Related papers: From differential equations to Boolean networks: A…
The solution of high-dimensional inference and prediction problems in computational biology is almost always a compromise between mathematical theory and practical constraints such as limited computational resources. As time progresses,…
Cellular response to environmental and internal signals can be modeled by dynamical gene regulatory networks (GRN). In the literature, three main classes of gene network models can be distinguished: (i) non-quantitative (or data-based)…
This article is set in the field of regulation networks modeled by discrete dynamical systems. It focuses on Boolean automata networks. In such networks, there are many ways to update the states of every element. When this is done…
We study two measures of the complexity of heterogeneous extended systems, taking random Boolean networks as prototypical cases. A measure defined by Shalizi et al. for cellular automata, based on a criterion for optimal statistical…
Gene expression-based heterogeneity analysis has been extensively conducted. In recent studies, it has been shown that network-based analysis, which takes a system perspective and accommodates the interconnections among genes, can be more…
The major biochemical networks of the living cell, the network of interacting genes and the network of biochemical reactions, are highly interdependent, however, they have been studied mostly as separate systems so far. In the last years an…
Network equilibrium models represent a versatile tool for the analysis of interconnected objects and their relationships. They have been widely employed in both science and engineering to study the behavior of complex systems under various…
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…
Global dynamics of a non-linear Cellular Automata is, in general irregular, asymmetric and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable. In the past efforts have been made to systematize…
Boolean networks serve as discrete models of regulation and signaling in biological cells. Identifying the key controllers of such processes is important for understanding the dynamical systems and planning further analysis. Here we…
Canalization is a key organizing principle in complex systems, particularly in gene regulatory networks. It describes how certain input variables exert dominant control over a function's output, thereby imposing hierarchical structure and…
Recent experimental advances in biology allow researchers to obtain gene expression profiles at single-cell resolution over hundreds, or even thousands of cells at once. These single-cell measurements provide snapshots of the states of 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…
Progress in cell type reprogramming has revived the interest in Waddington's concept of the epigenetic landscape. Recently researchers developed the quasi-potential theory to represent the Waddington's landscape. The Quasi-potential U(x),…
We realize autonomous Boolean networks by using logic gates in their autonomous mode-of-operation on a field-programmable gate array. This allows us to implement time-continuous systems with complex dynamical behaviors that can be…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides…
Recent progress in experimental techniques has enabled us to quantitatively study stochastic and flexible behavior of biological systems. For example, gene regulatory networks perform stochastic information processing and their…
A number of representation schemes have been presented for use within learning classifier systems, ranging from binary encodings to neural networks. This paper presents results from an investigation into using discrete and fuzzy dynamical…
In this review we discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on…