Related papers: Genetic networks with canalyzing Boolean rules are…
The evolutionary origins of structural features in reconstructed gene-regulatory networks (GRNs) remain poorly understood, especially given the random aspects of gene expression. Here, we extend a classical model of GRN evolution to allow a…
Feedback loops in a dynamic network play an important role in determining the dynamics of that network. Through a computational study, in this paper we show that networks with fewer independent negative feedback loops tend to exhibit more…
Regulatory networks consist of interacting molecules with a high degree of mutual chemical specificity. How can these molecules evolve when their function depends on maintenance of interactions with cognate partners and simultaneous…
In automata networks, it is well known that the way entities update their states over time has a major impact on their dynamics. In particular, depending on the chosen update schedule, the underlying dynamical systems may exhibit more or…
Dynamical properties of the transcriptional regulatory network of {\it Escherichia coli} and {\it Saccharomyces cerevisiae} are studied within the framework of random Boolean functions. The dynamical response of these networks to a single…
We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed in a previous paper we show some interesting properties of…
Deterministic and stochastic Boolean network models are build for the dynamics of negative feedback loops of the p53 pathways. It is shown that the main function of the negative feedback in the p53 pathways is to keep p53 at a low steady…
We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The…
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…
Biological processes, including cell differentiation, organism development, and disease progression, can be interpreted as attractors (fixed points or limit cycles) of an underlying networked dynamical system. In this paper, we study the…
Phylogenetic networks are becoming of increasing interest to evolutionary biologists due to their ability to capture complex non-treelike evolutionary processes. From a combinatorial point of view, such networks are certain types of rooted…
Genetic regulatory networks are defined by their topology and by a multitude of continuously adjustable parameters. Here we present a class of simple models within which the relative importance of topology vs. interaction strengths becomes…
Graph convolutional neural networks (GCNNs) have emerged as powerful tools for analyzing graph-structured data, achieving remarkable success across diverse applications. However, the theoretical understanding of the stability of these…
Genetic regulatory networks (GRNs) have been widely studied, yet there is a lack of understanding with regards to the final size and properties of these networks, mainly due to no network currently being complete. In this study, we analyzed…
Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by…
Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing…
The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local…
The effects of the finite size of the network on the evolutionary dynamics of a Boolean network are analyzed. In the model considered, Boolean networks evolve via a competition between nodes that punishes those in the majority. It is found…
Random Boolean networks, the Kauffman model, are revisited by means of a novel decimation algorithm, which reduces the networks to their dynamical cores. The average size of the removed part, the stable core, grows approximately linearly…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…