Topics range from analyzing mathematical properties of graph polynomials to applying the polynomials in several application areas, including discussion of the interlace polynomial, independence polynomials of k-trees and compound graphs, new aspects of the Abelian
sandpile model on graphs and their polynomials, second quantization of recurrences, the matching polynomial, the permanental polynomials of graphs, the general graph homomorphism polynomial, derivatives and real roots of graph polynomials, logic-based computation of graph polynomials, the alliance polynomial, and graph polynomials and set functions.
Seminal work by Newhouse offered the "
sandpile" hypothesis--supply will be higher in more populous areas with more demand, and then as the overall supply increases, supply in areas with lower demand will increase (Rosenthal, Zaslavsky, and Newhouse 2005).
On the final pages of one of their reports, Gregor's team included an unsubtle warning: a stock image of a man with his head submerged in a
sandpile.
The present-day site of Manila's Entertainment City and noteworthy edifices is built of select dredged fill, subsequently upgraded by
sandpile drains that were installed using the Fudo process (Japanese) on the recommendation of Kawasaki Engineers, Japan.
To understand grid behavior, let's start with a
sandpile or, better yet, a mound of rice.
Never one to be put off by, well, being put off, I gathered my notes, staggered out to the
sandpile and delivered it anyway, to my usual audience--my dog Sancho and several lizards.
However, the essentially equivalent notion of superstable configurations has been studied for longer in the context of the abelian
sandpile model; see (Hopkins and Perkinson, 2012a, [section]2.4) for a definition of these and their connection to parking functions.
For instance, in one room, the shoes of the laborers who helped set up the exhibition were exhibited; in another, strings of local marigolds were prominent; and in a third, a
sandpile, home to an insect colony, remained undisturbed.
In the DDM introduced by Goles and Kiwi in [4], denoted by SPM(n), a configuration is an integer partition a = ([a.sub.1],..., [a.sub.n]) of the positive integer n, and each summand of a is identified with a pile of sand grains; hence, the name is
sandpile model (briefly SPM).
Fittingly, network scientists call these avalanches "
sandpile cascades."