1,548 research outputs found
Recognizing Partial Cubes in Quadratic Time
We show how to test whether a graph with n vertices and m edges is a partial
cube, and if so how to find a distance-preserving embedding of the graph into a
hypercube, in the near-optimal time bound O(n^2), improving previous O(nm)-time
solutions.Comment: 25 pages, five figures. This version significantly expands previous
versions, including a new report on an implementation of the algorithm and
experiments with i
Happy endings for flip graphs
We show that the triangulations of a finite point set form a flip graph that
can be embedded isometrically into a hypercube, if and only if the point set
has no empty convex pentagon. Point sets of this type include convex subsets of
lattices, points on two lines, and several other infinite families. As a
consequence, flip distance in such point sets can be computed efficiently.Comment: 26 pages, 15 figures. Revised and expanded for journal publicatio
Mathematical story: a metaphor for mathematics curriculum
This paper proposes a theoretical framework for interpreting mathematical content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of mathematics curriculum as story and defines and illustrates the mathematical story elements of mathematical characters, action, setting, and plot. Drawn from literary theory, this framework supports the interpretation of mathematics curriculum as art, able to stimulate the imagination and curiosity of students and teachers alike. In doing so, it is argued, this framework offers teachers and other curriculum designers a conceptual tool that can be used to improve the mathematics curriculum offered to students in terms of both logic and aesthetic
Beyond XSPEC: Towards Highly Configurable Analysis
We present a quantitative comparison between software features of the defacto
standard X-ray spectral analysis tool, XSPEC, and ISIS, the Interactive
Spectral Interpretation System. Our emphasis is on customized analysis, with
ISIS offered as a strong example of configurable software. While noting that
XSPEC has been of immense value to astronomers, and that its scientific core is
moderately extensible--most commonly via the inclusion of user contributed
"local models"--we identify a series of limitations with its use beyond
conventional spectral modeling. We argue that from the viewpoint of the
astronomical user, the XSPEC internal structure presents a Black Box Problem,
with many of its important features hidden from the top-level interface, thus
discouraging user customization. Drawing from examples in custom modeling,
numerical analysis, parallel computation, visualization, data management, and
automated code generation, we show how a numerically scriptable, modular, and
extensible analysis platform such as ISIS facilitates many forms of advanced
astrophysical inquiry.Comment: Accepted by PASP, for July 2008 (15 pages
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