Logic Integer Programming Models for Signaling Networks

We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this we use the two different mathematical tools of Propositional Logic and Integer Programming. The power of discrete mathematics for handling qualitative as well as quantitative data has so far not been exploited in Molecular Biology, which is mostly driven by experimental research, relying on first-order or statistical models. The arising logic statements and integer programs are analyzed and can be solved with standard software. For a restricted class of problems the logic models reduce to a polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic model enables enumeration of possible time resolutions in poly-logarithmic time. Computational experiments are included

Note on Finite Convergence of Exterior Penalty Functions

It is shown that existence of a saddle point of the Lagrangian function in an optimization problem is sufficient to assure finite convergence of the linear exterior penalty function. Also, an estimate of the penalty weight is given that yields \epsilon -convergence for the quadratic exterior penalty function.

Implementation of a Unimodularity Test

Abstract. This paper describes implementation and computational results of a polynomial test of total unimodularity. The test is a simpli ed version of a prior method. The program also decides two related unimodularity properties. The software is available free of charge in source code form under the Boost Software License. Key words: unimodularity, total unimodularity, polynomial test