A discrete inhomogeneous model for the yeast cell cycle

We study the robustness and stability of the yeast cell regulatory network by using a general inhomogeneous discrete model. We find that inhomogeneity, on average, enhances the stability of the biggest attractor of the dynamics and that the large size of the basin of attraction is robust against changes in the parameters of inhomogeneity. We find that the most frequent orbit, which represents the cell-cycle pathway, has a better biological meaning than the one exhibited by the homogeneous model.Comment: 5 pages, 1 figur

A Framework for Combining Analysis and Verification

interpretation using this domain infers that x0, y0 are even at the end of the loop, although it cannot infer anything about x, y. Combining the results from the Hoare-style reasoner with this abstract interpretation results gives fx + y = x0 + y0 x \Gamma 1 ! y + 1 x y even(x0) even(y0)g, which now does imply x = y. This example illustrates the potential of cooperation between a verification engine and an analysis engine. However, it only shows how running verification and then analysis can give better results than either on its own. In fact the verification and analysis process are not independent -- results from one can be used to improve the results of the other and vice-versa. This interaction suggests a process consisting of a sequence of alternating analysis and verification phases. In this paper, we start with a representation of a program, user assertions, and a given analyzer for the program. The framework we describe induces an algorithm that exploits the assertions ..