The Effect of Noise on the Density Classification Task for Various Cellular Automata Rules.

Cellular automata (CA) are discrete dynamical systems with a prominent place in the history and study of artificial life. Here, we focus on the density classification task (DCT) in which a 1-dimensional lattice of Boolean (on/off) automata must perform a form of rudimentary quorum sensing. Typically, the ring lattice consists of 149 cells (though we consider other sizes as well) that update their state according to their own state and its six nearest neighbors in the previous time step.

The ultrametric backbone is the union of all minimum spanning forests.

Minimum spanning trees and forests are powerful sparsification techniques that remove cycles from weighted graphs to minimize total edge weight while preserving node reachability, with applications in computer science, network science, and graph theory. Despite their utility and ubiquity, they have several limitations, including that they are only defined for undirected networks, they significantly alter dynamics on networks, and they do not generally preserve important network features such as shortest distances, shortest path distribution, and community structure. In contrast, distance backbones, which are subgraphs formed by all edges that obey a generalized triangle inequality, are well defined in directed and undirected graphs and preserve those and other important network features.

Models of Cell Processes are Far from the Edge of Chaos.

Complex living systems are thought to exist at the "edge of chaos" separating the ordered dynamics of robust function from the disordered dynamics of rapid environmental adaptation. Here, a deeper inspection of 72 experimentally supported discrete dynamical models of cell processes reveals previously unobserved order on long time scales, suggesting greater rigidity in these systems than was previously conjectured. We find that propagation of internal perturbations is transient in most cases, and that even when large perturbation cascades persist, their phenotypic effects are often minimal.

Inferring gene regulatory networks using transcriptional profiles as dynamical attractors.

Genetic regulatory networks (GRNs) regulate the flow of genetic information from the genome to expressed messenger RNAs (mRNAs) and thus are critical to controlling the phenotypic characteristics of cells. Numerous methods exist for profiling mRNA transcript levels and identifying protein-DNA binding interactions at the genome-wide scale. These enable researchers to determine the structure and output of transcriptional regulatory networks, but uncovering the complete structure and regulatory logic of GRNs remains a challenge.

Effective Connectivity and Bias Entropy Improve Prediction of Dynamical Regime in Automata Networks.

Biomolecular network dynamics are thought to operate near the critical boundary between ordered and disordered regimes, where large perturbations to a small set of elements neither die out nor spread on average. A biomolecular automaton (e.g.

pystablemotifs: Python library for attractor identification and control in Boolean networks.

Summary: pystablemotifs is a Python 3 library for analyzing Boolean networks. Its non-heuristic and exhaustive attractor identification algorithm was previously presented in Rozum et al. (2021).

Self-sustaining positive feedback loops in discrete and continuous systems.

We consider a dynamic framework frequently used to model gene regulatory and signal transduction networks: monotonic ODEs that are composed of Hill functions. We derive conditions under which activity or inactivity in one system variable induces and sustains activity or inactivity in another. Cycles of such influences correspond to positive feedback loops that are self-sustaining and control-robust, in the sense that these feedback loops "trap" the system in a region of state space from which it cannot exit, even if the other system variables are externally controlled.