Related papers: On Analysis And Generation Of Biologically Importa…
Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by…
We prove that nested canalizing functions are the minimum-sensitivity Boolean functions for any given activity ratio and we characterize the sensitivity boundary which has a nontrivial fractal structure. We further observe, on an extensive…
We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number $b_t$ of nodes with value one, and the network sensitivity $\lambda$, and we…
Boolean functions can be represented in many ways including logical forms, truth tables, and polynomials. Additionally, Boolean functions have different canonical representations such as minimal disjunctive normal forms. Other canonical…
Canalization is a classic concept in Developmental Biology that is thought to be an important feature of evolving systems. In a Boolean network it is a form of network robustness in which a subset of the input signals control the behavior…
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…
The canalizing properties of biological functions have been mainly studied in the context of Boolean modelling of gene regulatory networks. An important mathematical consequence of canalization is a low average sensitivity, which ensures in…
Boolean networks constitute relevant mathematical models to study the behaviours of genetic and signalling networks. These networks define regulatory influences between molecular nodes, each being associated to a Boolean variable and a…
The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and…
Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
Interaction graphs provide an important qualitative modeling approach for System Biology. This paper presents a novel approach for construction of interaction graph with the help of Boolean function decomposition. Each decomposition part…
Many approaches such as Quine-McCluskey algorithm, Karnaugh map solving, Petrick's method and McBoole's method have been devised to simplify Boolean expressions in order to optimize hardware implementation of digital circuits. However, the…
We determine stability and attractor properties of random Boolean genetic network models with canalyzing rules for a variety of architectures. For all power law, exponential, and flat in-degree distributions, we find that the networks are…
Understanding design principles of molecular interaction networks is an important goal of molecular systems biology. Some insights have been gained into features of their network topology through the discovery of graph theoretic patterns…
Gene regulatory networks exhibit remarkable stability, maintaining functional phenotypes despite genetic and environmental perturbations. Discrete dynamical models, such as Boolean networks, provide systems biologists with a tractable…
Convolutional neural networks (CNNs) are being applied to an increasing number of problems and fields due to their superior performance in classification and regression tasks. Since two of the key operations that CNNs implement are…
Boolean networks are discrete dynamical systems in which the state (zero or one) of each node is updated at each time t to a state determined by the states at time t-1 of those nodes that have links to it. When these systems are used to…
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…
The concept of control is crucial for effectively understanding and applying biological network models. Key structural features relate to control functions through gene regulation, signaling, or metabolic mechanisms, and computational…