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Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or logical approaches. We propose a new modeling framework for gene regulatory networks, that combines the intuitive appeal of(More)
Weakly activated signaling cascades can be modeled as linear systems. The input-to-output transfer function and the internal gain of a linear system, provide natural measures for the propagation of the input signal down the cascade and for the characterization of the final outcome. The most efficient design of a cascade for generating sharp signals, is(More)
A hierarchy of models, ranging from high to lower levels of abstraction, is proposed to construct "minimal" but predictive and explanatory models of biological systems. Three hierarchical levels will be considered: Boolean networks, piecewise affine differential (PWA) equations, and a class of continuous, ordinary, differential equations' models derived(More)
— We consider the problem of estimating Boolean models of gene regulation networks from few and noisy measurements. To this end, we use a representation of Boolean functions as multi-affine polynomials, leading to a reformulation of the estimation problem as mixed integer linear program. We then show that the integer constraints can be omitted which(More)
The concept of robustness of regulatory networks has received much attention in the last decade. One measure of robustness has been associated with the volume of the feasible region, namely, the region in the parameter space in which the system is functional. In this paper, we show that, in addition to volume, the geometry of this region has important(More)
This paper studies aspects of the dynamics of a conventional mechanism of ligand-receptor interactions, with a focus on the stability and location of steady-states. A theoretical framework is developed, which is based upon the rich and deep formalism of irreducible biochemical networks. When represented in this manner, the mass action kinetics of(More)
In this paper we will consider a network of vehicles exchanging information among themselves with the intention of achieving a specified polygonal formation. A stochastic model for information transmission and reception is considered , allowing for the randomly breaking of the communication links among the vehicles. The network achieves the formation(More)