Research Spotlights

Abstract

This issue's Research Spotlights section contains three papers. First, “Pairwise Compatibility Graphs: A Survey," by Tiziana Calamoneri and Blerina Sinaimeri, describes computational graph theory methods as applied to computational biology. The evolutionary ancestral relationships of species can be described using a tree-like graph structure known as a phylogenetic tree. Using optimization techniques, the goal is to reconstruct the best possible tree structure starting from a set of biological data. However, the data sets are large and the phylogenetic tree reconstruction problem is known to be NP-hard. This article presents an approach using carefully chosen subsets of the original data set. The work is of particular interest to a reader interested in graph theory or computational biology. The second article in this section, “Computing Fundamental Matrix Decompositions Accurately via the Matrix Sign Function in Two Iterations: The Power of Zolotarev's Functions," by Yuji Nakatsukasa and Roland W. Freund, describes a new algorithm for matrix decomposition. The paper develops a high order method using functions of Zolotarev (1877) to calculate two standard matrix decompositions: singular value and symmetric eigenvalue decompositions. The method is designed to be well suited for parallel computing. This article gives a self-contained description of the method and its convergence. It will appeal to those interested in either the theory of numerical linear algebra or its application for large-scale matrix decompositions. The third paper, “Optimal Mixing Enhancement by Local Perturbation," by Gary Froyland, Cecilia González-Tokman, and Thomas M. Watson, develops optimal methods for applying local perturbations in order to most effectively increase the process of mixing in a dynamical system. The approach is a systematic way of turning a dynamical system into a convex optimization problem. This paper will appeal to a broad set of readers, as the control of fluid mixing not only is of theoretical interest but also has wide-ranging applications on many different length scales within engineering and natural sciences. For example, it is important in the speedup of industrial chemical mixing, the prevention of pollutant spread in oceanographic and atmospheric flow, and the control of microfluidics.