3,776 research outputs found
List rankings and on-line list rankings of graphs
A -ranking of a graph is a labeling of its vertices from
such that any nontrivial path whose endpoints have the same
label contains a larger label. The least for which has a -ranking is
the ranking number of , also known as tree-depth. The list ranking number of
is the least such that if each vertex of is assigned a set of
potential labels, then 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
- …