We prove that it is unlikely that $A$ has large condition number. Using this result, we prove it is unlikely that $A$ has large growth factor under Gaussian elimination without pivoting. By combining these results, we bound the smoothed precision needed by Gaussian elimination without pivoting. Our results improve the average-case analysis of Gaussian elimination without pivoting performed by Yeung and Chan (SIAM J. Matrix Anal. Appl., 1997).Comment: corrected some minor mistake

First-order transition features of the triangular Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions

We implement a new and accurate numerical entropic scheme to investigate the first-order transition features of the triangular Ising model with nearest-neighbor ($J_{nn}$) and next-nearest-neighbor ($J_{nnn}$) antiferromagnetic interactions in ratio $R=J_{nn}/J_{nnn}=1$. Important aspects of the existing theories of first-order transitions are briefly reviewed, tested on this model, and compared with previous work on the Potts model. Using lattices with linear sizes $L=30,40,...,100,120,140,160,200,240,360$ and 480 we estimate the thermal characteristics of the present weak first-order transition. Our results improve the original estimates of Rastelli et al. and verify all the generally accepted predictions of the finite-size scaling theory of first-order transitions, including transition point shifts, thermal, and magnetic anomalies. However, two of our findings are not compatible with current phenomenological expectations. The behavior of transition points, derived from the number-of-phases parameter, is not in accordance with the theoretically conjectured exponentially small shift behavior and the well-known double Gaussian approximation does not correctly describe higher correction terms of the energy cumulants. It is argued that this discrepancy has its origin in the commonly neglected contributions from domain wall corrections.Comment: 34 pages, 11 figure