186 research outputs found
Generic Cohen-Macaulay monomial ideals
Given a simplicial complex, it is easy to construct a generic deformation of
its Stanley-Reisner ideal. The main question under investigation in this paper
is how to characterize the simplicial complexes such that their Stanley-Reisner
ideals have Cohen-Macaulay generic deformations. Algorithms are presented to
construct such deformations for matroid complexes, shifted complexes, and tree
complexes.Comment: 18 pages, 8 figure
Generalized Mayer-Vietoris sequences in algebraic K-theory
AbstractLong exact sequences of algebraic K-groups for certain kinds of multiple pullback rings are constructed, with special emphasis on Dedekind-like rings. In the case where excision holds they reduce to the usual Mayer-Vietoris sequences. These sequences are then used to obtain information about the K-groups of integral group rings of abelian groups of square-free order; about certain rings of integers in number fields; and about the coordinate ring of n lines in the plane
Dimension Reduction of Large AND-NOT Network Models
Boolean networks have been used successfully in modeling biological networks
and provide a good framework for theoretical analysis. However, the analysis of
large networks is not trivial. In order to simplify the analysis of such
networks, several model reduction algorithms have been proposed; however, it is
not clear if such algorithms scale well with respect to the number of nodes.
The goal of this paper is to propose and implement an algorithm for the
reduction of AND-NOT network models for the purpose of steady state
computation. Our method of network reduction is the use of "steady state
approximations" that do not change the number of steady states. Our algorithm
is designed to work at the wiring diagram level without the need to evaluate or
simplify Boolean functions. Also, our implementation of the algorithm takes
advantage of the sparsity typical of discrete models of biological systems. The
main features of our algorithm are that it works at the wiring diagram level,
it runs in polynomial time, and it preserves the number of steady states. We
used our results to study AND-NOT network models of gene networks and showed
that our algorithm greatly simplifies steady state analysis. Furthermore, our
algorithm can handle sparse AND-NOT networks with up to 1000000 nodes
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