Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semipredictable dynamical systems   A new class of deterministic dynamical systems, termed semipredictable
dynamical systems, is presented. The spatiotemporal evolution of these systems
have both predictable and unpredictable traits, as found in natural complex
systems. We prove a general result: The dynamics of any deterministic nonlinear
cellular automaton (CA) with $p$ possible dynamical states can be decomposed at
each instant of time in a superposition of $N$ layers involving $p_{0}$,
$p_{1}$,... $p_{N-1}$ dynamical states each, where the $p_{k\in \mathbb{N}}$,
$k \in [0, N-1]$ are divisors of $p$. If the divisors coincide with the prime
factors of $p$ this decomposition is unique. Conversely, we also prove that $N$
CA working on symbols $p_{0}$, $p_{1}$,... $p_{N-1}$ can be composed to create
a graded CA rule with $N$ different layers. We then show that, even when the
full spatiotemporal evolution can be unpredictable, certain traits (layers) can
exactly be predicted. We present explicit examples of such systems involving
compositions of Wolfram's 256 elementary CA and a more complex CA rule acting
on a neighborhood of two sites and 12 symbols and whose rule table corresponds
to the smallest Moufang loop $M_{12}(S_{3},2)$.

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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an