Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the set of Fixed Points of the Parallel Symmetric Sand Pile Model   Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of
Self-Organized Criticality. From a configuration composed of a finite number of
stacked grains, we apply on every possible positions (in parallel) two grain
moving transition rules. The transition rules permit one grain to fall to its
right or left (symmetric) neighboring column if the difference of height
between those columns is larger than 2. The model is nondeterministic and
grains always fall downward. We propose a study of the set of fixed points
reachable in the Parallel Symmetric Sand Pile Model (PSSPM). Using a comparison
with the Symmetric Sand Pile Model (SSPM) on which rules are applied once at
each iteration, we get a continuity property. This property states that within
PSSPM we can't reach every fixed points of SSPM, but a continuous subset
according to the lexicographic order. Moreover we define a successor relation
to browse exhaustively the sets of fixed points of those models.

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The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph