An Investigation of Oriented Matroids Associated with a Petri Net
EMSL Project ID
2090
Abstract
As part of the Silicon Cell project (LDRD:Enabling the Silicon Cell: Development of Models of Cell-Signaling Pathways and Networks.) we have associated a Petri net with a reaction sequence. Petri nets have a number of mathematical invariants that come from the underlying linear algebra. These invariants carry much information about the net, particularly relating to pathways and cycles. Some of these (the S- and T-invariants) naturally give rise to oriented matroids.These matroids strip away the vector aspect of the invariants revealing essential structure that can be used for path searches and various optimization techniques. Oriented matroids have many equivalent forms, each one making a different piece of information accessible. Finding these equivalent forms is theoretically easy, but computationally difficult due to high space requirements. I propose to develop code that takes a Petri net, finds the desired invariant and produces several forms of the associated matroid. Having done this I intend to investigate (via examples and then theoretically as patterns become clear) the relationship between these different forms and the Petri net. For example, it appears that Petri nets coming from the reaction pathways of interest are built from a small number of elementary blocks. Does this transfer to the matroid, and if so (as might be expected), does it simplify optimization questions?
Project Details
Project type
Exploratory Research
Start Date
2000-11-03
End Date
2001-11-15
Status
Closed
Released Data Link
Team
Principal Investigator