相关论文: Piecewise linear and Boolean models of chemical re…

We show that certain non-linear dynamical systems with non-linearities in the form of Hill functions, can be approximated by piecewise linear dynamical systems. The resulting piecewise systems have closed form solutions that can be used to…

Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…

Boolean networks have been successfully used in modelling gene regulatory networks. In this paper we propose a reduction method that reduces the complexity of a Boolean network but keeps dynamical properties and topological features and…

Boolean networks are popular tools for the exploration of qualitative dynamical properties of biological systems. Several dynamical interpretations have been proposed based on the same logical structure that captures the interactions…

The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are…

This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network…

Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may,…

In this paper we consider piecewise affine differential equations modeling gene networks. We work with arbitrary decay rates, and under a local hypothesis expressed as an alignment condition of successive focal points. The interaction graph…

Reconstruction of biochemical reaction networks is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and…

Due to the scarcity of quantitative details about biological phenomena, quantitative modeling in systems biology can be compromised, especially at the subcellular scale. One way to get around this is qualitative modeling because it requires…

The design and synthesis of complex and large mimicked biochemical networks de novo is an unsolved problem in synthetic biology. To address this limitation without resorting to ad hoc computations and experiments, a predictive mathematical…

Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…

Boolean networks are powerful frameworks for capturing the logic of gene-regulatory circuits, yet their combinatorial explosion hampers exhaustive analyses. Here, we present a systematic reduction of a 31-node Boolean model that describes…

Neural networks are a popular tool for modeling sequential data but they generally do not treat time as a continuous variable. Neural ODEs represent an important exception: they parameterize the time derivative of a hidden state with a…

The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean…

Boolean networks have been used successfully in modeling biological networks and provide a good framework for theoretical analysis. However, the analysis of large networks is not trivial. In order to simplify the analysis of such networks,…

We study the problem of computing a minimal subset of nodes of a given asynchronous Boolean network that need to be controlled to drive its dynamics from an initial steady state (or attractor) to a target steady state. Due to the phenomenon…

Boolean networks have been used in a variety of settings, as models for general complex systems as well as models of specific systems in diverse fields, such as biology, engineering, and computer science. Traditionally, their properties as…

Boolean threshold networks have recently been proposed as useful tools to model the dynamics of genetic regulatory networks, and have been successfully applied to describe the cell cycles of \textit{S. cerevisiae} and \textit{S. pombe}.…

Interacting biological systems at all organizational levels display emergent behavior. Modeling these systems is made challenging by the number and variety of biological components and interactions (from molecules in gene regulatory…