2,147 research outputs found
Cellular automata and self-organized criticality
Cellular automata provide a fascinating class of dynamical systems capable of
diverse complex behavior. These include simplified models for many phenomena
seen in nature. Among other things, they provide insight into self-organized
criticality, wherein dissipative systems naturally drive themselves to a
critical state with important phenomena occurring over a wide range of length
and time scales.Comment: 23 pages, 12 figures (most in color); uses sprocl.tex; chapter
submitted for "Some new directions in science on computers," G. Bhanot, S.
Chen, and P. Seiden, ed
A theory of hyperfinite sets
We develop an axiomatic set theory -- the Theory of Hyperfinite Sets THS,
which is based on the idea of existence of proper subclasses of big finite
sets. We demonstrate how theorems of classical continuous mathematics can be
transfered to THS, prove consistency of THS and present some applications.Comment: 28 page
Counting spanning trees in a small-world Farey graph
The problem of spanning trees is closely related to various interesting
problems in the area of statistical physics, but determining the number of
spanning trees in general networks is computationally intractable. In this
paper, we perform a study on the enumeration of spanning trees in a specific
small-world network with an exponential distribution of vertex degrees, which
is called a Farey graph since it is associated with the famous Farey sequence.
According to the particular network structure, we provide some recursive
relations governing the Laplacian characteristic polynomials of a Farey graph
and its subgraphs. Then, making use of these relations obtained here, we derive
the exact number of spanning trees in the Farey graph, as well as an
approximate numerical solution for the asymptotic growth constant
characterizing the network. Finally, we compare our results with those of
different types of networks previously investigated.Comment: Definitive version accepted for publication in Physica
On the Exhaustive Generation of Plane Partitions
We present a CAT (Constant Amortized Time) algorithm for generating all plane partitions of an integer n, that is, all integer matrices with non-increasing rows and columns having sum n
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