Related papers: An open problem: Why are motif-avoidant attractors…
Random Boolean networks have been used widely to explore aspects of gene regulatory networks. A modified form of the model through which to systematically explore the effects of increasing the number of gene states has previously been…
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…
In this paper, we address the formal characterization of targets triggering cellular trans-differentiation in the scope of Boolean networks with asynchronous dynamics. Given two fixed points of a Boolean network, we are interested in all…
Boolean networks are powerful frameworks for capturing the logic of gene-regulatory circuits, yet their combinatorial explosion hampers exhaustive analyses. Here, we present a systematic reduction of a 31-node Boolean model that describes…
Disorder and noise in physical systems often disrupt spatial and temporal regularity, yet chaotic systems reveal how order can emerge from unpredictable behavior. Complex networks, spatial analogs of chaos, exhibit disordered, non-Euclidean…
A Boolean network (BN) is a transformation of the set of Boolean configurations of a given length. A trapspace of a BN is a subcube invariant by the BN; a principal trapspace is the smallest trapspace containing a given configuration; a…
The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy…
Boolean networks have been successfully used in modelling gene regulatory networks. In this paper we propose a reduction method that reduces the complexity of a Boolean network but keeps dynamical properties and topological features and…
Networks are a fundamental tool for modeling complex systems in a variety of domains including social and communication networks as well as biology and neuroscience. Small subgraph patterns in networks, called network motifs, are crucial to…
In this paper, we propose an approach for modeling and analysis of a number of phenomena of collective behavior. By collectives we mean multi-agent systems that transition from one state to another at discrete moments of time. The behavior…
The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations…
A Boolean network is a function $f:\{0,1\}^n\to\{0,1\}^n$ from which several dynamics can be derived, depending on the context. The most classical ones are the synchronous and asynchronous dynamics. Both are digraphs on $\{0,1\}^n$, but the…
Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability…
In dynamical systems with distinct time scales the time evolution in phase space may be influenced strongly by the fixed points of the fast subsystem. Orbits then typically follow these points, performing in addition rapid transitions…
A Boolean network (BN) is a discrete dynamical system defined by a Boolean function that maps to the domain itself. A trap space of a BN is a generalization of a fixed point, which is defined as the sub-hypercubes closed by the function of…
Multiple dynamic pathways always exist in biological networks, but their robustness against internal fluctuations and relative stability have not been well recognized and carefully analyzed yet. Here we try to address these issues through…
Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in…
Maxmin-$\omega$ is a new threshold model, where each node in a network waits for the arrival of states from a fraction $\omega$ of neighborhood nodes before processing its own state, and subsequently transmitting it to downstream nodes.…
Combinatorial threshold-linear networks (CTLNs) are a special class of inhibition-dominated TLNs defined from directed graphs. Like more general TLNs, they display a wide variety of nonlinear dynamics including multistability, limit cycles,…
In this paper we try to end the debate concerning the suitability of different updating schemes in random Boolean networks (RBNs). We quantify for the first time loose attractors in asyncrhonous RBNs, which allows us to analyze the…