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Discrete dynamical models underpin systems biology, but we still lack substrate-agnostic diagnostics for identifying finite-horizon dynamical signatures that may be relevant to open-ended evolution (OEE), such as the recurrent production of…
We study the stability of orbits in large Boolean networks with given complex topology. We impose no restrictions on the form of the update rules, which may be correlated with local topological properties of the network. While recent past…
An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over the field with two elements. For systems that can…
We investigate the dynamical behavior of simple modules composed of two genes with two or three regulating connections. Continuous dynamics for mRNA and protein concentrations is compared to a Boolean model for gene activity. Using a…
This paper addresses the problem of finding cycles in the state transition graphs of synchronous Boolean networks. Synchronous Boolean networks are a class of deterministic finite state machines which are used for the modeling of gene…
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…
We present dichotomy theorems regarding the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain {0,1}. For a class F of boolean functions and a…
Biological systems encode function not primarily in steady states, but in the structure of transient responses elicited by time-varying stimuli. Overshoots, biphasic dynamics, adaptation kinetics, fold-change detection, entrainment, and…
Effective control of biological systems can often be achieved through the control of a surprisingly small number of distinct variables. We bring clarity to such results using the formalism of Boolean dynamical networks, analyzing the…
The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function $f$, not of variables, having a…
Estimating the influence that individual nodes have on one another in a Boolean network is essential to predict and control the system's dynamical behavior, for example, detecting key therapeutic targets to control pathways in models of…
We study classes of dynamical systems that can be obtained by constructing recursive networks with monotone Boolean functions. Stack filters in nonlinear signal processing are special cases of such systems. We show an analytical connection…
A conjunctive Boolean network (CBN) is a finite state dynamical system, whose variables take values from a binary set, and the value update rule for each variable is a Boolean function consisting only of logic AND operations. We investigate…
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…
There is an obvious need for improving the performance and accuracy of a Bayesian network as new data is observed. Because of errors in model construction and changes in the dynamics of the domains, we cannot afford to ignore the…
Boolean circuit is a computational graph that consists of the dynamic directed graph structure and static functionality. The commonly used logic optimization and Boolean matching-based transformation can change the behavior of the Boolean…
This paper proposes a new parameter for studying Boolean networks: the independence number. We establish that a Boolean network is $k$-independent if, for any set of $k$ variables and any combination of binary values assigned to them, there…
We report a scalable hybrid quantum-classical machine learning framework to build Bayesian networks (BN) that captures the conditional dependence and causal relationships of random variables. The generation of a BN consists of finding a…
Regulatory networks (RNs) are a well-accepted modelling formalism in computational systems biology. The control of RNs is currently receiving a lot of attention because it provides a computational basis for cell reprogramming -- an…
This short paper presents an abstract, tunable model of genomic structural change within the cell lifecycle and explores its use with simulated evolution. A well-known Boolean model of genetic regulatory networks is extended to include…