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In the applications of Boolean networks to modeling biological systems, an important computational problem is the detection of the fixed points of these networks. This is an NP-complete problem in general. There have been various attempts…
The gene networks that comprise the circadian clock modulate biological function across a range of scales, from gene expression to performance and adaptive behaviour. The clock functions by generating endogenous rhythms that can be…
Asynchronous Boolean networks are a type of discrete dynamical system in which each variable can take one of two states, and a single variable state is updated in each time step according to pre-selected rules. Boolean networks are popular…
We present new applications of parity inversion and time-reversal to the emergence of complex behavior from simple dynamical rules in stochastic discrete models. Our parity-based encoding of causal relationships and time-reversal…
We evaluate the probability that a Boolean network returns to an attractor after perturbing h nodes. We find that the return probability as function of h can display a variety of different behaviours, which yields insights into the…
Boolean networks model finite discrete dynamical systems with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the…
In this paper we study the dynamical behavior of Boolean networks with firing memory, namely Boolean networks whose vertices are updated synchronously depending on their proper Boolean local transition functions so that each vertex remains…
In this report a systematic approach is used to determine the approximate genetic network and robust dependencies underlying differentiation. The data considered is in the form of a binary matrix and represent the expression of the nine…
In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a…
Understanding control mechanisms in biological systems plays a crucial role in important applications, for instance in cell reprogramming. Boolean modeling allows the identification of possible efficient strategies, helping to reduce the…
Boolean networks are a widely used modeling framework in systems biology for studying gene regulation, signal transduction, and cellular decision-making. Empirical studies indicate that biological Boolean networks exhibit a high degree of…
Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…
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…
Finding a globally optimal Bayesian Network using exhaustive search is a problem with super-exponential complexity, which severely restricts the number of variables that it can work for. We implement a dynamic programming based algorithm…
Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…
In a previous article, an algorithm for identifying therapeutic targets in Boolean networks modeling pathological mechanisms was introduced. In the present article, the improvements made on this algorithm, named kali, are described. These…
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…
Inferring microbial interaction networks from abundance patterns is an important approach to advance our understanding of microbial communities in general and the human microbiome in particular. Here we suggest discriminating two levels of…
Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks…
This paper presents an algorithm for approximating certain types of dynamical systems given by a system of ordinary delay differential equations by a Boolean network model. Often Boolean models are much simpler to understand than complex…