List rankings and on-line list rankings of graphs

A $k$-ranking of a graph $G$ is a labeling of its vertices from $\{1,\ldots,k\}$ such that any nontrivial path whose endpoints have the same label contains a larger label. The least $k$ for which $G$ has a $k$-ranking is the ranking number of $G$, also known as tree-depth. The list ranking number of $G$ is the least $k$ such that if each vertex of $G$ is assigned a set of $k$ potential labels, then $G$ can be ranked by labeling each vertex with a label from its assigned list. Rankings model a certain parallel processing problem in manufacturing, while the list ranking version adds scheduling constraints. We compute the list ranking number of paths, cycles, and trees with many more leaves than internal vertices. Some of these results follow from stronger theorems we prove about on-line versions of list ranking, where each vertex starts with an empty list having some fixed capacity, and potential labels are presented one by one, at which time they are added to the lists of certain vertices; the decision of which of these vertices are actually to be ranked with that label must be made immediately.Comment: 16 pages, 3 figure

Algorithms for Estimating Trends in Global Temperature Volatility

Trends in terrestrial temperature variability are perhaps more relevant for species viability than trends in mean temperature. In this paper, we develop methodology for estimating such trends using multi-resolution climate data from polar orbiting weather satellites. We derive two novel algorithms for computation that are tailored for dense, gridded observations over both space and time. We evaluate our methods with a simulation that mimics these data's features and on a large, publicly available, global temperature dataset with the eventual goal of tracking trends in cloud reflectance temperature variability.Comment: Published in AAAI-1

A primer on the mortgage market and mortgage finance

This article is a primer on mortgage finance. It discusses the basics of the mortgage market and mortgage finance. In so doing, it provides useful information that can aid individuals in making better mortgage finance decisions. The discussion and the tools are presented within the context of mortgage finance; however, these same principles and tools can be applied to a wide range of financial decisions.Mortgages