6 papers
Permutation theory governs long-term dynamics of critical Boolean networks
Venkata Sai Narayana Bavisetty, Matthew Wheeler, Julian Vignes +4
Boolean networks are widely used to model gene regulatory dynamics, where long-term behavior is organized by attractors - by both their number and their lengths. The number of attr…
Dynamics Decomposition of Boolean Networks: An algebraic foundation
Alan Veliz-Cuba, Claus Kadelka, David Murrugarra +4
Understanding the dynamics of Boolean networks is central to problems such as network reduction, design, control, and reverse engineering. As Boolean network models continue to gro…
Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Clouds
Hubert Wagner, Nickolas Arustamyan, Matthew Wheeler +1
We combine standard persistent homology with image persistent homology to define a novel way of characterizing shapes and interactions between them. In particular, we introduce: (1…
Upper bound for the stability of Boolean networks
Venkata Sai Narayana Bavisetty, Matthew Wheeler, Reinhard Laubenbacher +1
Boolean networks, inspired by gene regulatory networks, were developed to understand the complex behaviors observed in biological systems, with network attractors corresponding to…
Categorical foundations of discrete dynamical systems
Daniel Carranza, Chris Kapulkin, Nathan Kershaw +2
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the n…
Modular control of Boolean network models
David Murrugarra, Alan Veliz-Cuba, Elena Dimitrova +3
The concept of control is crucial for effectively understanding and applying biological network models. Key structural features relate to control functions through gene regulation,…