Topic
Boolean network
About: Boolean network is a research topic. Over the lifetime, 2568 publications have been published within this topic receiving 56267 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: Probabilistic Boolean Networks (PBN) are introduced that share the appealing rule-based properties of Boolean networks, but are robust in the face of uncertainty.
Abstract: Motivation: Our goal is to construct a model for genetic regulatory networks such that the model class: (i) incorporates rule-based dependencies between genes; (ii) allows the systematic study of global network dynamics; (iii) is able to cope with uncertainty, both in the data and the model selection; and (iv) permits the quantification of the relative influence and sensitivity of genes in their interactions with other genes. Results: We introduce Probabilistic Boolean Networks (PBN) that share the appealing rule-based properties of Boolean networks, but are robust in the face of uncertainty. We show how the dynamics of these networks can be studied in the probabilistic context of Markov chains, with standard Boolean networks being special cases. Then, we discuss the relationship between PBNs and Bayesian networks—a family of graphical models that explicitly represent probabilistic relationships between variables. We show how probabilistic dependencies between a gene and its parent genes, constituting the basic building blocks of Bayesian networks, can be obtained from PBNs. Finally, we present methods for quantifying the influence of genes on other genes, within the context of PBNs. Examples illustrating the above concepts are presented throughout the paper.
1,738 citations
Book•
8 Apr 2011TL;DR: A new matrix product, called semi-tensor product of matrices, is used, which can covert the Boolean networks into discrete-time linear dynamic systems and the controllability of Boolean control networks is considered in the paper as an application.
Abstract: A Boolean network is a logical dynamic system, which has been used to describe cellular networks. Using a new matrix product, called semi-tensor product of matrices, a logical function can be expressed as an algebraic function. This expression can covert the Boolean networks into discrete-time linear dynamic systems. Similarly, the Boolean control networks can also be converted into discrete time bilinear dynamic systems. Under these forms the standard matrix analysis can be used to consider the structure and the control problems of Boolean (control) networks. After the detailed description of this new approach, the controllability of Boolean control networks is considered in the paper as an application.
1,192 citations
24 Oct 1988
TL;DR: Methods from harmonic analysis are used to prove some general theorems on Boolean functions and enable them to prove theorem on the rapid mixing of the random walk on the cube and in the extremal theory of finite sets.
Abstract: Methods from harmonic analysis are used to prove some general theorems on Boolean functions. These connections with harmonic analysis viewed by the authors are very promising; besides the results on Boolean functions they enable them to prove theorems on the rapid mixing of the random walk on the cube and in the extremal theory of finite sets. >
884 citations
10 Dec 2002
TL;DR: The central theme in this paper is the Boolean formalism as a building block for modeling complex, large-scale, and dynamical networks of genetic interactions and its relationships to nonlinear digital filters.
Abstract: Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrative and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in disease. The central theme in this paper is the Boolean formalism as a building block for modeling complex, large-scale, and dynamical networks of genetic interactions. We discuss the goals of modeling genetic networks as well as the data requirements. The Boolean formalism is justified from several points of view. We then introduce Boolean networks and discuss their relationships to nonlinear digital filters. The role of Boolean networks in understanding cell differentiation and cellular functional states is discussed. The inference of Boolean networks from real gene expression data is considered from the viewpoints of computational learning theory and nonlinear signal processing, touching on computational complexity of learning and robustness. Then, a discussion of the need to handle uncertainty in a probabilistic framework is presented, leading to an introduction of probabilistic Boolean networks and their relationships to Markov chains. Methods for quantifying the influence of genes on other genes are presented. The general question of the potential effect of individual genes on the global dynamical network behavior is considered using stochastic perturbation analysis. This discussion then leads into the problem of target identification for therapeutic intervention via the development of several computational tools based on first-passage times in Markov chains. Examples from biology are presented throughout the paper.
712 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 32 |
| 2024 | 45 |
| 2023 | 75 |
| 2022 | 167 |
| 2021 | 62 |
| 2020 | 74 |