Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reverse engineering time discrete finite dynamical systems: A feasible
  undertaking?   With the advent of high-throughput profiling methods, interest in reverse
engineering the structure and dynamics of biochemical networks is high.
Recently an algorithm for reverse engineering of biochemical networks was
developed by Laubenbacher and Stigler. It is a top-down approach using time
discrete dynamical systems. One of its key steps includes the choice of a term
order. The aim of this paper is to identify minimal requirements on data sets
to be used with this algorithm and to characterize optimal data sets. We found
minimal requirements on a data set based on how many terms the functions to be
reverse engineered display. Furthermore, we identified optimal data sets, which
we characterized using a geometric property called "general position".
Moreover, we developed a constructive method to generate optimal data sets,
provided a codimensional condition is fulfilled. In addition, we present a
generalization of their algorithm that does not depend on the choice of a term
order. For this method we derived a formula for the probability of finding the
correct model, provided the data set used is optimal. We analyzed the
asymptotic behavior of the probability formula for a growing number of
variables n (i.e. interacting chemicals). Unfortunately, this formula converges
to zero as fast as r^(q^n), where q is a natural number and 0<r<1. Therefore,
even if an optimal data set is used and the restrictions in using term orders
are overcome, the reverse engineering problem remains unfeasible, unless
prodigious amounts of data are available. Such large data sets are
experimentally impossible to generate with today's technologies.

20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an