Upper bound for the stability of Boolean networks
Venkata Sai Narayana Bavisetty1, Matthew Wheeler1, Reinhard Laubenbacher1
1University of Florida, Department of Medicine, Gainesville, Florida.
Abstract:
Boolean networks, inspired by gene regulatory networks, were developed to understand the complex behaviors observed in biological systems, with network attractors corresponding to biological phenotypes or cell types. In this article, we present a proof for a conjecture by Williadsen, Triesch, and Wiles about upper bounds for the stability of basins of attraction in Boolean networks. We further extend this result from a single basin of attraction to the entire network. Specifically, we demonstrate that the asymptotic upper bound for the robustness and the basin entropy of a Boolean network are negatively linearly related.
Related Concept Videos
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
Pole and System Stability
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
Stability of structures
Stability of Equilibrium Configuration
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
Stability of Equilibrium Configuration: Problem Solving
Problem-solving in the context of the stability of equilibrium configuration...
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...

