Equally charged with orderly conduct

Orderly Spanning Trees with Applications

We introduce and study orderly spanning trees of plane graphs. This algorithmic tool generalizes canonical orderings, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning tree, we provide an algorithm to compute an orderly pair for any connected planar graph G, consisting of an embedded planar graph H isomorphic to G, and an orderly spanning ...

Orderly Analysis of Social Visualizations

Recent advances in technology have allowed people to shift many of their communication practices online. These practices, such as email, IM, VoIP, and video conferencing, can be archived to serve as digital artifacts from which social information, such as social networks, can be extracted. Social network analysis has emerged as a powerful method for understanding the importance of relationships...

Consecutive Integers with Equally Many Principal Divisors

Classifying the positive integers as primes, composites, and the unit, is so familiar that it seems inevitable. However, other classifications can bring interesting relationships to our attention. In that spirit, let us classify positive integers by the number of principal divisors they possess, where we define a principal divisor of a positive integer n to be any prime-power divisor pa|n which...

The orderly chaos of proteins.

Orderly spectra from random interactions

We investigate the low-lying spectra of many-body systems with random two-body interactions, specifying that the ensemble be invariant under particle-hole conjugation. Surprisingly we find patterns reminiscent of more orderly interactions, such as a predominance of J = 0 ground states separated by a gap from the excited states, and evidence of phonon vibrations in the low-lying spectra. c ©1998...