Directed hypergraphs and applications
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
An aperiodic set of 13 Wang tiles
Discrete Mathematics
A small aperiodic set of Wang tiles
Discrete Mathematics
The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Self-Organization in Biological Systems
Self-Organization in Biological Systems
Convex Optimization
Abstract interpretation of cellular signalling networks
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Testing structure freeness of regular sets of biomolecular sequences
DNA'04 Proceedings of the 10th international conference on DNA computing
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This paper concerns the problem of computing equilibrium of a chemical reaction system in which molecules are interacting locally in various ways and hybridize to produce a large assembly. Such a system can generate tremendously many assemblies from a small number of molecules, which makes it intractable to analyze the system. We call such a reaction system a Hybridization Reaction System (an HRS, for short) in this paper. In spite of its computational intractability, the analysis of HRSs is of rapidly increasing importance in many research fields. The goal of this paper is to present a general theory for the efficient computation of equilibria of HRSs. We will fuse hypergraph theory and optimization theory in order to overcome the combinatorial explosion problem of the number of resultant assemblies.